Indirect adaptive self-organizing RBF neural controller design with a dynamical training approach

This study proposes an indirect adaptive self-organizing RBF neural control (IASRNC) system which is composed of a feedback controller, a neural identifier and a smooth compensator. The neural identifier which contains a self-organizing RBF (SORBF) network with structure and parameter learning is designed to online estimate a system dynamics using the gradient descent method. The SORBF network can add new hidden neurons and prune insignificant hidden neurons online. The smooth compensator is designed to dispel the effect of minimum approximation error introduced by the neural identifier in the Lyapunov stability theorem. In general, how to determine the learning rate of parameter adaptation laws usually requires some trial-and-error tuning procedures. This paper proposes a dynamical learning rate approach based on a discrete-type Lyapunov function to speed up the convergence of tracking error. Finally, the proposed IASRNC system is applied to control two chaotic systems. Simulation results verify that the proposed IASRNC scheme can achieve a favorable tracking performance.     

Model predictive control of dissolved oxygen concentration based on a self-organizing RBF neural network

The dissolved oxygen (DO) concentration in activated sludge wastewater treatment processes (WWTPs) is difficult to control because of the complex nonlinear behavior involved. In this paper, a self-organizing radial basis function (RBF) neural network model predictive control (SORBF-MPC) method is proposed for controlling the DO concentration in a WWTP. The proposed SORBF can vary its structure dynamically to maintain prediction accuracy. The hidden nodes in the RBF neural network can be added or removed on-line based on node activity and mutual information (MI) to achieve the appropriate network complexity and the necessary dynamism. Moreover, the convergence of the SORBF is analyzed in both the dynamic process phase and the phase following the modification of the structure. Finally, the SORBF-MPC is applied to the Benchmark Simulation Model 1 (BSM1) WWTP to maintain the DO concentration. The results show that SORBF-MPC effectively provides process control. The performance comparison also indicates that the proposed model's predictive control strategy yields the most accurate for DO concentration, better effluent qualities, and lower average aeration energy (AE) consumption.     

Prediction of activated sludge bulking based on a self-organizing RBF neural network

Despite extensive research that has been done on sludge bulking, it remains a widespread problem in the operation of activated sludge processes, which brings severe economic and environmental consequences. In this study, a self-organizing radial basis function (SORBF) neural network method is utilized to predict the evolution of the sludge volume index (SVI). The hidden nodes in the SORBF neural network can be grown or pruned based on the node activity (NA) and mutual information (MI) to achieve the appropriate network complexity and maintain overall computational efficiency. The growing and pruning criteria of the SORBF can vary its structure dynamically with the objective to enhance its performance. Moreover, the input–output selection to calculate the SVI values is also discussed. The variables with key relations to the sludge bulking are used as the inputs for the SVI. Finally, the SORBF neural network is applied to the activated sludge wastewater treatment processes (WWTPs) for predicting the SVI, and then for predicting the sludge bulking. Experimental results show the excellent performance of the SORBF method. The performance comparison demonstrates the effectiveness of the proposed SORBF.     

Identification and modeling of nonlinear dynamical systems using a novel self-organizing RBF-based approach

In this paper, a novel self-organizing radial basis function (SORBF) neural network is proposed for nonlinear identification and modeling. The proposed SORBF consists of simultaneous network construction and parameter optimization. It offers two important advantages. First, the hidden neurons in the SORBF neural network can be added or removed, based on the neuron activity and mutual information (MI), to achieve the appropriate network complexity and maintain overall computational efficiency for identification and modeling. Second, the model performance can be significantly improved through the parameter optimization. The proposed parameter-adjustment-based optimization algorithm, utilizing the forward-only computation (FOC) algorithm instead of the traditionally forward-and-backward computation, simplifies neural network training, and thereby significantly reduces computational complexity. Additionally, the convergence of the SORBF is analyzed in both the structure organizing process phase and the phase following the modification. Lastly, the proposed approach is applied to model and identify the nonlinear dynamical systems. Simulation results demonstrate its effectiveness.     

