The Maximum principle in control theory provides necessary optimality conditions for a given trajectory in terms of the co-state, which is the solution of a suitable adjoint system. For constrained problems the adjoint system contains a measure supported at the boundary of the constraint set. In this paper we give a representation formula for such a measure for smooth constraint sets and nice Hamiltonians. As an application, we obtain a perimeter estimate for constrained attainable sets.
Cannarsa, P., Castelpietra, M., Cardaliaguet, P. (2008). Regularity properties of attainable sets under state constraints, 76, 120-135 [10.1142/9789812776075_0006].
Regularity properties of attainable sets under state constraints
CANNARSA, PIERMARCO;
2008-01-01
Abstract
The Maximum principle in control theory provides necessary optimality conditions for a given trajectory in terms of the co-state, which is the solution of a suitable adjoint system. For constrained problems the adjoint system contains a measure supported at the boundary of the constraint set. In this paper we give a representation formula for such a measure for smooth constraint sets and nice Hamiltonians. As an application, we obtain a perimeter estimate for constrained attainable sets.| File | Dimensione | Formato | |
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