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- Title
On the relaxation of state-constrained linear control problems via Henig dilating cones.
- Authors
Kogut, Peter I.; Leugering, Günter; Schiel, Ralph
- Abstract
We discuss a regularization of state-constrained optimal control problems via a Henig relaxation of ordering cones. Considering a state-constrained optimal control problem, the pointwise state constraint is replaced by an inequality condition involving a so-called Henig dilating cone. It is shown that this class of cones provides a reasonable solid approximation of the typically nonsolid ordering cones which correspond to pointwise state constraints. Thereby, constraint qualifications, which are based on the existence of interior points, can be applied to given problems. Moreover, we characterize admissibility and solvability of the original problem by analyzing the associated relaxed problem. We also show that the optimality system for the original problem can be obtained through the limit passage in the corresponding optimality system for the relaxed problem. As an example of our approach, we derive the optimality conditions for a state constrained Neumann boundary optimal control problem and show that in this case the corresponding Lagrange multipliers are more regular than Borel measures.
- Subjects
LINEAR control systems; OPTIMAL control theory; RELAXATION methods (Mathematics); CONES (Operator theory); NEUMANN boundary conditions; LAGRANGE multiplier; BOREL sets
- Publication
Control & Cybernetics, 2016, Vol 45, Issue 2, p131
- ISSN
0324-8569
- Publication type
Article