Online machine learning modeling and predictive control of nonlinear systems with scheduled mode transitions

This work develops a model predictive control (MPC) scheme using online learning of recurrent neural network (RNN) models for nonlinear systems switched between multiple operating regions following a prescribed switching schedule. Specifically, an RNN model is initially developed offline to model process dynamics using the historical operational data collected in a small region around a certain steady-state. After the system is switched to another operating region under a Lyapunov-based MPC with suitable constraints to ensure satisfaction of the prescribed switching schedule policy, RNN models are updated using real-time process data to improve closed-loop performance. A generalization error bound is derived for the updated RNN models using the notion of regret, and closed-loop stability results are established for the switched nonlinear system under RNN-based MPC. Finally, a chemical process example with the operation schedule that requires switching between two steady-states is used to demonstrate the effectiveness of the proposed RNN-MPC scheme.     

Statistical machine-learning–based predictive control of uncertain nonlinear processes

In this study, we present machine-learning–based predictive control schemes for nonlinear processes subject to disturbances, and establish closed-loop system stability properties using statistical machine learning theory. Specifically, we derive a generalization error bound via Rademacher complexity method for the recurrent neural networks (RNN) that are developed to capture the dynamics of the nominal system. Then, the RNN models are incorporated in Lyapunov-based model predictive controllers, under which we study closed-loop stability properties for the nonlinear systems subject to two types of disturbances: bounded disturbances and stochastic disturbances with unbounded variation. A chemical reactor example is used to demonstrate the implementation and evaluate the performance of the proposed approach.     

Machine learning-based predictive control of nonlinear processes. Part I: Theory

This article focuses on the design of model predictive control (MPC) systems for nonlinear processes that utilize an ensemble of recurrent neural network (RNN) models to predict nonlinear dynamics. Specifically, RNN models are initially developed based on a data set generated from extensive open-loop simulations within a desired process operation region to capture process dynamics with a sufficiently small modeling error between the RNN model and the actual nonlinear process model. Subsequently, Lyapunov-based MPC (LMPC) that utilizes RNN models as the prediction model is developed to achieve closed-loop state boundedness and convergence to the origin. Additionally, machine learning ensemble regression modeling tools are employed in the formulation of LMPC to improve prediction accuracy of RNN models and overall closed-loop performance while parallel computing is utilized to reduce computation time. Computational implementation of the method and application to a chemical reactor example is discussed in the second article of this series.     

ADAPTIVE NEURAL-NETWORK PREDICTIVE CONTROL FOR NONMINIMUM-PHASE NONLINEAR PROCESSES

An adaptive neural-network predictive control strategy for a class of nonlinear processes, which exhibit input multiplicities and change in the sign of steady-state gains, is presented. According to the graphic-based determination associated with prescribed input/output patterns, the feed-forward neural network (FNN) is attributed to reconstruct dynamic and steady-state characteristics of minimum-phase modes with specified operating ranges. The flexible predictive control strategy using on-line neuro-based adaptation is developed for enhancing the predictive capability of neural network. Finally, the proposed FNN-based implementation is illustrated on simulations of both isothermal and adiabatic CSTR systems.     

网络化动态矩阵控制及在倒立摆控制中的应用

针对不确定有界长时延网络控制系统,研究动态矩阵控制(DMC)算法及其稳定性问题。首先基于多输入多输出状态空间模型,推导针对长时延网络化控制系统的DMC算法;然后,利用Lyapunov稳定性理论和线性矩阵不等式方法,给出闭环控制系统渐近稳定的充分条件;最后,通过对倒立摆的实时控制验证笔者算法的有效性。     

Machine learning-based distributed model predictive control of nonlinear processes

This work explores the design of distributed model predictive control (DMPC) systems for nonlinear processes using machine learning models to predict nonlinear dynamic behavior. Specifically, sequential and iterative DMPC systems are designed and analyzed with respect to closed-loop stability and performance properties. Extensive open-loop data within a desired operating region are used to develop long short-term memory (LSTM) recurrent neural network models with a sufficiently small modeling error from the actual nonlinear process model. Subsequently, these LSTM models are utilized in Lyapunov-based DMPC to achieve efficient real-time computation time while ensuring closed-loop state boundedness and convergence to the origin. Using a nonlinear chemical process network example, the simulation results demonstrate the improved computational efficiency when the process is operated under sequential and iterative DMPCs while the closed-loop performance is very close to the one of a centralized MPC system.     

Operable adaptive sparse identification of systems: Application to chemical processes

Over the past few decades, several data-driven methods have been developed for identifying a model that accurately describes the process dynamics. Lately, sparse identification of nonlinear dynamics (SINDy) has delivered promising results for various nonlinear processes. However, at any instance of plant-model mismatch or process upset, retraining the model using SINDy is computationally expensive and cannot guarantee to catch up with rapidly changing dynamics. Hence, we propose operable adaptive sparse identification of systems (OASIS) framework that extends the capabilities of SINDy for accurate, automatic, and adaptive approximation of process models. First, we use SINDy to obtain multiple models from historical data for varying input settings. Next, using these models and their training data, we build a deep neural network that is incorporated in a model predictive control framework for closed-loop operation. We demonstrate the OASIS methodology on the identification and control of a continuous stirred tank reactor.     

