# Dynamic Tube MPC for Nonlinear Systems

## TL;DR

This paper introduces Dynamic Tube MPC, a novel control framework for nonlinear systems that optimizes both the tube geometry and trajectory simultaneously, reducing conservativeness and enhancing robustness against uncertainties and disturbances.

## Contribution

The paper proposes a new Dynamic Tube MPC framework that integrates tube geometry optimization with trajectory planning for nonlinear systems, improving robustness and reducing conservativeness.

## Key findings

- Enables simultaneous optimization of tube geometry and trajectory.
- Leverages state-dependent uncertainty to reduce conservativeness.
- Demonstrates robust obstacle avoidance capabilities.

## Abstract

Modeling error or external disturbances can severely degrade the performance of Model Predictive Control (MPC) in real-world scenarios. Robust MPC (RMPC) addresses this limitation by optimizing over feedback policies but at the expense of increased computational complexity. Tube MPC is an approximate solution strategy in which a robust controller, designed offline, keeps the system in an invariant tube around a desired nominal trajectory, generated online. Naturally, this decomposition is suboptimal, especially for systems with changing objectives or operating conditions. In addition, many tube MPC approaches are unable to capture state-dependent uncertainty due to the complexity of calculating invariant tubes, resulting in overly-conservative approximations. This work presents the Dynamic Tube MPC (DTMPC) framework for nonlinear systems where both the tube geometry and open-loop trajectory are optimized simultaneously. By using boundary layer sliding control, the tube geometry can be expressed as a simple relation between control parameters and uncertainty bound; enabling the tube geometry dynamics to be added to the nominal MPC optimization with minimal increase in computational complexity. In addition, DTMPC is able to leverage state-dependent uncertainty to reduce conservativeness and improve optimization feasibility. DTMPC is demonstrated to robustly perform obstacle avoidance and modify the tube geometry in response to obstacle proximity.