Neural‐network‐based predictive controller design: An application to temperature control of a plastic injection molding process

This paper presents a neural‐network‐based predictive control (NPC) method for a class of discrete‐time multi‐input multi‐output (MIMO) systems. A discrete‐time mathematical model using a recurrent neural network (RNN) is constructed and a learning algorithm adopting an adaptive learning rate (ALR) approach is employed to identify the unknown parameters in the recurrent neural network model (RNNM). The NPC controller is derived based on a modified predictive performance criterion, and its convergence is guaranteed by adopting an optimal algorithm with an adaptive optimal rate (AOR) approach. The stability analysis of the overall MIMO control system is well proven by the Lyapunov stability theory. A real‐time control algorithm is proposed which has been implemented using a digital signal processor, TMS320C31 from Texas Instruments. Two examples, including the control of a MIMO nonlinear system and the control of a plastic injection molding process, are used to demonstrate the effectiveness of the proposed strategy. Results from both numerical simulations and experiments show that the proposed method is capable of controlling MIMO systems with satisfactory tracking performance under setpoint and load changes. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

RBF-ARX model-based MPC strategies with application to a water tank system

A hybrid pseudo-linear RBF-ARX model that combines Gaussian radial basis function (RBF) networks and linear ARX model structure is utilized for representing the dynamic behavior of a class of smooth nonlinear and non-stationary systems. This model is locally linear at each working point and globally nonlinear within whole working range. Based on the structural characteristics of the RBF-ARX model, three receding horizon predictive control (RBF-ARX-MPC) strategies are designed: (1) the RBF-ARX-MPC algorithm based on single-point linearization (MPC-SPL); (2) the RBF-ARX-MPC algorithm based on multi-point linearization (MPC-MPL); and (3) the RBF-ARX-MPC algorithm based on globally nonlinear optimization (MPC-GNO). In the MPC-SPL, the future multi-step-ahead predictive output of the system is obtained based on the local linearization of the RBF-ARX model at only current working-point, while in the MPC-MPL the future long-term output prediction is obtained according to the future local characteristics from previous online optimization results of the RBF-ARX model based MPC. In the MPC-GNO, the globally nonlinear characteristics of the RBF-ARX model are fully used for online getting control variables of the MPC. Real-time control experiments for the three type MPCs are carried out on a water tank system, which are also compared with a classical PID control and a traditional linear ARX model-based MPC. The results verify that the modeling method and the model-based predictive control strategies are realizable and effective for the nonlinear and unstable system. Moreover, it is also shown that the MPC-GNO can obtain better control performance but need more computation time compared to the other MPCs, which makes it possible to be applied into some slowly varying processes.     

Robust event‐triggered model predictive control for cyber‐physical systems under denial‐of‐service attacks

This paper investigates the resilient control problem for constrained continuous‐time cyber‐physical systems subject to bounded disturbances and denial‐of‐service (DoS) attacks. A sampled‐data robust model predictive control law with a packet‐based transmission scheduling is taken advantage to compensate for the loss of the control data during the intermittent DoS intervals, and an event‐triggered control strategy is designed to save communication and computation resources. The robust constraint satisfaction and the stability of the closed‐loop system under DoS attacks are proved. In contrast to the existing studies that guarantee the system under DoS attacks is input‐to‐state stable, the predicted input error caused by the system constraints can be dealt with by the input‐to‐state practical stability framework. Finally, a simulation example is performed to verify the feasibility and efficiency of the proposed strategy.     

Nonlinear system modeling and predictive control using the RBF nets-based quasi-linear ARX model

On the basis of the single-input single-output (SISO) RBF-ARX model proposed in previous works [Peng, H., et al. (2003b). Stability analysis of the RBF-ARX model based nonlinear predictive control. In Proceedings of the ECC2003; Peng, H., et al. (2003c). Modeling and control of nonlinear nitrogen oxide decomposition process. In Proceedings of the CDC’03; Peng, H., et al. (2004). RBF-ARX model based nonlinear system modeling and predictive control with application to a NO_x decomposition process. Control Engineering Practice, 12, 191–203; Peng, H., et al. (2007). Nonlinear predictive control using neural nets-based local linearization ARX model—Stability and industrial application. IEEE Transactions on Control Systems Technology, 15, 130–143] the multi-input multi-output (MIMO) RBF-ARX model and its state-space representation are derived to describe the dynamics of a class of multivariable nonlinear systems whose working-point varies with time and which may be linearized around the working-point. The proposed MIMO RBF-ARX model has a basic regression-model structure that is analogous to the linear ARX model structure, and the elements of its regression matrices are composed of Gaussian radial basis function (RBF) neural networks that are dependent on the working-point state of the current system. An off-line estimation approach to parameters and orders of the MIMO RBF-ARX model is presented, and, on the basis of the estimated MIMO RBF-ARX model, a predictive control strategy is designed to control the underlying nonlinear system. A case study on a simulator of a thermal power plant is also given to illustrate the effectiveness of the nonlinear modeling and control method proposed in this paper.     

