An Iterative Method for Optimal Control of Nonlinear Quadratic Tracking Problems

Xin Ning, Walter Bomela, Shin Li
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Abstract

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.
非线性二次型跟踪问题最优控制的迭代方法
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。
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