On polyhedral projection and parametric programming

Submitted versio

The Explicit Solution of Constrained LP-Based Receding Horizon Control

For discrete-OjS linear time-) variant systems with constraints on inputs and states, we develop analgorithm to determine explicitly, as a function of the initial state, the solution to optimal control problems that can be formulated using a linear program. Inparticular, we focus our attention on a receding horizon control scheme where the performance criterion is based on a mixed 1/#-'DL (i.e., 1-e., with respect to time and #-SS3 with respect to space). We show that theoptimal control profile is a piecewise linear and continuous function of the initial state. Thus, when the optimal control problem is solved at each time step according to a moving horizon scheme, the on-]]L computation of the resultant MPC controller is reduced to a simple linear function evaluation, instead of the typical expensive linear program required up to now. The technique proposed has both theoretical and practical advantages. From a theoretical point of view, the explicit solution gives insight on the acti..