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Robustness of unmodified stochastic adaptive control algorithms

机译：未修改的随机自适应控制算法的鲁棒性

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摘要

Originally, adaptive control theory was developed for the ideal system models, i.e., linear system models under the assumption that relative degree and upper bounds on the order of the systems are known. In the early 1980s, adaptive control algorithms designed for such ideal system models were strongly attacked by many researchers due to “lack of robustness” in the presence of unmodeled dynamics and external disturbances. The purpose of the present paper is to relax existing constant pressure on the adaptive control algorithms originally designed for the ideal system models. It is shown that such adaptive control algorithms are globally stable and robust with respect to unmodeled dynamics and external disturbances without any modifications, such as iσ-modification, ε1-modification, relative dead-zone, projection of the parameter estimates, etc. Global stability of the unmodified algorithms is established by requiring the reference signal to be persistently exciting
机译：最初，在假定系统阶数的相对程度和上限是已知的前提下，针对理想的系统模型即线性系统模型开发了自适应控制理论。在1980年代初期，由于存在未建模的动力学和外部干扰，“缺乏鲁棒性”，为这种理想的系统模型设计的自适应控制算法遭到了许多研究人员的强烈抨击。本文的目的是在最初为理想系统模型设计的自适应控制算法上放松现有的恒定压力。结果表明，这种自适应控制算法对于未建模的动力学和外部干扰具有全局稳定性，并且没有任何修改（例如，iσ修改，ε1修改，相对死区，参数估计的投影等）就具有鲁棒性。全局稳定性通过要求参考信号持续激励来建立未经修改的算法

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