Maieutic, Natural, and Artificial Forms in Automatic Control Case Study

Abstract

Maieutics is a remarkable method for discovering new insights through deep dialogue. Defined as “relating to or resembling the Socratic method of eliciting new ideas from another”, the term originates from the Greek word for “midwifery”—as noted in the Merriam-Webster Dictionary. Recently, maieutics has gained renewed relevance in advanced discussions about artificial intelligence, the nature of the mind, and scientific inquiry. This contribution presents a real and extended dialogue, illustrating the power of the maieutic method in addressing key developments in the field of Automatic Control. Over the past 40 years, the authors have followed a unique intellectual path shaped by this method. Inspired by recent research, they have also applied maieutics in interaction with AI systems—particularly ChatGPT. This experiment aimed to replicate, in a condensed timeframe, the long intellectual journey taken over decades. The preliminary results suggest that although AI systems can retrieve historical information, they struggle to capture the deeper, guiding principles of this journey. The authors also identify a significant concern: while the maieutic approach with ChatGPT can serve as a valuable educational tool, it must be complemented by a strong knowledge of dynamical systems leading to innovative paradigms of learning.

1. Introduction

This paper presents an authentic dialogue among professionals operating in various domains of Electrical Engineering. Its objective is to explore the current state and future directions of Automatic Control by applying the maieutic method to guide the discussion. The strength of maieutics lies in its capacity to bring out evolving concepts through questioning. As the final session of this ongoing conversation reveals, each answer naturally gives rise to further questions—underscoring the method’s generative and recursive nature.

While still relatively novel within the field of Automatic Control and Systems Theory, the maieutic approach has recently attracted increasing interest, particularly in areas such as information science and neuroscience, as proposed in recent books [1,2]. These studies investigate topics at the intersection of artificial intelligence and emerging models of consciousness. A key inspiration for this paper came from engaging in a sustained dialogue with ChatGPT 4o, which raised thought-provoking questions about AI’s ability to mirror the intellectual process of human inquiry—as recently explored in the timely publication.

What is documented here is not a theoretical fiction but rather the reconstruction of a real and long-standing conversation that began over four decades ago and continues today. Its focus lies on the evolution of methodologies and perspectives in Automatic Control. This paper traces significant milestones along this journey and offers a conceptual framework for understanding the development of feedback control strategies over time.

Intrinsic feedback loops play a vital role in both physical and biological systems. Life itself would be inconceivable without feedback mechanisms: the human brain, for example, encompasses billions of such loops. Yet, despite their ubiquity, the design of feedback controllers has remained a major challenge [3]—even though feedback principles were already central to the First Industrial Revolution.

Although a rigorous mathematical theory of control was developed after World War II, many open questions persisted well into the 1980s, especially in light of new challenges introduced by the digital and information age. The rise of robotics intensified interest in integrating classical control methods with real-world industrial systems. This created a need to bridge traditional theory with emerging techniques in computer science. It was within this context that a long-standing collaboration among researchers took shape—even before the advent of the internet.

Looking back, the authors stress that the maieutic method has served as a productive and dynamic tool, fostering a continuous dialogue with ChatGPT. This conversational process has enabled them to remain intellectually agile, connected to practical challenges, and continuously open to conceptual evolution.

Structure of the Paper

• Section 2 examines the current challenges in Automatic Control.
• Section 3 presents a concise overview of the conceptual and historical significance of the maieutic method with a mathematical model example.
• Section 4 offers a transcription of a real dialogue that exemplifies the application of the method, with a mathematical model and a cognitive map of the learning process.
• Section 5 reflects on the experiment of engaging ChatGPT in this intellectual journey.
• Section 6 summarizes the main contributions of the paper.
• An appendix follows, showcasing a ChatGPT research proposal.

2. Conceiving the General Challenge Problem of Automatic Control

Let us consider a dynamical system [4]. The design of the compensator consists in designing another dynamical system [5] that assures that the closed-loop configuration is stable and that the behavior of the feedback system will achieve the desired performances in spite of the uncertainties, model imperfections, disturbances, and measurement noise.

As a dynamical system, we will refer our discussion to the following definition. It will be given a set of ordered real numbers T along with the following:

• The three sets: U, X, y
• A set of input functions $\mathsf{\Omega }$.
• The output transformation function, defined as

  $$\eta :T\times X\times U\to y.$$

  (1)
• The state transition function, defined as

  $$\mathsf{\Psi }:T\times T\times \mathsf{\Omega }\to X.$$

  (2)
  This transformation associates each initial state, initial time, and input function to the state X of the system.

In summary, the initial state and the forcing input function allow the evolution of the state by the function $\psi$. The state and the input by means of the transformation $\eta$ will give the answer as output (Figure 1).

Schematically, it is as follows:

Figure 1. Open-loop representation of a generic dynamical system and its state transitions after a forcing funcion is applied.

Figure 1. Open-loop representation of a generic dynamical system and its state transitions after a forcing funcion is applied.

In the closed-loop context Figure 2, we have to design a new dynamical system where the input of the controller is y, the output function, which gives the control law $\overline{u}$, is ${\psi }_1(\overline{x},y)$, with $\overline{x}$ being the state generated by the transfer state transition function ${\psi }_1(y,\overline{x})$.

In a feedback scheme, it is as follows:

Figure 2. Closed-loop control of a generic dynamical system with external disturbances applied.

Figure 2. Closed-loop control of a generic dynamical system with external disturbances applied.

In a real context, disturbances such as measurement noise, uncertainty in the adopted model, both of the state transition function and of the output function, must be considered as previously outlined.

