Variational stability of optimal control problems involving subdifferential operators
- Institute of System Dynamics and Control Theory, Siberian Branch of the Russian Academy of Sciences, Irkutsk (Russian Federation)
This paper is concerned with the problem of minimizing an integral functional with control-nonconvex integrand over the class of solutions of a control system in a Hilbert space subject to a control constraint given by a phase-dependent multivalued map with closed nonconvex values. The integrand, the subdifferential operators, the perturbation term, the initial conditions and the control constraint all depend on a parameter. Along with this problem, the paper considers the problem of minimizing an integral functional with control-convexified integrand over the class of solutions of the original system, but now subject to a convexified control constraint. By a solution of a control system we mean a 'trajectory-control' pair. For each value of the parameter, the convexified problem is shown to have a solution, which is the limit of a minimizing sequence of the original problem, and the minimal value of the functional with the convexified integrand is a continuous function of the parameter. This property is commonly referred to as the variational stability of a minimization problem. An example of a control parabolic system with hysteresis and diffusion effects is considered. Bibliography: 24 titles.
- OSTI ID:
- 21592556
- Journal Information:
- Sbornik. Mathematics, Vol. 202, Issue 4; Other Information: DOI: 10.1070/SM2011v202n04ABEH004157; Country of input: International Atomic Energy Agency (IAEA); ISSN 1064-5616
- Country of Publication:
- United States
- Language:
- English
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