Nonlinear Model Predictive Control Based on a Self-Organizing Recurrent Neural Network

Error-Triggered Adaptive Sparse Identification for Predictive Control and Its Application to Multiple Operating Conditions Processes

With the digital transformation of process manufacturing, identifying the system model from process data and then applying to predictive control has become the most dominant approach in process control. However, the controlled plant often operates under changing operating conditions. What is more, there are often unknown operating conditions such as first appearance operating conditions, which make traditional predictive control methods based on identified model difficult to adapt to changing operating conditions. Moreover, the control accuracy is low during operating condition switching. To solve these problems, this article proposes an error-triggered adaptive sparse identification for predictive control (ETASI4PC) method. Specifically, an initial model is established based on sparse identification. Then, a prediction error-triggered mechanism is proposed to monitor operating condition changes in real time. Next, the previously identified model is updated with the fewest modifications by identifying parameter change, structural change, and combination of changes in the dynamical equations, thus achieving precise control to multiple operating conditions. Considering the problem of low control accuracy during the operating condition switching, a novel elastic feedback correction strategy is proposed to significantly improve the control accuracy in the transition period and ensure accurate control under full operating conditions. To verify the superiority of the proposed method, a numerical simulation case and a continuous stirred tank reactor (CSTR) case are designed. Compared with some state-of-the-art methods, the proposed method can rapidly adapt to frequent changes in operating conditions, and it can achieve real-time control effects even for unknown operating conditions such as first appearance operating conditions.

Transfer Learning Algorithm With Knowledge Division Level

One of the major challenges of transfer learning algorithms is the domain drifting problem where the knowledge of source scene is inappropriate for the task of target scene. To solve this problem, a transfer learning algorithm with knowledge division level (KDTL) is proposed to subdivide knowledge of source scene and leverage them with different drifting degrees. The main properties of KDTL are three folds. First, a comparative evaluation mechanism is developed to detect and subdivide the knowledge into three kinds-the ineffective knowledge, the usable knowledge, and the efficient knowledge. Then, the ineffective and usable knowledge can be found to avoid the negative transfer problem. Second, an integrated framework is designed to prune the ineffective knowledge in the elastic layer, reconstruct the usable knowledge in the refined layer, and learn the efficient knowledge in the leveraged layer. Then, the efficient knowledge can be acquired to improve the learning performance. Third, the theoretical analysis of the proposed KDTL is analyzed in different phases. Then, the convergence property, error bound, and computational complexity of KDTL are provided for the successful applications. Finally, the proposed KDTL is tested by several benchmark problems and some real problems. The experimental results demonstrate that this proposed KDTL can achieve significant improvement over some state-of-the-art algorithms.

Global Predefined-Time Adaptive Neural Network Control for Disturbed Pure-Feedback Nonlinear Systems With Zero Tracking Error

This article presents a global adaptive neural-network-based control algorithm for disturbed pure-feedback nonlinear systems to achieve zero tracking error in a predefined time. Different from the traditional works that only solve the semiglobal bounded tracking problem for pure-feedback systems, this work not only achieves that the tracking error globally converges to zero but also guarantees that the convergence time can be predefined according to the user specification. In order to get the desired predefined-time controller, first, a mild semibound assumption for nonaffine functions is skillfully proposed so that the design difficulty caused by the structure of pure feedback can be easily solved. Then, we apply the property of radial basis function (RBF) neural networks (NNs) and Young's inequality to derive the upper bound of the term that contains the unknown nonlinear function and external disturbances, and the designed adaptive parameters decide the derived upper and robust control gain. Finally, the predefined-time virtual control inputs are presented whose derivatives are further estimated by utilizing finite-time differentiators. It is strictly proved that the proposed novel predefined-time controller can guarantee that the tracking error globally converges to zero within predefined time and a practical example is shown to verify the effectiveness and practicability of the proposed predefined-time control method.

