Point-to-point control near heteroclinic orbits: Plant and controller optimality conditions

In this paper we consider the simultaneous optimization of the controller and plant in a one degree-of-freedom system. In particular we are interested in optimal trajectories between fixed points connected by heteroclinic orbits. We find that designing the plant dynamics to have a heteroclinic connection between target states enables a low energy transfer between the states. We use a nested optimization strategy to find the optimal plant dynamics and control effort for the transition. Additionally, we uncover plant optimality conditions which reduce the complexity of the optimization.