Moreover, the compensator must not be fragile; this means that soft imperfections of the fixed parameters in the design do not lead to a catastrophe of the whole system. The formalization of the main systematic principles of Automatic Control started with the vacuum electronic amplifiers design [6], but in the last century, achieved widespread applications—from domestic apparatus like boilers to industrial robot applications.

During our life, unconsciously, we produce control laws; therefore, we are the compensator of one or more systems: during driving our car, during daily walking, and so on. Feedback and control are common. Moreover, the design, from an engineering point of view, is highly complex. This means that in order to guarantee the good performances of the system, the mathematical strategies and the design strategies must be adapted to the specific problem. Moreover, the nonlinearities of the controlled system add new difficulties. Today, there does not exist an a priori technique that assures the optimal design of a feedback loop [7].

Indeed, the difficulties increase if the system is made of a set of loops. This occurs in chemical processes or in large-scale electrical plants. The coordination of feedback control loops leads to the adoption of hierarchical control strategies and the development of both local control actions and centralized supervisor systems. This is what occurs in complex industrial plants.

Indeed, highly interconnected distributed nonlinear systems could result in self-organization. This means that the intrinsic feedback of each unit will work in an adaptive manner with the local one, allowing a robust global control system. This is what occurs in nature, in social systems, and in living systems.

Therefore, the suitable design of a system is complicated, and the control strategies could be improved step by step thanks to the contributions and ideas of multiple experts. In general, this occurs in many engineering fields and in science. Moreover, the control design topic deserves serious attention due to the fact that the closed-loop action is often critical and could lead to a collapse of the system.

The adoption of a strong dialogic method has been adopted to achieve good knowledge and success. It should be remarked that in the maieutic approach, there is a necessary condition for the task to be even partially achieved: the actors of the dialogue must achieve sufficient empathy. This is a peculiarity of human beings.

3. Maieutics as a Tool

3.1. A Brief Review

Maieutics is the method of Socrates: the art of following the bringing forth of ideas from the mind of a pupil by a series of pertinent question [8]. It is an old, efficient, and universal method. Below is a schematic overview of the various fields where maieutics has been employed:

• Science Education and Pedagogy: In science teaching, especially at higher levels, Socratic questioning helps students develop critical thinking and deepen conceptual understanding.
  Example: Teaching physics or biology through guided inquiry questions rather than formal lectures.
• Philosophy of Science and Scientific Inquiry: Philosophers of science use maieutic dialogue (as in PHI by Tononi) to explore foundational questions about consciousness, cognition, and scientific explanation. Dialogues help reveal assumptions and foster theoretical development.
• Interdisciplinary Research and Collaboration: When teams from different scientific fields collaborate, dialogical inquiry—akin to maieutics—helps integrate perspectives and clarify concepts. Questioning fosters mutual understanding and uncovers hidden premises.
• Qualitative Research Methods: In the social sciences (e.g., psychology, anthropology, sociology), maieutic-like interviewing (open-ended, reflective questioning) enables participants to articulate deeper insights about their experiences.
  Examples: Narrative interviews, phenomenological research.
• Cognitive Science and AI: In AI research and cognitive science, dialogue systems or interactive learning environments can be inspired by maieutic principles, encouraging both machines and users to uncover knowledge through structured questioning.

A brief selection of literature referring to maieutic methods includes the following:

• Plato, Meno: Classic example where Socrates helps a slave boy “remember” geometry through guided questioning [9].
• Plato, Theaetetus: Dialogue exploring the nature of knowledge through the questioning of assumptions [8]
• John L. Casti, The Cambridge Quintet: Fictional dialogue among great minds discussing AI and consciousness via Socratic exchange [1].
• Giulio Tononi, PHI: A Voyage from the Brain to the Soul: A fictional Galileo learns about consciousness through dialogical inquiry [2].
• Paulo Freire, Pedagogy of the Oppressed: Advocates dialogical education in which learners discover knowledge through critical questioning [10].
• Nancy Kline, Time to Think: Demonstrates how thoughtful questioning enables deep reflection and insight [11].
• Michael Bungay Stanier, The Coaching Habit: Applies maieutic techniques to coaching, using open questions to unlock client thinking [12].
• Carl Rogers, On Becoming a Person: Client-centered therapy where individuals discover their own truths through dialogic engagement [13].
• Danilo Dolci, Inventare il Futuro: Describes reciprocal maieutic dialogue for community education and empowerment [14].
• Boethius, The Consolation of Philosophy: A philosophical dialogue employing maieutic questioning to attain understanding [15].
• Vincenzo Manca, Conversazioni Artificiali—Conversazioni ai tempi dei Chatbot: A timely reflection linking maieutics to modern tools like ChatGPT, potentially becoming a landmark book on the topic [16].

3.2. Maieutics Is a Dynamical Process

Maieutics is considered from Socrates a method to discover knowledge through a dialogue by using a dialectic strategy when the interlocutor is guided to discover routes of knowledge. Maieutics is therefore considered a provocative question system not aiming to transfer information but making the interlocutor discover a pattern. Can maieutics lead to dialogic pattern recognition?

Maieutics is a retrieval process and it is nonlinear, iterative, recursive, and adaptive: it is, therefore, characterized by the properties of a dynamical system. Moreover, it is irreversible; in fact the maieutic systems are accumulative processes.

Schematically, it is characterized by the following entities:

• The Socratic Questioner (maieutic question);
• The interlocutor;
• The dialogic state space, including the set of possible cognitive states;
• Question, answer, operation.

