Stable Adaptive SystemsThis graduate-level text focuses on the stability of adaptive systems, and offers a thorough understanding of the global stability properties essential to designing adaptive systems. Its self-contained, unified presentation of well-known results establishes the close connections between seemingly independent developments in the field. Prerequisites include a knowledge of linear algebra and differential equations, as well as a familiarity with basic concepts in linear systems theory. The first chapter sets the tone for the entire book, introducing basic concepts and tracing the evolution of the field from the 1960s through the 1980s. The first seven chapters are accessible to beginners, and the final four chapters are geared toward more advanced, research-oriented students. Problems ranging in complexity from relatively easy to quite difficult appear throughout the text. Topics include results in stability theory that emphasize incidents directly relevant to the study of adaptive systems; the stability properties of adaptive observers and controllers; the important concept of persistent excitation; the use of error models in systems analysis; areas of intense research activity; and five detailed case studies of systems in which adaptive control has proved successful |
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adaptive control problem adaptive law adaptive observer adaptive systems assumed assumptions asymptotically stable augmented error Automatic Control boundedness Chapter chosen control input control parameters convergence coprime defined derived described determine differential equation discussed dynamical system e₁ e₁(t equilibrium error equation error model estimate exists exponentially feedback follows given Hence Hermite normal form Hp(s Hurwitz polynomial identification IEEE Transactions initial conditions known Lemma limt linear time-invariant Lyapunov function methods monic polynomial multivariable Narendra output error overall system parameter error parameter vector persistently exciting PID controller plant parameters polynomial positive-definite positive-definite matrix proof reference input reference model relative degree robot Rp(s scalar Section shown in Fig signals Simulation solutions of Eq stable matrix t₁ tends to zero Theorem time-varying Transactions on Automatic uniform asymptotic stability uniformly bounded values variables Wm(s Wp(s xp(t ym(t Yp(t Zp(s Ур