[Paper Review] Model Predictive Control meets robust Kalman filtering

Alberto Zenere, Mattia Zorzi|arXiv (Cornell University)|Mar 15, 2017

Advanced Control Systems Optimization13 references3 citations

TL;DR

This paper proposes a robust Model Predictive Control (MPC) framework that integrates a robust Kalman filter to enhance resilience against model uncertainties and noise. By replacing the standard Kalman filter in MPC with a risk-sensitive robust Kalman filter, the controller maintains MPC's intuitive structure while enabling tunable robustness via a tolerance parameter $ c $, significantly improving performance under model mismatch at the cost of increased control energy and reduced smoothness.

ABSTRACT

Model Predictive Control (MPC) is the principal control technique used in industrial applications. Although it offers distinguishable qualities that make it ideal for industrial applications, it can be questioned its robustness regarding model uncertainties and external noises. In this paper we propose a robust MPC controller that merges the simplicity in the design of MPC with added robustness. In particular, our control system stems from the idea of adding robustness in the prediction phase of the algorithm through a specific robust Kalman filter recently introduced. Notably, the overall result is an algorithm very similar to classic MPC but that also provides the user with the possibility to tune the robustness of the control. To test the ability of the controller to deal with errors in modeling, we consider a servomechanism system characterized by nonlinear dynamics.

Motivation & Objective

• To address the inherent vulnerability of standard MPC to model uncertainties and external noise in industrial applications.
• To preserve the simplicity and constraint-handling flexibility of MPC while enhancing its robustness.
• To enable user-tunable robustness through a parameterized robust Kalman filter without requiring deep mathematical expertise.
• To evaluate the performance of the robust MPC in a nonlinear servomechanism system under model mismatch.

Proposed method

• The proposed controller replaces the standard Kalman filter in MPC with a robust Kalman filter based on risk-sensitive filtering principles, as introduced in Levy and Nikoukhah (2013).
• The robust Kalman filter uses a tolerance parameter $ c $ to quantify uncertainty in the nominal model, allowing trade-offs between robustness and control effort.
• The MPC optimization problem is solved using a standard receding horizon formulation with quadratic cost functions on prediction errors and input variations.
• The state estimate $ \hat{x}_{t|t} $ is updated using the robust Kalman filter, which modifies the prediction step to account for model uncertainty.
• The controller is implemented using a standard MPC formulation with modified state estimates, preserving the algorithmic simplicity of classic MPC.
• Simulations are conducted on a nonlinear servomechanism system with a linearized nominal model, where model mismatch is introduced to test robustness.

Experimental results

Research questions

• RQ1 Can a robust Kalman filter be effectively integrated into the MPC framework to improve resilience against model uncertainties?
• RQ2 How does the tolerance parameter $ c $ in the robust Kalman filter affect the control performance and input characteristics?
• RQ3 Does the proposed robust MPC outperform standard MPC in tracking accuracy when the actual system deviates from the nominal model?
• RQ4 What is the trade-off between robustness, control energy, and smoothness in the proposed controller?

Key findings

• Under model-matching conditions, all controllers—S-MPC, R-MPC1 ($ c=0.1 $), and R-MPC2 ($ c=1 $)—achieved comparable tracking performance on the reference trajectory.
• When the actual system deviated from the nominal model, S-MPC failed to track the reference, while both R-MPC variants maintained stable and accurate control.
• R-MPC2 ($ c=1 $) outperformed R-MPC1 ($ c=0.1 $) in handling model mismatch, demonstrating improved robustness with higher tolerance.
• The control inputs for R-MPC1 and R-MPC2 were less smooth and required higher energy than S-MPC, with R-MPC2 exhibiting the most aggressive input profile.
• The increased robustness with higher $ c $ came at the cost of reduced input smoothness and higher energy consumption, confirming the expected trade-off.
• The proposed robust MPC maintained the structural simplicity of standard MPC while enabling tunable robustness through a single parameter $ c $.