Referring to these points, we will now further explain the following aspects:

• This is a stimulus or attentional cue that triggers neural processes towards a specific task.
• The interlocutor can be viewed as the network of neurons representing the current epistemic cognitive state. Each component corresponds to the activation level of a concept or memory mode.
• It represents the cognitive landscape of possible neural activation patterns like a high-dimensional attractor space in a recurrent neural network.
• That a mechanism possibly includes the external input neural computational layout made by sensory and cognitive prompts, with response of neuron population and generation of synapses or network level updates.

It is therefore appropriate to look at a dynamical system reviewed as follows: the maieutic question Q becomes a way to perturb the system until it goes into a new stable attractor $s_t$ basis. This means that Q is, in the formalism of dynamical system, the forcing function. The interlocutor (learning agent) is represented by the state vector of the system $x\in R^n$. The dimension of the state corresponds to the levels of a conceptual domain belief of attention focus. The values of the state component represent confidence, activation, or coherence. The values of the initial state are given, representing the initial learner.

Moreover, let $u\left(t\right)\in R^n$ be the question vector at the time t, while $y\left(t\right)=f(x,u)$ represents the response function. In the maieutic dialogue, u is the question vector Q, x is the state vector of the learner, and $y\left(t\right)$ is the response function $R_t$.

The following state space transition function is adopted:

$$x_{t+1}=x_t+\alpha \sigma (x_t,u_t)(u_t-x_t)$$

(3)

Of course, it is remarked that in the classical maieutic dialogue, $u_t$ is $Q_t$ and $x_t$ is the epistemic state vector $S_r$.

If $\alpha$ is our learning rate, and $\sigma$ the receptivity function classically used in neuron modeling,

$$\sigma (x_r,u_r)={\displaystyle \frac{1}{1+e^{-B(x_t{Q}_t^T-\theta )}}}$$

(4)

The following item is therefore remarked:

A question is a prompt vector of the same dimension of the epistemic state. The question vector is made by ∅ quantities with the number 1 in only one component. It forces the learner to reconsider or to develop its knowledge along a direction. Therefore, the learner updates its state $X\left(s\right)$ in accordance with the receptivity function and the learning rate.

A maieutic dialogue is now proposed. It is a very simple case that will introduce the problem with the purpose to model the process of guided self-discovery through iterative questions. The program models the process of reflections and belief revision step by step. The following task will be inferred:

• Step 1: A randomly generated epistemic state $x\left(s\right)$ is generated, being $[-0.63-0.0469$ $2.6830-1.14670.5530]$.
• Step 2: The socratic questioning is established. At each turn, the system selects the “weakest” dimension. That, in the selected example, is the smallest absolute value $min\left(abs\right(x\left)\right)$ in $x\left(s\right)$, that in our case, corresponds to the second element. The question vector Q that is, in the context of dynamical systems, the forcing vector u, is a vector of the same dimension of $x\left(s\right)$ made by zeros and a unity value that will result in $Q=\left[01000\right]$.
• Step 3: The receptivity to the question does work on how well aligned it is with the current state, where the alignment is equal to $x{Q}^T$.
• Step 4: The receptivity is modeled by using a classical sigmoidal function. The concept is that more alignment is considered receptivity:

  $$\mathrm{receptive}={\displaystyle \frac{1}{1+e^{-B\ast \mathrm{alignment}}}}$$

  (5)
• Step 5: The new state X and, therefore, the new epistemic state is given in accordance with expression (3):

  $$x_{new}=x+\alpha +\mathrm{receptive}\ast (Q-x)$$
• Step 6: The convergence is achieved; this means that the belief is reached if the norm of $x_{new}-S$ results to be less than a given threshold; otherwise, the procedure will start again from Step 2.

In Figure 3, the dynamical evolution of the epistemic state through maieutic dialogue is reported. It shows as the learner achieved the task of the questioner. The sequences of maieutic questions that allow one to achieve the results are shown in Figure 4.

This iterative formulation (Equations (3)–(5)) also resonates with recent advances in federated optimization. In particular, the Fed-OGD framework [17] addresses the straggler effect in distributed settings, offering algorithmic parallels to the update dynamics of the maieutic state transition model.

4. The Dialogic Approach in an Automatic Control Real Context

Premise: The dialogue began in 1988 and is still ongoing. The portion reported here spans from 1988 to 2022, even though the most recent conversations are from the last few years. Naturally, the starting point was rooted in classical concepts of Automatic Control and the prevailing technologies of that era. The responses from the participants are numbered.

1-Luigi: The design of compensators for linear time-invariant control of SISO systems relies heavily on both experience and trial-and-error methods. This is a traditional engineering approach. What do you think about introducing decision-based support systems to speed up the design process and help practicing engineers achieve effective results more quickly?

Giuseppe: We could try to develop an Expert System to support your goal. In fact, we can formalize the acquired knowledge into a set of rules—both for selecting elementary networks and for choosing suitable parameters. The system could interface with MATLAB for numerical computation and verification, all within a trial-and-error framework. I can start building the knowledge base as you suggest.

2-Luigi: I’m very glad that you support my proposal. I’ll provide you with my design rules, and you can begin developing the system.

Giuseppe: Luigi, I’ve prepared the system and also included rules that allow us to design PID controllers and select their gains. The Expert System enables a dialog-based interaction where we can choose between PID controllers and cascaded elementary networks. I believe the system is ready for testing. Provide me with classical examples, and I’ll present both the system and the case studies to students.

3-Luigi: Welcome, Giuseppe. Involving more people will strengthen our project and help disseminate our knowledge. Next week, you could discuss the project with Peter—he has extensive experience in control design and could help us make the project more robust.

