Optimal Control for Unknown Nonlinear System With Semi-Markovian Jump Parameters via Adaptive Dynamic Programming
研究了未知动力学的离散时间非线性半马尔可夫跳变系统的最优控制问题，利用半马尔可夫核方法处理模式切换，并通过神经网络辨识器和自适应动态规划求解哈密顿-雅可比-贝尔曼方程。
This article investigates the optimal control problem for the discrete-time (DT) nonlinear semi-Markovian jump systems (s-MJSs) that possess unknown dynamics. The study uses the semi-Markovian kernel approach to address the problem of mode-switching in these systems. This approach employs the transition probability and the sojourn-time distribution function to jointly determine the transitions between different modes. Then, with a neural network (NN) identifier, the demand for accurate information on the system dynamics is eliminated, and an optimal control method for the nonlinear s-MJSs is utilized to solve the Hamilton-Jacobi–Bellman equation (HJBE) built upon adaptive dynamic programming methodology. Additionally, a detailed analysis of the convergence of a value iteration-based algorithm, which solves the optimal control issue for the DT s-MJSs, is thoroughly discussed. Furthermore, an actor-critic NN is trained to attain an estimated solution to the relevant HJBE. Finally, to validate the designed approach, two simulations are performed to prove its effectiveness.