Discrete-time Contraction-based Control of Nonlinear Systems with Parametric Uncertainties using Neural Networks

Abstract

Flexible manufacturing in the process industry requires control systems to achieve time-varying setpoints (e.g., product specifications) based on market demand. Contraction theory provides a useful framework for reference-independent system analysis and tracking control for nonlinear systems. However, the determination of the control contraction metrics and control laws can be very difficult for general nonlinear systems. This work develops an approach to discrete-time contraction analysis and control using neural networks. The methodology involves training a neural network to learn a contraction metric and feedback gain. The resulting contraction-based controller embeds the trained neural network and is capable of achieving efficient tracking of time-varying references, with a full range of model uncertainty, without the need for controller structure redesign. This is a robust approach that can deal with bounded parametric uncertainties in the process model, which are commonly encountered in industrial (chemical) processes. Simulation examples are provided to illustrate the above approach.

Contraction Analysis and Control Synthesis for Discrete-time Nonlinear Processes

“…Based on the contraction (37) and differential dissipativity (42) conditions presented in Section 3, here we develop control synthesis approaches from these conditions using Sum of squares (SOS) programming (see [22] for an alternative neural network-based approach). Details for numerical implementation of a contraction-based controller are also provided.…”