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Time Optimal Control of a Clarke Subdifferential Type Stochastic Evolution Inclusion in Hilbert Spaces

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Abstract

This paper investigates the time optimal control for a class of non-instantaneous impulsive Clarke subdifferential type stochastic evolution inclusions in Hilbert spaces. We focus first on the existence of mild solutions for these systems by using the measure of non-compactness and a fixed-point theorem wth the properties of Clarke subdifferential. Then, the existence of time optimal control of governed by stochastic control systems is also obtained. We do not assume that the evolution operator and the values of multi-valued map are compact. Finally, an example is given to illustrate the effectiveness of the results.

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Acknowledgements

The author would like to thank the editor and the reviewer for their constructive comments and suggestions. This work is supported by the National Natural Science Foundation of China (11461019).

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  1. Department of Mathematics, Hexi University, Zhangye, 734000, Gansu, People’s Republic of China

    Zuomao Yan

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Yan, Z. Time Optimal Control of a Clarke Subdifferential Type Stochastic Evolution Inclusion in Hilbert Spaces. Appl Math Optim 84, 3083–3110 (2021). https://doi.org/10.1007/s00245-020-09740-w

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