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- W4226420004 abstract "In this paper we consider the problem of the optimal control of an ensemble of affine-control systems. After proving the well-posedness of the minimization problem under examination, we establish a $Gamma$-convergence result that allows us to substitute the original (and usually infinite) ensemble with a sequence of finite increasing-in-size sub-ensembles. The solutions of the optimal control problems involving these sub-ensembles provide approximations in the $L^2$-strong topology of the minimizers of the original problem. Using again a $Gamma$-convergence argument, we manage to derive a Maximum Principle for ensemble optimal control problems with end-point cost. Moreover, in the case of finite sub-ensembles, we can address the minimization of the related cost through numerical schemes. In particular, we propose an algorithm that consists of a subspace projection of the gradient field induced on the space of admissible controls by the approximating cost functional. In addition, we consider an iterative method based on the Pontryagin Maximum Principle. Finally, we test the algorithms on an ensemble of linear systems in $mathbb{R}^2$." @default.
- W4226420004 created "2022-05-05" @default.
- W4226420004 creator A5045644680 @default.
- W4226420004 date "2022-03-30" @default.
- W4226420004 modified "2023-09-29" @default.
- W4226420004 title "Optimal Control of ensembles of dynamical systems" @default.
- W4226420004 doi "https://doi.org/10.48550/arxiv.2203.16485" @default.
- W4226420004 hasPublicationYear "2022" @default.
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