Multiple Shooting Technique for Optimal Control Problems with Application to Power Aware Networks*

This paper presents a shooting method for a class of optimal control problems where the input u(t) is expressed analytically in terms of its associated state x(t) and costate (adjoint) p(t) along the optimal trajectory. The problem is formulated in terms of computing the initial costate that drives the final costate to a prescribed value. We solve this problem by a combination of gradient descent and multiple shooting. The proposed technique is applied to a power-aware problem of co-optimizing motion and transmission power in networks of mobile agents, and fast convergence is discerned from simulation of a fifty-agent system.