L-Q optimal control for discrete descriptor systems with a complete set of boundary information

Abstract

This paper presents the linear-quadratic optimal control problem for the discrete-time descriptor systems Exk+1 = Axk + Buk, where E is a singular matrix, the system structure is, in general, non-causal and its boundary conditions information is specified in terms of d initial conditions and (n – d) final conditions, where d = deg {det (λE – A)}. It is shown that the optimal control law depends only on the d-dimensional state variables of the causal subsystem, and the optimal cost-to-go is a general quadratic expression of the causal state variables and does not depend on the entire descriptor vector. This result constitutes an extension to the non-causal system case of Larson et al. (1978), where the structure of the descriptor system had been assumed causal.