Synthesis of Optimal Feedback Control Systems With Model Feedback Observers

Abstract

This paper deals with an inaccessible control problem for a discrete time linear fixed parameter system. It is well known that when the state vector is completely detectable, an optimal feedback control system can be constructed for the so-called linear quadratic problem, at least theoretically. When the state vector is not completely detectable, the problem is not so straightforward, and many different approaches or devices have been tried. In this paper, the state vector of the controlled system is restored by an observer in order to generate optimal control. Under some appropriate assumptions, the state vector is restored within at most v stages, where v is the quotient of n divided by m (n = dimension of state vector, m = dimension of output vector, with divisibility assumed in this paper). The design method for such an observer reduces to the design of a minimum stage regulator and is explained in detail in this paper. Finally, the characteristics of the feedback control system with an observer are examined numerically and compared with those of an optimal feedback control system with complete state detectability.