Abstract
This paper deals with a method of synthesizing optimal control for a class of multivariable linear stochastic discrete-time systems with parameter variations. As is well known, for this type of control problem, the “self-tuning regulator” is proposed. The regulator recursively identifies and corrects the model, which is used to derive the control law, until the model matches the controlled object. The self-tuning regulator becomes effective, however, only when the parameters of the controlled object are unknown constants or very slow variables. In the other case, namely, when a variable which represents the cause of parameter variations varies around its nominal value, the concept of sensitivities seems to be applicable. In this paper, the closed-loop control law which minimizes a quadratic performance index containing sensitivity variable is derived. The optimal control becomes a linear dynamical system. All the equations to be solved are linear, but there are equations having no unique solution. Therefore, it is shown that every solution yields the same control law, and any solution might as well be used to synthesize an optimal control system.
