Adaptive Control: Stability, Convergence and Robustness
With a focus on linear, continuous time, single-input, single-output systems, this volume surveys the major results and techniques of analysis in the field of adaptive control. The authors offer a clear, conceptual presentation of adaptive methods, enabling a critical evaluation of these techniques and suggesting avenues of further development.
A brief historical overview of adaptive control is followed by a review of mathematical preliminaries and the development of several adaptive identification algorithms. Succeeding chapters examine averaging techniques, the robustness of adaptive schemes, and advanced topics — including the use of prior information and multivariable adaptive control — followed by a concise introduction to the control of a class of nonlinear systems. The treatment is largely self-contained, assuming only some graduate-level background in basic control systems and in linear systems theory.
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and Identiﬁcation Algorithms
Parameter Convergence Using Averaging Techniques
adap adaptive control scheme adaptive system analysis assumed assumption asymptotically asymptotically stable autocovariance averaged system bounded bounded function Chapter closed-loop Consider control law controller parameters coprime deﬁned deﬁnition derivative differential equation direct adaptive control eigenvalues error direct adaptive estimates exists exponential convergence exponentially decaying exponentially stable feedback Figure ﬁltering ﬁnd ﬁxed follows frequency gradient algorithm guaranteed Hermite normal form Hurwitz polynomial identiﬁcation algorithm identiﬁer error identiﬁer parameter identiﬁer structure initial conditions input error scheme instability lemma linear error equation Lyapunov function matrix minimum phase model reference adaptive modiﬁed Note obtained original system parameter convergence parameter error parameter update persistently exciting plant parameters polynomial positive deﬁnite Proof of Lemma Proof of Theorem proposition rate of convergence reference adaptive control reference input reference model regressor relative degree robustness satisﬁed Section signals SISO speciﬁc strictly proper suﬂiciently tion trajectories unmodeled dynamics update law vector yp(t