非线性二次型跟踪问题最优控制的迭代方法

Xin Ning, Walter Bomela, Shin Li
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摘要

本文研究了一般仿射非线性二次跟踪问题最优控制的迭代计算方法。控制律是通过求解一系列线性二次跟踪问题来迭代计算的,特别是由求解由Hamilton-Jacobi-Bellman方程导出的一组耦合微分方程组成。通过构造一个收缩映射并利用不动点定理证明了迭代格式的收敛性。通过对三种结构不同的非线性系统的数值模拟,验证了该方法的通用性和有效性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
An Iterative Method for Optimal Control of Nonlinear Quadratic Tracking Problems
In this paper, we investigate an iterative method for computing optimal controls for general affine nonlinear quadratic tracking problems. The control law is computed iteratively by solving a sequence of linear quadratic tracking problems and, in particular, it consists of solving a set of coupled differential equations derived from the Hamilton-Jacobi-Bellman equation. The convergence of the iterative scheme is shown by constructing a contraction mapping and using the fixed-point theorem. The versatility and effectiveness of the proposed method is demonstrated in numerical simulations of three structurally different nonlinear systems.
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