Flexible-step Model Predictive Control based on Generalized Lyapunov Functions

TL;DR

This paper introduces a flexible-step nonlinear MPC scheme utilizing generalized Lyapunov functions, allowing variable control inputs per iteration while ensuring stability and feasibility, demonstrated on nonholonomic systems.

Contribution

It proposes a novel MPC approach based on average descent Lyapunov functions, enabling flexible control input implementation with guaranteed stability.

Findings

Ensures recursive feasibility and stability with flexible control steps.

Demonstrates improved convergence in nonholonomic systems.

Provides computationally attractive control scheme.

Abstract

We present a novel nonlinear model predictive control (MPC) scheme with relaxed stability criteria, based on the idea of generalized discrete-time control Lyapunov functions. These functions need to satisfy an average descent over a finite window of time, rather than a descent at every time step. One feature of this scheme is that it allows for implementing a flexible number of control inputs in each iteration, in a computationally attractive manner, while guaranteeing recursive feasibility and stability. The benefits of our flexible-step implementation are also demonstrated in an application to nonholonomic systems, where the one-step standard implementation may suffer from lack of asymptotic convergence.