[Paper Review] Robust Adaptive MPC in the Presence of Nonlinear Time-Varying Uncertainties: An Uncertainty Compensation Approach

Ran Tao, Pan Zhao+2 more|arXiv (Cornell University)|Feb 27, 2026

Advanced Control Systems Optimization0 citations

TL;DR

The paper proposes UC-MPC, a robust adaptive MPC framework that compensates for nonlinear time-varying matched and unmatched uncertainties using an L1 adaptive controller and an LMI-designed robust feedback controller, with constraint tightening based on uniform error bounds.

ABSTRACT

This paper introduces an uncertainty compensation-based robust adaptive model predictive control (MPC) framework for linear systems with nonlinear time-varying uncertainties. The framework integrates an L1 adaptive controller to compensate for the matched uncertainty and a robust feedback controller, designed using linear matrix inequalities, to mitigate the effect of unmatched uncertainty on target output channels. Uniform bounds on the errors between the system's states and control inputs and those of a nominal (i.e., uncertainty-free) system are derived. These error bounds are then used to tighten the actual system's state and input constraints, enabling the design of an MPC for the nominal system under these tightened constraints. Referred to as uncertainty compensation-based MPC (UC-MPC), this approach ensures constraint satisfaction while delivering enhanced performance compared to existing methods. Simulation results for a flight control example and a spacecraft landing on an asteroid demonstrate the effectiveness of the proposed framework.

Motivation & Objective

• Develop a robust adaptive MPC framework that guarantees constraint satisfaction for linear systems with nonlinear time-varying matched and unmatched uncertainties.
• Integrate an L1 adaptive controller to compensate matched uncertainties and a robust LMI-based feedback controller to mitigate unmatched effects.
• Derive uniform bounds on state/input deviations to tighten MPC constraints for the nominal, uncertainty-free system.
• Provide theoretical guarantees for constraint satisfaction, recursive feasibility, and nominal closed-loop stability.
• Validate the framework via flight control and spacecraft landing scenarios under uncertainty.

Proposed method

• Decompose total uncertainty into matched and unmatched components using B and B_u with B_u^T B = 0.
• Design an L1 adaptive controller to estimate and cancel the matched uncertainty within the L1 filter bandwidth.
• Develop an LMI-based robust feedback controller to attenuate the impact of unmatched uncertainty on target outputs.
• Form an equivalent nominal system and perform MPC on tightened constraints derived from uniform error bounds.
• Establish conditions for constraint satisfaction, recursive feasibility, and nominal stability within UC-MPC.
• Provide a scaling mechanism and per-channel performance bounds to reduce conservativeness in constraint tightening.

Experimental results

Research questions

• RQ1 How can UC-MPC guarantee constraint satisfaction for linear systems with nonlinear time-varying matched and unmatched uncertainties?
• RQ2 Can L1 adaptive compensation be integrated with MPC in a theoretically grounded way to tighten constraints while ensuring feasibility?
• RQ3 What uniform bounds on state/input deviations can be derived to enable effective constraint tightening?
• RQ4 How do scaling of unmatched uncertainties and per-channel bounds affect performance and feasibility?
• RQ5 What are the theoretical guarantees (constraint satisfaction, stability, recursive feasibility) of the proposed UC-MPC framework?

Key findings

• UC-MPC integrates L1 adaptive compensation with an LMI-based robust controller to handle both matched and unmatched nonlinear time-varying uncertainties.
• Uniform bounds on deviations between actual and nominal systems are derived and used to tighten MPC constraints.
• A scaling mechanism and per-channel bounds reduce conservativeness and improve constraint tightening.
• Equivalent nominal formulation reveals a connection between UC-MPC and tube MPC, enabling standard MPC analysis for feasibility and stability.
• Case studies on flight control and asteroid-enabled spacecraft landing demonstrate the method’s ability to ensure safety and performance under uncertainty.