面向偏微分方程的连续反演控制算法综述

Continuum backstepping control algorithms in partial differential equation orientation:a review

连续反演控制算法是一种面向偏微分方程(partial differential equations,PDEs)模型控制对象,配合边界控制方式的分布参数系统(distributed parameter systems,DPSs)控制算法.该算法基于Volterra映射运算,思路较为新颖,具有鲁棒性、逆最优性,便于获得显式的精确控制律和闭环系统的精确解,并能结合观测器、自适应控制等领域已取得的成果拓展应用范围.本文概述了连续反演算法的基本原理和设计过程,总结了该算法在抛物线偏微分模型、双曲线偏微分模型、复合偏微分模型、非线性偏微分模型等各方面的最新进展,最后归纳了该算法的主要特点,并探讨了未来研究的发展方向.

The continuum backstepping （C-BKST） control algorithm cooperated with boundary control approaches is proposed for distributed parameter systems （DPSs） modeled in partial differential equations （PDEs）. The algorithm based on the Volterra transformation is robust, inverse optimal, and potential for explicit exact control laws and exact solutions of closed-loop systems. The C-BKST control algorithm is novel and can be combined with the achievements of the observer theory and the adaptive control theory to extend its application fields. The basic principles and design procedures of the algorithm are introduced in this paper. The recent development of this algorithm is concluded, covering the aspects of parabolic PDEs, hyperbolic PDEs, complex PDEs, and nonlinear PDEs. Finally the main characteristics of the algorithm are summarized, and the development direction of the algorithm is discussed.