Giuseppe: Welcome, Peter.

Giuseppe: Peter, I’d like to introduce you to our Expert System, which integrates designer knowledge into the compensator design process, enabling rapid development. We’ve already proposed several examples, and the students have shown great interest.

Peter: I’m excited to work with you, Giuseppe, and to explore more examples together. The cases you’ve presented align with those found in classical control textbooks. However, I must point out that these texts often don’t clearly specify when a system can be compensated using a stable compensator, including the types you propose. Here’s an example: $G\left(s\right)={\displaystyle \frac{s-2}{(s-1)s}}$. Try this one, Giuseppe.

Giuseppe: Our system cannot find suitable networks for this case. This doesn’t mean the system is incorrect—it’s just incomplete.

Peter: Exactly. The system I provided lacks the PIP property and cannot be stabilized using elementary stable networks.

4-Luigi: Excellent point, Peter. We need to expand the knowledge base and deepen our understanding. What strategy do you suggest for approaching this issue?

Peter: We should discuss a general strategy for robust control during upcoming seminars. I’ll present my approach in detail then [18].

5-Luigi: Peter, your method assumes a well-known plant model and a mathematically derived compensator. What’s your view on using Fuzzy Logic for designing control compensators?

Peter: I don’t have enough expertise in Fuzzy Logic. I recommend exploring various fields to fully understand the problem and identify the most effective control strategy.

6-Luigi: I’ll try to contact Lofti Zadeh.

7-Luigi: Dear Lofti, I’m interested in evaluating multiple strategies for controller design, particularly involving Fuzzy Logic [19].

Lofti: Welcome, Luigi. I’m aware that a company is developing a Fuzzy Logic-based microcontroller that could be useful for your aims. The company is STMicroelectronics, located in your city. Contact Gianguido.

8-Luigi: Gianguido, I understand you’re coordinating a project on a Fuzzy Logic-based microcontroller. I’m eager to explore real-world applications of advanced control systems, and your work is of great interest to me.

Gianguido: Wonderful, Luigi. We’ll collaborate on this. The microcontroller is called WARP 1. I’ll introduce you to its capabilities.

9-Luigi: It’s a powerful microcontroller. I propose using it both for system modeling—based on process control expertise—and for implementing controllers derived from systems engineering. Even when a precise mathematical model is unavailable, we can build a fuzzy dynamic model using measurements and expert knowledge, enabling faster controller development.

Gianguido: Excellent idea, Luigi. The company finds this approach very promising. I should add that WARP 1 will be followed by WARP II. These are not conventional microcontrollers with software-based fuzzy logic—they use hardware-implemented fuzzy inference.

Lofti: Your approach is innovative and offers great potential for the control community. Keep going and develop further results.

10-Luigi: Gianguido, I had a meeting with researchers working on backpropagation. They introduced me to multilayer perceptrons and associative memory. It’s a fascinating area. I believe neural networks could be used for modeling, while WARP devices can handle control.

Gianguido: That sounds promising. But be cautious with learning algorithms—they can be numerically weak. Try using global optimization techniques to enhance them.

Matteo: To accelerate convergence during learning, we could use auxiliary neural networks to speed up the weight adjustment process. Therefore, we could couple the technique of learning with the dynamical prediction techniques, also based on neural network-based predictors. Therefore, Networks of Networks for learning.

11-Luigi: George, I’m working on neural networks for modeling, and I’m interested in robotics applications where quaternion-based modeling is relevant. Have you studied interpolation problems in the quaternion field?

George: That’s an excellent question, Luigi. So you’re trying to invent quaternion-based neural networks! […] I encourage you to follow your research about. I invite you also to consider using quaternion-based networks for hyperchaotic time series prediction [20].

12-Luigi: Leon, I’ve explained my research activities in system modeling and control. Do you have any suggestions?

Leon: Luigi, you started with analog controllers and have now reached complex AI-based systems. I recommend exploring Cellular Nonlinear Networks (CNNs). […]

Tamas: Your research is impressive, Luigi. I also see your interest in chaos control. I think you now have a great opportunity to integrate all these topics. Cellular Neural Networks architectures are similar to the Cellular Automata

13-Luigi: Thank you, my friends. Your encouragement has led me to talk with Gianguido about building a CNN-based microcontroller with a 128 × 128 array of analog cells. […]

Tamas and Leon: That would be fantastic!

14-Luigi: Gianguido, I propose developing the ACE 128 × 128. A CNN-based microcontroller could be a game-changer for distributed, emergent systems. […]

Gianguido: Let’s do it!

Mario: We’re organizing the project, the consortium, and the deliverables. Everything should be ready by 2002.

Leon and Tamas: The ACE device opens new frontiers. It can implement reaction-diffusion equations in hardware. […] [21].

15-Luigi: Your encouragement is vital. I’d like to share my latest insights. We’ve discovered that due to imperfections in analog electronic technology, each CNN cell is slightly different. […]

Henry: I fully agree. I recommend experimenting with MEG data to quickly demonstrate the practical impact [22].

16-Luigi: I propose involving Maide in this research. She could come to San Diego and possibly suggest further applications.

Leon, Lofti, Gianguido: That’s a great opportunity, Luigi. What are your new ideas?

17-Luigi: Leon invented CNNs, and Lofti introduced Fuzzy Logic. Gianguido has supported both hardware projects. My idea is to combine them—to develop a Fuzzy Logic-based CNN! […]

Leon: Why?

Lofti: Can we integrate our theories?

Gianguido: Designing the hardware won’t be straightforward. […] Start formalizing the architecture and begin new research.

