Paola Loreti
Abstract
We consider an optimal control problem with space constraints and we show some properties of the optimal cost function. Our main result is the equality between the value functions of four optimal control problems and the constrained viscosity solution of the Hamilton–Jacobi–Bellman equation.
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We consider an optimal control problem with space constraints and we show some properties of the optimal cost function. Our main result is the equality between the value functions of four optimal control problems and the constrained viscosity solution of the Hamilton–Jacobi–Bellman equation.
Key concepts: Hamilton–Jacobi equation, Viscosity solution, Mathematics, Bellman equation, Optimal control, Hamilton–Jacobi–Bellman equation, Viscosity, Applied mathematics