Robustly Linearized Model Predictive Control for Nonlinear Infinite-Dimensional Systems

This work presents a computationally efficient approach to robustly linearized model predictive control for nonlinear affine-in-control evolution equations on infinite-dimensional system state. In this setting, robust linearization refers to a need to account for the approximation errors in linearization and discretization in the model predictive control law, such that the original output constraints are not violated on the true system, a feature that present model predictive control frameworks lack. The main purpose of this work is to enable tractable model predictive control for nonlinear distributed parameter systems while accounting for these approximation errors by means of output constraints. These output constraints are derived using tight integral inequalities that rest on mild assumptions on the nonlinear system dynamics, and are easy to evaluate in real-time. Using our method, linearization and discretization errors are explicitly accounted for, producing for the first time a model predictive control law that is robust to approximation errors. This approach hence enables a trade-off between computational efficiency and strictness of output constraints, much akin to robust control methods. We demonstrate our method on a nonlinear distributed parameter system, namely a one-dimensional heat equation with a velocity-controlled moveable heat source, motivated by autonomous energy-based surgery.