Regularized Model Predictive Control

TL;DR

This paper introduces a Riccati equation-based regularization method for model predictive control, improving real-time performance by adaptively adjusting the cost design matrices within the MPC framework.

Contribution

It proposes a novel regularized MPC algorithm using Riccati equations and penalized least squares, with convergence and stability analysis demonstrating its advantages.

Findings

Enhanced control performance over traditional MPC methods.

Successful recursive updating of the design matrix via Riccati equations.

Numerical results confirm improved stability and efficiency.

Abstract

In model predictive control (MPC), the choice of cost-weighting matrices and designing the Hessian matrix directly affects the trade-off between rapid state regulation and minimizing the control effort. However, traditional MPC in quadratic programming relies on fixed design matrices across the entire horizon, which can lead to suboptimal performance. This study presents a Riccati equation-based method for adjusting the design matrix within the MPC framework, which enhances real-time performance. We employ a penalized least-squares (PLS) approach to derive a quadratic cost function for a discrete-time linear system over a finite prediction horizon. Using the method of weighting and enforcing the equality constraint by introducing a large penalty parameter, we solve the constrained optimization problem and generate control inputs for forward-shifted horizons. This process yields a recursive PLS-based Riccati equation that updates the design matrix as a regularization term in each shift, forming the foundation of the regularized MPC (Re-MPC) algorithm. To accomplish this, we provide a convergence and stability analysis of the developed algorithm. Numerical analysis demonstrates its superiority over traditional methods by allowing Riccati equation-based adjustments.