Research on an online self-organizing radial basis function neural network

A new growing and pruning algorithm is proposed for radial basis function (RBF) neural network structure design in this paper, which is named as self-organizing RBF (SORBF). The structure of the RBF neural network is introduced in this paper first, and then the growing and pruning algorithm is used to design the structure of the RBF neural network automatically. The growing and pruning approach is based on the radius of the receptive field of the RBF nodes. Meanwhile, the parameters adjusting algorithms are proposed for the whole RBF neural network. The performance of the proposed method is evaluated through functions approximation and dynamic system identification. Then, the method is used to capture the biochemical oxygen demand (BOD) concentration in a wastewater treatment system. Experimental results show that the proposed method is efficient for network structure optimization, and it achieves better performance than some of the existing algorithms.     

Decoupling control for wastewater treatment process based on recurrent fuzzy neural network

Due to the characteristics of strong coupling and high nonlinearity in the control process, an intelligent decoupling control strategy based on recurrent fuzzy neural network (RFNN) is proposed in this paper to control the wastewater treatment process (WWTP). Firstly, the architecture of the RFNN controller is designed with a mechanism analysis of WWTP. Secondly, a decoupling strategy in combination with a gradient descent search algorithm is used to decouple the control loop of dissolved oxygen (D_O) concentration and nitrate nitrogen (S_NO) concentration. Finally, stability analysis based on a Lyapunov function is investigated. The proposed approach has been applied to the WWTP simulation model. Compared to model predictive control, echo state network‐based HDP (E‐HDP), conventional RFNN, and neural network on‐line modelling and controlling methods, the proposed method has better control performance.     

Multi‐Variable Direct Self‐Organizing Fuzzy Neural Network Control for Wastewater Treatment Process

A multi‐variable direct self‐organizing fuzzy neural network control (M‐DSNNC) method is proposed for the multi‐variable control of the wastewater treatment process (WWTP). In this paper, the proposed control system is an essential multi‐variable control method for the WWTP. No exact plant model is required, which avoids the difficulty of establishing the mathematics model of WWTP. The M‐DSNNC system is comprised of a fuzzy neural network controller and a compensation controller. The fuzzy neural network is used for approximating the ideal control law under a general nonlinear system. Moreover, the neural network is designed in a self‐organizing mode to adapt the uncertainty environment. Simulation results, based on the international benchmark simulation model No.1 (BSM1), demonstrate that the control accuracy is improved under the proposed M‐DSNNC method, and the controller has a much stronger decoupling ability.     

Modeling of Energy Consumption and Effluent Quality Using Density Peaks-based Adaptive Fuzzy Neural Network

Modeling of energy consumption (EC) and effluent quality (EQ) are very essential problems that need to be solved for the multiobjective optimal control in the wastewater treatment process (WWTP). To address this issue, a density peaks-based adaptive fuzzy neural network (DP-AFNN) is proposed in this study. To obtain suitable fuzzy rules, a DP-based clustering method is applied to fit the cluster centers to process nonlinearity. The parameters of the extracted fuzzy rules are fine-tuned based on the improved Levenberg-Marquardt algorithm during the training process. Furthermore, the analysis of convergence is performed to guarantee the successful application of the DPAFNN. Finally, the proposed DP-AFNN is utilized to develop the models of EC and EQ in the WWTP. The experimental results show that the proposed DP-AFNN can achieve fast convergence speed and high prediction accuracy in comparison with some existing methods.      

