https://ieco.usb.ac.ir/ International Journal of Industrial Electronics Control and Optimization en daily 1 Tue, 01 Sep 2026 00:00:00 +0330 Tue, 01 Sep 2026 00:00:00 +0330 https://ieco.usb.ac.ir/article_9445.html A home energy management system optimizes the electrical demand of household appliances according to price-based demand response programs. In this paper, we proposed a price-based demand response for a smart home with different types of appliances according to customer satisfaction, which also used electric and thermal storage systems. In the proposed method, various appliances were considered in the smart home modeled by the energy hub system. A multi-objective daily management is proposed which considered electricity costs and customer satisfaction simultaneously to provide comprehensive management for smart homes. This paper presents a multi-objective optimization approach that not only minimizes operating costs and maximizes customer satisfaction but also reduces environmental impacts through emission reduction, creating a more sustainable energy management system. After solving the multi-objective problem, the technique for order preference by similarity to the ideal solution was used to rank the solutions, considering the preference of the decision-maker. The proposed model investigates the response of the smart home energy system in different conditions. Also, stochastic optimization was applied to model the probabilistic nature of demands, PV, and wind energy. The simulation results demonstrate that the proposed method reduces the consumer dissatisfaction by 79.9% and reduces the range from 199 to 40 https://ieco.usb.ac.ir/article_9463.html This paper introduces a novel optimal iterative learning control scheme for continuous-time systems with multiple-inputs and multiple-outputs and linear time-varying dynamics. While iterative learning control has been extensively studied in the discrete-time domain, the development of optimal iterative learning control for continuous-time systems remains limited due to the lack of lifted-formulations and associated mathematical challenges. The proposed method transforms the original optimal iterative learning control problem into a linear quadratic tracking-like problem, enabling the derivation of an explicit close-loop control law that ensures both tracking performance and control effort minimization. Unlike many existing approaches that rely on learning algorithms involving derivative terms, which are often sensitive to measurement noise, the proposed design avoids such terms and remains computationally efficient. Moreover, the monotonic convergence of the tracking error and the associated cost function are proved by rigorous mathematical analysis. Theoretical results are supported by four comprehensive simulation examples, including comparisons with several existing iterative learning control methods. Quantitative evaluations confirm that the proposed optimal scheme significantly outperforms previous techniques in terms of convergence speed and error reduction rate. This contribution offers a new framework for the optimal control of continuous-time systems with multiple inputs and outputs in repetitive tasks and provides a foundation for future extensions to constrained, nonlinear, or partially measurable systems. https://ieco.usb.ac.ir/article_9484.html High-speed rail systems, operating at speeds up to 350 km/h, face significant challenges in delivering reliable network connectivity due to frequent handovers, signal degradation, and network congestion. This paper proposes the 5G-R framework, an optimized solution integrating beamforming, network slicing, railway-specific Long Short-Term Memory (LSTM) algorithms, and Multi-Access Edge Computing (MEC) to enhance connectivity performance. By leveraging real-time train data, such as speed and GPS location, the framework optimizes handover prediction and traffic management, achieving robust performance in diverse environments. Compared to 4G LTE and standard 5G, the 5G-R framework demonstrates significant improvements, including a 250 Mbps throughput, 15 ms latency, and 95% handover success rate. Network slicing optimizes resource allocation, reducing congestion by approximately 30%, while MEC enables low-latency control for train systems. Field trials along the Beijing-Zhangjiakou railway (174 km, urban/suburban) and simulations validate the framework’s adaptability across urban and rural routes. Designed for compatibility with the Future Railway Mobile Communication System (FRMCS), the 5G-R framework lays a foundation for future advancements, including 6G and satellite communications. Future research should focus on optimizing performance in extreme environments and densely populated routes to support autonomous transport systems. This optimization-driven approach establishes a scalable model for next-generation rail communication systems. https://ieco.usb.ac.ir/article_9501.html This work proposes an adaptive resilient control for uncertain nonlinear cyber-physical systems (CPSs) under deception