Compensation‐based data‐driven ILC with input and output package dropouts

This paper explores the problem of random data loss at both input and output sides and proposes a compensation‐based data‐driven iterative learning control (cDDILC) to refrain from deteriorating of the control performance due to the data loss. A linear data model is first established to describe the input‐output dynamics of a repetitive control system in the iteration domain. The linear data model, which only virtually exists in the computer without any physical backgrounds, is employed as a predictive model to estimate and compensate the lost output data. Meanwhile, the lost input data is replaced by the corresponding input of the same time instant in the latest previous iterations. Then, a cDDILC is proposed by introducing two Bernoulli random variables to describe the stochastic data loss at both input and output sides. The proposed cDDILC method is data driven and independent of a precise plant model. Although the design and analysis of the cDDILC start from a MIMO linear repetitive system, one can easily extend the results to a MIMO nonlinear nonaffine one. Theoretical analysis and simulations confirm the efficiency of the proposed cDDILC method.     

Distributed MPC for Tracking and Formation of Homogeneous Multi‐agent System with Time‐Varying Communication Topology

The distributed model predictive control (MPC) is studied for the tracking and formation problem of multi‐agent system with time‐varying communication topology. At each sampling instant, each agent solves an optimization problem respecting input and state constraints, to obtain its optimal control input. In the cost function for the optimization problem of each agent, the formation weighting coefficient is properly updated so that the adverse effect of the time‐varying communication topology on the closed‐loop stability can be counteracted. It is shown that the overall multi‐agent system can achieve the desired tracking and formation objectives. The effectiveness of the results is demonstrated through two examples.     

A Nonsmooth Nonlinear Programming Based Predictive Control for Mechanical Servo Systems with Backlash‐like Hysteresis

In this paper, a multi‐step‐ahead predictive control approach for dynamic systems with preceded backlash‐like hysteresis based on nonsmooth nonlinear programming is proposed. In this approach, a nonsmooth multi‐step‐ahead predictive model is developed for long‐range prediction of the controlled dynamic systems with preceded backlash‐like hysteresis. Then, the predictive control strategy is treated as a problem of on‐line nonsmooth nonlinear programming. Subsequently, the stability of the nonsmooth predictive control system is analyzed and the corresponding stability condition is derived. Afterward, a numerical example and a simulation based on a mechanical servo system are presented, respectively.     

Quad‐Rotor Modeling and Attitude Control Using State‐Dependent ARX Type Model

A state‐dependent autoregressive with exogenous variables (SD‐ARX) model whose functional coefficients are approximated by sets of radial basis function (RBF) networks is proposed to describe the dynamic behavior of a quad‐rotor in this paper. This model is identified offline and used as an internal predictor of a receding horizon predictive controller to address the quad‐rotor's attitude control issue. In addition, the physical constraints of the system have been also taken into account during the controller design process. The results of real‐time control on a quad‐rotor aircraft illustrate satisfactory modeling accuracy in a large operating range and good performance of control approach proposed in this paper.     

A compact multi‐band multi‐input multi‐output antenna for 4G/5G and IoT devices using theory of characteristic modes

A compact four element multi‐band multi‐input multi‐output (MIMO) antenna system for 4G/5G and IoT applications is presented in this paper. The proposed antenna is developed using the theory of characteristic modes helping in systematic design of MIMO antenna system. It consists of four L‐shaped planar inverted‐F antenna (PIFA) elements each operating at 3.5, 12.5, and 17 GHz bands with the bandwidth of 359 MHz, 1 GHz, and more than 3.7 GHz, respectively. The proposed antenna system is suitable for both 4G/5G and internet of things devices as it shows the satisfactory MIMO system performance. Good isolation characteristics are observed by implementing complimentary Metamaterial structure on the ground plane resulting in isolation level lower than ?21 dB between the antenna elements. The proposed antenna is fabricated and experimental results are also presented and discussed.     

