Advances in Applied Optimization in Automatic Control and Systems Engineering

Applied optimization in automatic control and systems engineering involves developing and implementing mathematical methods to improve the performance and efficiency of automated systems. This interdisciplinary field combines principles from control theory and computational algorithms to design and fine-tune systems for optimal operation. Techniques such as linear programming, nonlinear optimization, and dynamic programming are used to solve complex problems in real time, ensuring that systems respond effectively to changing conditions and constraints. Applications range from industrial automation and robotics to aerospace and energy systems, where optimizing parameters such as speed, accuracy, and resource use 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.

This Special Issue aims to highlight the importance of optimization techniques in automatic control and engineering systems. To this end, it brings together fifteen high-quality articles that address diverse problems, including tuning fractional-order and proportional–integral–derivative controllers, sliding-mode strategies, and deep-learning-based supervisory systems. All of these articles share the goal to apply optimization methods to improve system stability, robustness, responsiveness, and efficiency.

Meena et al. [1] provide an overview of algorithms for analyzing power flows and short-circuit modes in microgrids across two operating modes: network and isolated. The results of a comparative analysis of various methods, such as Newton–Raphson and backward/forward sweeps, for analyzing power flows and short-circuit modes, as well as approaches to modeling various components of microgrids. The article’s content is of interest, as the mass development of microgrids requires the use of the most technically effective methods with minimal financial costs for implementation.

Zambou et al. [2] introduce a hybrid algorithm for maximum power point tracking (MPPT) of a photovoltaic system under partial shading conditions, achieving fast convergence and low oscillation. This is done by integrating a nonlinear discrete proportional–derivative (PID) controller with the classical perturbation–observation algorithm. The PID controller parameters are optimized using particle swarm optimization (PSO). The result is a scheme that improves response speed, reduces oscillations around the operating point, and increases efficiency under various environmental conditions.

Mansouri et al. [3] present a fault-tolerant control (FTC) strategy for Linear Parameter Varying (LPV) systems with variable delays combining an observer and a sliding-mode controller. The proposed scheme formulates the FTC design problem using Lyapunov–Krasovskii functionals and multi-objective Linear Matrix Inequality (LMI) conditions to balance robustness, performance, and stability. The adaptability of the FTC approach effectively handles uncertainties, nonlinearities, and delay variations, demonstrating effective integration with optimization tools.

Clempner [4] addresses the long-standing challenge of incomplete information in security games by using a Bayesian Markov game model and an associated reinforcement learning (RL) technique. This research problem is indeed important in security game research and has caught wide attention from the security community. The main contribution of the manuscript is a systematic method that combines stochastic modeling, a proximal gradient approach for equilibrium computation, a Bayesian RL technique, and a random-walk approach for implementation.

Montoya et al. [5] present a work on the formulation and solution of the power flow problem for bipolar direct current networks with unbalanced constant power loads. An integrated nonlinear model is proposed that represents monopolar and bipolar load configurations, as well as voltage coupling between conductors. Different iterative algorithms based on Newtonian and quasi-Newtonian methods with constant Jacobian approximations are developed and compared. The proposed approach provides key elements for efficiently resolving operational and planning problems in modern electrical networks.

Gu and Xi [6] introduce an integral strategy for the optimal design of the diagnosticability of unmanned aerial vehicles, combining structural analysis with a quantitative metric based on the mean and covariance discrepancy and an optimization scheme using the Grey-Wolf algorithm. Starting with the generation of residuals using structurally overdetermined sets, a framework is established that enables the evaluation and improvement of fault detection and isolation capabilities, while accounting for the system’s causal relationships. The proposal is validated in simulation, demonstrating significant improvements with respect to other methods in the literature.

Phan Thi et al. [7] tackle the problem of secure control and communication of electric drive systems in wireless environments. It combines a neural network-based controller with fuzzy emotional learning and a disturbance observer to enhance robustness against uncertainties and attacks. The approach is implemented on an embedded ESP32 microcontroller to conduct experimental tests validating secure real-time transmission.

Ahmed et al. [8] have developed an energy management system for electric vehicles. This system optimally manages batteries and ultracapacitors using control strategies to distribute power dynamics and recover energy through regenerative braking. The system improves overall efficiency, dynamic performance, and the lifespan of the energy storage system. The proposal is validated in numerical simulations and experimentally.

Barroso-García et al. [9] present a comprehensive evaluation of the energy performance of a compressed air system based on a screw compressor operating under real-world, variable-load conditions. It combines experimental measurements and thermodynamic modeling to identify significant deviations from nominal efficiency. Based on this analysis, operational limitations associated with low-demand regimes are identified, and techno-economic strategies, such as reactive power compensation and the adoption of more flexible operating schemes, are proposed to improve overall system performance.

Ben Alaia et al. [10] propose an adaptive observer with fixed-time convergence for perturbed systems with varying parameters, incorporating an online perturbation learning mechanism that eliminates the need for prior bounds and significantly improves noise rejection through a non-diagonal gain structure. Using a formulation based on parameter-dependent Lyapunov functions and less conservative LMI conditions, the method enables a systematic design that balances performance, robustness, and computational feasibility, as demonstrated in power system applications with substantial improvements in convergence speed and steady-state error.

Obeidat et al. [11] present a systematic literature review on the Preference Selection Index (PSI) within the framework of multi-criteria decision-making. The review consists of a detailed critical analysis of over 100 studies, identifying the strengths and weaknesses of PSIs. The review includes the methodological background, areas of application, and integration with other techniques and ends with proposed future research directions to improve robustness and adaptability.

Du and Mao [12] propose a controller design approach for active suspensions based on modal-structure optimization, integrating partial self-structure allocation with a dynamic-response optimization scheme. By formulating a minimization problem that simultaneously considers vibration performance and energy consumption, the method enables the redistribution of dominant modes and the adjustment of system dynamics to improve vehicle comfort and stability. Numerical results demonstrate significant reductions in acceleration and body roll, as well as adequate robustness to uncertainties.

Sullivan et al. [13] introduce a novel framework for analyzing the behavior of convolutional neural networks from a data-centric perspective through the programmatic generation of synthetic sets that allow for the isolation and quantification of the contribution of specific features. Based on a theoretical formulation that links CNN learning with apriori-type pattern counting principles, the authors demonstrate that feature overlap across datasets can accurately predict model performance, eliminating the need for extensive training. The results show that intrinsic object characteristics dominate generalization capacity and validate a similarity algorithm that acts as a performance estimator.

Kumar and Shaik [14] present a reformulation of a mixed-integer programming model for medium- and long-term planning and scheduling in multi-stage biopharmaceutical processes. The representation of product life cycles and inventory management is modified using new binary variables and linear constraints. This modification helps to reduce computational complexity and to increase the cost-effectiveness and quality of solutions compared to previous approaches. Results obtained from case studies demonstrate greater efficiency in resource allocation and in meeting demands under realistic operational constraints.

Liu et al. [15] address the problem of emergency facility location and layout, which are critical to the efficiency of emergency rescue and resource allocation. For this, they formulate an optimization model that maximizes satisfaction with respect to response time. The problem addressed considers facility failures caused by uncertain factors and complex polygonal barriers that hinder transportation. The Artificial Ecosystem Optimization (AEO) algorithm is employed to obtain the solution. Numerical experiments and a practical case study are used to validate the method’s effectiveness.

The papers in this Special Issue show how applied optimization continues to evolve and improve the field of automatic control and systems engineering. We thank all authors for their valuable contributions and the reviewers for their careful and constructive evaluations. We hope this Special Issue inspires further innovation and collaboration.