attacks. It is assumed that attacker injects false data into the commands exchanged between the controller and actuator over the communication channels. The injected false data affects the control input in both additive and multiplicative forms. To deal with the uncertain dynamics of the system and additive term of cyber-attacks, the radial basis function-neural networks (RBF-NNs) are invoked. Also, to handle adverse effects of multiplicative term of cyber-attack, the Nussbaum-type gain function is employed. Then, by integrating the RBF-NN model and Nussbaum function into the command filtered backstepping (CFB) approach, the proposed resilient control scheme is designed. Compared with the existing works, the proposed control eliminates the “explosion of complexity” problem in the conventional backstepping approach, removes the trial and error in choosing time constant of the first order filters in the dynamics surface control (DSC) approach, compensates the filtering error and deals with both additive and multiplicative cyber-attacks in “controller to actuator” channel, simultaneously. Also, it mitigates the effects of the cyber-attack without requiring separate attack estimation unit, controller reconfiguration or readjustment algorithm. Simulation results on the robotic arm under different cyber-attacks verify effective resilient performance of the proposed control scheme. https://ieco.usb.ac.ir/article_9521.html Low back pain and spinal disorders are widespread issues affecting individuals globally, often requiring effective rehabilitation methods. This paper proposes a cable-driven parallel robot designed to assist in rehabilitation by moving patients' legs along frontal and sagittal axes. A novel Current Iterative Learning Control (CILC) algorithm is introduced to enhance the system's precision and reliability. The CILC ensures the convergence of system states and outputs to desired trajectories, maintaining bounded tracking errors even under disturbances, noise, or initial condition inaccuracies. Simulations demonstrate the controller's effectiveness when applied to the robotic structure, highlighting its potential for accurate and robust rehabilitation applications. By addressing challenges such as system nonlinearity and external uncertainties, the proposed solution offers a promising advancement in electromechanical rehabilitation equipment. This innovation not only improves patient outcomes but also provides a cost-effective and adaptable tool for diverse therapeutic needs. The integration of advanced control strategies with robotic systems marks a significant step forward in spinal rehabilitation technology. https://ieco.usb.ac.ir/article_9762.html The pursuit of time-optimal performance is a fundamental objective for high-speed robotic and mechatronic systems, where minimizing settling-time directly enhances throughput and operational efficiency. Despite its importance, deriving exact solutions for practical systems remains a formidable challenge. Existing methodologies, which predominantly rely on numerical optimization or simplified plant models, often yield suboptimal results; they fail to provide guarantees of global optimality and frequently prove inadequate when confronting realistic system constraints such as actuator saturation. To address this critical gap, this paper introduces an analytical framework for synthesizing time-optimal control laws for a class of second-order systems. The proposed method is based on phase portrait analysis, a powerful geometric approach that facilitates the direct derivation of the exact switching curve. This curve is the critical element that defines the globally optimal, bang-bang controller. The final control law is presented in a closed-form expression, thereby enabling computationally efficient and straightforward implementation. Simulation results validate the theoretical framework, demonstrating that the proposed controller consistently achieves the theoretical performance by tracking the optimal trajectory perfectly. https://ieco.usb.ac.ir/article_9766.html Today, power system operators face two major challenges: (1) determining the flexibility region for generators due to the increasing penetration of renewable generation in power systems, and (2) the rise in ambient temperature. Structural limitations in a power network and changes in its topology significantly affect the generator's flexibility region. In this paper, in addition to describing the structure of the flexibility region, the variability of these regions due to changes in the network topology is thoroughly demonstrated. For this purpose, the problem of determining the flexibility region of the generators (GFR) is integrated with the Optimal Transmission Switching (OTS) and Dynamic Line Rating (DLR) problems to develop the flexibility region and maximize the use of renewable power generation. To reduce the computational time and increase the effectiveness of the proposed method, an innovative method (referred to as Radar Scanning) is used to categorize the data related to the