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.     

Neural Network Based Control of the Acrylonitrile Polymerization Process

Acrylic fiber is commercially produced by free radical polymerization, initiated by a redox system. Industrial production of polyacrylonitrile is a variant of aqueous dispersion polymerization, which takes place in a homogenous phase under isothermal conditions with perfect mixing. The fact that the kinetics are a lot more complicated than those of ordinary polymerization systems makes it difficult to control the molecular weight. On the other hand, abundant data is being gathered in industrial polymerization systems, and this information makes the neural network based controllers a good candidate for managing such a difficult control problem. Multilayer neural networks have been applied successfully in the identification and control of dynamic systems. In this work, the neural network based control of continuous acrylonitrile (ACN) polymerization is studied, based on a previously developed new rigorous dynamic model for the polymerization of acrylonitrile. Two typical neural network controllers are investigated, i.e., model predictive control and NARMA‐L2 (Nonlinear Auto Regressive Moving Average) control. These controllers are representative of the variety of common ways in which multilayer networks are used in control systems. The results present a comparison of the two common neural network controllers, and indicate that the model predictive controller requires a larger computational time.     

基于控制性能比较的非线性不对称系统预测控制

生产过程某些非线性系统常常表现出不对称动态特性,相对于其在工业工程中经常出现的理论研究特别是控制方法研究则十分有限。本文针对基于正反方向上的两个线性模型分别设计PID控制器的缺陷,提出根据正反方向上的线性模型分别设计相应的状态反馈预测控制器。在每一步的控制率计算中,正反方向的控制器分别计算控制作用,并通过比较正反控制器的控制性能指标来确定最终采用的控制作用。通过pH值控制的仿真实验证明其对非线性不对称系统的控制效果明显优于传统的在正反方向分别采用PID控制的控制效果。     

Distributed model predictive control of switched nonlinear systems with scheduled mode transitions

A method for the design of distributed model predictive control (DMPC) systems for a class of switched nonlinear systems for which the mode transitions take place according to a prescribed switching schedule is presented. Under appropriate stabilizability assumptions on the existence of a set of feedback controllers that can stabilize the closed‐loop switched, nonlinear system, a cooperative DMPC architecture using Lyapunov‐based model predictive control (MPC) in which the distributed controllers carry out their calculations in parallel and communicate in an iterative fashion to compute their control actions is designed. The proposed DMPC design is applied to a nonlinear chemical process network with scheduled mode transitions and its performance and computational efficiency properties in comparison to a centralized MPC architecture are evaluated through simulations. © 2013 American Institute of Chemical Engineers AIChE J, 59:860‐871, 2013     

The control of MSF desalination plants based on inverse model control by neural network

In this paper, a nonlinear inverse model control strategy based on neural network is proposed for MSF desalination plant. Artificial neural networks (ANNs) can handle complex and nonlinear process relationships, and are robust to noisy data. The designed neural networks consist of three layers identified from input–output data and trained with a descent gradient algorithm. The set point tracking performance of the proposed method was studied when the disturbance is present in the MSF system. Three controllers are designed for controlling the top brine temperature, the level of last stage and salinity. These results show that a neural network inverse model control strategy (NNINVMC) is robust and highly promising to be implemented in such nonlinear systems. Also the comparison between the top brine temperature of the proposed model and NN predicted data from the literature supports the accuracy of the model.     

Sequential and iterative architectures for distributed model predictive control of nonlinear process systems

In this work, we focus on distributed model predictive control of large scale nonlinear process systems in which several distinct sets of manipulated inputs are used to regulate the process. For each set of manipulated inputs, a different model predictive controller is used to compute the control actions, which is able to communicate with the rest of the controllers in making its decisions. Under the assumption that feedback of the state of the process is available to all the distributed controllers at each sampling time and a model of the plant is available, we propose two different distributed model predictive control architectures. In the first architecture, the distributed controllers use a one‐directional communication strategy, are evaluated in sequence and each controller is evaluated only once at each sampling time; in the second architecture, the distributed controllers utilize a bi‐directional communication strategy, are evaluated in parallel and iterate to improve closed‐loop performance. In the design of the distributed model predictive controllers, Lyapunov‐based model predictive control techniques are used. To ensure the stability of the closed‐loop system, each model predictive controller in both architectures incorporates a stability constraint which is based on a suitable Lyapunov‐based controller. We prove that the proposed distributed model predictive control architectures enforce practical stability in the closed‐loop system and optimal performance. The theoretical results are illustrated through a catalytic alkylation of benzene process example. © 2010 American Institute of Chemical Engineers AIChE J, 2010     