Multiobjective PID control design in uncertain robotic systemsusing neural network elimination scheme

A PID-type controller incorporating neural network elimination scheme and sliding-mode control action for different objectives including H₂ tracking performance, H_∞ tracking performance, and regional pole constraints is developed in robotic systems under plant uncertainties and external disturbances. The adaptive neural networks are used to compensate the plant uncertainties. The sliding-mode control action is included to eliminate the effect of approximation error via neural network approximation. The sufficient conditions are developed for different objectives in terms of linear matrix inequality (LMI) formulations. The interesting combinations of different objectives are considered in this paper, which include H_∞ PID tracking control design with regional pole constraints and mixed H₂/H_∞ PID tracking control design with regional pole constraints. These multiobjective PID control problems are characterized in terms of eigenvalue problem (EVP). The EVP can be efficiently solved by the LMI toolbox in Matlab. The proposed methods are simple and the PID control gain for different objectives can be obtained systematically     

基于数据ADP算法的一类带有执行器饱和的未知离散时间系统最优跟踪控制

针对一类带有执行器饱和的未知动态离散时间非线性系统, 提出了一种新的最优跟踪控制方案. 该方案基于迭代自适应动态规划算法, 为了实现最优控制, 首先建立了未知系统动态的数据辨识器. 通过引入M网络, 获得了稳态控制的精确表达式. 为了消除执行器饱和的影响, 提出了一个非二次的性能指标函数. 然后提出了一种迭代自适应动态规划算法获得最优跟踪控制的解, 并给出了收敛性分析. 为了实现最优控制方案, 神经网络被用来构建数据辨识器、计算性能指标函数、近似最优控制策略和求解稳态控制. 仿真结果验证了本文所提出的最优跟踪控制方法的有效性.     

Dynamic multi-objective optimization control for wastewater treatment process

A dynamic multi-objective optimization control (DMOOC) scheme is proposed in this paper for the wastewater treatment process (WWTP), which can dynamically optimize the set-points of dissolved oxygen concentration and nitrate level with multiple performance indexes simultaneously. To overcome the difficulty of establishing multi-objective optimization (MOO) model for the WWTP, a neural network online modeling method is proposed, requiring only the process data of the plant. Then, the constructed MOO model with constraints is solved based on the NSGA-II (non-dominated sorting genetic algorithm-II), and the optimal set-point vector is selected from the Pareto set using the defined utility function. Simulation results, based on the benchmark simulation model 1 (BSM1), demonstrate that the energy consumption can be significantly reduced applying the DMOOC than the default PID control with the fixed set-points. Moreover, a tradeoff between energy consumption and effluent quality index can be considered.

     

Self-organizing adaptive fuzzy neural control for the synchronization of uncertain chaotic systems with random-varying parameters

This paper proposes a self-organizing adaptive fuzzy neural control (SAFNC) for the synchronization of uncertain chaotic systems with random-varying parameters. The proposed SAFNC system is composed of a computation controller and a robust controller. The computation controller containing a self-organizing fuzzy neural network (SOFNN) identifier is the principle controller. The SOFNN identifier is used to online estimate the compound uncertainties with the structure and parameter learning phases of fuzzy neural network (FNN), simultaneously. The structure-learning phase consists of the growing of membership functions, the splitting of fuzzy rules and the pruning of fuzzy rules, and thus the SOFNN identifier can avoid the time-consuming trial-and-error tuning procedure for determining the network structure of fuzzy neural network. The robust controller is used to attenuate the effects of the approximation error so that the synchronization of chaotic systems is achieved.All the parameter learning algorithms are derived based on the Lyapunov stability theorem to ensure network convergence as well as stable synchronization performance. To demonstrate the effectiveness of the proposed method, simulation results are illustrated in this paper.     

Real-time torque control using discrete-time recurrent high-order neural networks

