Second Order Sufficient Optimality Conditions for a Control Problem with Continuous and Bang-Bang Control Components: Riccati Approach
نویسندگان
چکیده
Second order sufficient optimality conditions for bang-bang control problems in a very general form have been obtained in [15, 21, 13, 12, 1]. These conditions require the positive definiteness (coercivity) of an associated quadratic form on the finite-dimensional critical cone. In the present paper, we investigate similar conditions for optimal control problems with a control variable having two components: a continuous unconstrained control appearing nonlinearly and a bang-bang control appearing linearly and belonging to a convex polyhedron. The coercivity of the quadratic form can be verified by checking solvability of an associated matrix Riccati equation. The results are applied to an economic control problem in optimal production and maintenance, where existing sufficient conditions fail to hold.
منابع مشابه
Equivalence of second order optimality conditions for bang – bang control problems
Second order optimality conditions have been derived in the literature in two different forms. Osmolovskii (1988a, 1995, 2000, 2004) obtained second order necessary and sufficient conditions requiring that a certain quadratic form be positive (semi)-definite on a critical cone. Agrachev, Stefani, Zezza (2002) first reduced the bang-bang control problem to finite-dimensional optimization and the...
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