In this study, a model-free $P{I}^{\phi }$-sliding mode control ( $P{I}^{\phi }$-SMC) methodology is proposed to synchronize a specific class of chaotic fractional-order memristive neural network systems (FOMNNSs) with delays and input saturation. The fractional-order Lyapunov stability theory is used to design a two-level $P{I}^{\phi }$-SMC which can effectively manage the inherent chaotic behavior of delayed FOMNNSs and achieve finite-time synchronization. At the outset, an initial sliding surface is introduced. Subsequently, a robust $P{I}^{\phi }$-sliding surface is designed as a second sliding surface, based on proportional–integral (PI) rules. The finite-time asymptotic stability of both surfaces is demonstrated. The final step involves the design of a dynamic-free control law that is robust against system uncertainties, input saturations, and delays. The independence of control rules from the functions of the system is accomplished through the application of the norm-boundedness property inherent in chaotic system states. The soft actor-critic (SAC) algorithm based deep Q-Learning is utilized to optimally adjust the coefficients embedded in the two-level $P{I}^{\phi }$-SMC controller’s structure. By maximizing a reward signal, the optimal policy is found by the deep neural network of the SAC agent. This approach ensures that the sliding motion meets the reachability condition within a finite time. The validity of the proposed protocol is subsequently demonstrated through extensive simulation results and two numerical examples.

In this work, a dynamic-free adaptive sliding mode control (adaptive-SMC) methodology for the synchronization of a specific class of chaotic delayed fractional-order neural network systems in the presence of input saturation is proposed. By incorporating the frequency distributed model (FDM) and the fractional version of the Lyapunov stability theory, a dynamic-free adaptive SMC methodology is designed to effectively overcome the inherent chaotic behavior exhibited by the delayed FONNSs to achieve synchronization. Notably, the decoupling of the control laws from the nonlinear/linear dynamical components of the system is ensured, taking advantage of the norm-boundedness property of the states in chaotic systems. The effectiveness of the suggested adaptive-SMC method for chaos synchronization in delayed fractional-order Hopfield neural network systems is validated through numerical simulations, demonstrating its robustness and efficiency. The proposed dynamic-free adaptive-SMC approach, incorporating the FDM and fractional Lyapunov stability theorem, offers a promising solution for synchronizing chaotic delayed FONNSs with input saturation, with potential applications in various domains requiring synchronization of such systems.

Fractional-order four-wing (FO 4-wing) systems are of significant importance due to their complex dynamics and wide-ranging applications in secure communications, encryption, and nonlinear circuit design, making their control and stabilization a critical area of study. In this research, a novel model-free finite-time flexible sliding mode control (FTF-SMC) strategy is developed for the stabilization of a particular category of hyperchaotic FO 4-wing systems, which are subject to unknown uncertainties and input saturation constraints. The proposed approach leverages fractional-order Lyapunov stability theory to design a flexible sliding mode controller capable of effectively addressing the chaotic dynamics of FO 4-wing systems and ensuring finite-time convergence. Initially, a dynamic sliding surface is formulated to accommodate system variations. Following this, a robust model-free control law is designed to counteract uncertainties and input saturation effects. The finite-time stability of both the sliding surface and the control scheme is rigorously proven. The control strategy eliminates the need for explicit system models by exploiting the norm-bounded characteristics of chaotic system states. To optimize the parameters of the model-free FTF-SMC, a deep reinforcement learning framework based on the adaptive dynamic programming (ADP) algorithm is employed. The ADP agent utilizes two neural networks (NNs)—action NN and critic NN—aiming to obtain the optimal policy by maximizing a predefined reward function. This ensures that the sliding motion satisfies the reachability condition within a finite time frame. The effectiveness of the proposed methodology is validated through comprehensive simulations, numerical case studies, and comparative analyses.

In this paper, the concept of fractional calculus (FC) is introduced into the sliding mode control (SMC), named fractional order SMC (FOSMC), for the load frequency control (LFC) of an islanded microgrid (MG). The studied MG is constructed from different autonomous generation components such as diesel engines, renewable sources, and storage devices, which are optimally planned to benefit customers. The coefficients embedded in the FOSMC structure play a vital role in the quality of controller commands, so there is a need for a powerful heuristic methodology in the LFC study to adjust the design coefficients in such a way that better transient output may be achieved for resistance to renewable sources fluctuations. Accordingly, the Sine Cosine algorithm (SCA) is effectively combined with the harmony search (HS) for the optimal setting of the controller coefficients. The Lyapunov function based on the FOSMC is formulated to guarantee the stability of the LFC mechanism for the test MG. Finally, the hardware-in-the-loop (HIL) experiments are carried out to ensure that the suggested controller can suppress the frequency fluctuations effectively, and that it provides more robust MG responses in comparison with the prior art techniques.