18-Luigi: Many applications benefit from expert knowledge and would also leverage CNN-based architectures. […]

Leon: Absolutely. Also, don’t forget about the memristor! […] Idea Luigi: Memristors based CNN!

The following recently happened:

19-Luigi: Can we undertake a systematic study of human-machine interface modeling? This is a timely and important topic. […]

Adriano: Absolutely. We can apply neural networks and dynamical systems theory. I also have an industrial robot in my lab that we can use as a basis for the study. I propose making this the subject of my PhD thesis!

20-Luigi: I suggest to link the subject to mathematical models.

The cited actors were Luigi Fortuna, Giuseppe Nunnari, Maide Bucolo (University of Catania); Peter Dorato (University of Albuquerque, USA); Lofti Zaded, Leon Chua (University of California, Berkeley, USA); Gianguido Rizzotto, Mario Lavorgna, Matteo Lo Presti (St Microelectronics), Henry Abarbanel (University of California San Diego).

It is worth remarking that the dialogue has not only led to reinforcing the research and educational program of the University of Catania, but also to strongly reinforcing the electronic company activity in the Etna territory [23].

Each participant is an AI agent. In our case, the agents are

• Luigi;
• Giuseppe;
• Peter;
• Lofti;
• Gianguido;
• Matteo;
• George;
• Leon;
• Tamas;
• Henry;
• Adriano;
• Maide;
• Mario.

Each AI agent has a knowledge state $k_i\left(t\right)$ that evolves during the time that is characterized by the dialogue steps. In maieutics, each dialogue exchange can be seen as a stimulus-response pair and a knowledge upgrade. Therefore, it is

$$K_i(t+1)=k_i\left(t\right)+f_i(k_i\left(t\right),{\{k_j/\left(t\right)\}}_{j\in {\tilde{N}}_i})+u_i\left(t\right).$$

(6)

Here, $f_i$ can be considered the capture questioning, the guidance or corrective feedback control of the maieutics. The term $u_i$ represents an external input or stimulus that externally influences the system each step.

In our case, the model being taken into account is purely dialogue-driven; therefore, $u_i=0\forall i$. The evaluation depends only on dialogue influence (what you learn from the others) and on the reflective term (how you think about it and internalize it). In particular, in the considered model, it is

$$k_i(t+1)=k_i\left(t\right)+\sum _j{A}_{ij}\sigma (k_j\left(t\right)-k_i\left(t\right))+B\sigma \left(d_i\left(t\right)\right)$$

(7)

where the second term represent the dialogue influence, equal to $d_i\left(t\right)$. The nonlinearity is in the classical nonlinear saturation function: $\tanh \left(x\right)$. The following connection weight matrix is adopted:

$$A=\left\{A_{ij}\right\}$$

with

$$\begin{array}{ccc}\hfill & A(1,2)=0.6;\mathrm{Luigi}\to \mathrm{Giuseppe}\hfill & \hfill A(2,1)=0.5;\mathrm{Giuseppe}\to \mathrm{Luigi}\\ \hfill & A(1,3)=0.4;\mathrm{Luigi}\to \mathrm{Peter}\hfill & \hfill A(3,1)=0.5;\mathrm{Peter}\to \mathrm{Luigi}\\ \hfill & A(1,4)=0.3;\mathrm{Luigi}\to \mathrm{Lofti}\hfill & \hfill A(1,5)=0.5;\mathrm{Luigi}\to \mathrm{Gianguido}\\ \hfill & A(5,1)=0.4;\mathrm{Gianguido}\to \mathrm{Luigi}\hfill & \hfill A(1,6)=0.3;\mathrm{Luigi}\to \mathrm{Matteo}\\ \hfill & A(6,1)=0.2;\mathrm{Matteo}\to \mathrm{Luigi}\hfill & \hfill A(1,7)=0.3;\mathrm{Luigi}\to \mathrm{George}\\ \hfill & A(7,1)=0.2;\mathrm{George}\to \mathrm{Luigi}\hfill & \hfill A(1,8)=0.3;\mathrm{Luigi}\to \mathrm{Leon}\\ \hfill & A(1,9)=0.3;\mathrm{Luigi}\to \mathrm{Tamas}\hfill & \hfill A(1,10)=0.2;\mathrm{Luigi}\to \mathrm{Henry}\\ \hfill & A(1,11)=0.2;\mathrm{Luigi}\to \mathrm{Adriano}\hfill & \hfill A(11,1)=0.2;\mathrm{Adriano}\to \mathrm{Luigi}\\ \hfill & A(1,12)=0.2;\mathrm{Luigi}\to \mathrm{Maide}\hfill & \hfill A(1,13)=0.2;\mathrm{Luigi}\to \mathrm{Mario}\end{array}$$

(8)

To initialize the dynamical process, a random knowledge $k_i$ is selected. Based on our discourse, the time horizon of the dialogue is $T=20$, which is characterized by the question index that is said by Agent 1. The B coefficient is assumed to be equal to $0.1$ for each time. The simulator trends of nonlinear maieutic knowledge evolution from dialogue are shown in Figure 5. The graph shows an oscillatory trend in the knowledge of various agents. Moreover, the agents that are only cited maintain a constant knowledge.

Agent 1 requires knowledge from the other agents. It achieves the maximum when the other supplies knowledge. An antiphase behavior with the other actors with the agent is remarked. When the stronger Agent 1 achieves the maximum of knowledge, which prompts another question, it suffers a crisis: this is the up and down meaning of the knowledge trend of Agent 1.