Machine-learning-based construction of barrier functions and models for safe model predictive control

In this paper, we propose a control Lyapunov-barrier function-based model predictive control method utilizing a feed-forward neural network specified control barrier function (CBF) and a recurrent neural network (RNN) predictive model to stabilize nonlinear processes with input constraints, and to guarantee that safety requirements are met for all times. The nonlinear system is first modeled using RNN techniques, and a CBF is characterized by constructing a feed-forward neural network (FNN) model with unique structures and properties. The FNN model for the CBF is trained based on data samples collected from safe and unsafe operating regions, and the resulting FNN model is verified to demonstrate that the safety properties of the CBF are satisfied. Given sufficiently small bounded modeling errors for both the FNN and the RNN models, the proposed control system is able to guarantee closed-loop stability while preventing the closed-loop states from entering unsafe regions in state-space under sample-and-hold control action implementation. We provide the theoretical analysis for bounded unsafe sets in state-space, and demonstrate the effectiveness of the proposed control strategy using a nonlinear chemical process example with a bounded unsafe region.     

基于神经网络的pH中和过程非线性预测控制

针对pH中和过程这一化工过程系统中的典型非线性对象特点，应用神经网络建模思想和模型预测控制方法，并结合Hammerstein模型特点，研究pH中和过程非线性系统的两种新型模型预测控制手段，分别建立基于神经网络的非线性预测控制系统整体求解策略和基于Hammerstein模型的两步法预测控制策略，并用MATLAB对其进行仿真。控制仿真结果表明，建立的神经网络预测控制策略和非线性Hammerstein模型预测控制均优于传统PID控制方法，具有良好的设定值跟踪效果和抗干扰控制响应，说明这两种控制策略是非线性过程的有效控制方法。     

Neural‐Networks‐Based Feedback Linearization versus Model Predictive Control of Continuous Alcoholic Fermentation Process

In this work advanced nonlinear neural networks based control system design algorithms are adopted to control a mechanistic model for an ethanol fermentation process. The process model equations for such systems are highly nonlinear. A neural network strategy has been implemented in this work for capturing the dynamics of the mechanistic model for the fermentation process. The neural network achieved has been validated against the mechanistic model. Two neural network based nonlinear control strategies have also been adopted using the model identified. The performance of the feedback linearization technique was compared to neural network model predictive control in terms of stability and set point tracking capabilities. Under servo conditions, the feedback linearization algorithm gave comparable tracking and stability. The feedback linearization controller achieved the control target faster than the model predictive one but with vigorous and sudden controller moves.     

Multivariable Nonlinear Proportional-Integral-Derivative Decoupling Control Based on Recurrent Neural Networks

A nonlinear proportional-integral-derivative (PID) controller is constructed based on recurrent neural networks. In the control process of nonlinear multivariable systems, several nonlinear PID controllers have been adopted in parallel. Under the decoupling cost function, a decoupling control strategy is proposed. Then the stability condition of the controller is presented based on the Lyapunov theory. Simulation examples are given to show effectiveness of the proposed decoupling control.     

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.     

基于递归神经网络的多变量非线性PID解耦控制

A nonlinear proportional-integral-derivative (PID) controller is constructed based on recurrent neural networks. In the control process of nonlinear multivariable systems, several nonlinear PID controllers have been adopted in parallel. Under the decoupling cost function, a decoupling control strategy is proposed. Then the stability condition of the controller is presented based on the Lyapunov theory. Simulation examples are given to show effectiveness of the proposed decoupling control.     

