非线性广义最小方差控制律综述

如何设计简单的控制策略对复杂非线性系统进行控制是控制界还未解决的难题．非线性广义最小方差控制律的提出使得非线性控制器的设计可以基于更为一般的非线性模型，并且控制器易于实现．整个系统包含时滞环节，稳定的非线性输入子系统和一个可以用多项式或者状态空间描述的子系统．通过最小化由误差加权项、状态加权项和输入加权项组成的信号的方差得到优化控制器．在系统为开环稳定的情况下，可用史密斯预估器进行控制．本文首先介绍了非线性广义最小方差控制的发展进程，然后综述了基于状态空间和多项式描述的系统的非线性广义最小方差控制器的设计以及其现状和今后的发展方向．

Nonlinear generalized minimum variance control: a review

The Nonlinear Generalized Minimum Variance (NGMV) controller introduced in this paper is an optimal control strategy for a class of nonlinear plants. It is assumed that the plant model can be decomposed into a set of delay terms, a stable input nonlinear subsystem and a linear subsystem which can be represented in either polynomial or state space forms. The optimal controller is obtained by minimizing the variance of the generalized signal consisted of error weighting, state weighting and control signal weighting. The controller is easy to compute and the resulting nominal closed loop system is stable. The controller can be represented in the Smith predictor form while the system is open loop stable. In this paper,the development of Nonlinear Generalized Minimum Variance control theory is reviewed in details. Next, NGMV controller design methods for the systems in both state space form and polynomial form are introduced. Finally, future work directions as well as challenging research problems in this area are addressed.