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We study a constrained optimal control problem for an ensemble of controlsystems. Each sub-system (or plant) evolves on a matrix Lie group, and mustsatisfy given state and control action constraints pointwise in time. Inaddition, certain multiplexing requirement is imposed: the controller must beshared between the plants in the sense that at any time instant the controlsignal may be sent to only one plant. We provide first-order necessaryconditions for optimality in the form of suitable Pontryagin maximum principlein this problem. Detailed numerical experiments are presented for a system oftwo satellites performing energy optimal maneuvers under the preceding familyof constraints.

On optimal multiplexing of an ensemble of discrete-time constrained control systems on matrix Lie groups