Exploiting Characteristics in Stationary Action Problems

Connections between the principle of least action and optimal control are explored with a view to describing trajectories energy conserving systems, subject temporal boundary conditions, as solutions corresponding systems characteristics equations on arbitrary time horizons. Motivated by relaxation stationary for longer horizons, due loss convexity functional, problems is considered. In characterizing attendant controls, generalized velocity trajectories, an auxiliary problem posed respect characteristic system interest. Using this problem, it shown that controls rendering functional horizons have state feedback representation, via verification theorem, consistent short An example provided illustrate application simple mass-spring system.