Certainty-equivalent adaptive MPC for uncertain nonlinear systems

TL;DR

This paper introduces a robust adaptive MPC method for uncertain nonlinear systems that guarantees performance and constraint satisfaction by combining certainty-equivalent control with least-mean-square parameter adaptation, applicable to large uncertainties.

Contribution

It develops a novel certainty-equivalent MPC framework with strong robustness guarantees that requires no offline system-specific design and handles large parametric uncertainties.

Findings

Linear scaling of tracking error with noise and disturbance energy

Effective control of nonlinear unstable quadrotor with obstacle navigation

Applicability to large parametric uncertainties in simulations

Abstract

We provide a method to design adaptive controllers for nonlinear systems using model predictive control (MPC). By combining a certainty-equivalent MPC formulation with least-mean-square parameter adaptation, we obtain an adaptive controller with strong robust performance guarantees: The cumulative tracking error and violation of state constraints scale linearly with noise energy, disturbance energy, and path length of parameter variation. A key technical contribution is developing the underlying certainty-equivalent MPC that tracks output references, accounts for actuator limitations and desired state constraints, requires no system-specific offline design, and provides strong inherent robustness properties. This is achieved by leveraging finite-horizon rollouts, artificial references, recent analysis techniques for optimization-based controllers, and soft state constraints. For open-loop stable systems, we derive a semi-global result that applies to arbitrarily large measurement noise, disturbances, and parametric uncertainty. For stabilizable systems, we derive a regional result that is valid within a given region of attraction and for sufficiently small uncertainty. Applicability and benefits are demonstrated with numerical simulations involving systems with large parametric uncertainty: a linear stable chain of mass-spring-dampers and a nonlinear unstable quadrotor navigating obstacles.