Adaptive control: A simplified approach.

*(English)*Zbl 0689.93036
System identification and adaptive control, Pt. 1, Control Dyn. Syst., Adv. Theory Appl. 25, 187-235 (1987).

[For the entire collection see Zbl 0643.00033.]

One of the main purposes of the author is to develop simple and robust model-reference adaptive control algorithms with necessary conditions for implementation in realistic complex and multivariable systems. The procedure is applicable to time-variable input commands and to any system that can be stabilized via constant output feedback. The article presents simplified adaptive control algorithms, which can be applied if an approximate reduced-order model of the plant is known, with and without full knowledge of the constant output feedback configuration. Also, it presents the basic ideas related to the positive realness and robustness of adaptive control. Almost strictly positive real (ASPR) systems are defined and it has shown how parallel feedforward can be used to satisfy the ASPR conditions if some output feedback configuration is known. Based on the linear following control method, the algorithm is generalized for systems in which no relevant prior knowledge is given. It is shown that the algorithm guarantees global stability in the presence of any bounded input or output disturbances. The algorithm uses proportional and integral gains in order to achieve perfect tracking.

Seven example illustrate the application of the main results.

One of the main purposes of the author is to develop simple and robust model-reference adaptive control algorithms with necessary conditions for implementation in realistic complex and multivariable systems. The procedure is applicable to time-variable input commands and to any system that can be stabilized via constant output feedback. The article presents simplified adaptive control algorithms, which can be applied if an approximate reduced-order model of the plant is known, with and without full knowledge of the constant output feedback configuration. Also, it presents the basic ideas related to the positive realness and robustness of adaptive control. Almost strictly positive real (ASPR) systems are defined and it has shown how parallel feedforward can be used to satisfy the ASPR conditions if some output feedback configuration is known. Based on the linear following control method, the algorithm is generalized for systems in which no relevant prior knowledge is given. It is shown that the algorithm guarantees global stability in the presence of any bounded input or output disturbances. The algorithm uses proportional and integral gains in order to achieve perfect tracking.

Seven example illustrate the application of the main results.

Reviewer: H.H.van de Ven

##### MSC:

93C40 | Adaptive control/observation systems |

93D05 | Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory |

93D15 | Stabilization of systems by feedback |

93C35 | Multivariable systems, multidimensional control systems |

93B35 | Sensitivity (robustness) |