(402c) When Deep Learning Meets Sparse Model Identification: Online Adaptive Sparse Identification of Systems (OASIS)

Over the past few decades, nonlinear model-based control is receiving significant attention as linear models are inadequate in describing inherently nonlinear and complex industrial processes. This requires developing methods for nonlinear model identification. Modeling using first-principles is desirable only when there is sufficient knowledge of the process available. For the processes that are complex and poorly understood, it is difficult to derive such models. In view of this, there has been an increasing interest in data-driven system identification for prediction and control purposes. Specifically, subspace identification methods such as multi-variable output-error-state-space (MOESP) [1], numerical algorithms for subspace state-space identification (N4SID) [2], and canonical variate analysis [3] are popular in the process control domain. Although these methods are successful in identifying state-space models for various industrial applications using input-output data, they do not provide a physical understanding of the process. More importantly, for adaptive modeling applications, it is advantageous to have a model that can provide interpretability of the changing dynamics, which will help guide in evaluating the process operating conditions to take appropriate actions. Lately, sparse identification of nonlinear dynamics (SINDy) has delivered promising results for various nonlinear processes [4]. The SINDy algorithm is based on the techniques of sparse regression and compressive sensing. It fits the input-output data to a library of candidate functions such that only the functions describing the original dynamics are identified. Thereby, using this approach, a parsimonious and interpretable model is obtained. Additionally, any prior knowledge about the process from, for example, physics and thermodynamic laws can be included in the candidate library to quicken the model identification process. Due to these reasons, there has been a growing interest in applying SINDy to a variety of applications, which includes identifying rational nonlinearities [5], sparse learning of reaction kinetics [6], reduced-order modeling of a complex process [7], model recovery from abrupt system changes [8], and for control [9].

Despite the simplicity of SINDy algorithm, it is challenging to use SINDy for model-based control, especially at any instance of plant-model mismatch or process upset. This is because re-training the model using SINDy is computationally expensive and cannot guarantee to catch up with rapidly changing dynamics. Hence, we propose online adaptive sparse identification of systems (OASIS) framework that extends the capabilities of SINDy for accurate, automatic, and adaptive approximation of process models. The key novelty is to combine the usefulness of SINDy in discovering an interpretable model with a deep neural network (DNN) to adaptively model and control the process dynamics in real-time. The proposed method is implemented in two steps: system identification and controller design. For the system identification step, we utilize several sets of process historical data that are available for various input settings and identify their corresponding models using SINDy. Next, we train a DNN using the previously collected historical data sets and their respective SINDy models such that the DNN approximates the relationship between process data and SINDy models. We use this trained DNN to design a controller wherein the DNN updates the SINDy model by utilizing a new set of measurements at every sampling time to accurately predict the future process behavior. In this way, the OASIS method supports the application of SINDy for real-time model identification and control. We demonstrate the OASIS methodology on the model identification and control of a continuous stirred tank reactor. The closed-loop results showed that the proposed OASIS framework can be effectively used for adaptive modeling and control of nonlinear processes.

Literature cited:

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