Stability, convergence, and robustness of deterministic multivariable self-tuning control
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摘要: 本文用基于傳遞函數概念的虛擬等價系統方法統一分析各種類型的多變量確定性自校正控制系統的穩定性、收斂性和魯棒性，分別針對參數估計收斂到真值、參數估計收斂到非真值以及參數估計不收斂的3種情況給出若干定理、推論和注釋.在各個判據的基礎上，進一步深化對確定性多變量自校正控制系統的理解.所得結論說明：參數估計的收斂性不是確定性多變量自校正控制系統穩定和收斂的必要條件；系統自身的反饋信息對確定性多變量自校正控制是充分的，即外加激勵信號不是必要的.Abstract: 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.
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圖 3 自校正控制系統對應的定常系統
Figure 3. Non-adaptive control system for deterministic self-tuning control system
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