Abstract
In this paper, we study the controllability and optimal control for a class of time-delayed fractional stochastic integro-differential system with Poisson jumps. A set of sufficient conditions is established for complete and approximate controllability by assuming non-Lipschitz conditions and pth mean square norm. We also give an existence of optimal control for Bolza problem. Our result is valid for fractional order \(\alpha >\frac{p-1}{p},\ p\ge 2.\) Finally, an example is provided to illustrate the efficiency of the obtained theoretical results.
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This work is partially supported by the National Natural Science Foundation of China (11661016), Training Object of High Level and Innovative Talents of Guizhou Province ((2016)4006), Major Research Project of Innovative Group in Guizhou Education Department ([2018]012) and Guizhou Data Driven Modeling Learning and Optimization Innovation Team ([2020]5016).
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Sathiyaraj, T., Wang, J. & Balasubramaniam, P. Controllability and Optimal Control for a Class of Time-Delayed Fractional Stochastic Integro-Differential Systems. Appl Math Optim 84, 2527–2554 (2021). https://doi.org/10.1007/s00245-020-09716-w
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DOI: https://doi.org/10.1007/s00245-020-09716-w