Discrete-time contraction-based control of nonlinear systems with parametric uncertainties using neural networks

Abstract

In response to the continuously changing feedstock supply and market demand for products with different specifications, industrial processes need to be operated at time-varying operating conditions and targets (e.g., setpoints) to improve their economy, in contrast to traditional process operations around predetermined equilibriums. In this paper, a novel control approach is developed for nonlinear chemical processes to achieve time-varying reference tracking, by combining the universal approximation characteristics of neural networks with the rigor of discrete-time contraction analysis and control. This is a robust approach that can deal with bounded parametric uncertainties in the process model, which are commonly encountered in industrial processes. A new synthesis approach is developed that involves training a neural network representation of a contraction metric and differential feedback gain for a full range of parametric uncertainty. This network is then embedded in a contraction-based control structure. A separate neural network is also incorporated into the control-loop to perform online identification of uncertain system model parameters. The resulting control scheme is capable of achieving efficient offset-free tracking of time-varying references under the parametric uncertainty, without the need for controller redesign as the reference changes. Process stability is also ensured during online simultaneous learning and control. Simulation examples are provided to illustrate the approach.