Applied Optimization in Automatic Control and Systems Engineering

A special issue of Mathematical and Computational Applications (ISSN 2297-8747). This special issue belongs to the section "Engineering".

Deadline for manuscript submissions: 31 December 2025 | Viewed by 5275

Special Issue Editor


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Tecnológico Nacional de México/Instituto Tecnológico de Hermosillo, Ave. Tecnológico y Periférico Poniente SN, Hermosillo 83170, Mexico
Interests: predictive control; optimization; LPV systems; fault detection and isolation
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Special Issue Information

Dear Colleagues,

Applied optimization in automatic control and systems engineering involves the development and implementation of mathematical strategies to improve the performance and efficiency of automated systems. This interdisciplinary field combines principles from control theory, operations research, and computational algorithms to design and fine-tune systems for optimal operation. Techniques such as linear programming, nonlinear optimization, and dynamic programming are employed to solve complex problems in real-time, ensuring systems respond effectively to changing conditions and constraints. Applications range from industrial automation and robotics to aerospace and energy systems, where optimizing parameters like speed, accuracy, and resource usage is crucial for achieving desired outcomes. Through continuous advancements, applied optimization in automatic control and systems engineering drives innovation and enhances the capabilities of modern automated systems.

In this Special Issue, the aim is to discuss the state of the art of the most advanced optimization techniques (online and offline) and their applications in automatic control and systems engineering. Potential topics include (but are not limited to) the following:

  • Optimal control of nonlinear systems;
  • Optimal control of complex systems;
  • Optimal observer design;
  • Predictive control;
  • Neuronal networks;
  • Control systems;
  • Fault detection;
  • Fault tolerant control.

Prof. Dr. Guillermo Valencia-Palomo
Guest Editor

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Keywords

  • LMIs
  • optimal control
  • systems engineering

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Published Papers (6 papers)