基于Tent混沌优化的神经网络预测控制

With the unique ergodicity, irregularity, and special ability to avoid being trapped in local optima, chaos optimization has been a novel global optimization technique and has attracted considerable attention for application in various fields, such as nonlinear programming problems. In this article, a novel neural network nonlinear predictive control (NNPC) strategy based on the new Tent-map chaos optimization algorithm (TCOA) is presented. The feedforward neural network is used as the multi-step predictive model. In addition, the TCOA is applied to perform the nonlinear rolling optimization to enhance the convergence and accuracy in the NNPC. Simulation on a laboratory-scale liquid-level system is given to illustrate the effectiveness of the proposed method.     

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.     

SYSTEMATIC DERIVATIONS OF MODEL PREDICTIVE CONTROL BASED ON ARTIFICIAL NEURAL NETWORK

This article presents systematic derivations of setting up a nonlinear model predictive control based on the artifical neural network. Unlike most research in the past, the control law is mathematically developed in detail so that the performance of the ANN-based controller can be improved. In this paper, a three-layer feedforward neural network with hyperbolic tangent functions in the hidden layer and with a linear function in the output layer is used. The two-stage scheme including pseudo Gauss-Newton and least squares is proposed for training ANN. This training method is better than the traditional algorithm in terms of training speed. The Levenberg-Marquardt approximation is also utilized for the minimum of the predictive control criterion. Two typical chemical processes are simulated and the ANN model predictive control applications can reach fairly good results.     

基于Hammerstein-Wiener模型的连续搅拌反应釜神经网络预测控制

针对化工过程中广泛使用的连续搅拌反应釜(CSTR),提出一种基于神经网络的模型预测控制策略,采用分段最小二乘支持向量机辨识Hammerstein-Wiener模型系数的方法,在此基础上建立线性自回归模式〖DK〗(ARX)结构和高斯径向基神经网络串联的非线性预测控制器。利用BP神经网络训练预测控制输入序列和拟牛顿算法求解非线性预测控制律,从而实现一种基于支持向量机Hammerstein-Wiener辨识模型的非线性神经网络预测控制算法。对CSTR的仿真结果表明,该方法能够更有效地跟踪控制反应物浓度。     

不对称系统输入反馈预测控制及可控性分析

研究了生产过程中一类特殊的非线性系统,不对称系统的预测控制方法。在正反方向的控制作用下,这类系统表现出不对称动态特性。此类系统的理论研究特别是控制方法研究十分有限。针对基于正反方向上的线性模型设计的正反模型预测控制方法与传统预测控制方法在结构上的差异进行了分析,说明了由于这种结构上的差异可能导致的模型失配及控制效果不佳,然后采用输入反馈方法对不对称系统正反模型预测控制方法进行了修正,将实际施加给对象的控制作用通过反馈形式纳入到下一步正反方向控制律的求解中。并且在无约束的条件下分析了正反模型预测控制方法的可控性。最后通过pH值控制的仿真实验验证了此两种不对称系统正反模型预测控制方法的控制效果。     

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.     

Dynamics And Assessment of Some Control Strategies of a Simulated Industrial Rotary Dryer

Rotary dryers are widely used for the continuous drying of minerals and chemicals on a large scale. Hot gases are passed parallel to the flowing solid to achieve the desired product moisture content. Because these dryers are energy intensive, it is mandatory to operate them as efficiently as possible to respond to economic pressures. Using a dynamic rotary dryer simulator for mineral concentrate, five control strategies are evaluated and compared. Two control strategies are based on PI controllers and the others use neural network models. Results clearly show that a feedforward action, in conjunction with a PI controller or incorporated within the structure of a neural network model, led to the best performances provided an accurate measurement of the feed moisture content is available.     

基于改进回声状态网络的游离氧化钙预测控制

在非线性时延水泥烧成系统中,针对传统预测控制方法调节时间长、控制精度不高的问题,提出一种改进的在线型回声状态网络预测控制模型。首先将带有L1范数约束项的递归最小二乘法与回声状态网络相结合构建在线型预测模型,解决传统预测控制模型辨识精度较低、无法进行实时预测的问题;然后基于改进的回声状态网络预测模型,构建预测控制模型结构,并采用具有全局优化能力的粒子群算法进行滚动优化,保证实际输出量快速、准确、平稳地跟随被控量的设定值;最后利用改进的预测控制模型对水泥烧成系统中的游离氧化钙含量进行预测控制仿真实验,结果表明改进的预测控制模型具有良好的性能和应用前景。