Adaptive control via adaptive observation and asymptotic feedback matrix synthesis

For unknown linear, time invariant systems an adaptive feedback control scheme is established. It is composed of a stable adaptive state and parameter observation part, and a stable asymptotic synthesis of an adaptive feedback matrix part, the latter based on the current parameter estimates. Both adaptive state feedback control and adaptive feedback control, using the adaptively observed state instead of the true state, are shown to result in closed loop control systems, which behave globally asymptotically stable in the sense of Lyapunov with respect to the initial uncertainty, provided only that the input of the unknown system is sufficiently excited by means of an external command signal. Thereby an algebraic separation property for adaptive state feedback control is also established, extending an earlier nonadaptive result. In particular, no assumptions on the parameters of the unknown system nor on the speed of the adaptive observer and the adaptive feedback matrix generator are made.

[1]  W. Hahn.  Theorie und Anwendung der direkten Methode von Ljapunov , 1959 .

[2]  R. E. Kalman,et al.  Control System Analysis and Design Via the “Second Method” of Lyapunov: I—Continuous-Time Systems , 1960 .

[3]  K. Narendra,et al.  An adaptive observer and identifier for a linear system , 1973 .

[4]  R. Carroll,et al.  An adaptive observer for single-input single-output linear systems , 1973 .

[5]  Brian D. O. Anderson.  Adaptive identification of multiple-input multiple-output plants , 1974, CDC 1974.

[6]  I. D. Landau,et al.  A survey of model reference adaptive techniques - Theory and applications , 1973, Autom..

[7]  R. Monopoli.  Model reference adaptive control with an augmented error signal , 1974 .

[8]  L. Kraft.  Controllable form state variables obtained from an arbitrarily fast adaptive observer , 1976, 1976 IEEE Conference on Decision and Control including the 15th Symposium on Adaptive Processes.

[9]  K. Narendra,et al.  Stable adaptive observers and controllers , 1976, Proceedings of the IEEE.

[10]  G. Kreisselmeier.  Adaptive observers with exponential rate of convergence , 1977 .

[11]  Jürgen Ackermann,et al.  On the synthesis of linear control systems with specified characteristics , 1975, Autom..

[12]  C. Johnson,et al.  Adaptive implementation of one-step-ahead optimal control via input matching , 1977, 1977 IEEE Conference on Decision and Control including the 16th Symposium on Adaptive Processes and A Special Symposium on Fuzzy Set Theory and Applications.

[13]  A. Morse,et al.  Adaptive control of single-input, single-output linear systems , 1977, 1977 IEEE Conference on Decision and Control including the 16th Symposium on Adaptive Processes and A Special Symposium on Fuzzy Set Theory and Applications.

[14]  Lennart Ljung,et al.  Model Reference Adaptive Systems and Self-Tuning Regulators - Some Connections , 1978 .

[15]  W. Wolovich,et al.  Parameter adaptive identification and control , 1978 .

[16]  Kumpati S. Narendra,et al.  Direct and Indirect Adaptive Control , 1978 .

[17]  K. Narendra,et al.  Stable adaptive controller design--Direct control , 1978 .

[18]  S. Nuyan,et al.  Minimal order arbitrarily fast adaptive observers and identifiers , 1979 .

[19]  Kumpati S. Narendra,et al.  Direct and indirect model reference adaptive control , 1979, Autom..

[20]  G. Kreisselmeier,et al.  The generation of adaptive law structures for globally convergent adaptive observers , 1979 .

[21]  G. Kreisselmeier,et al.  Algebraic separation in realizing a linear state feedback control law by means of an adaptive observer , 1980 .