Adaptive Neural Backstepping Terminal Sliding Mode Control of a DC-DC Buck Converter

In this paper, an adaptive backstepping terminal sliding mode control (ABTSMC) method based on a double hidden layer recurrent neural network (DHLRNN) is proposed for a DC-DC buck converter. The DHLRNN is utilized to approximate and compensate for the system uncertainty. On the basis of backstepping control, a terminal sliding mode control (TSMC) is introduced to ensure the finite-time convergence of the tracking error. The effectiveness of the composite control method is verified on a converter prototype in different test conditions. The experimental comparison results demonstrate the proposed control method has better steady-state performance and faster transient response.

Intelligent Optimization Design of a Phononic Crystal Air-Coupled Ultrasound Transducer

To further improve the operational performance of a phononic crystal air-coupled ultrasonic transducer while reducing the number of simulations, an intelligent optimization design strategy is proposed by combining finite element simulation analysis and artificial intelligence (AI) methods. In the proposed strategy, the structural design parameters of 1-3 piezoelectric composites and acoustic impedance gradient matching layer are sampled using the optimal Latin hypercube sampling (OLHS) method. Moreover, the COMSOL software is utilized to calculate the performance parameters of the transducer. Based on the simulation data, a radial basis function neural network (RBFNN) model is trained to establish the relationship between the design parameters and the performance parameters. The accuracy of the approximation model is verified through linear regression plots and statistical methods. Finally, the NSGA-II algorithm is used to determine the design parameters of the transducer. After optimization, the band gap widths of the piezoelectric composites and acoustic impedance gradient matching layer are increased by 16 kHz and 13.5 kHz, respectively. Additionally, the -6 dB bandwidth of the transducer is expanded by 11.5%. The simulation results and experimental results are consistent with the design objectives, which confirms the effectiveness of the design strategy. This work provides a feasible strategy for the design of high-performance air-coupled ultrasonic transducers, which is of great significance for the development of non-destructive testing technology.

Event-Triggered Tracking Control for Adaptive Anti-Disturbance Problem in Systems with Multiple Constraints and Unknown Disturbances

Aimed at the objective of anti-disturbance and reducing data transmission, this article discusses a novel dynamic neural network (DNN) modeling-based anti-disturbance control for a system under the framework of an event trigger. In order to describe dynamical characteristics of irregular disturbances, exogenous DNN disturbance models with different excitation functions are firstly introduced. A novel disturbance observer-based adaptive regulation (DOBAR) method is then proposed, which can capture the dynamics of unknown disturbance. By integrating the augmented triggering condition and the convex optimization method, an effective anti-disturbance controller is then found to guarantee the system stability and the convergence of the output. Meanwhile, both the augmented state and the system output are constrained within given regions. Moreover, the Zeno phenomenon existing in event-triggered mechanisms is also successfully avoided. Simulation results for the A4D aircraft models are shown to verify the availability of the algorithm.

Dissolved oxygen control strategies for water treatment: a review

Dissolved oxygen (DO) is one of the most important water quality factors. Maintaining the DO concentration at a desired level is of great value to both wastewater treatment plants (WWTPs) and aquaculture. This review covers various DO control strategies proposed by researchers around the world in the past 20 years. The review focuses on published research related to determination and control of DO concentrations in WWTPs in order to improve control accuracy, save aeration energy, improve effluent quality, and achieve nitrogen removal. The strategies used for DO control are categorized and discussed through the following classification: classical control such as proportional-integral-derivative (PID) control, advanced control such as model-based predictive control, intelligent control such as fuzzy and neural networks, and hybrid control. The review also includes the prediction and control strategies of DO concentration in aquaculture. Finally, a critical discussion on DO control is provided. Only a few advanced DO control strategies have achieved successful implementation, while PID controllers are still the most widely used and effective controllers in engineering practice. The challenges and limitations for a broader implementation of the advanced control strategies are analyzed and discussed.

Hybrid deep learning diagonal recurrent neural network controller for nonlinear systems

In the present paper, a hybrid deep learning diagonal recurrent neural network controller (HDL-DRNNC) is proposed for nonlinear systems. The proposed HDL-DRNNC structure consists of a diagonal recurrent neural network (DRNN), whose initial values can be obtained through deep learning (DL). The DL algorithm, which is used in this study, is a hybrid algorithm that is based on a self-organizing map of the Kohonen procedure and restricted Boltzmann machine. The updating weights of the DRNN of the proposed algorithm are developed using the Lyapunov stability criterion. In this concern, simulation tasks such as disturbance signals and parameter variations are performed on mathematical and physical systems to improve the performance and the robustness of the proposed controller. It is clear from the results that the performance of the proposed controller is better than other existent controllers.