changes in the output power of renewable generation units. To evaluate the proposed method, the IEEE 30-bus and 118-bus power systems are employed, and the numerical results obtained from the simulation show that: first, OTS and DLR can enhance and improve the flexibility region of the generators in a power system; and second, by employing the proposed algorithm, the flexibility region of 30- and 118-bus power systems are determined by examining only a limited number of data (less than 30%), resulting in a 92% and 89% reduction in computational time, respectively. https://ieco.usb.ac.ir/article_9452.html This paper presents a comparative study on the application of artificial intelligence for optimizing External Lightning Protection Systems (ELPS) in photovoltaic power (PV) plants. The research addresses the critical need for advanced protection systems in solar installations, which are particularly vulnerable to lightning strikes due to their expansive outdoor configurations. Through a detailed comparative analysis, the study evaluates multiple AI approaches, including metaheuristic algorithms and machine learning models. The investigation reveals that metaheuristic algorithms often have lower accuracy compared to modern AI techniques. All comparisons are based on a multi-level optimization framework, systematically addressing air termination design, grounding system configuration, and overall system integration. The results show superiority in sensitivity analysis in the transformer model. Compared to other models, the random forest (RF) model, along with the artificial neural network (ANN) model, has a higher speed in data analysis. However, physics-informed neural networks (PINN) achieve remarkable improvements, delivering 93% protection coverage with only 3.2% grounding error while significantly reducing design convergence times. https://ieco.usb.ac.ir/article_9684.html As the field of nanotechnology rapidly advances and the need for faster processing in smaller dimensions grows, as does the integration of Very Large-Scale Integration (VLSI) technology. These difficulties include things like large-scale area needs, high power consumption, and low operating speeds, which call for new approaches to lessen these constraints. Developed and implemented at the nano-based, Quantum-Dot Cellular Automata (QCA) technology presents itself as a viable way around these obstacles. The advent of QCA technology heralds our entry into the nano-scale realm, where the advantages of enhanced processing speeds, reduced dimensions, and minimal power consumption become manifest. This article focuses on the 7-input majority gate, a fundamental component in QCA technology, distinguished by its fault-tolerant characteristics. The primary objective is to present the design and simulation of this key gate within the context of QCA technology. Noteworthy among the merits of the 7-input majority gate is its capacity to implement logic gates with a greater number of inputs, consolidating multiple functionalities within a single gate. QCADesigner and QCAPro software have simulated the given gate, and the results demonstrate the exact and correct operation of the gate. This gate generates the output signal every 0.25 clock cycles and is built with 66 quantum cells within a 0.03 µm2. The simulation results demonstrate the precision of the circuit's operation. Additionally, basic fault-tolerant gates such as 4-input AND, and 4-input OR using a 7-input fault-tolerant majority gate have been suggested in order to illustrate the proper operation of the new gate. https://ieco.usb.ac.ir/article_9767.html In many data mining problems, leveraging structural and local connectivity information can significantly improve clustering performance. This paper presents a novel semi-supervised clustering framework that integrates weighted feature information, Delaunay-based graph construction, and pairwise constraints. First, feature weights are computed based on within-class pairwise variability, emphasizing dimensions that contribute most to local cluster structure. Weighted distances between samples are then calculated, and a Delaunay graph is constructed and filtered using an influence radius, preserving meaningful local geometric relationships while removing redundant edges. To capture higher-order neighborhood information, a GraphSAGE-style embedding propagates feature information through the graph, generating enriched low-dimensional representations of the data. Pairwise constraints are incorporated into the similarity matrix to encode prior knowledge about sample relationships, guiding the clustering process. Finally, semi-supervised clustering is performed using constraint-based spectral clustering. Experiments on benchmark datasets demonstrate that the combination of structural graph information, feature weighting, and pairwise constraints substantially improves clustering accuracy. The proposed framework is flexible and can be effectively applied across diverse data domains. https://ieco.usb.ac.ir/article_9795.html Effective energy