Update-Aware Robust Optimal Model Predictive Control for Nonlinear Systems

TL;DR

This paper introduces an update-aware robust MPC method for nonlinear systems that explicitly considers future control updates, leading to less conservative solutions and improved worst-case performance bounds.

Contribution

It proposes a novel update-aware robust MPC algorithm formulated as nested SIPs, expanding feasible solutions and enhancing performance over traditional fixed-horizon methods.

Findings

Outperforms existing methods in a planar quadrotor simulation

Guarantees improved worst-case performance bounds

Expands feasible solution set compared to traditional approaches

Abstract

Robust optimal or min-max model predictive control (MPC) approaches aim to guarantee constraint satisfaction over a known, bounded uncertainty set while minimizing a worst-case performance bound. Traditionally, these methods compute a trajectory that meets the desired properties over a fixed prediction horizon, apply a portion of the resulting input, and then re-solve the MPC problem using newly obtained measurements at the next time step. However, this approach fails to account for the fact that the control trajectory will be updated in the future, potentially leading to conservative designs. In this paper, we present a novel update-aware robust optimal MPC algorithm for decreasing horizon problems on nonlinear systems that explicitly accounts for future control trajectory updates. This additional insight allows our method to provably expand the feasible solution set and guarantee improved worst-case performance bounds compared to existing techniques. Our approach formulates the trajectory generation problem as a sequence of nested existence-constrained semi-infinite programs (SIPs), which can be efficiently solved using local reduction techniques. To demonstrate its effectiveness, we evaluate our approach on a planar quadrotor problem, where it clearly outperforms an equivalent method that does not account for future updates at the cost of increased computation time.