A Radial Basis Function Neural Network Approach to Predict Preschool Teachers' Technology Acceptance Behavior

With the continual development of artificial intelligence and smart computing in recent years, quantitative approaches have become increasingly popular as an efficient modeling tool as they do not necessitate complicated mathematical models. Many nations have taken steps, such as transitioning to online schooling, to decrease the harm caused by coronaviruses. Inspired by the demand for technology in early education, the present research uses a radial basis function (RBF) neural network (NN) modeling technique to predict preschool instructors' technology usage in classes based on recognized determinant characteristics of technology acceptance. In this regard, this study utilized the RBFNN approach to predict preschool teachers' technology acceptance behavior, based on the theory of planned behavior, which states that behavioral achievement, in our case the actual technology use in class, depends on motivation, intention and ability, and behavioral control. Thus, this research design is based on an adapted version of the technology acceptance model (TAM) with eight dimensions: D1. Perceived usefulness, D2. Perceived ease of use, D3. Perceived enjoyment, D4. Intention to use, D5. Actual use, D6. Compatibility, D7. Attitude, and D8. Self-efficacy. According to the TAM, actual usage is significantly predicted by the other seven dimensions used in this research. Instead of using the classical multiple linear regression statistical processing of data, we opted for a NN based on the RBF approach to predict the actual usage behavior. This study included 182 preschool teachers who were randomly chosen from a project-based national preschool teacher training program and who responded to our online questionnaire. After designing the RBF function with the actual usage as an output variable and the other seven dimensions as input variables, in the model summary, we obtained in the training sample a sum of squares error of 37.5 and a percent of incorrect predictions of 43.3%. In the testing sample, we obtained a sum of squares error of 14.88 and a percent of incorrect predictions of 37%. Thus, we can conclude that 63% of the classified data are correctly assigned to the models' dependent variable, i.e., actual technology use, which is a significant rate of correct predictions in the testing sample. This high significant percentage of correct classification represents an important result, mainly because this is the first study to apply RBFNN's prediction on psychological data, opening up a new interdisciplinary field of research.

Adaptive Anti-Disturbance Control for Systems With Saturating Input via Dynamic Neural Network Disturbance Modeling

This article discusses the issue of disturbance rejection and anti-windup control for a class of complex systems with both saturating actuators and diverse types of disturbances. At the input port, to better characterize those irregular disturbances, exogenous dynamic neural network (DNN) models with adjustable weight parameters are first introduced. A novel disturbance observer-based adaptive control (DOBAC) technique is then established, which realizes the dynamic monitoring for the unknown input disturbance. To handle the system disturbance with a bounded norm, the attenuation performance is concurrently analyzed by optimizing the L₁ gain index. Moreover, the PI-type dynamic tracking controller is proposed by integrating the polytopic description of the saturating input with the estimation of the input disturbance. The favorable stability, tracking, and robustness performances of the augmented system are achieved within a given domain of attraction by employing the convex optimization theory. Finally, using DNN-based modeling for three kinds of different irregular disturbances, simulation studies for an A4D aircraft model are conducted to substantiate the superiority of the designed algorithm.

A Brain-Inspired Approach for Collision-Free Movement Planning in the Small Operational Space

In a small operational space, e.g., mesoscale or microscale, we need to control movements carefully because of fragile objects. This article proposes a novel structure based on spiking neural networks to imitate the joint function of multiple brain regions in visual guiding in the small operational space and offers two channels to achieve collision-free movements. For the state sensation, we simulate the primary visual cortex to directly extract features from multiple input images and the high-level visual cortex to obtain the object distance, which is indirectly measurable, in the Cartesian coordinates. Our approach emulates the prefrontal cortex from two aspects: multiple liquid state machines to predict distances of the next several steps based on the preceding trajectory and a block-based excitation-inhibition feedforward network to plan movements considering the target and prediction. Responding to "too close" states needs rich temporal information, and we leverage a cerebellar network for the subconscious reaction. From the viewpoint of the inner pathway, they also form two channels. One channel starts from state extraction to attraction movement planning, both in the camera coordinates, behaving visual-servo control. The other is the collision-avoidance channel, which calculates distances, predicts trajectories, and reacts to the repulsion, all in the Cartesian coordinates. We provide appropriate supervised signals for coarse training and apply reinforcement learning to modify synapses in accordance with reality. Simulation and experiment results validate the proposed method.

