Variable structure controller with neural compensator

This paper proposes a new variable structure controller combined with a multilayer neural network using an error back-propagation learning algorithm. The neural network acts as a compensator for a conventional variable structure controller in order to improve the control performance when the initial assumptions of the uncertainty bounds of the system parameters are violated. Also, the proposed controller can reduce the steady-state error of a conventional variable structure controller using the boundary layer technique. Computer simulation results show that the proposed method is effective in controlling dynamic systems with unexpected large uncertainties.     

Derivation of a parameter stabilizing training criterion for adaptive neuro-fuzzy inference systems in motion control

This paper presents a novel training algorithm for adaptive neuro-fuzzy inference systems. The algorithm combines the error back-propagation algorithm with the variable structure systems approach. Expressing the parameter update rule as a dynamic system in continuous time and applying sliding mode control (SMC) methodology to the dynamic model of the gradient based training procedure results in the parameter stabilizing part of training algorithm. The proposed combination therefore exhibits a degree of robustness to the unmodelled multivariable internal dynamics of the gradient-based training algorithm. With conventional training procedures, the excitation of this dynamics during a training cycle can lead to instability, which may be difficult to alleviate owing to the multidimensionality of the solution space and the ambiguities concerning the environmental conditions. This paper shows that a neuro-fuzzy model can be trained such that the adjustable parameter values are forced to settle down (parameter stabilization) while minimizing an appropriate cost function (cost optimization), which is based on state tracking performance. In the application example, trajectory control of a two degrees of freedom direct drive robotic manipulator is considered. As the controller, an adaptive neuro-fuzzy inference mechanism is used and, in the parameter tuning, the proposed algorithm is utilized.     

An efficient compensatory neuro-fuzzy system and its applications

In this study, a compensatory neuro-fuzzy system (CNFS) is proposed. The compensatory fuzzy reasoning method uses adaptive fuzzy operations of a neuro-fuzzy system to make the fuzzy logic system more adaptive and effective. Furthermore, an online learning algorithm that consists of structure learning and parameter learning is proposed to automatically construct the CNFS. The structure learning is based on the fuzzy similarity measure to determine the number of fuzzy rules, and the parameter learning is based on backpropagation algorithm to adjust the parameters. The simulation results have shown that (1) the CNFS model converges quickly and (2) the CNFS model has a lower root mean square (RMS) error than other models.     

Neuro-fuzzy control based on the NEFCON-model: recent developments

 Fuzzy systems are currently being used in a wide field of industrial and scientific applications. Since the design and especially the optimization process of fuzzy systems can be very time consuming, it is convenient to have algorithms which construct and optimize them automatically. One popular approach is to combine fuzzy systems with learning techniques derived from neural networks. Such approaches are usually called neuro-fuzzy systems. In this paper we present our view of neuro-fuzzy systems and an implementation in the area of control theory: the NEFCON-Model. This model is able to learn and optimize the rule base of a Mamdani like fuzzy controller online by a reinforcement learning algorithm that uses a fuzzy error measure. Therefore, we also describe some methods to determine a fuzzy error measure for a dynamic system. In addition we present some implementations of the model and an application example. The presented implementations are available free of charge for non-commercial purposes.     

Observer-Based Adaptive Controller Design of Flexible Manipulators Using Time-Delay Neuro-Fuzzy Networks

In this paper, a dynamical time-delay neuro-fuzzy controller is proposed for the adaptive control of a flexible manipulator. It is assumed that the robotic manipulator has only joint angle position measurements. A linear observer is used to estimate the robot joint angle velocity. For a perfect tracking control of the robot, the output redefinition approach is used in the adaptive controller design using time-delay neuro-fuzzy networks. The time-delay neuro-fuzzy networks with the rule representation of the TSK type fuzzy system have better learning ability for complex dynamics as compared with existing neural networks. The novel control structure and learning algorithm are given, and a simulation for the trajectory tracking of a flexible manipulator illustrates the control performance of the proposed control approach.     

