Computation of the constrained infinite time linear quadratic regulator

This paper presents an efficient algorithin for coiiiputing the solution to the constrained infinite time linear quadratic regulator (CLQR) problem for discrete time systems. The algorithm coinbiiies multi-parametric quadratic programming with reachability analysis to obtain the optiinal piecewise affine (PWA) feedback law. The algorithm reduces the time necessary to compute the PWA solution for tlie CLQR when compared to other approaches. It also determines the minimal finite horizon N,c, such that the constrained finite horizon LQR problem equals tlie CLQR problem for a compact set of states S. The on-line computational effort for the implementation of the CLQR caii be significantly reduced as well, either hy evaluating the PWA solution or hy solving the finite dimensional quadratic program associatcd with tlie CLQR for a horizon of N = Ns.