A Variable-Parameter Noise-Tolerant Zeroing Neural Network for Time-Variant Matrix Inversion With Guaranteed Robustness

Matrix inversion frequently occurs in the fields of science, engineering, and related fields. Numerous matrix inversion schemes are often based on the premise that the solution procedure is ideal and noise-free. However, external interference is generally ubiquitous and unavoidable in practice. Therefore, an integrated-enhanced zeroing neural network (IEZNN) model has been proposed to handle the time-variant matrix inversion issue interfered with by noise. However, the IEZNN model can only deal with small time-variant noise interference. With slightly larger noise interference, the IEZNN model may not converge to the theoretical solution exactly. Therefore, a variable-parameter noise-tolerant zeroing neural network (VPNTZNN) model is proposed to overcome shortcomings and improve the inadequacy. Moreover, the excellent convergence and robustness of the VPNTZNN model are rigorously analyzed and proven. Finally, compared with the original zeroing neural network (OZNN) model and the IEZNN model for matrix inversion, numerical simulations and a practical application reveal that the proposed VPNTZNN model has the best robust property under the same external noise interference.

Recurrent Neural Dynamics Models for Perturbed Nonstationary Quadratic Programs: A Control-Theoretical Perspective

Recent decades have witnessed a trend that control-theoretical techniques are widely leveraged in various areas, e.g., design and analysis of computational models. Computational methods can be modeled as a controller and searching the equilibrium point of a dynamical system is identical to solving an algebraic equation. Thus, absorbing mature technologies in control theory and integrating it with neural dynamics models can lead to new achievements. This work makes progress along this direction by applying control-theoretical techniques to construct new recurrent neural dynamics for manipulating a perturbed nonstationary quadratic program (QP) with time-varying parameters considered. Specifically, to break the limitations of existing continuous-time models in handling nonstationary problems, a discrete recurrent neural dynamics model is proposed to robustly deal with noise. This work shows how iterative computational methods for solving nonstationary QP can be revisited, designed, and analyzed in a control framework. A modified Newton iteration model and an improved gradient-based neural dynamics are established by referring to the superior structural technology of the presented recurrent neural dynamics, where the chief breakthrough is their excellent convergence and robustness over the traditional models. Numerical experiments are conducted to show the eminence of the proposed models in solving perturbed nonstationary QP.

Grey Wolf Optimizer in Design Process of the Recurrent Wavelet Neural Controller Applied for Two-Mass System

In this paper, an adaptive speed controller of the electrical drive is presented. The main part of the control structure is based on the Recurrent Wavelet Neural Network (RWNN). The mechanical part of the plant is considered as an elastic connection of two DC machines. Oscillation damping and robustness against parameter changes are achieved using network parameters updates (online). Moreover, the various combinations of the feedbacks from the state variables are considered. The initial weights of the neural network and the additional gains are tuned using a modified version of the Grey Wolf Optimizer. Convergence of the calculation is forced using a new definition. For theoretical analysis, numerical tests are presented. Then, the RWNN is implemented in a dSPACE card. Finally, the simulation results are verified experimentally.

An inertial neural network approach for robust time-of-arrival localization considering clock asynchronization

This paper presents an inertial neural network to solve the source localization optimization problem with l₁-norm objective function based on the time of arrival (TOA) localization technique. The convergence and stability of the inertial neural network are analyzed by the Lyapunov function method. An inertial neural network iterative approach is further used to find a better solution among the solutions with different inertial parameters. Furthermore, the clock asynchronization is considered in the TOA l₁-norm model for more general real applications, and the corresponding inertial neural network iterative approach is addressed. The numerical simulations and real data are both considered in the experiments. In the simulation experiments, the noise contains uncorrelated zero-mean Gaussian noise and uniform distributed outliers. In the real experiments, the data is obtained by using the ultra wide band (UWB) technology hardware modules. Whether or not there is clock asynchronization, the results show that the proposed approach always can find a more accurate source position compared with some of the existing algorithms, which implies that the proposed approach is more effective than the compared ones.

