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- Title
Approximate optimal control of fractional stochastic hemivariational inequalities of order (1, 2] driven by Rosenblatt process.
- Authors
Yan, Zuomao
- Abstract
We study the approximate optimal control for a class of fractional stochastic hemivariational inequalities with non-instantaneous impulses driven by Rosenblatt process in a Hilbert space. Firstly, a suitable definition of piecewise continuous mild solution is introduced, and by using stochastic analysis, properties of α -order sine and cosine family and Picard type approximate sequences, we show the existence and uniqueness of approximate mild solutions for the inequality problems of fractional order (1, 2] under the non-Lipschitz conditions. Secondly, we provide the existence conditions of approximate solutions to optimal control problems driven by the presented control systems with the help of a new minimizing sequence method. Finally, an example is provided to illustrate the theory.
- Subjects
STOCHASTIC control theory; STOCHASTIC analysis; HILBERT space; OPTIMAL control theory; SEQUENCE spaces
- Publication
Fractional Calculus & Applied Analysis, 2024, Vol 27, Issue 2, p848
- ISSN
1311-0454
- Publication type
Article
- DOI
10.1007/s13540-024-00257-5