具有扰动的非线性系统最优控制问题

An Optimal Control Problem for Nonlinear Systems with Perturbations

摘要: 在本文中，我们发展了一类具有扰动的非线性系统最优控制理论。该问题的目标是通过建立一个框架来解决最优控制问题，使得参数化的代价函数是最小的。为了避免求解哈密顿雅可比贝尔曼方程的稳态形式，我们设计了一个代价函数，它依赖于动态系统，Lyapunov函数，通过求解哈密顿雅可比贝尔曼方程获得了一个稳定的反馈控制器的具体表达式，并且该反馈控制器使得系统是渐近稳定的。最后通过一个实例来说明本文所提方法的有效性。

Abstract: In this paper, we develop a class of optimal control theory for nonlinear systems with perturbations. The objective of this problem is to establish a framework to solve the optimal control problem so that the parameterized cost function is minimized. In order to avoid solving the steady- state form of the Hamilton-Jacobi-Bellman equation, we design a cost function, which depends on the dynamic system, Lyapunov function. By solving the Hamilton-Jacobi-Behrman equation, we obtain a concrete expression of a stable feedback controller, and the feedback controller makes the system asymptotically stable. Finally, an example is given to illustrate the effectiveness of the proposed method.