Adaptive Meshes and Contraction Condition Certification for Nonlinear Control Synthesis Using Machine Learning

In response to the continuously changing feedstock supply, time-varying utility (e.g., energy) costs and product market demand, the process operation strategy, modern chemical plants (which are typically nonlinear) need to be operated to achieve time-varying operation targets (e.g., production rates and specifications) to improve the process economy. As such the control system should be able to track time-varying references, i.e., flexible manufacturing. By leveraging the differential dynamics, contraction theory provides a tool for control design to deliver reference-independent stability (incremental stability). To address the difficulties in contraction-based control synthesis, a machine learning approach was proposed to determine the contraction metric and controller. However, this approach often requires a very large data set for neural network training which can be very computationally complex. In this article, we extend the above approach with an adaptive mesh to reduce the required size of training data sets and thus improve the efficiency of neural network training. The main contribution of this work is the development of the contraction condition certification ensuring that the contraction metric and corresponding controller, which are learned from limited number of data points, are valid for the entire state and input space.