Abstract
This paper presents some solution approaches to the problem of optimal energy-regenerative model predictive control for linear systems subject to stability and/or dissipativity constraints, as well as hard constraints on the state and control vectors. The problem is generally non-convex in the objective and some of the constraints, thereby resulting in a non-convex optimization problem to be solved at each time step. Multiple extended convex relaxation approaches are considered. As a result, a more conservative semi-definite programming problem is proposed to be solved at each time step. The feasibility and stability of the resulting closed-loop system are also examined. The approaches are validated using a numerical example of maximizing energy regeneration from a single degree of freedom vibrating system subject to a level-set constraint on some performance metric characterizing the quality of vibration isolation achieved by the system. The constraint is described in terms of an upper bound on the L2 gain of the system from the input to a vector of appropriately selected system outputs.