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Optimal Multiplexing of Discrete-Time Constrained Control Systems on Matrix Lie Groups

In this article, we study a constrained optimal control problem for an ensemble of control systems in a centralized setting. Each system evolves on a matrix Lie group, and must satisfy given state and control action constraints pointwise in time. In addition, the controller must be shared between the plants in the sense that at any time instant the control signal may be sent to only one plant while minimizing a given objective function. We provide first-order necessary conditions for optimality in the form of a Pontryagin maximum principle for such optimal control problems.