Neural Network Filtering Control Design for Nontriangular Structure Switched Nonlinear Systems in Finite Time

No prior work had resolved the challenge of managing nonstrict-feedback nonlinear switched systems within a finite-time framework. These systems often exhibit unpredictable state transitions that complicate traditional stability analysis. Prior research has shown that immeasurable states frequently hinder the implementation of effective feedback controllers. That uncertainty drove the need for advanced estimation techniques to recover missing information. Existing literature often struggles to maintain performance when system dynamics are unknown or highly complex. This gap motivated the development of robust approximation strategies to handle such nonlinearities. Researchers have long sought methods to ensure system signals remain bounded during arbitrary switching events. This paper addresses these limitations by integrating intelligent approximation with state estimation tools.

This study aims to develop a finite-time switching control method for nonstrict-feedback nonlinear systems. The researchers address the challenge of controlling plants that feature immeasurable states and arbitrary switching. A major motivation is the presence of unknown functions that depend on the entire state vector. The authors seek to overcome the limitations of existing controllers that struggle with such complex dynamics. By designing a filter-based state observer, they intend to recover the missing information required for feedback. The project also incorporates neural networks to approximate the uncertain system components. The researchers aim to ensure that closed-loop signals remain bounded throughout the operation. Ultimately, the goal is to achieve rapid tracking of reference signals within a finite timeframe.

The researchers employ a filter-based state observer to estimate hidden variables within the controlled plants. A backstepping recursive technique serves as the primary design framework for constructing the control law. Neural networks are utilized to approximate unknown functions inherent in the nonlinear system dynamics. The team applies a common Lyapunov function method to verify stability across all switching modes. This design approach focuses on ensuring finite-time convergence for the tracking errors. The study utilizes a mass-spring-damper system as a practical application to demonstrate the proposed methodology. Mathematical modeling defines the plant behavior under arbitrary switching conditions. The overall approach integrates these diverse tools to manage complex, nonstrict-feedback architectures effectively.

The proposed control method successfully ensures that all closed-loop signals remain bounded during arbitrary switching. System outputs demonstrate the ability to track desired reference signals within a finite time interval. The neural network approximation effectively simulates the unknown functions present in the nonlinear plants. The filter-based observer provides accurate estimates for the immeasurable states. Application to a mass-spring-damper system confirms the practical utility of the developed strategy. The results indicate that the integration of backstepping and common Lyapunov functions maintains stability throughout the process. The system achieves rapid convergence compared to traditional asymptotic control methods. These findings validate the theoretical design for nonstrict-feedback switched systems.

The authors demonstrate that their finite-time switching control strategy successfully maintains bounded closed-loop signals. This approach allows system outputs to track desired reference trajectories rapidly. The study confirms that the proposed method remains effective even under arbitrary switching conditions. By utilizing a common Lyapunov function, the researchers ensure stability across all system modes. The application to a mass-spring-damper system provides empirical evidence for the theoretical claims. These results suggest that the observer-based design effectively manages immeasurable states in nonlinear plants. The synthesis of backstepping techniques and neural approximation offers a viable path for complex system regulation. The authors conclude that their framework provides a reliable solution for nonstrict-feedback architectures.