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Discrete-Time Impulsive Adaptive Dynamic Programming.

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    A novel iterative adaptive dynamic programming (ADP) algorithm solves optimal impulsive control for nonlinear systems. This method ensures convergence to optimal control laws for discrete-time systems with impulsive intervals.

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    Area of Science:

    • Control Theory
    • Nonlinear Systems
    • Dynamic Programming

    Background:

    • Optimal control problems for infinite horizon discrete-time nonlinear systems are challenging.
    • Impulsive control introduces complexities due to constrained intervals.

    Purpose of the Study:

    • Develop a new iterative adaptive dynamic programming (ADP) algorithm.
    • Solve optimal impulsive control problems for infinite horizon discrete-time nonlinear systems.
    • Address constraints of the impulsive interval.

    Main Methods:

    • Iterative adaptive dynamic programming (ADP) approach.
    • Obtain iterative impulsive value function for each possible impulsive interval.
    • Achieve iterative value function and iterative control law.
    • Develop a new convergence analysis method.
    • Analyze properties of the iterative control law.

    Main Results:

    • The iterative value function converges to the optimum as the iteration index increases.
    • The developed algorithm effectively solves optimal impulsive control problems.
    • Two simulation examples demonstrate the method's effectiveness.

    Conclusions:

    • The proposed iterative ADP algorithm is effective for optimal impulsive control.
    • The convergence analysis guarantees the optimality of the control law.
    • The method provides a practical approach for complex control problems.