Nonlinear MPC lower bounds via robust simulation

Model predictive control (MPC) for nonlinear systems typically involves a non-convex optimization problem. As with all non-convex optimizations, a local minimum is found, but nothing can be said about the global minimum. With a careful choice of cost, constraints, and system representation, robust simulation gives a lower bound on the optimal cost. If this bound differs greatly from the MPC cost, then additional optimization may be desired. Furthermore, the robust simulation results can be used to initialize additional MPC optimizations. This technique is demonstrated on a simple example