The explicit linear quadratic regulator for constrained systems Academic Article uri icon


  • For discrete-time linear time invariant systems with constraints on inputs and states, we develop an algorithm to determine explicitly, the state feedback control law which minimizes a quadratic performance criterion. We show that the control law is piece-wise linear and continuous for both the finite horizon problem (model predictive control) and the usual infinite time measure (constrained linear quadratic regulation). Thus, the on-line control computation reduces to the simple evaluation of an explicitly defined piecewise linear function. By computing the inherent underlying controller structure, we also solve the equivalent of the Hamilton-Jacobi-Bellman equation for discrete-time linear constrained systems. Control based on on-line optimization has long been recognized as a superior alternative for constrained systems. The technique proposed in this paper is attractive fora wide range of practical problems where the computational complexity of on-line optimization is prohibitive. It also provides an insight into the structure underlying optimization-based controllers. 2001 Elsevier Science Ltd. All rights reserved.

published proceedings


altmetric score

  • 9

author list (cited authors)

  • Bemporad, A., Morari, M., Dua, V., & Pistikopoulos, E. N.

citation count

  • 2285

complete list of authors

  • Bemporad, A||Morari, M||Dua, V||Pistikopoulos, EN

publication date

  • January 2002