An E‐HOIM Based Data‐Driven Adaptive TILC of Nonlinear Discrete‐Time Systems for Non‐Repetitive Terminal Point Tracking

This work proposes a new adaptive terminal iterative learning control approach based on the extended concept of high‐order internal model, or E‐HOIM‐ATILC, for a nonlinear non‐affine discrete‐time system. The objective is to make the system state or output at the endpoint of each operation track a desired target value. The target value varies from one iteration to another. Before proceeding to the data‐driven design of the proposed approach, an iterative dynamical linearization is performed for the unknown nonlinear systems by using the gradient of the nonlinear system with regard to the control input as the iteration‐and‐time‐varying parameter vector of the equivalent linear I/O data model. By virtue of the basic idea of the internal model, the inverse of the parameter vector is approximated by a high‐order internal model. The proposed E‐HOIM‐ATILC does not use measurements of any intermediate points except for the control input and terminal output at the endpoint. Moreover, it is data‐driven and needs merely the terminal I/O measurements. By incorporating additional control knowledge from the known portion of the high order internal model into the learning control law, the control performance of the proposed E‐HOIM‐ATILC is improved. The convergence is shown by rigorous mathematical proof. Simulations through both a batch reactor and a coupled tank system demonstrate the effectiveness of the proposed method.     

Adaptive Fault‐Tolerant Control of Uncertain MIMO Systems with Reduced Requirement on Desired Trajectory Under Unknown Control Direction

This paper aims at investigating the tracking control problem for a class of multi‐input multi‐output (MIMO) nonlinear systems with non‐square control gain matrix subject to unknown control direction and uncertain desired trajectory. By using the artificial neural network (NN) reconstructs the target trajectory with actual disguised trajectory, we are able to design a practical and stable tracking control scheme without the need for the unavailable desired trajectory. Nussbaum‐type function is incorporated in the control law to handle the unknown control direction. The remarkable feature of the proposed scheme is that it is robust against modeling uncertainties and tolerant to actuation faults, yet guarantees that the closed‐loop system is stable in the sense of ultimately uniformly bounded (UUB). The effectiveness of the proposed control schemes are illustrated through simulation results.     

Disturbance observer–based adaptive boundary layer sliding mode controller for a type of nonlinear multiple‐input multiple‐output system

In this paper, a disturbance observer–based adaptive boundary layer sliding mode controller (ABLSMC) is proposed to compensate external disturbance and system uncertainty for a class of output coupled multiple‐input multiple‐output (MIMO) nonlinear systems. To show the effectiveness of the proposed ABLMSC, a traditional adaptive sliding mode controller (ASMC) is also designed. The stability of the closed‐loop system is examined by using the Lyapunov stability approach. The proposed control approach is implemented for a class of nonlinear output coupled MIMO systems. For real‐time validation, a coupled tank system is considered for study. Finally, simulation and real‐time results show that the proposed ABLMSC gives better performance such as reduced chattering and energy efficiency than that of the ASMC and some reported works in the literature.     

High‐order sliding‐mode observer–based input‐output linearization

The problem of output control in multiple‐input–multiple‐output nonlinear systems is addressed. A high‐order sliding‐mode observer is used to estimate the states of the system and identify the discrepancy between the nominal model and the real plant. The exact and finite‐time estimation may be tackled as long as the system presents the algebraic strong observability property. Thus, a continuous robust input‐output linearization strategy can be obtained with respect to a prescribed output. As a consequence, the closed‐loop dynamics performs robustly to uncertainties/perturbations. To illustrate the advantages of the proposed method, we introduce a study case that demands a robust linear system behavior: the self‐oscillations induced in an underactuated mechanical system through a two‐relay controller. Experiments with an inertial wheel pendulum illustrate the feasibility of the proposed approach.     

