The explicit solution of constrained LP-based receding horizon control

For discrete-time linear time-invariant systems with constraints on inputs and states, we develop an algorithm to determine explicitly, as a function of the initial state, the solution to optimal control problems that can be formulated using a linear program. In particular, we focus our attention on a receding horizon control scheme where the performance criterion is based on a mixed 1/∞-norm. We show that the optimal 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 online computation of the resultant model predictive 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. The proposed technique is attractive for a wide range of applications where the simplicity of the online computational complexity is a crucial requirement