Control Of Uncertain Dynamical Systems Research Articles

A New Class of Stabilizing Controllers for Uncertain Dynamical Systems

This paper is concerned with the problem of designing a stabilizing controller for a class of uncertain dynamical systems. The vector of uncertain parameters $q( \cdot )$ is time-varying, and its values $q(t)$ lie within a prespecified bounding set Q in $R^p $. Furthermore, no statistical description of $q( \cdot )$ is assumed, and the controller is shown to render the closed loop system “practically stable” in a so-called guaranteed sense; that is, the desired stability properties are assured no matter what admissible uncertainty $q( \cdot )$ is realized. Within the perspective of previous research in this area, this paper contains one salient feature: the class of stabilizing controllers which we characterize is shown to include linear controllers when the nominal system happens to be linear and time-invariant. In contrast, in much of the previous literature (see, for example, [1], [2], [7], and [9]), a linear system is stabilized via nonlinear control. Another feature of this paper is the fact that the methods of analysis and design do not rely on transforming the system into a more convenient canonical form; e.g., see [3]. It is also interesting to note that a linear stabilizing controller can sometimes be constructed even when the system dynamics are nonlinear. This is illustrated with an example.

Sufficiently informative functions and the minimax feedback control of uncertain dynamic systems

The problem of optimal feedback control of uncertain discrete-time dynamic systems is considered where the uncertain quantities do not have a stochastic description but instead are known to belong to given sets. The problem is converted to a sequential minimax problem and dynamic programming is suggested as a general method for its solution. The notion of a sufficiently informative function, which parallels the notion of a sufficient statistic of stochastic optimal control, is introduced, and conditions under which the optimal controller decomposes into an estimator and an actuator are identified. A limited class of problems for which this decomposition simplifies the computation and implementation of the optimal controller is delineated.