Contraction Analysis and Control Synthesis for Discrete-time Nonlinear Processes

TL;DR

This paper develops a contraction-based control framework for discrete-time nonlinear processes, enabling adaptive, stable, and disturbance-rejecting control suitable for next-generation smart chemical plants.

Contribution

It introduces a systematic contraction analysis method using SOS programming for control synthesis in discrete-time nonlinear systems, with practical implementation guidance.

Findings

Derived contraction conditions for exponential convergence.

Developed a discrete-time differential dissipativity condition.

Validated approach through a numerical case study.

Abstract

Shifting away from the traditional mass production approach, the process industry is moving towards more agile, cost-effective and dynamic process operation (next-generation smart plants). This warrants the development of control systems for nonlinear chemical processes to be capable of tracking time-varying setpoints to produce products with different specifications as per market demand and deal with variations in the raw materials and utility (e.g., energy). This article presents a systematic approach to the implementation of contraction-based control for discrete-time nonlinear processes. Through the differential dynamic system framework, the contraction conditions to ensure the exponential convergence to feasible time-varying references are derived. The discrete-time differential dissipativity condition is further developed, which can be used for control designs for disturbance rejection. Computationally tractable equivalent conditions are then derived and additionally transformed into an SOS programming problem, such that a discrete-time control contraction metric and stabilising feedback controller can be jointly obtained. Synthesis and implementation details are provided and demonstrated through a numerical case study.