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The explicit linear quadratic regulator for constrained systems


M. Morari

Pittsburgh, PA, USA, Seminar at the Department of Chemical Engineering, Carnegie Mellon University.

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 piecewise 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 computation is reduced to a simple linear function evaluation, instead of the expensive quadratic program required up to now. 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 prohibitive.


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