Observer-Based Neuro-Adaptive Optimized Control of Strict-Feedback Nonlinear Systems With State Constraints

No prior work has fully resolved the challenge of managing strict-feedback nonlinear systems when internal dynamics remain unknown and state variables are both hidden and restricted. Existing literature often struggles to maintain stability while simultaneously satisfying strict boundary conditions for these complex architectures. That uncertainty drove the need for more robust estimation techniques. Prior research has shown that traditional feedback mechanisms frequently fail when faced with unobservable states. This gap motivated the development of advanced approximation tools. It was already known that neural networks could model complex functions, yet integrating them into constrained optimal control remains difficult. That limitation hindered progress in automated system regulation. Researchers have sought better ways to ensure system safety without sacrificing performance optimization.

The primary aim of this study is to develop an adaptive neural network output feedback optimized control design for strict-feedback nonlinear systems. Researchers seek to address the challenge of managing systems with unknown internal dynamics. The project focuses on scenarios where system states are immeasurable and must be constrained within predefined compact sets. This work intends to provide a robust solution for maintaining stability in such complex environments. The authors aim to improve upon existing control strategies by reducing the restrictive conditions required for optimal performance. They propose using an adaptive neural network state observer to estimate hidden variables accurately. The study also explores the application of barrier Lyapunov functions to ensure strict adherence to safety boundaries. Ultimately, the researchers strive to validate their new control framework through both numerical and practical testing.

The investigators utilize a backstepping framework to structure the control design for strict-feedback dynamics. They implement an actor-critic architecture to solve the optimal control problem iteratively. A barrier Lyapunov function serves as the primary tool for maintaining state constraints. The team develops an adaptive observer to reconstruct the immeasurable state variables. Neural networks provide the approximation capability for unknown internal system components. The study employs numerical simulations to test the theoretical performance of the proposed strategy. Practical examples further demonstrate the utility of the control design in realistic scenarios. This comprehensive evaluation approach confirms the stability and constraint satisfaction of the developed methodology.

The proposed strategy successfully ensures that all closed-loop signals remain bounded during the entire operation. The researchers demonstrate that system states are consistently confined within preselected compact sets. This performance is achieved through the integration of barrier Lyapunov functions and adaptive neural network observers. The study indicates that the controller effectively handles unknown internal dynamics without requiring excessive system information. Numerical simulations confirm that the optimal control design maintains stability under strict-feedback conditions. Practical examples validate the robustness of the approach in real-world settings. The authors report that their method requires fewer conditions on system dynamics than previous optimal control techniques. These results collectively highlight the efficiency and reliability of the neuro-adaptive framework.

The authors propose that their strategy effectively maintains all closed-loop signals within bounded ranges during operation. They demonstrate that system states remain confined within preselected compact sets throughout the entire process. The researchers claim that their barrier Lyapunov function approach provides a reliable mechanism for enforcing these strict constraints. Their synthesis suggests that the actor-critic architecture successfully facilitates optimal control performance. The study implies that this design requires fewer restrictive conditions on system dynamics than previous methodologies. They conclude that the integration of state observers and neural networks enhances overall system robustness. The findings indicate that the proposed framework is applicable to various nonlinear system configurations. Finally, the authors confirm that numerical and practical examples validate the effectiveness of their control scheme.