Control Contraction Metric Synthesis for Discrete-time Nonlinear Systems

TL;DR

This paper introduces a systematic method for contraction analysis and control synthesis of discrete-time nonlinear systems using Discrete-time Control Contraction Metrics, enabling tracking of time-varying targets in flexible manufacturing.

Contribution

It extends contraction theory to discrete-time systems and develops a synthesis approach using SOS programming for control design.

Findings

Effective discrete-time contraction analysis method

Control synthesis demonstrated on illustrative example

Enables tracking of time-varying targets in manufacturing

Abstract

Flexible manufacturing has been the trend in the area of the modern chemical process nowadays. One of the essential characteristics of flexible manufacturing is to track time-varying target trajectories (e.g. diversity and quantity of products). A possible tool to achieve time-varying targets is contraction theory. However, the contraction theory was developed for continuous time systems and there lacks analysis and synthesis tools for discrete-time systems. This article develops a systematic approach to discrete-time contraction analysis and control synthesis using Discrete-time Control Contraction Metrics (DCCM) which can be implemented using Sum of Square (SOS) programming. The proposed approach is demonstrated by illustrative example.