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Inverse Optimal Control : theoretical study

Abstract : This PhD thesis is part of a larger project, whose aim is to address the mathematical foundations of the inverse problem in optimal control in order to reach a general methodology usable in neurophysiology. The two key questions are : (a) the uniqueness of a cost for a given optimal synthesis (injectivity) ; (b) the reconstruction of the cost from the synthesis. For general classes of costs, the problem seems very difficult even with a trivial dynamics. Therefore, the injectivity question was treated for special classes of problems, namely, the problems with quadratic cost and a dynamics, which is either non-holonomic (sub-Riemannian geometry) or control-affine. Based on the obtained results, we propose a reconstruction algorithm for the linear-quadratic problem.
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Submitted on : Monday, December 10, 2018 - 3:52:07 PM
Last modification on : Wednesday, May 11, 2022 - 12:06:06 PM
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  • HAL Id : tel-01950176, version 1


Sofya Maslovskaya. Inverse Optimal Control : theoretical study. Optimization and Control [math.OC]. Université Paris-Saclay, 2018. English. ⟨NNT : 2018SACLY013⟩. ⟨tel-01950176⟩



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