Control of discrete-time nonlinear systems via finite-step control Lyapunov functions

TL;DR

This paper introduces novel control design methods for discrete-time nonlinear systems using finite-step control Lyapunov functions, formulated as optimization problems within a model predictive control framework, suitable for scenarios with intermittent information exchange.

Contribution

It develops new control design approaches based on finite-step CLFs, formulated as MPC problems, and compares their performance with classic MPC in discrete-time nonlinear systems.

Findings

Contractive multi-step MPC with reoptimization improves stability.

Finite-step CLFs enable control under intermittent communication.

The proposed methods outperform classic MPC in specific scenarios.

Abstract

In this work, we establish different control design approaches for discrete-time systems, which build upon the notion of finite-step control Lyapunov functions (fs-CLFs). The design approaches are formulated as optimization problems and solved in a model predictive control (MPC) fashion. In particular, we establish contractive multi-step MPC with and without reoptimization and compare it to classic MPC. The idea behind these approaches is to use the fs-CLF as running cost. These new design approaches are particularly relevant in situations where information exchange between plant and controller cannot be ensured at all time instants. An example shows the different behavior of the proposed controller design approaches.