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Research

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28 pages, 7329 KiB  
Article
Causal Diagnosability Optimization Design for UAVs Based on Maximum Mean Covariance Difference and the Gray Wolf Optimization Algorithm
by Xuping Gu and Xianjun Shi
Math. Comput. Appl. 2025, 30(3), 55; https://doi.org/10.3390/mca30030055 - 14 May 2025
Viewed by 138
Abstract
Given the growing complexity and variability of application scenarios, coupled with increasing operational demands, unmanned aerial vehicles (UAVs) are prone to faults. To enhance diagnosability and reliability in this context, this study proposes a causal diagnosability optimization strategy based on the Maximum Mean [...] Read more.
Given the growing complexity and variability of application scenarios, coupled with increasing operational demands, unmanned aerial vehicles (UAVs) are prone to faults. To enhance diagnosability and reliability in this context, this study proposes a causal diagnosability optimization strategy based on the Maximum Mean and Covariance Discrepancy (MMCD) metric and the Grey Wolf Optimization (GWO) algorithm. First, a qualitative assessment method for causal diagnosability is introduced, leveraging structural analysis to evaluate the detectability and isolability of faults. Next, residuals are generated using Minimal Structurally Overdetermined (MSO) sets, and a quantitative diagnosability assessment framework is developed based on the MMCD metric. This framework measures the complexity of diagnosability through the analysis of residual deviations under fault conditions. Finally, a diagnosability optimization technique utilizing the GWO algorithm is proposed. This approach minimizes diagnostic system design costs while maximizing its performance. Simulation results for a UAV structural model demonstrate that the proposed strategy achieves a 100% fault detection rate and fault isolation rate while reducing design costs by 70.59%. Full article
(This article belongs to the Special Issue Applied Optimization in Automatic Control and Systems Engineering)
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20 pages, 350 KiB  
Article
A Family of Newton and Quasi-Newton Methods for Power Flow Analysis in Bipolar Direct Current Networks with Constant Power Loads
by Oscar Danilo Montoya, Juan Diego Pulgarín Rivera, Luis Fernando Grisales-Noreña, Walter Gil-González and Fabio Andrade-Rengifo
Math. Comput. Appl. 2025, 30(3), 50; https://doi.org/10.3390/mca30030050 - 6 May 2025
Viewed by 184
Abstract
This paper presents a comprehensive study on the formulation and solution of the power flow problem in bipolar direct current (DC) distribution networks with unbalanced constant power loads. Using the nodal voltage method, a unified nonlinear model is proposed which accurately captures both [...] Read more.
This paper presents a comprehensive study on the formulation and solution of the power flow problem in bipolar direct current (DC) distribution networks with unbalanced constant power loads. Using the nodal voltage method, a unified nonlinear model is proposed which accurately captures both monopolar and bipolar load configurations as well as the voltage coupling between conductors. The model assumes a solid grounding of the neutral conductor and known system parameters, ensuring reproducibility and physical consistency. Seven iterative algorithms are developed and compared, including three Newton–Raphson-based formulations and four quasi-Newton methods with constant Jacobian approximations. The proposed techniques are validated on two benchmark networks comprising 21 and 85 buses. Numerical results demonstrate that Newton-based methods exhibit quadratic convergence and high accuracy, while quasi-Newton approaches significantly reduce computational time, making them more suitable for large-scale systems. The findings highlight the trade-offs between convergence speed and computational efficiency, and they provide valuable insights for the planning and operation of modern bipolar DC grids. Full article
(This article belongs to the Special Issue Applied Optimization in Automatic Control and Systems Engineering)
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21 pages, 519 KiB  
Article
Learning Deceptive Tactics for Defense and Attack in Bayesian–Markov Stackelberg Security Games
by Julio B. Clempner
Math. Comput. Appl. 2025, 30(2), 29; https://doi.org/10.3390/mca30020029 - 17 Mar 2025
Viewed by 320
Abstract
In this paper, we address the challenges posed by limited knowledge in security games by proposing a novel system grounded in Bayesian–Markov Stackelberg security games (SSGs). These SSGs involve multiple defenders and attackers and serve as a framework for managing incomplete information effectively. [...] Read more.
In this paper, we address the challenges posed by limited knowledge in security games by proposing a novel system grounded in Bayesian–Markov Stackelberg security games (SSGs). These SSGs involve multiple defenders and attackers and serve as a framework for managing incomplete information effectively. To tackle the complexity inherent in these games, we introduce an iterative proximal-gradient approach to compute the Bayesian Equilibrium, which captures the optimal strategies of both defenders and attackers. This method enables us to navigate the intricacies of the game dynamics, even when the specifics of the Markov games are unknown. Moreover, our research emphasizes the importance of Bayesian approaches in solving the reinforcement learning (RL) algorithm, particularly in addressing the exploration–exploitation trade-off. By leveraging Bayesian techniques, we aim to minimize the expected total discounted costs, thus optimizing decision-making in the security domain. In pursuit of effective security game implementation, we propose a novel random walk approach tailored to fulfill the requirements of the scenario. This innovative methodology enhances the adaptability and responsiveness of defenders and attackers, thereby improving overall security outcomes. To validate the efficacy of our proposed strategy, we provide a numerical example that demonstrates its benefits in practice. Through this example, we showcase how our approach can effectively address the challenges posed by limited knowledge, leading to more robust and efficient security solutions. Overall, our paper contributes to advancing the understanding and implementation of security strategies in scenarios characterized by incomplete information. By combining Bayesian and Markov Stackelberg games, reinforcement learning algorithms, and innovative random walk techniques, we offer a comprehensive framework for enhancing security measures in real-world applications. Full article
(This article belongs to the Special Issue Applied Optimization in Automatic Control and Systems Engineering)
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30 pages, 858 KiB  
Article
Sliding Mode Fault-Tolerant Control for Nonlinear LPV Systems with Variable Time-Delay
by Omayma Mansouri, Ali Ben Brahim, Fayçal Ben Hmida and Anis Sellami
Math. Comput. Appl. 2024, 29(6), 96; https://doi.org/10.3390/mca29060096 - 26 Oct 2024
Viewed by 1116
Abstract
This paper presents a robust sliding mode fault-tolerant control (FTC) strategy for a class of linear parameter variant (LPV) systems with variable time-delays and uncertainties. First fault estimation (FE) is conducted using a robust sliding mode observer, synthesized to simultaneously estimate the states [...] Read more.
This paper presents a robust sliding mode fault-tolerant control (FTC) strategy for a class of linear parameter variant (LPV) systems with variable time-delays and uncertainties. First fault estimation (FE) is conducted using a robust sliding mode observer, synthesized to simultaneously estimate the states and actuator faults of LPV polytopic delayed systems. Second, a sliding mode FTC is developed, ensuring all states of the closed-loop system converge to the origin. This paper presents an integrated sliding mode FTC strategy to achieve optimal robustness between the observer and controller models. The integrated design approach offers several advantages over traditional separated FTC methods. Our novel approach is based on incorporating adaptive law into the design of the Lyapunov–Krasovskii functional to improve both robustness and performance. This is achieved by combining the concept of sliding mode control (SMC) with the Lyapunov–Krasovskii function under the H criteria, which plays a key role in guaranteeing the stability of this class of system. The effectiveness of the proposed method is demonstrated through a diesel engine example, which highlights the validity and benefits of the integrated and separated FTC strategy for uncertain nonlinear systems with time delays and the sliding mode control. Full article
(This article belongs to the Special Issue Applied Optimization in Automatic Control and Systems Engineering)
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14 pages, 3165 KiB  
Article
Optimized Nonlinear PID Control for Maximum Power Point Tracking in PV Systems Using Particle Swarm Optimization
by Maeva Cybelle Zoleko Zambou, Alain Soup Tewa Kammogne, Martin Siewe Siewe, Ahmad Taher Azar, Saim Ahmed and Ibrahim A. Hameed
Math. Comput. Appl. 2024, 29(5), 88; https://doi.org/10.3390/mca29050088 - 2 Oct 2024
Cited by 4 | Viewed by 1512 | Correction
Abstract
This paper proposes a high-performing, hybrid method for Maximum Power Point Tracking (MPPT) in photovoltaic (PV) systems. The approach is based on an intelligent Nonlinear Discrete Proportional–Integral–Derivative (N-DPID) controller with the Perturb and Observe (P&O) method. The feedback gains derived are optimized by [...] Read more.
This paper proposes a high-performing, hybrid method for Maximum Power Point Tracking (MPPT) in photovoltaic (PV) systems. The approach is based on an intelligent Nonlinear Discrete Proportional–Integral–Derivative (N-DPID) controller with the Perturb and Observe (P&O) method. The feedback gains derived are optimized by a metaheuristic algorithm called Particle Swarm Optimization (PSO). The proposed methods appear to present adequate solutions to overcome the drawbacks of existing methods despite various weather conditions considered in the analysis, providing a robust solution for dynamic environmental conditions. The results showed better performance and accuracy compared to those encountered in the literature. We also recall that this technique provides a systematic design procedure in the search for the MPPT in photovoltaic (PV) systems that has not yet been documented in the literature to the best of our knowledge. Full article
(This article belongs to the Special Issue Applied Optimization in Automatic Control and Systems Engineering)
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Review

