Hierarchical Sliding-Mode Surface-Based Adaptive Actor-Critic Optimal Control for Switched Nonlinear Systems With...

No prior work has fully resolved the challenge of maintaining stability in switched nonlinear systems subject to unknown external disturbances. Existing control frameworks often struggle when system parameters shift abruptly during operation. That uncertainty drove researchers to investigate more flexible, adaptive architectures. Prior research has shown that traditional sliding-mode techniques provide robustness but frequently suffer from chattering effects. This gap motivated the development of hierarchical structures to smooth control transitions. It was already known that actor-critic neural networks offer powerful tools for solving complex optimization problems. However, integrating these networks with hierarchical surfaces for switched systems remained an open question. This study addresses these limitations by proposing a novel observer-based adaptive control strategy.

The aim of this study is to develop a hierarchical sliding-mode surface-based adaptive optimal control strategy for switched continuous-time nonlinear systems. The researchers seek to address the problem of unknown perturbations that often degrade system performance. This issue poses a significant challenge for maintaining stability in complex, multi-mode environments. The authors intend to integrate an actor-critic neural network architecture to solve the Hamilton-Jacobi-Bellman equation efficiently. They aim to eliminate the restrictive persistence of excitation condition typically required in reinforcement learning. By constructing a specialized cost function, the team plans to convert the original control problem into a series of optimal policy searches. The study also focuses on designing a perturbation observer with a nested parameter adaptive law for accurate estimation. Ultimately, the work strives to provide a robust, stable control solution for nonlinear dynamics.

Review approach involves designing a novel perturbation observer equipped with a nested parameter adaptive law. The investigators construct a specialized cost function linked directly to the hierarchical sliding-mode surface. They convert the primary control challenge into a sequence of optimal policy determinations. The team employs an actor-critic neural network architecture to solve the Hamilton-Jacobi-Bellman equation. Updating laws for both the actor and critic components are developed to execute reinforcement learning strategies. The critic update law utilizes a gradient descent approach combined with the principle of standardization. Stability analysis relies on Lyapunov theory to ensure all signals remain bounded. Finally, the researchers perform numerical simulations to verify the effectiveness of the proposed control framework.

The strongest finding indicates that the proposed control scheme achieves uniformly ultimate boundedness for all closed-loop signals. The study confirms that the hierarchical sliding-mode surface effectively facilitates the approximation of optimal control policies. By utilizing the principle of standardization, the critic update law successfully eliminates the need for persistence of excitation. The perturbation observer accurately tracks unknown disturbances through the nested parameter adaptive law. Simulation results demonstrate that the system maintains stability even when switching between different nonlinear modes. The actor-critic architecture provides a consistent method for solving the Hamilton-Jacobi-Bellman equation in real-time. All signals within the switched nonlinear systems are strictly proven to stay within defined bounds. The adaptive laws ensure that the controller adapts to unknown perturbations without requiring prior knowledge of the disturbance dynamics.

The authors demonstrate that their hierarchical sliding-mode approach effectively manages unknown perturbations in switched systems. Synthesis and implications suggest that this method achieves uniformly ultimate boundedness for all closed-loop signals. By removing the persistence of excitation requirement, the researchers offer a more practical implementation for real-time control. The study confirms that the actor-critic neural network architecture successfully approximates optimal control policies. These findings imply that nested parameter adaptive laws significantly improve disturbance estimation accuracy. The work provides a robust framework for handling nonlinear dynamics without needing precise model knowledge. Future applications could leverage this control scheme to enhance stability in complex, multi-mode industrial processes. The results validate the theoretical stability proofs through comprehensive simulation testing.