An Analysis of Closed-Loop Stability for Linear Model Predictive Control Based on Time-Distributed Optimization

TL;DR

This paper analyzes the stability of linear MPC when using Time-distributed Optimization, providing explicit bounds and multiple mechanisms to ensure closed-loop stability while reducing computational load.

Contribution

It derives analytic expressions and stability bounds for TDO-based MPC, offering practical guidelines for stability guarantees in linear and potentially nonlinear MPC.

Findings

Explicit stability bounds for TDO-based MPC

Multiple mechanisms to guarantee closed-loop stability

Insights applicable to nonlinear MPC

Abstract

Time-distributed Optimization (TDO) is an approach for reducing the computational burden of Model Predictive Control (MPC). When using TDO, optimization iterations are distributed over time by maintaining a running solution estimate and updating it at each sampling instant. In this paper, TDO applied to input constrained linear MPC is studied in detail, and analytic expressions for the system gains and a bound on the number of optimization iterations per sampling instant required to guarantee closed-loop stability is derived. Further, it is shown that the closed-loop stability of TDO-based MPC can be guaranteed using multiple mechanisms including increasing the number of solver iterations, preconditioning the optimal control problem, adjusting the MPC cost matrices, and reducing the length of the receding horizon. These results in a linear system setting also provide insights and guidelines that could be more broadly applicable, e.g., to nonlinear MPC.