Abstract
A parametric constrained convex optimal control problem, where the initial state is perturbed and the linear state equation contains a noise, is considered in this paper. Formulas for computing the subdifferential and the singular subdifferential of the optimal value function at a given parameter are obtained by means of some recent results on differential stability in mathematical programming. The computation procedures and illustrative examples are presented.
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Acknowledgements
This work was supported by College of Sciences, Thai Nguyen University (Vietnam), the Grant MOST 105-2221-E-039-009-MY3 (Taiwan), and National Foundation for Science & Technology Development (Vietnam). The authors would like to thank the anonymous referees for their careful readings and valuable suggestions for corrections, which have helped to improve the paper presentation.
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An, D.T.V., Yao, JC. & Yen, N.D. Differential Stability of a Class of Convex Optimal Control Problems. Appl Math Optim 81, 1–22 (2020). https://doi.org/10.1007/s00245-017-9475-4
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DOI: https://doi.org/10.1007/s00245-017-9475-4
Keywords
- Parametric constrained convex optimal control problem
- Linear ordinary differential equation
- Sobolev space
- Parametric mathematical programming problem
- Optimal value function
- Subdifferential
- Singular subdifferential