Computation of the constrained infinite time linear quadratic regulator

Authors:
Pascal Grieder;Francesco Borrelli;Fabio Torrisi;Manfred Morari
Affiliations:
Institut für Automatik, ETH, Swiss Federal Institute of Technology, Physikstrasse 3, CH-8092 Zürich, Switzerland;Institut für Automatik, ETH, Swiss Federal Institute of Technology, Physikstrasse 3, CH-8092 Zürich, Switzerland;Institut für Automatik, ETH, Swiss Federal Institute of Technology, Physikstrasse 3, CH-8092 Zürich, Switzerland;Institut für Automatik, ETH, Swiss Federal Institute of Technology, Physikstrasse 3, CH-8092 Zürich, Switzerland
Venue:
Automatica (Journal of IFAC)
Year:
2004

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Abstract

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