Optimal Control Problem for Minimization of Net Energy Consumption at Metro

The optimal control currently decides the minimum energy consumption within the problems attached to subways. Among other things, we formulate and solve an optimal bi-control problem, the two controls being the acceleration and the feed-back of a Riemannian connection. The control space is a square, and the optimal controls are of the bang-bang type. The third component of the optimal solution is the maximum value function, as a solution of the Hamilton-Jacobi-Bellman PDE. The examples of energy optimal trajectories refer to the lines of the Bucharest subway.