Superposition in efficient robust constrained predictive control (Q1614309)

A stabilizing control algorithm for linear systems with polytopic uncertainties and hard input constraints which does not require on-line optimization is proposed. The method is based on a constrained robust model predictive control approach by the authors [IEEE Trans. Autom. Control 45, 1765-1770 (2000; Zbl 0990.93116)] which adopts the union of polytopic invariant target sets and optimizes a cost which is linear in the degree of freedom. The linearity of the cost combined with the linearity of the constraints enables the deployment of superposition so that a feasible control sequence for a particular state can be found as a linear combination of feasible control sequences of other states. Based on this observation, a stabilizing control algorithm which uses pre-computed optimal sequences for selected canonical states is elaborated. Provided that the initial condition lies in the convex hull of the canonical states, it is trivial to calculate on-line the trajectories for which the receding horizon implementation will robustly stabilize the given linear system and then choose the one that indicates the smallest cost.