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Pontryagin principle for state-constrained control problems governed by a first-order PDE system
(2000)
Second order sufficient conditions for optimal control subject to first order state constraints
(2005)
Regulator Problems on Unbounded Domains : Stationarity–Optimal Control–Asymptotic Controllability
(2018)
In this paper, we consider a class of infinite horizon variational and control problems arising from economics, quantum mechanics, and stabilization. Herein, we assume that the objective is of regulator type. The problem setting implies a weighted Sobolev space as the state space. For this class of problems, we establish necessary optimality conditions in a form of a Pontryagin type maximum principle. A duality concept of convex analysis is provided and used to find sufficient optimality conditions and to motivate a dual approximation scheme. We apply the theoretical results to find an asymptotically stabilizing control for a linearized Lotka–Volterra type system.
In this paper a class of infinite horizon optimal control problems with an isoperimetrical constraint, also interpreted as a budget constraint, is considered. Herein a linear both in the state and in the control dynamic is allowed. The problem setting includes a weighted Sobolev space as the state space. For this class of problems, we establish the necessary optimality conditions in form of a Pontryagin Type Maximum Principle including a transversality condition. The proved theoretical result is applied to a linear-quadratic regulator problem.
In this paper a class of linear-quadratic infinite horizon optimal control problems is considered. Problems of this type are not only of practical interest. They also appear as an approximation of nonlinear problems. The key idea is to introduce weighted Sobolev spaces as state space and weighted Lebesgue spaces as control spaces into the problem setting. We investigate the question of existence of an optimal solution in these spaces and establish a Pontryagin type Maximum Principle as a necessary optimality condition including transversality conditions.
In this paper we consider a class of infinite horizon variational problems resulting from a transformation of singular variational problems. Herein we assume that the objective is convex. The problem setting implies a weighted Sobolev space as state space. For this class of problems we establish necessary optimality
conditions in form of a Pontryagin type maximum principle. A duality concept of convex analysis is provided and used to establish sufficient optimality conditions. We apply the theoretical results proven to the problem of the Brachistochrone.