A Reinforcement Learning-Based Vehicle Platoon Control Strategy for Reducing Energy Consumption in Traffic Oscillations

The vehicle platoon will be the most dominant driving mode on future roads. To the best of our knowledge, few reinforcement learning (RL) algorithms have been applied in vehicle platoon control, which has large-scale action and state spaces. Some RL-based methods were applied to solve single-agent problems. If we need to tackle multiagent problems, we will use multiagent RL algorithms since the parameters space grows exponentially with the increasing number of agents involved. Previous multiagent RL algorithms generally may provide redundant information to agents, indicating a large amount of useless or unrelated information, which may cause to be difficult for convergence training and pattern extractions from shared information. Also, random actions usually contribute to crashes, especially at the beginning of training. In this study, a communication proximal policy optimization (CommPPO) algorithm was proposed to tackle the above issues. In specific, the CommPPO model adopts a parameter-sharing structure to allow the dynamic variation of agent numbers, which can well handle various platoon dynamics, including splitting and merging. The communication protocol of the CommPPO consists of two parts. In the state part, the widely used predecessor-leader follower typology in the platoon is adopted to transmit global and local state information to agents. In the reward part, a new reward communication channel is proposed to solve the spurious reward and "lazy agent" problems in some existing multiagent RLs. Moreover, a curriculum learning approach is adopted to reduce crashes and speed up training. To validate the proposed strategy for platoon control, two existing multiagent RLs and a traditional platoon control strategy were applied in the same scenarios for comparison. Results showed that the CommPPO algorithm gained more rewards and achieved the largest fuel consumption reduction (11.6%).

Recent Advances in Dynamic Modeling and Process Control of PVA Degradation by Biological and Advanced Oxidation Processes: A Review on Trends and Advances

Polyvinyl alcohol (PVA) is an emerging pollutant commonly found in industrial wastewater, owing to its extensive usage as an additive in the manufacturing industry. PVA’s popularity has made wastewater treatment technologies for PVA degradation a popular research topic in industrial wastewater treatment. Although many PVA degradation technologies are studied in bench-scale processes, recent advancements in process optimization and control of wastewater treatment technologies such as advanced oxidation processes (AOPs) show the feasibility of these processes by monitoring and controlling processes to meet desired regulatory standards. These wastewater treatment technologies exhibit complex reaction mechanisms leading to nonlinear and nonstationary behavior related to variability in operational conditions. Thus, black-box dynamic modeling is a promising tool for designing control schemes since dynamic modeling is more complicated in terms of first principles and reaction mechanisms. This study seeks to provide a survey of process control methods via a comprehensive review focusing on PVA degradation methods, including biological and advanced oxidation processes, along with their reaction mechanisms, control-oriented dynamic modeling (i.e., state-space, transfer function, and artificial neural network modeling), and control strategies (i.e., proportional-integral-derivative control and predictive control) associated with wastewater treatment technologies utilized for PVA degradation.

Virtual Inertia Control Methods in Islanded Microgrids

Although the deployment and integration of isolated microgrids is gaining widespread support, regulation of microgrid frequency under high penetration levels of renewable sources is still being researched. Among the numerous studies on frequency stability, one key approach is based on integrating an additional loop with virtual inertia control, designed to mimic the behavior of traditional synchronous machines. In this survey, recent works related to virtual inertia control methods in islanded microgrids are reviewed. Based on a contextual analysis of recent papers from the last decade, we attempt to better understand why certain control methods are suitable for different scenarios, the currently open theoretical and numerical challenges, and which control strategies will predominate in the following years. Some of the reviewed methods are the coefficient diagram method, H-infinity-based methods, reinforcement-learning-based methods, practical-swarm-based methods, fuzzy-logic-based methods, and model-predictive controllers.