In order to have a view of the cognitive schemes of the discussed process, the graph of the shared knowledge space is given in Figure 6, where the agents in the knowledge domain are reported. Moreover, in Figure 7, the cumulative knowledge over turns is shown. As cumulative knowledge is intended, the number of concepts and new subjects learned during the dialogue by Agent 1 is presented.

5. The a Posteriori Answers Based on ChatGPT Maieutic Appoach

This section will be the dialogue between the authors and ChatGPT [24,25]. The previous 20 questions in a real historic discussion are formalized in two groups: the first one of 20 and the second of 21 questions. In the first part of this section are reported the formulated 20 first commands and the summary of answers given by the GPT tool. The same has been carried out for the second part of questions and answers directly.

5.1. The First 20 Questions

Q1 

Is the design of a control system based on experience?

Q2 

Could we use expert systems to assist in the design of compensators?

Q3 

I mean using expert systems to help select the elementary networks.

Q4 

Yes, I mean selecting the lead-lag parameters with the help of expert systems.

Q5 

Under which conditions can expert systems select the appropriate compensator?

Q6 

That’s not entirely accurate. Some systems cannot be compensated using simple lead-lag networks.

Q7 

I know that the double PIP property is required to choose a lead-lag network as a compensator.

Q8 

Therefore, to design the expert system, we need a knowledge base that includes topics in robust control. That’s not entirely accurate. Some systems cannot be compensated using simple lead-lag networks.I know that the double PIP property is required to choose a lead-lag network as a compensator. Therefore, to design the expert system, we need a knowledge base that includes topics in robust control.

Q9 

Could I have a discussion with Prof. Zadeh to get suggestions on incorporating fuzzy concepts into my expert system for compensator design?

Q10 

I understand. Moreover, I need a fast controller that can handle more detailed process information. How can this be practically implemented?

Q11 

Dear Prof. Zadeh, I will speak with Dr. Gianguido Rizzotto about the possibility of designing a fuzzy controller platform.

Q12 

The project we developed is based on the WARP 1 fuzzy microcontroller. Are you familiar with it?

Q13 

Very good. Are you also familiar with the WARP 2 device?

Q14 

Ideally, I want a system that can both identify a fuzzy model and generate a fuzzy controller to ensure desired closed-loop performance. Can the WARP 2 handle this?

Q15 

Indeed, the problem is easier to manage if process control specialists are involved in the controller design. But what can I do if they are not?

Q16 

Does this mean using neural networks for system identification?

Q17 

That’s a good idea. However, isn’t the backpropagation algorithm poorly conditioned for learning?

Q18 

Good point. Additionally, I have an idea: using global optimization algorithms to overcome the drawbacks you mentioned.

Q19 

Using a classical multilayer perceptron introduces some issues. I’m considering extending the theory to complex and quaternion-based networks. What’s your opinion?

Q20 

I would like to propose using quaternion-based networks for both system identification and controller implementation.

Q21 

Indeed, this approach should ultimately be implemented on digital systems. But I’m also curious—what about implementation using analog systems?

The questions are reported before without the answer due to the fact that a detailed discussion will be too tedious. Moreover, ChatGPT will provide us with a summary of the discussion, as reported in the next section.

5.2. GPT Answers

Here is a structured but conversational discussion addressing your points, integrating the ideas you presented:

A1 

Is the design of a control system based on experience?

Yes, in many practical scenarios, control system design often relies on the engineer’s experience and intuition. Classical control design techniques like tuning PID or lead-lag compensators have traditionally involved trial-and-error or heuristic methods developed through accumulated expertise.

A2–4 

Could expert systems assist in the design of compensators, particularly in selecting elementary networks and lead-lag parameters?

Absolutely. Expert systems can encapsulate design heuristics and rules derived from expert knowledge to help automate compensator design. For example, an expert system could analyze system characteristics and recommend lead-lag parameters based on a knowledge base of control principles and prior designs.

A5–7 

Under what conditions can expert systems select the appropriate compensator?

Expert systems can effectively select compensators when the design problem matches the assumptions embedded in their knowledge base. For instance, the classic lead-lag network is suitable when the system satisfies properties like the Parity Interlacing Property (PIP) property. If the system doesn’t meet these conditions, simpler compensators may not suffice.

A8 

Importance of robust control knowledge base

To design a competent expert system, the knowledge base must cover advanced control concepts, including robust control. This allows the system to handle uncertainties and more complex dynamics, extending beyond simple compensator selection.

A9–11 

Incorporating fuzzy concepts and fast controllers

Discussing with experts like Prof. Zadeh is a great step for integrating fuzzy logic into the compensator design process. Fuzzy controllers can handle uncertainties and nonlinearities better, and platforms like the WARP 1 fuzzy microcontroller provide practical hardware implementation. This leads to fast controllers that process detailed information effectively.

A12–14 

Familiarity with WARP devices and fuzzy modeling

The WARP 1 device is a known fuzzy microcontroller platform; WARP 2 offers improvements and could support both fuzzy model identification and controller generation, providing an integrated solution for robust closed-loop performance.

A15 

What if process control specialists are unavailable?

When specialists are not accessible, automated design tools—combining expert systems, fuzzy logic, and machine learning—can help bridge the gap by embedding expert knowledge and adaptive algorithms.

A16–18 

Neural networks and learning challenges

Neural networks are indeed promising for system identification, but classical algorithms like backpropagation can struggle with convergence and conditioning. Incorporating global optimization methods can help avoid local minima and improve learning robustness.

A19–20 

Extending neural networks with complex and quaternion-based approaches

Extending theory to complex and quaternion-valued neural networks is an exciting frontier. These can naturally handle multidimensional signals and rotational symmetries, offering potentially more efficient and richer representations for system identification and control.