基于精确线性化的MIMO双线性系统预测函数控制

针对典型多输入多输出双线性系统, 提出了基于非线性过程精确反馈解耦线性化的预测函数控制方法这是一种分层的控制策略, 首先设计一个静态的非线性状态反馈, 使得闭环系统是输入输出解耦和线性的;然后设计一组单输入单输出预测函数控制器, 下层为上层预测函数控制提供一组单输入单输出模型, 而上层预测函数控制以其固有的鲁棒性来补偿参数变化和解耦线性化的近似性, 并以纸机加压网前箱为例进行了仿真实验, 结果是令人满意的.     

多变量动态矩阵控制系统的闭环稳定性

定量分析了无约束多输入多输出（MIMO）动态矩阵控制系统的闭环稳定条件,首先基于脉冲响应模型重新描述了动态矩阵控制（DMC）算法;在此基础上,推导得到了MIMODMC系统的闭环稳定条件,以便于预测控制系统的分析与设计。     

Robust‐decentralized tracking control for a class of uncertain MIMO nonlinear systems with time‐varying delays

A new control design method based on signal compensation is proposed for a class of uncertain multi‐input multi‐output (MIMO) nonlinear systems in block‐triangular form with nonlinear uncertainties, unknown virtual control coefficients, strongly coupled interconnections, time‐varying delays, and external disturbances. By this method, the controller design is performed in a backstepping manner. At each step of backstepping procedure, a nominal virtual controller is first designed to get desired output tracking for the nominal disturbance‐free subsystem, and then a robust virtual compensator is designed to restrain the effect of the uncertainties, delays involved in the subsystem, and the couplings among the subsystems. The designed controller is linear and time‐invariant, so the explosion of complexity in the control law is avoid. It is proved that robust stability and robust practical tracking property of the closed‐loop system can be ensured, and the tracking errors can be made as small as desired. Copyright © 2013 John Wiley & Sons, Ltd.     

A predictive controller based on dynamic matrix control for a non-minimum phase robot manipulator

In this paper a hybrid control strategy is presented based on Dynamic Matrix Control (DMC) and feedback linearization methods for designing a predictive controller of five bar linkage manipulator as a MIMO system (two inputs and two outputs). Analyzing the internal dynamic of robot shows the open loop system is unstable and non-minimum phase, so in order to apply the predictive controller, special modifications are needed. These modifications on non-minimum phase behavior are performed using feedback linearization procedure based on state space realization. The design objective is to track a desirable set point as well as time varying trajectories as a command references with globally asymptotical stabilization. The proposed controller is applied to nonlinear fully coupled model of the typical five bar linkage manipulator with non-minimum phase behavior. Simulation results show that the proposed controller has good efficiency. The step responses of system with and without feedback linearization process illustrated that the mentioned modification for stabilizing is performed properly. After applying the proposed predictive controller, the joint angle of robot tracks the reference input while another input acts as the disturbance and vice versa.     

Nonlinear system modeling and robust predictive control based on RBF-ARX model

An integrated modeling and robust model predictive control (MPC) approach is proposed for a class of nonlinear systems with unknown steady state. First, the nonlinear system is identified off-line by RBF-ARX model possessing linear ARX model structure and state-dependent Gaussian RBF neural network type coefficients. On the basis of the RBF-ARX model, a combination of a local linearization model and a polytopic uncertain linear parameter-varying (LPV) model are built to approximate the present and the future system's nonlinear behavior, respectively. Subsequently, based on the approximate models, a min–max robust MPC algorithm with input constraint is designed for the output-tracking control of the nonlinear system with unknown steady state. The closed-loop stability of the MPC strategy is guaranteed by the use of parameter-dependent Lyapunov function and the feasibility of the linear matrix inequalities (LMIs). Simulation study to a NO_x decomposition process illustrates the effectiveness of the modeling and robust MPC approaches proposed in this paper.     

Linearized min‐max robust model predictive control: Application to the control of a bioprocess

This work deals with the problem of trajectory tracking for a nonlinear system with unknown but bounded model parameter uncertainties. First, this work focuses on the design of a robust nonlinear model predictive control (RNMPC) law subject to model parameter uncertainties implying solving a min‐max optimization problem. Secondly, a new approach is proposed, consisting in relating the min‐max problem to a more tractable optimization problem based on the use of linearization techniques to ensure a good trade‐off between tracking accuracy and computation time. The developed strategy is applied in simulation to a simplified macroscopic continuous photobioreactor model and is compared to the RNMPC and nonlinear model predictive controllers. Its efficiency and its robustness against parameter uncertainties and/or perturbations are illustrated through numerical results.