management in renewable-based microgrids demands advanced optimization and forecasting strategies capable of addressing the intrinsic uncertainties of solar generation and load demand. This paper proposes a comprehensive day-ahead scheduling framework based on Model Predictive Control (MPC) to enhance the operational efficiency of a grid-connected microgrid comprising photovoltaic units, microturbines, fuel cells, and battery energy storage. The MPC structure incorporates 24-hour-ahead forecasts of load and solar irradiance generated through multiple deep learning architectures, enabling dynamic adaptation to rapidly changing environmental and consumption conditions. To solve the underlying optimization problem, a novel Quadratic Interpolation Optimization (QIO) algorithm is employed, offering improved convergence behavior and robustness in comparison with conventional metaheuristic methods. The integrated forecasting–optimization methodology ensures optimal dispatch of distributed resources, effective utilization of storage systems, and economically efficient power exchange with the utility grid. Extensive simulations validate the superiority of the proposed MPC-QIO framework in reducing operational costs, enhancing renewable energy penetration, and maintaining system reliability even under forecasting uncertainties. The results confirm that the synergy between deep learning-based prediction and advanced optimization significantly strengthens the controllability and resilience of modern microgrids, highlighting the method’s strong potential for real-world deployment. https://ieco.usb.ac.ir/article_9887.html This paper presents a new comprehensive study on multi-phase interleaved DC-DC boost converters for fuel cell power interface. High power density DC-DC converters are usually required due to the volumetric and gravimetric constraints in the various fuel cell power system applications. On the other hand, in sensitive applications such as vehicular systems, using a reliable converter is a critical feature. Therefore, different multi-phase configurations with various phase numbers are investigated to find the configuration with the highest power density and reliability. Boost converters with single, two, and four-phase configurations are designed with considerably low input current and output voltage ripples compatible with the fuel cell application. Their performance parameters (especially their power densities) are investigated using the analytical and simulation results. To discuss their reliability, a reliability analysis based on a mathematical model and Markov diagram is employed to calculate the converters’ expected load loss values. In the end, among the considered configurations, the two-phase boost converter is selected to be used in fuel cell applications due to its superior performance in terms of power density and reliability. The selected boost configuration is implemented to extract the experimental results and verify the accuracy of the calculation and simulation results. https://ieco.usb.ac.ir/article_9935.html Enhancing the energy output of photovoltaic (PV) systems is essential due to their inherently limited efficiency. Consequently, maximum power point tracking (MPPT) techniques have become a crucial component in photovoltaic systems for improving energy harvesting efficiency. However, conventional MPPT methods often require accurate mathematical modeling of PV systems, which remains a significant challenge due to their highly nonlinear behavior. To address this issue, researchers have proposed various MPPT strategies. The complex nonlinear behavior of PV systems makes pattern extraction difficult, often leading to simplified assumptions that may reduce tracking accuracy and overall system performance. This study investigates the performance of five metaheuristic optimization algorithms for MPPT under partial shading conditions (PSC) to improve PV system efficiency. The considered algorithms include Particle Swarm Optimization Algorithm (PSOA), Grey Wolf Optimization Algorithm (GWOA), Cuckoo Search Optimization Algorithm (CSOA), Genetic Algorithm (GA), and Quantum-Inspired Evolutionary Algorithm (QIEA). Although several studies have investigated metaheuristic MPPT techniques under partial shading conditions, relatively limited research has provided a comprehensive comparative evaluation of swarm-based, evolutionary-based, and physics-inspired optimization approaches considering tracking efficiency and dynamic response characteristics. The results demonstrate that the physics-inspired QIEA achieves a superior balance between exploration and exploitation, thereby enhancing its ability to accurately identify the global maximum power point. https://ieco.usb.ac.ir/article_9772.html Organisms continuously adapt to changing resources and environmental conditions to ensure survival. Such adaptations may involve shifts in diet, habitat, or hunting strategies. Species that fail to adapt often face extinction, as evidenced by many species that no longer exist. Adaptation can generally be