Adaptive control. Stability, convergence and robustness.

*(English)*Zbl 0721.93046
Prentice Hall Information and System Sciences Series; Prentice-Hall Advanced Reference Series. Englewood Cliffs, NJ: Prentice-Hall International, Inc. xvii, 377 p. $ 35.95 (1989).

This book presents the deterministic theory of identification and adaptive control, focussing on linear, continuous time single-input single-output plants, with extensions to some classes of multivariable and nonlinear plants. A mayor goal of the authors is to include a number of recent techniques and new directions for analysing stability, parameter convergence and robustness of the complicated nonlinear dynamics inherent in adaptive control schemes.

After a brief historical overview of adaptive control and identification and an outline of the key stability theorems, several algorithms for the adaptive identification and control along with their stability and parameter convergence properties are provided. An output error scheme, an input error scheme and an indirect scheme are derived in a unified framework. For the study of robustness, Lyapunov techniques and the recently introduced averaging methods are exploited. The latter turns out to be a valuable tool to assess the stability in presence of unmodeled dynamics and to understand mechanisms of instability. Several advanced topics in identification and adaptive control are presented, such as the use of prior information in the context of identification, flexible indirect adaptive control schemes, and the extension of model reference adaptive control schemes to multivariable systems based on a factorization approach. One chapter is devoted to adaptive control of a class of nonlinear systems, using the theory of linearization by exact cancellation of nonlinear terms via state feedback. Parameter adaptive control is proposed to get asymptotically exact cancellation in case of uncertainty in the knowledge of the nonlinearity. The book concludes with some suggestions about the areas of future research such as rule-based, expert and learning control systems.

This book is more than a “toolkit” of methods for the design and analysis of adaptive control algorithms. It is an excellent representation, on an advanced level, of the state of the art of the deterministic theory of identification and adaptive control.

After a brief historical overview of adaptive control and identification and an outline of the key stability theorems, several algorithms for the adaptive identification and control along with their stability and parameter convergence properties are provided. An output error scheme, an input error scheme and an indirect scheme are derived in a unified framework. For the study of robustness, Lyapunov techniques and the recently introduced averaging methods are exploited. The latter turns out to be a valuable tool to assess the stability in presence of unmodeled dynamics and to understand mechanisms of instability. Several advanced topics in identification and adaptive control are presented, such as the use of prior information in the context of identification, flexible indirect adaptive control schemes, and the extension of model reference adaptive control schemes to multivariable systems based on a factorization approach. One chapter is devoted to adaptive control of a class of nonlinear systems, using the theory of linearization by exact cancellation of nonlinear terms via state feedback. Parameter adaptive control is proposed to get asymptotically exact cancellation in case of uncertainty in the knowledge of the nonlinearity. The book concludes with some suggestions about the areas of future research such as rule-based, expert and learning control systems.

This book is more than a “toolkit” of methods for the design and analysis of adaptive control algorithms. It is an excellent representation, on an advanced level, of the state of the art of the deterministic theory of identification and adaptive control.

Reviewer: D.Franke (Hamburg)

##### MSC:

93C40 | Adaptive control/observation systems |

93-02 | Research exposition (monographs, survey articles) pertaining to systems and control theory |

93D15 | Stabilization of systems by feedback |

93B30 | System identification |

93B35 | Sensitivity (robustness) |

93C35 | Multivariable systems, multidimensional control systems |