Formation control using optimal time multiplexing

Lack of availability of adequate bandwidth for simultaneous communication between a large number of agents and the central processing unit motivates us to study a multi-agent system employing time multiplexed control. Achieving a formation under such time-multiplexing constraints is posed as a discrete constrained optimal control problem. Employing the discrete Pontryagin Maximum Principle (DMP) we obtain first order necessary conditions to be satisfied by an optimal control law, which tackles both problems of formation control and time multiplexing simultaneously. The information structure of relative states is embedded into the problem using a graph theoretic framework. The necessary conditions appear in the form of a two-point boundary value problem and this is solved using a multiple shooting method. The results are then validated through numerical experiments for various cases.