TY - JOUR
T1 - Optimal control of ensembles of dynamical systems
AU - Scagliotti, Alessandro
N1 - Publisher Copyright:
© 2023 The authors. Published by EDP Sciences, SMAI.
PY - 2023
Y1 - 2023
N2 - 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 λ-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 L2-strong topology of the minimizers of the original problem. Using again a λ-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 2.
AB - 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 λ-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 L2-strong topology of the minimizers of the original problem. Using again a λ-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 2.
KW - Gradient-based minimization
KW - Optimal control
KW - Pontryagin Maximum Principle
KW - Simultaneous control
KW - λ-convergence
UR - http://www.scopus.com/inward/record.url?scp=85151156759&partnerID=8YFLogxK
U2 - 10.1051/cocv/2023011
DO - 10.1051/cocv/2023011
M3 - Article
AN - SCOPUS:85151156759
SN - 1292-8119
VL - 29
JO - ESAIM - Control, Optimisation and Calculus of Variations
JF - ESAIM - Control, Optimisation and Calculus of Variations
M1 - 22
ER -