Robustly Linearized Model Predictive Control for Nonlinear Infinite-Dimensional Systems.

Area of Science:

• Control Theory
• Applied Mathematics
• Systems Engineering

Background:

• Model predictive control (MPC) is widely used but struggles with nonlinear systems and approximation errors.
• Existing MPC frameworks often fail to guarantee output constraints on the true system due to linearization and discretization inaccuracies.
• Nonlinear distributed parameter systems (DPS) present significant control challenges due to their infinite-dimensional state space.

Purpose of the Study:

• To develop a computationally efficient and robust model predictive control (MPC) method for nonlinear evolution equations in infinite-dimensional systems.
• To explicitly account for linearization and discretization errors in the MPC law, ensuring output constraint satisfaction on the actual system.
• To enable tractable MPC for nonlinear DPS by incorporating these approximation errors via output constraints.

Main Methods:

• A robust linearization approach is proposed for nonlinear affine-in-control evolution equations.
• Tight integral inequalities are derived under mild assumptions on nonlinear system dynamics to formulate output constraints.
• These constraints are designed to be easily evaluated in real-time, balancing computational efficiency and constraint strictness.

Main Results:

• The developed method produces a model predictive control law that is robust to approximation errors for the first time.
• Linearization and discretization errors are explicitly handled, guaranteeing constraint satisfaction on the true system.
• The approach allows for a trade-off between computational efficiency and the strictness of output constraints.

Conclusions:

• This work enables robust and computationally efficient model predictive control for nonlinear distributed parameter systems.
• The novel approach ensures output constraint satisfaction by rigorously accounting for approximation errors.
• The method has potential applications in fields like autonomous energy-based surgery, demonstrated on a 1D heat equation example.