A21 

Implementation on digital vs. analog systems

While digital implementation is dominant due to flexibility and scalability, analog systems still hold interest for ultra-fast or low-power applications. Exploring analog or hybrid architectures for these advanced controllers could open new possibilities.

If you’d like, I can help you develop detailed explanations or draft specific questions or proposals for your discussions with Prof. Zadeh or Dr. Rizzotto on fuzzy and neural control systems. Would that be helpful?

5.3. Second Part GPT Questions and ChatGPT Answers

The second set of questions with ChatGPT has been direct and a short summary of the answers is immediately reported:

Question 1: I was just discussing the possibilities of implementing control for complex systems using analog processors.

GPT: That’s a very timely topic—analog processors, especially when designed for parallel computation, offer significant advantages in speed and energy efficiency for real-time control of complex, nonlinear systems.

Question 2.: What would you suggest?

GPT: I suggest exploring hybrid analog–digital architectures. Analog processors can handle continuous-time dynamics efficiently, while digital components can manage high-level logic and long-term adaptation.

Question 3.: What is your opinion on Cellular Nonlinear Networks (CNNs)?

GPT: CNNs are a powerful paradigm for distributed, parallel processing. Their local connectivity and nonlinear dynamics make them ideal for implementing spatiotemporal control laws, especially in systems requiring real-time response.

Question 4.: But what is your opinion on the role of this approach?

GPT: I believe CNNs represent a foundational approach for emergent control. Their role is especially important in modeling systems where global behavior arises from local interactions, such as swarm robotics or distributed sensor networks.

Question 5.: What is your opinion on the ACE device?

GPT: The ACE (Analogic Cellular Engine) device is a landmark in analog VLSI computing. It demonstrates the practical viability of CNN-based processing for applications like image processing and edge detection at high speeds and low power consumption.

Question 6.: What has Luigi Fortuna contributed to the field of CNNs?

GPT: Luigi Fortuna has made substantial contributions, particularly in extending CNN theory to practical applications. His work has bridged the gap between nonlinear dynamics, analog computing, and control, pushing forward real-world implementations of CNNs.

Question 7.: Did you know that the ACE 128 × 128 was implemented by STMicroelectronics?

GPT: Yes, that implementation was significant—it showed that industrial-scale fabrication of CNN-based processors was feasible. It also validated CNN hardware in real-world signal processing tasks.

Question 8.: What is your opinion on the potential of designing controllers based on CNNs?

GPT: I think there is great potential, especially for embedded, real-time systems where fast, distributed decision-making is crucial. CNNs could form the backbone of adaptive and decentralized controllers, particularly in fields like robotics and autonomous systems.

Question 9.: Lotfi Zadeh, Leon Chua, and Luigi Fortuna are discussing their joint research. What is the topic?

GPT: They are most likely discussing the convergence of fuzzy logic, nonlinear dynamics, and cellular architectures—specifically, Cellular Nonlinear Fuzzy Networks.

Question 10.: I’ll give you the correct answer: they are discussing Cellular Nonlinear Fuzzy Networks!

GPT: That makes perfect sense. Cellular Nonlinear Fuzzy Networks combine the strengths of fuzzy inference with the structural efficiency of CNNs, enabling flexible yet localized decision-making.

Question 11.: Fuzzy Cellular Nonlinear Networks are distributed, locally connected architectures in which each cell is represented by a dynamical system governed by fuzzy rules.

GPT: Exactly. This architecture allows for adaptive control with high fault tolerance, ideal for systems with uncertain, nonlinear, or time-varying dynamics.

Question 12.: Therefore, the concept of emergent control for distributed systems arises.

GPT: Indeed. Emergent control leverages local rules and interactions to produce globally coherent behavior—a hallmark of many natural and engineered systems.

Question 13.: But what is your opinion on brain-based control architectures?

GPT: They are not only fascinating but increasingly practical. Brain-based architectures offer models for distributed, adaptive, and robust control strategies, drawing inspiration from neurodynamics, plasticity, and hierarchical organization.

Question 14.: Indeed, there is a clear coherence between distributed emergent control and principles of brain function.

GPT: Yes, both rely on decentralized processing, local feedback, and adaptive learning—principles that enable resilience and flexibility.

Question 15.: Today, we have the possibility of using Brain-Computer Interfaces (BCIs). What do you think about that?

GPT: BCIs open a transformative pathway for control systems. They enable direct integration between neural signals and engineered systems, which could revolutionize fields like assistive robotics, prosthetics, and cognitive automation.

Question 16.: This represents a crucial link between brain engineering and advanced control systems.

GPT: Absolutely. The feedback loop between neural intent and machine execution is a frontier for both neuroscience and control engineering.

Question 17.: Moreover, the modeling and control of human-machine systems is a highly relevant topic today.

GPT: It’s central to modern cyber-physical systems. As machines become more integrated into daily life, modeling the dynamics of human-machine interaction becomes critical for safety, performance, and user experience.

Question 18.: Essentially, the models are relatively simple—such as in human car-driving control.

GPT: True. In some cases, simple models suffice, but even these can exhibit complex behaviors when feedback, delays, and environmental uncertainty are included.

Question 19.: In my opinion, modeling such systems requires time-delay theory and accurate knowledge of the actual feedback parameters. What do you think?

GPT: I agree. Time delays and feedback loops are central to accurately modeling human-in-the-loop systems. Without accounting for them, models may fail to predict key dynamics like instability or overcorrection.

Question 20.: In your opinion, what are the future perspectives in this area?