Machine learning-based model predictive control of hybrid dynamical systems

This article presents a machine learning-based model predictive control (MPC) scheme for stabilization of hybrid dynamical systems, for which the evolution of states exhibits both continuous and discrete dynamics described by differential and difference equations, respectively. We first present the development of two recurrent neural networks (RNNs) for approximating continuous- and discrete-time dynamics of hybrid dynamical systems, respectively, and then construct a unified hybrid RNN by integrating the two RNN models to capture both continuous and discrete dynamics. The hybrid RNN is used as the prediction model in Lyapunov-based MPC (RNN-LMPC), under which closed-loop stability of hybrid dynamical systems is established. Finally, two case studies including a bouncing ball example and a chemical process are utilized to illustrate the open- and closed-loop performance of the proposed RNN-LMPC scheme.     

High-order iterative learning model predictive control for batch chemical processes

In order to address two-dimensional (2D) control issue for a class of batch chemical processes, we propose a novel high-order iterative learning model predictive control (HILMPC) method in this paper. A set of local state-space models are first constructed to represent the batch chemical processes by adopting the just-in-time learning (JITL) technique. Meanwhile, a pre-clustered strategy is used to lessen the computational burden of the modelling process and improve the modelling efficiency. Then, a two-stage 2D controller is designed to achieve integrated control by combining high-order iterative learning control (HILC) on the batch domain with model predictive control (MPC) on the time domain. The resulting HILMPC controller can not only guarantee the convergence of the system on the batch domain, but also guarantee the closed-loop stability of the system on the time domain. The convergence of the HILMPC method is ensured by rigorous analysis. Two examples are presented in the end to demonstrate that the developed method provides better control performance than its previous counterpart.     

Differential recurrent neural network based predictive control

In this paper an efficient algorithm to train general differential recurrent neural network (DRNN) is developed. The trained network can be directly used in the nonlinear model predictive control (NMPC) context. The neural network is represented in a general nonlinear state-space form and used to predict the future dynamic behavior of the nonlinear process in real time. In the new training algorithms, the ODEs of the model and the dynamic sensitivity are solved simultaneously using Taylor series expansion and automatic differentiation (AD) techniques. The same approach is also used to solve the online optimization problem in the predictive controller. The efficiency and effectiveness of the DRNN training algorithm and the NMPC approach are demonstrated through a two-CSTR case study. A good model fitting for the nonlinear plant at different sampling rates is obtained using the new method. A comparison with other approaches shows that the new algorithm can considerably reduce network training time and improve solution accuracy. The DRNN based NMPC approach results in good control performance under different operating conditions.     

基于复合神经网络的离散非线性系统建模与控制

An adaptive inverse controller for nonliear discrete-time system is proposed in this paper. A compound neural network is constructed to identify the nonlinear system, which includes a linear part to approximate the nonlinear system and a recurrent neural network to minimize the difference between the linear model and the real nonlinear system. Because the current control input is not included in the input vector of recurrent neural network (RNN), the inverse control law can be calculated directly. This scheme can be used in real-time nonlinear single-input single-output (SISO) and multi-input multi-output (MIMO) system control with less computation work. Simulation studies have shown that this scheme is simple and affects good control accuracy and robustness.     

Modeling and predictive control of nonlinear processes using transfer learning method

This work develops a transfer learning (TL) framework for modeling and predictive control of nonlinear systems using recurrent neural networks (RNNs) with the knowledge obtained in modeling one process transferred to another. Specifically, transfer learning uses a pretrained model developed based on a source domain as the starting point, and adapts the model to a target process with similar configurations. The generalization error for TL-based RNN (TL-RNN) is first derived to demonstrate the generalization capability on the target process. The theoretical error bound that depends on model capacity and the discrepancy between source and target domains is then utilized to guide the development of pretrained models for improved model transferability. Subsequently, the TL-RNN model is utilized as the prediction model in model predictive controller (MPC) for the target process. Finally, the simulation study of chemical reactors via Aspen Plus Dynamics is used to demonstrate the benefits of transfer learning.     

NEURAL NETWORK-BASED PREDICTIVE CONTROL FOR MULTIVARIABLE PROCESSES

In this paper, the systematic derivations of setting up a nonlinear model predictive control based on the neural network are presented. This extends our previous work (Chen, 1998) into a multivariable system to explore the characteristics of the design. There are two stages for the development of nonlinear neural network predictive control: a neural network model and a control design. In the neural network model design, a parallel multiple-input, single-output neural network autoregressive with a model of exogenous inputs (NNARX) is proposed for multistep ahead predictions. In control design, the controller with extended control horizon is developed. The Levenberg-Marquardt algorithm is applied to training the NNARX model. Also, the sequential quadratic programming is used to search for the optimal manipulated inputs. The gradient of the objective function and constraints that require computation of Jacobian matrices are completely derived for optimization calculation. To demonstrate the control ability of MIMO cases, the proposed method is applied through two nonlinear simulation problems.     

