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Adaptive Dynamic Programming for Model-Free Global Stabilization of Control Constrained Continuous-Time Systems.

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    This study introduces a model-free control method using adaptive dynamic programming for global stabilization of linear systems with control constraints. The approach ensures system stability by preventing control saturation.

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    Area of Science:

    • Control Systems Engineering
    • Adaptive Dynamic Programming
    • System Stabilization

    Background:

    • Continuous-time linear systems often face challenges with control constraints, leading to saturation and instability.
    • Model-free approaches are desirable for systems where dynamics are unknown or complex.
    • Achieving global stabilization under control constraints is a critical problem in control theory.

    Purpose of the Study:

    • To develop a model-free control strategy for global stabilization of continuous-time linear systems with control constraints.
    • To design a gain-scheduled low-gain feedback scheme that actively prevents control saturation.
    • To utilize adaptive dynamic programming for solving control design problems without explicit system models.

    Main Methods:

    • A gain-scheduled low-gain feedback control scheme was designed using parameterized algebraic Riccati equations (AREs).
    • An iterative adaptive dynamic programming (ADP) algorithm was developed to solve the parameterized ARE without system dynamics knowledge.
    • Both state feedback and output feedback algorithms were formulated and analyzed.

    Main Results:

    • The proposed ADP method successfully finds solutions to parameterized AREs, determining optimal low-gain parameters.
    • Closed-loop stability of the system under the proposed control scheme was rigorously proven.
    • Convergence of the iterative ADP algorithm to the nominal solution of the parameterized ARE was demonstrated.

    Conclusions:

    • The model-free, gain-scheduled low-gain feedback approach effectively achieves global stabilization for linear systems with control constraints.
    • The adaptive dynamic programming method provides a viable solution for designing controllers without system identification.
    • Simulation results confirm the practical effectiveness and robustness of the proposed control strategy.