On optimal multiplexing of an ensemble of discrete-time constrained control systems on matrix Lie groups
Provides theoretical optimality conditions for a constrained multiplexing control problem on Lie groups, relevant for multi-agent systems with shared controllers.
The paper derives first-order necessary optimality conditions (Pontryagin maximum principle) for multiplexed control of an ensemble of systems on matrix Lie groups with state and control constraints. Numerical experiments on two satellites show energy-optimal maneuvers under multiplexing.
We study a constrained optimal control problem for an ensemble of control systems. Each sub-system (or plant) evolves on a matrix Lie group, and must satisfy given state and control action constraints pointwise in time. In addition, certain multiplexing requirement is imposed: 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. We provide first-order necessary conditions for optimality in the form of suitable Pontryagin maximum principle in this problem. Detailed numerical experiments are presented for a system of two satellites performing energy optimal maneuvers under the preceding family of constraints.