A Convex Relaxation for Model Predictive Control of a Class of Hammerstein Systems

This letter provides conditions under which a structured optimization problem has a convex relaxation. In this optimization problem, the objective function and constraints can be expressed as a function of an optimization variable and a nonlinear function of this variable. A natural application of this optimization problem is model predictive control of a system that has linear dynamics, but for which the input is a non-invertible nonlinear function of an input signal. An example of such a problem is provided in the application of advanced battery management.