Computation of the constrained infinite time linear quadratic regulator
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 NS, 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=NS.
Conference Proceeding: Multiparametric Linear Complementarity Problems[show abstract] [hide abstract]
ABSTRACT: The linear complementarity problem (LCP) is a general problem that unifies linear and quadratic programs and bimatrix games. In this paper, we present an efficient algorithm for the solution to multiparametric linear complementarity problems (pLCPs) that are defined by positive semi-definite matrices. This class of problems includes the multiparametric linear (pLP) and semi-definite quadratic programs (pQP), where parameters are allowed to appear linearly in the cost and the right hand side of the constraints. We demonstrate that the proposed algorithm is equal in efficiency to the best of current pLP and pQP solvers for all problems that they can solve, and yet extends to a much larger classDecision and Control, 2006 45th IEEE Conference on; 01/2007
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ABSTRACT: A continuous time infinite horizon linear quadratic regulator with input constraints is studied. Optimality conditions, both in the open loop and feedback form, and continuity and differentiability properties of the optimal value function and of the optimal feedback are shown. Arguments rely on basic ideas of convex conjugacy, and in particular, use a dual optimal control problemIEEE Transactions on Automatic Control 06/2007; · 2.11 Impact Factor
Conference Proceeding: On the infinite horizon constrained switched LQR problem[show abstract] [hide abstract]
ABSTRACT: This paper studies the Discrete-Time Switched LQR problem over an infinite time horizon subject to polyhedral constraints on state and control input. The overall constrained, infinite-horizon problem is split into two subproblems: (i) an unconstrained, infinite-horizon problem and (ii) a constrained, finite-horizon one. We derive a stationary suboptimal policy for problem (i) with analytical bounds on its optimality, and develop a formulation of problem (ii) as a Mixed-Integer Quadratic Program. By introducing the concept of a safe set, the solutions of the two subproblems are combined to achieve the overall control objective. It is shown that, by proper choice of the design parameters, the error of the overall sub-optimal solution can be made arbitrarily small. The approach is tested through a numerical example.Decision and Control (CDC), 2010 49th IEEE Conference on; 01/2011