Design of an optimal preview controller for linear discrete-time causal descriptor systems

This article is concerned with preview control problems for linear discrete-time and causal descriptor systems. First, by applying the first order forward difference operator to the equation of the states, error vectors and predictable target signals, the optimal control problems of the original systems are turned into generalised-expanded error systems. In the meantime, theoretical studies have shown that if the original systems, which are regular, stabilisable and detectable meet appropriate strengthening conditions, the generalised-expanded error systems are regular, stabilisable, and detectable. With the quadratic cost functional, the optimal controller for the generalised-expanded error systems is derived by using optimal control theory of generalised systems. Finally, a controller with preview action is obtained for the original systems. The stabilisability and detectability for generalised-expanded error systems are also discussed in detail in this article. An example is given to illustrate the correctness of the theory.