This paper presents a discrete-time direct current (DC) motor torque tracking controller, based on a recurrent high-order neural network to identify the plant model. In order to train the neural identifier, the extended Kalman filter (EKF) based training algorithm is used. The neural identifier is in series-parallel configuration that constitutes a well approximation method of the real plant by the neural identifier. Using the neural identifier structure that is in the nonlinear controllable form, the block control (BC) combined with sliding modes (SM) control techniques in discrete-time are applied. The BC technique is used to design a nonlinear sliding manifold such that the resulting sliding mode dynamics are described by a desired linear system. For the SM control technique, the equivalent control law is used in order to the plant output tracks a reference signal. For reducing the effect of unknown terms, it is proposed a specific desired dynamics for the sliding variables. The control problem is solved by the indirect approach, where an appropriate neural network (NN) identification model is selected; the NN parameters (synaptic weights) are adjusted according to a specific adaptive law (EKF), such that the response of the NN identifier approximates the response of the real plant for the same input. Then, based on the designed NN identifier a stabilizing or reference tracking controller is proposed (BC combined with SM). The proposed neural identifier and control applicability are illustrated by torque trajectory tracking for a DC motor with separate winding excitation via real-time implementation.     

A hybrid metaheuristic for multiobjective unconstrained binary quadratic programming

The conventional unconstrained binary quadratic programming (UBQP) problem is known to be a unified modeling and solution framework for many combinatorial optimization problems. This paper extends the single-objective UBQP to the multiobjective case (mUBQP) where multiple objectives are to be optimized simultaneously. We propose a hybrid metaheuristic which combines an elitist evolutionary multiobjective optimization algorithm and a state-of-the-art single-objective tabu search procedure by using an achievement scalarizing function. Finally, we define a formal model to generate mUBQP instances and validate the performance of the proposed approach in obtaining competitive results on large-size mUBQP instances with two and three objectives.     

Neural network based dynamic modeling of flexible‐link manipulators with application to the SSRMS

This paper presents an approach for dynamic modeling of flexible‐link manipulators using artificial neural networks. A state‐space representation is considered for a neural identifier. A recurrent network configuration is obtained by a combination of feedforward network architectures with dynamical elements in the form of stable filters. To guarantee the boundedness of the states, a joint PD control is introduced in the system. The method can be considered both as an online identifier that can be used as a basis for designing neural network controllers as well as an offline learning scheme to compute deflections due to link flexibility for evaluating forward dynamics. Unlike many other methods, the proposed approach does not assume knowledge of the nonlinearities of the system nor that the nonlinear system is linear in parameters. The performance of the proposed neural identifier is evaluated by identifying the dynamics of different flexible‐link manipulators. To demonstrate the effectiveness of the algorithm, simulation results for a single‐link manipulator, a two‐link planar manipulator, and the Space Station Remote Manipulator System (SSRMS) are presented. ©2000 John Wiley & Sons, Inc.     

基于信息强度的RBF神经网络结构设计研究

在系统研究前馈神经网络的基础上,针对径向基函数(Radial basis function, RBF) 网络的结构设计问题,提出一种弹性RBF神经网络结构优化设计方法. 利用隐含层神经元的输出信息(Output-information, OI)以及隐含层神经元与输出层神经元间的交互信息(Multi-information, MI)分析网络的连接强度, 以此判断增加或删除RBF神经网络隐含层神经元, 同时调整神经网络的拓扑结构,有效地解决了RBF神经网络结构设计问题; 利用梯度下降的参数修正算法保证了最终RBF网络的精度, 实现了神经网络的结构和参数自校正. 通过对典型非线性函数的逼近与污水处理过程关键水质参数建模, 结果证明了该弹性RBF具有良好的动态特征响应能力和逼近能力, 尤其是在训练速度、泛化能力、最终网络结构等方面较之最小资源神经网络(Minimal resource allocation net works, MRAN)、增长修剪RBF 神经网络(Generalized growing and pruning RBF, GGAP-RBF)和自组织RBF神经网络(Self-organizing RBF, SORBF)有较大的提高.     

Multiobjective evolution of deep learning parameters for robot manipulator object recognition and grasping

Deep Learning (DL) is currently very popular because of its similarity to the hierarchical architecture of human brain with multiple levels of abstraction. DL has many parameters that influence the network performance. In this paper, we introduce a multiobjective evolutionary algorithm (MOEA) to optimize the DBNN parameters subject to the error rate and the network training time as two conflicting objectives. To verify the effectiveness, the proposed method is applied to the robot object recognition and grasping task. We compare the performance of the optimized DBNN model with a) DBNN with arbitrarily selected parameters and b) Deep Belief Network-Deep Neural Network (DBN-DNN). The results show that optimized DL has a superior performance in terms of training time and recognition success rate. In addition, the optimized DBNN model is effective for real-time robotic implementations.     

