Quadratic order necessary and sufficient conditions for a Pontryagin minimum for singular extremals touching the boundary of admissible control set
For the control system {dot x} = f (x, t) + F (x, t)u a general optimal control problem is considered, involving terminal equality and inequality constraints, terminal functional to be minimized and a pointwise constraint u {element_of} U(t), where U(t) is a polyhedron. Given a singular extremal in this problem, necessary and sufficient conditions of a quadratic order {gamma} for a Pontryagin minimum are obtained. Here {gamma}({delta}x, {delta}u) is a quadratic function of estimation characteristics to this class of problems; it does`nt contain the control variations, but only variations of state variables. A Pontryagin minimum is an L{sub 1} - minimum with respect to the control on any uniformly bounded control set (thus, it allows to take needle-type variations of the control). The results are similar to those in the analysis and the classical calculus of variations in the sense that the necessary and sufficient conditions form an adjoining pair; the former transforms into the latter only by strengthening an inequality. These conditions include new Legendre type conditions, which take into account not only the second variations of Lagrange functions, but also their third variations and the admissible control set U (t).
- OSTI ID:
- 35955
- Report Number(s):
- CONF-9408161-; TRN: 94:009753-0221
- Resource Relation:
- Conference: 15. international symposium on mathematical programming, Ann Arbor, MI (United States), 15-19 Aug 1994; Other Information: PBD: 1994; Related Information: Is Part Of Mathematical programming: State of the art 1994; Birge, J.R.; Murty, K.G. [eds.]; PB: 312 p.
- Country of Publication:
- United States
- Language:
- English
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