Model Reduction for Control System Design

Abstract

The classical methods of the theory of automatic control are meant for linear systems and represent the control in the form of a linear operator applied to the current phase state of the system. Shortcomings of this approach are obvious both in the vicinity of the prescribed terminal state as well as far from it. Near the terminal state, the magnitude of the control becomes small, so that control possibilities are not fully realized. As a result, the time of the control process occurs to be, strictly speaking, infinite, and the phase state can only tend asymptotically to the terminal state as time goes to infinity. On the other hand, far from the terminal state, the control magnitude becomes large and can violate the constraints usually imposed on the control. That is why it is difficult and often impossible to take account of the constraints imposed when the linear methods are used. Moreover, the classical methods based on linear models are usually inapplicable to nonlinear systems; at least, their applicability should be justified thoroughly.