Markov Data-Based LQG Control1

Abstract

In this paper the Markov data-based LQG control problem is considered. The Markov data-based LQG control problem is to find the optimal control sequence which minimizes a quadratic cost function over some finite interval [0, N]. To solve this problem, we show that a complete input-output description of the system is not necessary. Obviously, a complete state space model is not necessary for this problem either. The main contributions of this paper include: (i) develop a new data-based LQG controller in a recursive form and a batch-form, (ii) derive a closed-form expression for the system’s optimal performance in terms of the Markov parameters, (iii) develop an algorithm for choosing the output weighting matrix, and (iv) demonstrate that the amount of information about the system required by the data-based controller design is less than the amount required to construct the full state space model. A numerical example is given to show the effectiveness of the data-based design method. [S0022-0434(00)02503-X]