Optimal control and Hamiltonian dynamics
نویسندگان
چکیده
Optimal control problems for systems linearly deopending on the control input often admit bang-bang type solutions where control takes exclusively extremal values. Over the last years substantial results on optimality conditions and the solution structure stability have been obtained. In the paper, we analyze once more the related finite-dimensional program with switching points localizations taken as decision variables. For linear as well as semilinear systems, we find an explicit representation for the Hessian w.r.t. switching times and deduce sufficient optimality conditions. The criteria are compared to duality based optimality results which are particularly simple for the linear system case. Further, certain multi-point boundary value problems are derived for the calculation of sensitivity differentials, and appropriate bang-bang controllability assumptions are discussed. Regularity of the boundary of reachable sets and semiconcavity of the value function
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