understood as a two-stage process. The first stage encompasses phenotypic adjustments, which occur in response to factors such as climate change, food availability, or the development of adaptive behaviors. These short-term changes increase the chances of survival for individuals by favoring the fittest under immediate conditions. The second stage involves genetic changes, where offspring chromosomes are formed through crossover and mutation of parental chromosomes. These genetic variations may either enhance the survival of the next generation or reduce it, thereby influencing long-term evolutionary success. In this study, a novel metaheuristic algorithm is introduced, inspired by the adaptability of socially living animals. The proposed algorithm was evaluated on a set of standard benchmark functions and compared with several well-established optimization methods. The results indicate that the proposed algorithm outperforms others in terms of convergence speed, solution accuracy, and robustness. Finally, to demonstrate its practical applicability, the algorithm was applied to an engineering problem involving air-conditioner load scheduling, where it achieved superior performance. https://ieco.usb.ac.ir/article_9791.html Railway traction vehicles transfer forces between rails and wheels through an adhesion ‎coefficient. In order to prevent wheel locking and shorten stopping distances, ‎estimating the adhesion conditions between rails and wheels is an essential task in ‎railway operations. Since the adhesion condition is influenced thru many factors, its ‎estimation technique is complex. This paper presents an intelligent square root ‎cubature Kalman filter (ISRCKF) to estimate adhesion force. The proposed method ‎has the advantage that it does not require to know the noise statistics. This method ‎integrates the differential evolution (DE) algorithm to tune the SRCKF by solving the ‎optimal values of the covariance matrix Q and measurement noise matrix R. It can ‎also decrease the error because of unknown noise, and increase the accuracy. ‎Furthermore, it exhibits a consistent enhancement in numerical stability due to the ‎assurance that all resultant covariance matrices remain positive semi-definite. This ‎innovative approach plays an active role in optimizing the utilization of the current ‎adhesion while reducing wheel wear by mitigating high creep values. The outcomes ‎demonstrate that the suggested approach yields superior estimation accuracy and ‎exhibits a swifter convergence rate in comparison to alternative methods.‎ https://ieco.usb.ac.ir/article_9805.html This paper presents an innovative adaptive sliding mode controller with disturbance rejection for robotic manipulators. The proposed approach employs orthogonal functions-based estimation to handle system uncertainties, while an adaptive mechanism is introduced to estimate the unknown upper bounds of external disturbances. Moreover, the dynamics of the robot actuators, namely the motors, are explicitly considered in the control law design. Three adaptive laws are proposed in this work. The first addresses the estimation of the parameters of orthogonal functions, the second deals with the approximation error, and the third concerns the estimation of the upper bound of external disturbances. Furthermore, a robust control term is proposed to compensate for the approximation error. Stability of the closed-loop system is ensured using Lyapunov theory. The performance of the proposed controller is evaluated through simulations on a SCARA robotic manipulator and compared with conventional and dynamic sliding mode control schemes in terms of tracking accuracy, control effort, and disturbance rejection. https://ieco.usb.ac.ir/article_9890.html Protective relay in the transformer may accept inrush current as fault current, thus, distinguishing the inrush current from the internal fault current is important in transformers. To estimate the transformer inrush current, the extended Kalman filter (EKF) is applied in this paper. Therefore, three phase transformer initial inrush currents are estimated using the extended Kalman filter formulation and a nonlinear model is used to simulate inrush currents. Then, type of current, whether it is a fault or an inrush current, is determined by comparing this current and the current calculated from the transformer model. It is considered as a fault current, if the inrush current estimation error surpasses a certain limit compared to the transformer actual inrush current. On the other hand, connection of the winding to the ground fault location has been also presented in this paper which has been less investigated in previous studies. Also, the relation of the fault location to the estimation error standard deviation is also studied and an index  is introduced. If the value of this index is greater than a specific value in any phase of the transformer, a fault condition is identified. Finally, the proposed technique is implemented for another transformer to calculate the estimation error standard deviation and