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arXiv · 2302.03404

Exact Controllability for Mean-Field Type Linear Game-Based Control Systems

Cui Chen·Zhiyong Yu
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Abstract

Motivated by the self-pursuit of controlled objects, we consider the exact controllability of a linear mean-field type game-based control system (MF-GBCS, for short) generated by a linear-quadratic (LQ, for short) Nash game. A Gram-type criterion for the general timevarying coefficients case and a Kalman-type criterion for the special time-invariant coefficients case are obtained. At the same time, the equivalence between the exact controllability of this MF-GBCS and the exact observability of a dual system is established. Moreover, an admissible control that can steer the state from any initial vector to any terminal random variable is constructed in closed form.

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Cui Chen, Zhiyong Yu. 2023-02-07. Exact Controllability for Mean-Field Type Linear Game-Based Control Systems. https://arxiv.org/abs/2302.03404

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