A State-Dependent Updating Period For Certified Real-Time Model Predictive Control

TL;DR

This paper introduces a state-dependent control updating scheme for real-time Model Predictive Control that guarantees stability and constraint satisfaction, validated through theoretical bounds and an illustrative example.

Contribution

It presents a novel state-dependent updating period framework with certified stability for real-time MPC, including explicit bounds and application to linear systems.

Findings

Certified stability and constraint satisfaction achieved

Explicit computation of control updating scheme demonstrated

Validation through a chain of integrators example

Abstract

In this paper, a state-dependent control updating period framework is proposed that leads to real-time implementable Model Predictive Control with certified practical stability results and constraints satisfaction. The scheme is illustrated and validated using new certification bound that is derived in the case where the Fast Gradient iteration is used through a penalty method to solve generally constrained convex optimization problems. Both the certification bound computation and its use in the state-dependent updating period framework are illustrated in the particular case of linear MPC. An illustrative example involving a chain of four integrators is used to show the explicit computation of the state-dependent control updating scheme.