Optimal feedback controls. (English) Zbl 0684.49008

The author considers the following control problem: select a control \(u^*\) from a class of admissible controls such that if s(\(\cdot)\) the solution of \(\dot x=f(t,x,u^*)\), \(x(\tau)=\xi\), there exists a \(t_ f\) such that \((t_ f,s(t_ f))\) belongs to an assigned terminal set and minimizes the values of a given function g. He is interested in finding the optimal feedback synthesis.
He proves under suitable assumptions that the value function is locally Lipschitz; a necessary condition in terms of lower directional Dini derivatives of the value function is given. A feedback control and a procedure for approximating optimal controls is provided under further assumptions.
Reviewer: R.Bianchini


49K15 Optimality conditions for problems involving ordinary differential equations
49L99 Hamilton-Jacobi theories
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