确定性多变量自校正控制的稳定性、收敛性和鲁棒性

本文用基于传递函数概念的虚拟等价系统方法统一分析各种类型的多变量确定性自校正控制系统的稳定性、收敛性和鲁棒性，分别针对参数估计收敛到真值、参数估计收敛到非真值以及参数估计不收敛的3种情况给出若干定理、推论和注释.在各个判据的基础上，进一步深化对确定性多变量自校正控制系统的理解.所得结论说明:参数估计的收敛性不是确定性多变量自校正控制系统稳定和收敛的必要条件；系统自身的反馈信息对确定性多变量自校正控制是充分的，即外加激励信号不是必要的. 

Stability,convergence, and robustness of deterministic multivariable self-tuning control

Self-tuning control is an important approach to intelligent control system design because this kind of control system uses online parameter estimation (or learning) to derive the model of the plant, and as a result of model parameter estimation (or learning), the controller parameters can be adjusted online. However, we still lack a unified analysis tool (which is independent of specific controller design strategy and parameter estimation algorithm) that can be used by engineers to easily understand and judge the stability, convergence, and robustness of this kind of self-tuning control system. This study is focused on a unified analysis of deterministic multivariable self-tuning control systems with the help of the virtual equivalent system (VES) approach based on the transfer function concept. For different parameter estimation situations (three cases are considered, i.e., parameter estimation converges to its true value, parameter estimation converges to other values, and parameter estimation does not converge), four theorems and two corollaries on the stability, convergence, and robustness of deterministic multivariable self-tuning control systems are given with some remarks. These results are independent of specific controller design strategy and parameter estimation algorithm. From the results obtained in this study, it is concluded that the convergence of parameter estimates is unnecessary for the stability and convergence of a self-tuning control system. The feedback information of the self-tuning control system itself is sufficient to achieve the control objective, i.e., the external excitation signal is unnecessary for the deterministic multivariable self-tuning control system. Moreover, on the basis of the results of the stability, convergence, and robustness of deterministic multivariable self-tuning control systems, we have obtained a profound understanding of the self-tuning control system design method. This understanding will provide more flexibility for engineers in real applications of this kind of controller design strategy.