Robust Adaptive Model Predictive Control with Uncertainty Compensation for Linear Systems with Matched and Unmatched Uncertainties

Core Concepts

This paper presents a robust adaptive model predictive control (MPC) framework that leverages an L1 adaptive controller to compensate for matched uncertainties and provide guaranteed uniform bounds on the error between the states and control inputs of the actual system and a nominal system. These bounds are then used to tighten the state and control constraints of the actual system, and an MPC is designed for the nominal system with the tightened constraints.

Abstract

The paper presents a robust adaptive MPC framework, termed UC-MPC, for linear systems with both matched and unmatched nonlinear uncertainties subject to state and input constraints. The key aspects are:

1. The framework uses an L1 adaptive controller (L1AC) to compensate for the matched uncertainties and provide uniform bounds on the error between the states and inputs of the actual system and a nominal system.

2. These uniform bounds are used to tighten the state and control constraints of the actual system, and an MPC is designed for the nominal system with the tightened constraints.

3. The proposed UC-MPC guarantees constraint satisfaction and achieves improved performance compared to existing robust or tube MPC methods.

4. Simulation results on a flight control example demonstrate the benefits of the proposed framework, showing that UC-MPC can achieve better tracking performance than MPC and tube MPC while enforcing the constraints.

5. The key advantages of UC-MPC are: 1) it can handle a broad class of uncertainties that are time-varying and state-dependent without a parametric structure, 2) it can handle unmatched disturbances, and 3) it improves tracking performance compared to existing robust or tube MPC solutions.

Stats

The system dynamics are given by:
˙x(t) = Ax(t) + B(u(t) + f(t, x(t))) + Buw(t)
y(t) = Cx(t)
where f(t, x(t)) represents the matched uncertainty and w(t) represents the unmatched uncertainty.
The state and control input constraints are:
x(t) ∈ X
u(t) ∈ U
where X and U are pre-specified convex and compact sets.

Quotes

None.

Key Insights Distilled From

Robust Adaptive MPC Using Uncertainty Compensation

by Ran Tao,Pan ... at arxiv.org 04-04-2024

https://arxiv.org/pdf/2309.13743.pdf

Deeper Inquiries

How could the proposed UC-MPC framework be extended to handle more general nonlinear systems beyond the linear case considered in this paper

To extend the proposed UC-MPC framework to handle more general nonlinear systems beyond the linear case considered in the paper, several modifications and adaptations would be necessary. One approach could involve incorporating nonlinear state and input constraints into the MPC design. This would require the development of nonlinear constraint satisfaction techniques within the optimization framework. Additionally, the uncertainty compensation approach would need to be tailored to handle nonlinear uncertainties, possibly through the use of adaptive control strategies that can effectively estimate and compensate for these nonlinear uncertainties. Furthermore, the model predictive controller itself would need to be reformulated to accommodate the complexities of nonlinear dynamics, possibly through the use of techniques such as nonlinear model predictive control (NMPC) or feedback linearization. Overall, extending the UC-MPC framework to nonlinear systems would involve a combination of advanced control techniques and algorithmic developments to address the challenges posed by nonlinear dynamics and constraints.

What are the potential limitations or drawbacks of the uncertainty compensation approach used in UC-MPC, and how could they be addressed in future work

While the uncertainty compensation approach used in UC-MPC offers significant benefits in terms of improving tracking performance and robustness, there are potential limitations and drawbacks that need to be considered. One limitation is the reliance on accurate modeling of uncertainties, which may not always be feasible in practical applications. Inaccurate estimation of uncertainties could lead to suboptimal performance or even instability in the control system. To address this limitation, future work could focus on developing adaptive algorithms that can dynamically adjust the uncertainty compensation based on real-time measurements and feedback. Additionally, the computational complexity of the uncertainty compensation approach could be a drawback, especially for real-time implementation. Future research could explore ways to streamline the computation and implementation of uncertainty compensation algorithms to reduce computational burden without compromising performance.

The paper focuses on improving tracking performance compared to existing robust MPC methods. Are there other performance metrics, beyond tracking error, that could be considered and optimized for in the UC-MPC design

While the paper primarily focuses on improving tracking performance compared to existing robust MPC methods, there are other performance metrics that could be considered and optimized for in the UC-MPC design. One important metric is control effort or energy consumption, which is crucial for practical applications where energy efficiency is a concern. By incorporating control effort minimization objectives into the MPC optimization problem, the UC-MPC framework could be further enhanced to achieve not only improved tracking performance but also reduced control effort. Additionally, robustness metrics such as disturbance rejection capabilities and sensitivity to modeling errors could be integrated into the design to ensure that the controller performs well under various operating conditions. By optimizing for a combination of tracking performance, control effort, robustness, and other relevant metrics, the UC-MPC framework can be further tailored to meet the specific requirements of different applications.