index  in the faulty condition. The results show the index β values are in agreement with the index limits and validate the accuracy of the proposed method. https://ieco.usb.ac.ir/article_9768.html This paper presents a novel non-isolated DC-DC converter topology with several significant advantages. First, the input current remains continuous, thereby reducing the current stress on the input filter capacitor. Second, the converter utilizes the same number of inductors as conventional topologies such as SEPIC, Zeta, and Ćuk converters. Third, it achieves high voltage gain at relatively low duty cycles. Fourth, the maximum voltage stress on the semiconductors remains well below the output voltage, ensuring improved device reliability. Fifth, the design incorporates only a single switch, simplifying the drive circuitry. Sixth, the voltage stress on the switch is significantly lower than the output voltage. Seventh, a quadruple voltage-lift is realized using an enhanced diode–capacitor voltage multiplier integrated at both stages of the converter. Finally, although the power circuit employs 15 diodes and 14 capacitors, the topology maintains a high voltage gain density, justifying the component count. Experimental results are provided to validate the theoretical analysis. The implemented prototype successfully boosts an input voltage of 20 V to an output of 1200 V at a 50% duty cycle, delivering an output power of less than 200 W. https://ieco.usb.ac.ir/article_9933.html This paper presents a multi-objective energy management strategy for a hybrid electricity-hydrogen microgrid (MG) aimed at improving economic and operational performance. The proposed framework simultaneously minimizes total operating cost and reduces peak load, which are conflicting objectives in MG operation. To address this challenge, the problem is formulated as a multi-objective optimization model using a normalized weighted sum approach, enabling an effective trade-off between objectives while preventing the creation of new peaks in the load profile. The studied hydrogen-based MGs includes renewable energy sources such as solar and wind power, a battery energy storage system (BESS), a diesel generator, and demand response programs. Hydrogen is also utilized as an energy carrier to enhance system flexibility and support improved integration of renewable generation. Coordinated scheduling of generation units, storage systems, and flexible loads improves system efficiency. To enhance model accuracy, a long short-term memory (LSTM) forecasting method is applied to predict solar irradiance and wind speed using historical data, supporting more reliable scheduling decisions. The proposed model is validated through a general case study. Simulation results show a peak load reduction of 442 kW and an improvement in the load factor of 16.75%, confirming the effectiveness of the proposed approach https://ieco.usb.ac.ir/article_9934.html This paper proposes a multi-rate hybrid control framework for modeling and managing Coronary Heart Disease (CHD) risk dynamics. Unlike conventional statistical and machine learning approaches that treat clinical variables as static predictors without dynamic interaction or stability guarantees, the proposed method formulates cardiovascular risk progression as a hybrid dynamical system with fast–slow time-scale decomposition and logical switching between physiological subsystems. A nonlinear switching controller incorporating decay synchronization is developed to regulate the evolution of risk states. Sufficient stability conditions are rigorously derived using a Lyapunov–Krasovskii functional, ensuring boundedness and convergence of the closed-loop system under disturbances and multi-rate sampling. The framework was evaluated using 152 clinical records collected from Iranian hospitals, with stratified training and testing procedures to ensure reliable evaluation. The proposed method achieved an accuracy of 82% and an F1-score of 0.83, demonstrating improved predictive consistency compared with conventional baseline models. The results indicate that the proposed hybrid control formulation provides both theoretical stability guarantees and practical predictive capability for dynamic health risk management. https://ieco.usb.ac.ir/article_9984.html A comparative approach is pretend in this paper that evaluates different Artificial Intelligence (AI) methods for diagnosing power transformer faults using Dissolved Gas Analysis (DGA). Traditional approaches like the Rogers Ratio Method and Duval Triangle have been used for many years, but offer unreliable results for complex cases. Although, newer AI methods present better results, but still vary in how well they work. In this paper, several AI approaches are evaluated including Support Vector Machines (SVMs), Random Forest (RF), Gradient Boosting Machines (GBMs), Deep Neural Networks (DNNs) and a new combinational model is proposed based on comparing results. A real DGA dataset is used for covering six different fault types for the proposed testing. The results show that