The explicit linear quadratic regulator for constrained systems

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 "nite horizon problem (model predictive control) and the usual in"nite time measure (constrained linear quadratic regulation). Thus, the on-line control computation reduces to the simple evaluation of an explicitly de"ned 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 for a wide range of practical problems where the computational complexity of on-line optimization is...

• Type: Journal
• Year: 2002
• Where: AUTOMATICA
• Authors: Alberto Bemporad, Manfred Morari, Vivek Dua, Efstratios N. Pistikopoulos
• Keywords: AUTOMATICA 2002, Discrete-time Linear, Discrete-time Linear Time, Linear