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25 pages, 1607 KiB  
Review
Optimizing Power Flow and Stability in Hybrid AC/DC Microgrids: AC, DC, and Combined Analysis
by Ghanshyam Meena, Veerpratap Meena, Akhilesh Mathur, Vinay Pratap Singh, Ahmad Taher Azar and Ibrahim A. Hameed
Math. Comput. Appl. 2024, 29(6), 108; https://doi.org/10.3390/mca29060108 - 24 Nov 2024
Cited by 3 | Viewed by 1387
Abstract
A microgrid (MG) is a unique area of a power distribution network that combines distributed generators (conventional as well as renewable power sources) and energy storage systems. Due to the integration of renewable generation sources, microgrids have become more unpredictable. MGs can operate [...] Read more.
A microgrid (MG) is a unique area of a power distribution network that combines distributed generators (conventional as well as renewable power sources) and energy storage systems. Due to the integration of renewable generation sources, microgrids have become more unpredictable. MGs can operate in two different modes, namely, grid-connected and islanded modes. MGs face various challenges of voltage variations, frequency deviations, harmonics, unbalances, etc., due to the uncertain behavior of renewable sources. To study the impact of these issues, it is necessary to analyze the behavior of the MG system under normal and abnormal operating conditions. Two different tools are used for the analysis of microgrids under normal and abnormal conditions, namely, power flow and short-circuit analysis, respectively. Power flow analysis is used to determine the voltages, currents, and real and reactive power flow in the MG system under normal operating conditions. Short-circuit analysis is carried out to analyze the behavior of MGs under faulty conditions. In this paper, a review of power flow and short-circuit analysis algorithms for MG systems under two different modes of operation, grid-connected and islanded, is presented. This paper also presents a comparison of various power flow as well as short-circuit analysis techniques for MGs in tabular form. The modeling of different components of MGs is also discussed in this paper. Full article
(This article belongs to the Special Issue Applied Optimization in Automatic Control and Systems Engineering)
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