Deterministic control of uncertain systems.

*(English)*Zbl 0667.93060
Modelling and adaptive control, Proc. IIASA Conf., Sopron/Hung. 1986, Lect. Notes Control Inf. Sci. 105, 108-133 (1988).

[For the entire collection see Zbl 0643.00032.]

The objective of the paper is to present an approach to the control of uncertain systems by employing deterministic concepts. This approach considers the problem of obtaining memoryless stabilizing feedback controllers for uncertain dynamical systems, described by ordinary differential equations. Various classes of controllers are presented in the paper, while the design of all of these controllers is based on Lyapunov theory.

Before proceeding with the problem, the authors introduce some basic notions and results for ordinary differential equations, concerning the existence and continuation of solutions, the boundedness and stability, the Lyapunov functions and the representation of systems with control. Furthermore, the authors present the models of the uncertain systems and the statement of the initial problem regarding system stabilization and control. Finally, the previous concepts are applied to the problem of uncertain systems control, by making a relaxed problem statement for the practical stabilization of the real world systems.

The paper is well organized and written and highly suggested to those involved in the corresponding area of interest.

The objective of the paper is to present an approach to the control of uncertain systems by employing deterministic concepts. This approach considers the problem of obtaining memoryless stabilizing feedback controllers for uncertain dynamical systems, described by ordinary differential equations. Various classes of controllers are presented in the paper, while the design of all of these controllers is based on Lyapunov theory.

Before proceeding with the problem, the authors introduce some basic notions and results for ordinary differential equations, concerning the existence and continuation of solutions, the boundedness and stability, the Lyapunov functions and the representation of systems with control. Furthermore, the authors present the models of the uncertain systems and the statement of the initial problem regarding system stabilization and control. Finally, the previous concepts are applied to the problem of uncertain systems control, by making a relaxed problem statement for the practical stabilization of the real world systems.

The paper is well organized and written and highly suggested to those involved in the corresponding area of interest.

Reviewer: A.V.Machias

##### MSC:

93C15 | Control/observation systems governed by ordinary differential equations |

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 |