A Novel Intelligent Multiobjective Simulated Annealing Algorithm for Designing Robust PID Controllers

This paper proposes an intelligent multiobjective simulated annealing algorithm (IMOSA) and its application to an optimal proportional integral derivative (PID) controller design problem. A well-designed PID-type controller should satisfy the following objectives: 1) disturbance attenuation; 2) robust stability; and 3) accurate setpoint tracking. The optimal PID controller design problem is a large-scale multiobjective optimization problem characterized by the following: 1) nonlinear multimodal search space; 2) large-scale search space; 3) three tight constraints; 4) multiple objectives; and 5) expensive objective function evaluations. In contrast to existing multiobjective algorithms of simulated annealing, the high performance in IMOSA arises mainly from a novel multiobjective generation mechanism using a Pareto-based scoring function without using heuristics. The multiobjective generation mechanism operates on a high-score nondominated solution using a systematic reasoning method based on an orthogonal experimental design, which exploits its neighborhood to economically generate a set of well-distributed nondominated solutions by considering individual and overall objectives. IMOSA is evaluated by using a practical design example of a super-maneuverable fighter aircraft system. An efficient existing multiobjective algorithm, the improved strength Pareto evolutionary algorithm, is also applied to the same example for comparison. Simulation results demonstrate high performance of the IMOSA-based method in designing robust PID controllers.     

基于单网络ADP的一类未知非线性系统的近似最优控制

针对一类未知的连续非线性系统,提出一个基于单网络近似动态规划(ADP)的近似最优控制方案。该方案通过设计一个新型的递归神经网络(RNN)辨识器放松了系统模型需已知或部分已知的要求,并利用一个神经网络(NN)近似系统的性能指标函数消除了常规ADP方法中的控制网络。通过Lyapunov理论分析严格证明了闭环系统内所有信号一致最终有界,并且所获得的性能指标函数和控制输入分别收敛到最优性能指标函数和最优控制输入的小邻域内。仿真结果验证了所提出控制方案的有效性。     

Tuning of PID controller based on a multiobjective genetic algorithm applied to a robotic manipulator

Most controllers optimization and design problems are multiobjective in nature, since they normally have several (possibly conflicting) objectives that must be satisfied at the same time. Instead of aiming at finding a single solution, the multiobjective optimization methods try to produce a set of good trade-off solutions from which the decision maker may select one. Several methods have been devised for solving multiobjective optimization problems in control systems field. Traditionally, classical optimization algorithms based on nonlinear programming or optimal control theories are applied to obtain the solution of such problems. The presence of multiple objectives in a problem usually gives rise to a set of optimal solutions, largely known as Pareto-optimal solutions. Recently, Multiobjective Evolutionary Algorithms (MOEAs) have been applied to control systems problems. Compared with mathematical programming, MOEAs are very suitable to solve multiobjective optimization problems, because they deal simultaneously with a set of solutions and find a number of Pareto optimal solutions in a single run of algorithm. Starting from a set of initial solutions, MOEAs use iteratively improving optimization techniques to find the optimal solutions. In every iterative progress, MOEAs favor population-based Pareto dominance as a measure of fitness. In the MOEAs context, the Non-dominated Sorting Genetic Algorithm (NSGA-II) has been successfully applied to solving many multiobjective problems. This paper presents the design and the tuning of two PID (Proportional–Integral–Derivative) controllers through the NSGA-II approach. Simulation numerical results of multivariable PID control and convergence of the NSGA-II is presented and discussed with application in a robotic manipulator of two-degree-of-freedom. The proposed optimization method based on NSGA-II offers an effective way to implement simple but robust solutions providing a good reference tracking performance in closed loop.