Neural network-based predictive control for multivariable processes

In this paper, the systematic derivations of setting up a nonlinear model predictive control based on the neural network are presented. This extends our previous work (Chen, 1998) into a multivariable system to explore the characteristics of the design. There are two stages for the development of nonlinear neural network predictive control: a neural network model and a control design. In the neural network model design, a parallel multiple-input, single-output neural network autoregressive with a model of exogenous inputs (NNARX) is proposed for multistep ahead predictions. In control design, the controller with extended control horizon is developed. The Levenberg-Marquardt algorithm is applied to training the NNARX model. Also, the sequential quadratic programming is used to search for the optimal manipulated inputs. The gradient of the objective function and constraints that require computation of Jacobian matrices are completely derived for optimization calculation. To demonstrate the control ability of MIMO cases, the proposed method is applied through two nonlinear simulation problems.     

基于神经网络和多模型的非线性自适应PID控制及应用

针对一类未知的单输入单输出离散非线性系统,提出了基于神经网络和多模型的非线性自适应PID控制方法。该方法由线性自适应PID控制器、神经网络非线性自适应PID控制器以及切换机构组成。采用线性自适应PID控制器可保证闭环系统所有信号有界;采用神经网络非线性自适应PID控制器可改善系统性能;通过引入合理的切换机制,能够在保证闭环系统稳定的同时,提高系统性能。理论分析表明,该方法能够保证闭环系统所有信号有界,如果适当地选择神经网络的结构和参数,系统的跟踪误差将收敛于任意给定的紧集。将所提出的方法应用于连续搅拌反应釜,仿真结果验证了所提出方法的有效性。由于该方法基于增量式数字PID控制器,在工业过程中有着广阔的应用前景。     

The design of experiments,training and implementation of nonlinear controllers based on neural networks

In the area of nonlinear predictive control, several control schemes using artificial neural networks have been proposed. In this work, the issues relating to the information contents of the data used to train the neural network components of these nonlinear predictive control schemes are considered. This raises questions about the design of experiments. A class of feedback-feedforward nonlinear controller based on the model predictive structure (also known as Internal Model Control, IMC, structure) is investigated. The implementation and performance of these neural network based controllers, together with comparisons to other nonlinear and linear controllers, are illustrated on two nonlinear continuous-stirred-tank-reactor simulations.     

Encrypted model predictive control design for security to cyberattacks

In recent years, cyber-security of networked control systems has become crucial, as these systems are vulnerable to targeted cyberattacks that compromise the stability, integrity, and safety of these systems. In this work, secure and private communication links are established between sensor–controller and controller–actuator elements using semi-homomorphic encryption to ensure cyber-security in model predictive control (MPC) of nonlinear systems. Specifically, Paillier cryptosystem is implemented for encryption-decryption operations in the communication links. Cryptosystems, in general, work on a subset of integers. As a direct consequence of this nature of encryption algorithms, quantization errors arise in the closed-loop MPC of nonlinear systems. Thus, the closed-loop encrypted MPC is designed with a certain degree of robustness to the quantization errors. Furthermore, the trade-off between the accuracy of the encrypted MPC and the computational cost is discussed. Finally, two chemical process examples are employed to demonstrate the implementation of the proposed encrypted MPC design.     

Predictive control of particlesize distribution of crystallization process using deep learning based image analysis

The challenges to regulate the particle-size distribution (PSD) stem from on-line measurement of the full distribution and the distributed nature of crystallization process. In this article, a novel nonlinear model predictive control method of PSD for crystallization process is proposed. Radial basis function neural network is adopted to approximate the PSD such that the population balance model with distributed nature can be transformed into the ordinary differential equation (ODE) models. Data driven nonlinear prediction model of the crystallization process is then constructed from the input and output data and further be used in the proposed nonlinear model predictive control algorithm. A deep learning based image analysis technology is developed for online measurement of the PSD. The proposed PSD control method is experimentally implemented on a jacketed batch crystallizer. The results of crystallization experiments demonstrate the effectiveness of the proposed control method.     

Data-driven prediction model of indoor air quality in an underground space

Several data-driven prediction methods based on multiple linear regression (MLR), neural network (NN), and recurrent neural network (RNN) for the indoor air quality in a subway station are developed and compared. The RNN model can predict the air pollutant concentrations at a platform of a subway station by adding the previous temporal information of the pollutants on yesterday to the model. To optimize the prediction model, the variable importance in the projection (VIP) of the partial least squares (PLS) is used to select key input variables as a preprocessing step. The prediction models are applied to a real indoor air quality dataset from telemonitoring systems data (TMS), which exhibits some nonlinear dynamic behaviors show that the selected key variables have strong influence on the prediction performances of the models. It demonstrates that the RNN model has the ability to model the nonlinear and dynamic system, and the predicted result of the RNN model gives better modeling performance and higher interpretability than other data-driven prediction models.