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Spiking Adaptive Dynamic Programming Based on Poisson Process for Discrete-Time Nonlinear Systems.

Qinglai Wei, Liyuan Han, Tielin Zhang

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    Summary
    This summary is machine-generated.

    A novel iterative spiking adaptive dynamic programming (SADP) method using Poisson processes solves optimal impulsive control problems. This approach ensures value functions converge to optimal performance, validated by simulations.

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    Area of Science:

    • Control Theory
    • Dynamic Programming
    • Stochastic Processes

    Background:

    • Optimal impulsive control problems are challenging due to discrete state transitions.
    • Existing methods may struggle with the complexity of real-time control systems.

    Purpose of the Study:

    • To develop a new iterative spiking adaptive dynamic programming (SADP) method for optimal impulsive control.
    • To address the computational challenges in solving these complex control problems.

    Main Methods:

    • The study introduces an iterative SADP method incorporating the Poisson process.
    • Maximum Likelihood Estimation (MLE) is used to compute state, spiking interval, and Poisson distribution probability.
    • Property analysis demonstrates the convergence of value functions.

    Main Results:

    • The developed algorithm effectively computes iterative value functions and control laws.
    • Value functions are shown to converge to the optimal performance index.
    • Simulation examples confirm the algorithm's effectiveness.

    Conclusions:

    • The proposed SADP method provides an effective solution for optimal impulsive control problems.
    • The algorithm demonstrates robust convergence properties.
    • This work offers a valuable tool for advanced control system design.