GPT: Future perspectives include adaptive control informed by neurocognitive data, closed-loop BCI-driven systems, and analog-digital hybrid architectures capable of learning from sparse, noisy inputs.

Question 21.: That’s not a satisfactory answer—I was referring to real-world applications.

GPT: Understood. Real-world applications include adaptive exoskeletons, autonomous vehicles with human override systems, intelligent neuroprosthetics, and haptic-feedback surgical robots.

Question 22.: That’s a better answer now. I would also add surgical robots as an example.

GPT: Absolutely—surgical robots are a key example where high-precision control, real-time feedback, and human intent interpretation converge.

5.4. Summary of the Perceived Results

Of course, the set of answers proposed by ChatGPT depends on the well-formulated questions, due to the real dialogue developed over the years. Moreover, the answers depend on the accuracy of ChatGPT’s information. That depends, of course, on the accrual research status that also includes more of the topic previously faced in the real dialogue.

Referring to the first set of questions, the proposed answers are detailed, and a prospective project is proposed by ChatGPT.

Table 1. In this table, the opinion of the authors regarding the GPT answers for questions 1 to 22 is reported.

Question	Sufficient	Good	Very Good
Q1		x
Q2		x
Q3			x
Q4			x
Q5		x
Q6			x
Q7		x
Q8		x
Q9		x
Q10		x
Q11		x
Q12		x
Q13		x
Q14	x
Q15		x
Q16		x
Q17	x
Q18	x
Q19	x
Q20		x
Q21		x
Q22		x

shows the GPT scores for each answer of this first set according to the authors. Indeed, the project details that are included in Appendix A are well known in the community, and more educational tools that have just been adopted reflect the items of the ChatGPT proposal. In the table, we adopted BLEW scores as follows:

• 0.3–0.5 sufficient;
• 0.5–0.7 good;
• 0.7–0.9 very good.

The table is built by using reference-specific books such as the Handbook of Automatic Control [7,26], and the evaluation of anonymous professors of Automatic Control.

In regard to the second set of questions, the system answers in a general manner and, of course, cannot have the capabilities to give real advanced perspectives. Moreover, the system capabilities to make reports, to summarize contents, and to create artificial papers and documents are relevant.

Figure 8 reports the cognitive map referred to the ChatGPT dialogue on control systems. It mainly shows the relationship among the various discussed topics referred to the first part of the dialogue. More similarity links among the graphs shown in Figure 5 and in this one are shown. The graph also emphasizes the more strongly connected items.

In Figure 9, the cognitive map of the dialogue on emerging control architecture, developed in the second part of the dialogue with ChatGPT, is presented. Indeed, by looking at these two figures and comparing them with the cognitive map that was obtained by the real dialogue, some analogies can be observed. This means that ChatGPT’s dialogue is efficient in giving a full representation of the real one.

Furthermore, these findings can be contextualized within the broader AI–Control co-design literature. Recent contributions in federated and generative learning provide interesting parallels with the maieutic framework. For instance, IFL-GAN [27] introduces an MMD-based aggregation strategy that resonates with distributed cognitive processes; Fed-OGD [17] addresses straggler effects in federated optimization, which can be compared to the iterative refinement mechanism of dialogic questioning; finally, DLS-GAN [28] proposes defect-sensitive data augmentation that strengthens robustness, especially in industrial robotics contexts. Together, these algorithmic paradigms illustrate how advances in AI–Control integration can be seen as complementary to the maieutic approach, emphasizing distributed cognition, robustness, and adaptive co-evolution of knowledge.

6. Conclusions

In this paper, we propose a discussion aimed at highlighting how the maieutic method can serve as a general tool for investigation, clarification, and the promotion of innovation in the field of Automatic Control. This approach has been developed over several years and has led to the formulation of broad concepts that guide researchers and engineers toward advanced and efficient solutions. Maieutics facilitates the emergence of synergistic resources, often leading to unexpected and innovative results. In this respect, it resonates with the fundamental task of modern science, which is interaction, with dialogue being its essential mechanism. Face-to-face dialogue remains particularly effective, although remote dialogue is also of great value and increasingly appreciated. The initial exploration of this approach was summarized in more than 40 questions, through which a set of satisfactory insights was achieved. Building upon this, the authors now propose the development of a maieutic process using ChatGPT. The knowledge available today—especially through AI tools like ChatGPT—is significantly more comprehensive than what was available in the past. Importantly, ChatGPT can also leverage concepts developed by the authors in earlier studies.

Moreover, since the authors are already familiar with the desired outcomes, they can formulate questions in a way that steers the dialogue toward those insights. To obtain a more schematic and complete understanding of the topics at hand, the authors propose an expanded set of 45 questions. This larger structure aims not only to elicit correct answers but also to stimulate problem awareness and conceptual exploration.

Thoughtful suggestions and prompts can help guide ChatGPT to provide more informative and insightful responses, and the learning that occurs during the dialogue improves the system’s ability to move beyond schematic or overly technical replies. In the authors’ view, many of ChatGPT’s responses are factually correct but do not always encourage problem posing or deep engagement. For this reason, effective use of the tool requires substantial knowledge of the subject matter and high logical and critical thinking skills on the part of the user.

In this paper, both mathematical models of the dialogue are introduced and details about the cognitive models of it are derived, also referring to the virtual ChatGPT discourse.

Ultimately, the proposed approach seeks to make ChatGPT a partner in interactive learning and conceptual development, expanding the scope of maieutic dialogue in the context of Automatic Control innovation. In Appendix A, a proposal made by ChatGPT is reported. It is of the opinion of the authors that the long dialogue addressed to that should lead to a project.