Showing papers by "Wpmh Maurice Heemels published in 1997"
01 Jan 1997
TL;DR: In this article, a numerical algorithm for the computation of the optimal control for the linear quadratic regulator problem with a positivity constraint on the admissible control set is presented, and sufficient conditions for optimality are presented in terms of inner products, projections on closed convex sets, Pontryagin's maximum principle and dynamic programming.
Abstract: In this paper, the Linear Quadratic Regulator Problem with a positivity constraint on the admissible control set is addressed. Necessary and sufficient conditions for optimality are presented in terms of inner products, projections on closed convex sets, Pontryagin's maximum principle and dynamic programming. The main results are concerned with smoothness of the optimal control and the value function. The maximum principle will be extended to the infinite horizon case. Based on these analytical methods, we propose a numerical algorithm for the computation of the optimal controls for the finite and infinite horizon problem. The numerical methods will be justified by convergence properties between the finite and infinite horizon case on one side and discretized optimal controls and the true optimal control on the other.
25 citations
10 Dec 1997
TL;DR: This work presents a precise definition of linear complementary-slackness systems and gives sufficient conditions for existence and uniqueness of solutions and the theory is illustrated by mechanical systems.
Abstract: We introduce the class of linear complementary-slackness systems. The time evolution of these systems typically consists of a series of continuous phases separated by "events" which cause a change in dynamics and possibly a jump in the state vector. The occurrence of events is governed by certain inequalities similar to those appearing in the linear complementarity problem of mathematical programming. The framework we describe is motivated by physical models in which both differential equations and inequalities play a role. We present a precise definition of linear complementary-slackness systems and give sufficient conditions for existence and uniqueness of solutions. The theory is illustrated by mechanical systems.
16 citations
01 Jan 1997
TL;DR: In this paper, the authors introduce a new class of dynamical systems called "linear complementarity systems" where the time evolution of these systems consists of a series of continuous phases separated by "events" which cause a change in dynamics and possibly a jump in the state vector.
Abstract: We introduce a new class of dynamical systems called "linear complementarity systems." The time evolution of these systems consists of a series of continuous phases separated by "events" which cause a change in dynamics and possibly a jump in the state vector. The occurrence of events is governed by certain inequalities similar to those appearing in the linear complementarity problem of mathematical programming. The framework we describe is suitable for certain situations in which both differential equations and inequalities play a role; for instance, in mechanics, electrical networks, piecewise linear systems, and dynamic optimization. We present a precise definition of the solution concept of linear complementarity systems and give sufficient conditions for existence and uniqueness of solutions.
13 citations
01 Jul 1997
TL;DR: In this article, the linear quadratic regulator problem with a positively constraint on the admissible control set is addressed, and necessary and sufficient conditions for optimality are presented in terms of inner products, projections on closed convex sets.
Abstract: In this paper, the Linear Quadratic Regulator Problem with a positively constraint on the admissible control set is addressed. Necessary and sufficient conditions for optimality are presented in terms of inner products, projections on closed convex sets. Pontryagin's maximum principle and dynamic programming. Sufficient and sometimes necessary conditions for the existence of positive stabilizing controls are incorporated. Convergence properties between the finite and infinite horizon case are presented. Besides these analytical methods, we describe briefly a method for the approximation of the optimal controls for the finite and infinite horizon problem.