Model Predictive Control for Seizure Suppression Based on Nonlinear Auto-Regressive Moving-Average Volterra Model

This article investigates a closed-loop brain stimulation method based on model predictive control strategy to suppress epileptic seizures. A neural mass model (NMM), exhibiting the normal and various epileptic seizures by changing physiologically meaningful parameters, is used as a black-box model of the brain. Based on system identification, an auto-regressive moving-average Volterra model is established to reveal the relationship between stimulation and neuronal responses. Then, the model predictive control strategy is implemented based the Volterra model, which can generate an optimal stimulation waveform to eliminate epileptiform waves. The computational simulation results indicate the proposed closed-loop control strategy can optimize the stimulation waveform without particular knowledge of the physiological properties of the system. The robustness of the proposed control strategy to system disturbances makes it more appropriate for future clinical application.

RBFNN-Based Data-Driven Predictive Iterative Learning Control for Nonaffine Nonlinear Systems

In this paper, a novel data-driven predictive iterative learning control (DDPILC) scheme based on a radial basis function neural network (RBFNN) is proposed for a class of repeatable nonaffine nonlinear discrete-time systems subjected to nonrepetitive external disturbances. First, by utilizing the dynamic linearization technique (DLT) with a newly introduced and unknown system parameter pseudopartial derivative (PPD) and designing a new RBFNN estimation algorithm along the iterative learning axis for addressing the unknown PPD and the unknown nonrepetitive external disturbances, a data-driven prediction model is established. It is theoretically shown that by constructing a composite energy function (CEF) with respect to the modeling error for the first time, the convergence of the modeling error via the proposed DLT-based RBFNN modeling method can be guaranteed, and the convergence speed is tunable. Then, a DDPILC with a disturbance compensation term is designed, and the convergence of the tracking control error is analyzed. Finally, simulations of a train operation system reveal that even if the train suffers from randomly varying load disturbances and nonlinear running resistance, the proposed scheme can make both the modeling error and the tracking control error decrease successively with increasing operation number.

Online prediction of effluent COD in the anaerobic wastewater treatment system based on PCA-LSSVM algorithm

Since anaerobic wastewater treatment is a nonlinear and complex biochemical process, reasonable monitoring and control are needed to keep it operating stably and efficiently. In this paper, a least-square support-vector machine (LS-SVM) was employed to construct models for the prediction of effluent chemical oxygen demand (COD) in an anaerobic wastewater treatment system. The result revealed that the performance of the steady-state model based on LS-SVM for predicting effluent COD was acceptable, with the maximum relative error (RE) of 11.45%, the mean average percentage error (MAPE) of 0.79% and the root mean square error (RMSE) of 3.08 when training, and the performance fell slightly when testing. Even though, the correlation coefficient value (R) between the predicted value and the actual value of 0.9752 could be achieved, which means this model can predict the variation of effluent COD in general. The dynamic-state models under three kinds of shock loads, which were concentration, hydraulic, and bicarbonate buffer absent, showed good forecasting performance, the correlation coefficient values (R) all excelled 0.99. Among these three shocks, the dynamic LS-SVM model under bicarbonate buffer absent shock achieved the optimal performance and followed by the dynamic-state model under hydraulic shock. This paper provides a meaningful reference to improve the monitoring level of the anaerobic wastewater treatment process.

Self-Organizing RBF Neural Network Using an Adaptive Gradient Multiobjective Particle Swarm Optimization

One of the major obstacles in using radial basis function (RBF) neural networks is the convergence toward local minima instead of the global minima. For this reason, an adaptive gradient multiobjective particle swarm optimization (AGMOPSO) algorithm is designed to optimize both the structure and parameters of RBF neural networks in this paper. First, the AGMOPSO algorithm, based on a multiobjective gradient method and a self-adaptive flight parameters mechanism, is developed to improve the computation performance. Second, the AGMOPSO-based self-organizing RBF neural network (AGMOPSO-SORBF) can optimize the parameters (centers, widths, and weights), as well as determine the network size. The goal of AGMOPSO-SORBF is to find a tradeoff between the accuracy and the complexity of RBF neural networks. Third, the convergence analysis of AGMOPSO-SORBF is detailed to ensure the prerequisite of any successful applications. Finally, the merits of our proposed approach are verified on multiple numerical examples. The results indicate that the proposed AGMOPSO-SORBF achieves much better generalization capability and compact network structure than some other existing methods.