while all AI methods do better than traditional approaches, the combinational approach performs the best with 92.3% accuracy. This is found 20.2% better than traditional methods and 4.8% better than the best single AI model. Rational explanation is provided for how each method works and practical recommendation is presented for choosing the right approach based on particular requirements and available resources in real practices. https://ieco.usb.ac.ir/article_9985.html The rapid expansion of the Internet of Things (IoT) has raised critical security concerns across its heterogeneous and resource-constrained networks. Ensuring robust protection with minimal overhead requires identifying a minimal set of key nodes that can provide wide security coverage. This study introduces a novel framework that integrates graph-theoretic modeling with metaheuristic optimization to enhance IoT network security. The proposed approach formulates the problem as an External Independent Dominating Set (EIDS), where selected security nodes ensure full coverage while maintaining independence to reduce correlated vulnerabilities. Four metaheuristic algorithms—Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Bee Colony Optimization (BCO), and Simulated Annealing (SA)—are implemented and compared using multiple network topologies, including random graphs, wireless sensor networks, and real-world smart city infrastructures. Experimental results show that SA achieves the best coverage-to-cost ratio, while PSO offers superior computational efficiency. BCO demonstrates strong independence enforcement, and GA provides balanced performance. The proposed framework achieves over 90% coverage with minimal node overhead, demonstrating scalability and robustness. This work establishes a foundation for hybrid and adaptive metaheuristic strategies in large-scale IoT security deployment. https://ieco.usb.ac.ir/article_9996.html In this paper, an adaptive observer-based cyber-attack detection and estimation problem is studied for smart grid under false data injection attack (FDIA). By invoking mathematical model of the smart grid, sliding mode observer (SMO) is proposed for estimating grid states and generating residual signal. By monitoring grid status, evaluating residual signal and comparing it with the appropriate threshold level, attack detection is done and alarm signal is generated. Upon alarm generation, attack estimation algorithm is activated to estimate the FDIA occurred at the vulnerable buses. In the proposed detection scheme, only the frequency deviations of the generator buses are required; also, no off-line learning phase and no prior knowledge about attack signal are required. Moreover, the proposed scheme is able to detect FDIA and exactly estimates the severity of the detected attack. The Lyapunov stability theorem is used to guarantee stability of the proposed state observer and the proposed attack estimation algorithm, separately. Simulation results for the IEEE six-bus network under single-point and multi-point FDIAs show that upon attack occurrence, the defined evaluation function exceeds from a defined threshold level, which makes attack detection after some milliseconds. Also, the reported mean square error shows that the proposed attack estimation strategy can precisely estimate the attack shape and severity and identify the under-attack bus. https://ieco.usb.ac.ir/article_10091.html Fractional-order PID (FOPID) controllers offer enhanced flexibility and robustness compared to classical integer-order PID controllers, making them well suited for complex and nonlinear control systems. However, the optimal tuning of FOPID parameters remains a challenging task due to the increased number of tuning parameters and the nonlinear nature of the resulting optimization problem. In this paper, a chaos-enhanced Grey Wolf Optimization (CGWO) algorithm is proposed for the optimal tuning of a FOPID controller applied to a DC motor system.Chaotic maps are integrated into the standard Grey Wolf Optimizer to improve population diversity, enhance global search capability, and mitigate premature convergence. Logistic and Tent chaotic maps are employed to dynamically regulate the control parameters of the optimizer throughout the optimization process. The proposed CGWO algorithm is implemented in a MATLAB/Simulink environment, and the controller performance is evaluated using the Integral of Time-Weighted Absolute Error (ITAE) as the optimization objective.Simulation results demonstrate that the proposed CGWO-FOPID controller outperforms both the conventional PID controller and the standard GWO-based FOPID controller in terms of transient response, convergence behavior, and control accuracy. Specifically, reduced overshoot, shorter settling time, and lower ITAE values are achieved. These results confirm that incorporating chaotic dynamics into metaheuristic optimization significantly enhances the tuning performance of fractional-order controllers and provides an effective and practical solution for industrial control applications.