This paper is concerned with an optimal control problem where the state is constrained to stay either in a smooth open set Omega or in its closure <(Omega)over bar>. Under a ''higher-order'' sufficient condition for the viability of Omega and <(Omega)over bar>. we prove that the optimal cost function upsilon(Omega) is the unique continuous constrained solution of the Hamilton-Jacobi-Bellman equation. Furthermore, we show that upsilon(Omega) coincides with the optimal cost function upsilon(<(Omega)over) (bar>) on Omega.
On Nonlinear Optimal Control Problems with State Constraints
MOTTA, MONICA
1995
Abstract
This paper is concerned with an optimal control problem where the state is constrained to stay either in a smooth open set Omega or in its closure <(Omega)over bar>. Under a ''higher-order'' sufficient condition for the viability of Omega and <(Omega)over bar>. we prove that the optimal cost function upsilon(Omega) is the unique continuous constrained solution of the Hamilton-Jacobi-Bellman equation. Furthermore, we show that upsilon(Omega) coincides with the optimal cost function upsilon(<(Omega)over) (bar>) on Omega.
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