Coordinated Optimization for the Descent Gradient of Technical Index in the Iron Removal Process

In the iron removal process, which is composed of four cascaded reactors, outlet ferrous ion concentration (OFIC) is an important technical index for each reactor. The descent gradient of OFIC indicates the reduced degree of ferrous ions in each reactor. Finding the optimal descent gradient of OFIC is tightly close to the effective iron removal and the optimal operation of the process. This paper proposes a coordinated optimization strategy for setting the descent gradient of OFIC. First, an optimal setting module is established to determine the initial set-points of the descent gradient. The oxygen utilization ratio (OUR), an important parameter in this module, cannot be measured online. Therefore, a self-adjusting RBF (SARBF) neural network with an adaptive learning rate is developed to estimate the OUR. The convergence of the SARBF neural network is discussed. Then, a coordinated optimization strategy is proposed to adjust the set-points of the descent gradient when the measured OFICs drift away from their desired set-pints. If the final OFIC does not satisfy the process requirements, a compensation mechanism is developed to provide a compensation for the set-points of the descent gradient. Finally, industrial experiments in the largest zinc hydrometallurgy plant validate the effectiveness of the proposed coordinated optimization strategy. Our strategy improves the qualified ratio of the OFIC and the quality of the goethite precipitate. More profit is created to the iron removal process after our strategy is applied.

Modeling and Analysis of Beta Oscillations in the Basal Ganglia

Enhanced beta (12-30 Hz) oscillatory activity in the basal ganglia (BG) is a prominent feature of the Parkinsonian state in animal models and in patients with Parkinson's disease. Increased beta oscillations are associated with severe dopaminergic striatal depletion. However, the mechanisms underlying these pathological beta oscillations remain elusive. Inspired by the experimental observation that only subsets of neurons within each nucleus in the BG exhibit oscillatory activities, a computational model of the BG-thalamus neuronal network is proposed, which is characterized by subdivided nuclei within the BG. Using different currents externally applied to the neurons within a given nucleus, neurons behave according to one of the two subgroups, named "-N" and "-P," where "-N" and "-P" denote the normal and the Parkinsonian states, respectively. The ratio of "-P" to "-N" neurons indicates the degree of the Parkinsonian state. Simulation results show that if "-P" neurons have a high degree of connectivity in the subthalamic nucleus (STN), they will have a significant downstream effect on the generation of beta oscillations in the globus pallidus. Interestingly, however, the generation of beta oscillations in the STN is independent of the selection of the "-P" neurons in the external segment of the globus pallidus (GPe), despite the reciprocal structure between STN and GPe. This computational model may pave the way to revealing the mechanism of such pathological behaviors in a realistic way that can replicate experimental observations. The simulation results suggest that the STN is more suitable than GPe as a deep brain stimulation target.

Diagonal recurrent neural network based adaptive control of nonlinear dynamical systems using lyapunov stability criterion

In this paper adaptive control of nonlinear dynamical systems using diagonal recurrent neural network (DRNN) is proposed. The structure of DRNN is a modification of fully connected recurrent neural network (FCRNN). Presence of self-recurrent neurons in the hidden layer of DRNN gives it an ability to capture the dynamic behaviour of the nonlinear plant under consideration (to be controlled). To ensure stability, update rules are developed using lyapunov stability criterion. These rules are then used for adjusting the various parameters of DRNN. The responses of plants obtained with DRNN are compared with those obtained when multi-layer feed forward neural network (MLFFNN) is used as a controller. Also, in example 4, FCRNN is also investigated and compared with DRNN and MLFFNN. Robustness of the proposed control scheme is also tested against parameter variations and disturbance signals. Four simulation examples including one-link robotic manipulator and inverted pendulum are considered on which the proposed controller is applied. The results so obtained show the superiority of DRNN over MLFFNN as a controller.