Numerical Discrete-Time Implementation of Continuous-Time Linear-Quadratic Model Predictive Control

TL;DR

This paper develops a numerical discretization method for continuous-time linear-quadratic model predictive control, demonstrating improved performance over traditional discrete-time approaches as sampling time increases.

Contribution

It introduces a novel discretization approach for CT-LMPC that converts the control problem into a quadratic program, enhancing performance with larger sampling times.

Findings

CT-LMPC outperforms conventional DT-LMPC at larger sampling times.

The discretization method effectively transforms the control problem into a quadratic program.

Numerical experiments validate the improved closed-loop performance.

Abstract

This study presents the design, discretization and implementation of the continuous-time linear-quadratic model predictive control (CT-LMPC). The control model of the CT-LMPC is parameterized as transfer functions with time delays, and they are separated into deterministic and stochastic parts for relevant control and filtering algorithms. We formulate time-delay, finite-horizon CT linear-quadratic optimal control problems (LQ-OCPs) for the CT-LMPC. By assuming piece-wise constant inputs and constraints, we present the numerical discretization of the proposed LQ-OCPs and show how to convert the discrete-time (DT) equivalent into a standard quadratic program. The performance of the CT-LMPC is compared with the conventional DT-LMPC algorithm. Our numerical experiments show that, under fixed tunning parameters, the CT-LMPC shows better closed-loop performance as the sampling time increases than the conventional DT-LMPC.