带饱和执行器非线性时滞系统的自适应动态规划

Adapted dynamic programming for nonlinear systems with saturated actuator and time-delay

针对带饱和执行器及状态时滞的一类非线性系统最优控制问题,提出基于迭代自适应动态规划算法的控制方法。用泛函性能指标处理执行器的饱问题,推导出非线性时滞系统对应的哈密顿-雅克比-贝尔曼(HJB)方程。针对其性能指标函数含有状态时滞耦合项和抗饱和函数是非二次型,难以求解HJB方程的问题,采用自适应动态规划算法来获得最优控制。通过收敛性分析证明性能指标可迭代达到最优。对比仿真试验结果验证以上方法的有效和求解的优越性。

An optimal control scheme based on using a new iterative adaptive dynamic programming （ADP） algorithm was presented to solve a class of nonlinear system with saturating actuator and time-delay in state. The Hamilton-Jacobi-Bellman （HJB） equation corresponding to constrained control was formulated using a nonquadratic function. Because the index function includes with state time-delay coupling and anti-saturation function was nonquadratic, and it was difficult to solve the HJB equation, the optimal control was obtained using the adaptive dynamic programming. Convergence analysis was presented to prove that the performance index function can reach the optimum by the iterative. Contrast simulation test results demonstrate the effectiveness of the above method and the superiority of the solution.