Sufficiency in optimal control without the strengthened condition of Legendre
نویسنده
چکیده
In this paper we derive a sufficiency theorem of an unconstrained fixed-endpoint problem of Lagrange which provides sufficient conditions for processes which do not satisfy the standard assumption of nonsingularity, that is, the new sufficiency theorem does not impose the strengthened condition of Legendre. The proof of the sufficiency result is direct in nature since the former uses explicitly the positivity of the second variation, in contrast with possible generalizations of conjugate points, solutions of certain matrix Riccati equations, invariant integrals, or the Hamiltonian-Jacobi theory. Mathematics Subject Classification : 49K15
منابع مشابه
Sufficiency and singularity in optimal control
optimization problem in a Banach space. The assumption that the strengthened Legendre– Clebsch condition holds is crucial. In particular, we refer the reader to Milyutin & Osmolovskiı̌ (1998) where the importance of this condition is fully explained. In this paper, we consider a fixed-endpoint optimal control problem with equality control constraints and provide a new set of sufficient condition...
متن کاملSufficient Variational Conditions for Isoperimetric Control Problems
For optimal control problems involving isoperimetric constraints, by using a two-norm approach, a new sufficiency theorem for a proper strong minimum is obtained. It is applicable to processes that satisfy the Legendre-Clebsch necessary condition but its strict version is not imposed, that is, the processes may be singular. The conditions are expressed explicitly in terms of the second variatio...
متن کاملSecond order conditions for periodic optimal control problems
This paper concerns second order sufficient conditions of optimality, involving the Riccati equation, for optimal control problems with periodic boundary conditions. The problems considered involve no pathwise constraints and are ‘regular’, in the sense that the strengthened Legendre-Clebsch condition is assumed to be satisfied. A well-known sufficient condition, which we refer to as the Riccat...
متن کاملA New Modification of Legendre-Gauss Collocation Method for Solving a Class of Fractional Optimal Control Problems
In this paper, the optimal conditions for fractional optimal control problems (FOCPs) were derived in which the fractional differential operators defined in terms of Caputo sense and reduces this problem to a system of fractional differential equations (FDEs) that is called twopoint boundary value (TPBV) problem. An approximate solution of this problem is constructed by using the Legendre-Gauss...
متن کاملStability Analysis of Optimal Control Problems with a Second-Order State Constraint
This paper gives stability results for nonlinear optimal control problems subject to a regular state constraint of second-order. The strengthened Legendre-Clebsch condition is assumed to hold, and no assumption on the structure of the contact set is made. Under a weak second-order sufficient condition (taking into account the active constraints), we show that the solutions are Lipschitz continu...
متن کامل