A modified gradient-based neuro-fuzzy learning algorithm and its convergence

Neuro-fuzzy approach is known to provide an adaptive method to generate or tune fuzzy rules for fuzzy systems. In this paper, a modified gradient-based neuro-fuzzy learning algorithm is proposed for zero-order Takagi-Sugeno inference systems. This modified algorithm, compared with conventional gradient-based neuro-fuzzy learning algorithm, reduces the cost of calculating the gradient of the error function and improves the learning efficiency. Some weak and strong convergence results for this algorithm are proved, indicating that the gradient of the error function goes to zero and the fuzzy parameter sequence goes to a fixed value, respectively. A constant learning rate is used. Some conditions for the constant learning rate to guarantee the convergence are specified. Numerical examples are provided to support the theoretical findings.     

RCMAC-based adaptive control for uncertain nonlinear systems.

An adaptive control system, using a recurrent cerebellar model articulation controller (RCMAC) and based on a sliding mode technique, is developed for uncertain nonlinear systems. The proposed dynamic structure of RCMAC has superior capability to the conventional static cerebellar model articulation controller in an efficient learning mechanism and dynamic response. Temporal relations are embedded in RCMAC by adding feedback connections in the association memory space so that the RCMAC provides a dynamical structure. The proposed control system consists of an adaptive RCMAC and a compensated controller. The adaptive RCMAC is used to mimic an ideal sliding mode controller, and the compensated controller is designed to compensate for the approximation error between the ideal sliding mode controller and the adaptive RCMAC. The online adaptive laws of the control system are derived based on the Lyapunov stability theorem, so that the stability of the system can be guaranteed. In addition, in order to relax the requirement of the approximation error bound, an estimation law is derived to estimate the error bound. Finally, the simulation and experimental studies demonstrate the effectiveness of the proposed control scheme for the nonlinear systems with unknown dynamic functions.     

A Combined Adaptive Law for Fuzzy Iterative Learning Control of Nonlinear Systems With Varying Control Tasks

To deal with the iterative control of uncertain nonlinear systems with varying control tasks, nonzero initial resetting state errors, and nonrepeatable mismatched input disturbance, a new adaptive fuzzy iterative learning controller is proposed in this paper. The main structure of this learning controller is constructed by a fuzzy learning component and a robust learning component. For the fuzzy learning component, a fuzzy system used as an approximator is designed to compensate for the plant nonlinearity. For the robust learning component, a sliding-mode-like strategy is applied to overcome the nonlinear input gain, input disturbance, and fuzzy approximation error. Both designs are based on a time-varying boundary layer which is introduced not only to solve the problem of initial state errors but also to eliminate the possible undesirable chattering behavior. A new adaptive law combining time- and iteration-domain adaptation is derived to search for suitable values of control parameters and then guarantee the closed-loop stability and error convergence. This adaptive algorithm is designed without using projection or deadzone mechanism. With a suitable choice of the weighting gain, the memory size for the storage of parameter profiles can be greatly reduced. It is shown that all the adjustable parameters as well as internal signals remain bounded for all iterations. Moreover, the norm of tracking state error vector will asymptotically converge to a tunable residual set even when the desired tracking trajectory is varying between successive iterations.     

Adaptive recurrent neural network control using a structure adaptation algorithm

This paper proposes an adaptive recurrent neural network control (ARNNC) system with structure adaptation algorithm for the uncertain nonlinear systems. The developed ARNNC system is composed of a neural controller and a robust controller. The neural controller which uses a self-structuring recurrent neural network (SRNN) is the principal controller, and the robust controller is designed to achieve L ² tracking performance with desired attenuation level. The SRNN approximator is used to online estimate an ideal tracking controller with the online structuring and parameter learning algorithms. The structure learning possesses the ability of both adding and pruning hidden neurons, and the parameter learning adjusts the interconnection weights of neural network to achieve favorable approximation performance. And, by the L ² control design technique, the worst effect of approximation error on the tracking error can be attenuated to be less or equal to a specified level. Finally, the proposed ARNNC system with structure adaptation algorithm is applied to control two nonlinear dynamic systems. Simulation results prove that the proposed ARNNC system with structure adaptation algorithm can achieve favorable tracking performance even unknown the control system dynamics function.     

Learning control of process systems with hard input constraints

In this paper, a novel and simple learning control strategy based on using a bounded nonlinear controller for process systems with hard input constraints is proposed. To enable the bounded nonlinear controller to learn to control a changing plant by merely observing the process output errors, a simple learning algorithm for parameter updating is derived based on the Lyapunov stability theorem. The learning scheme is easy to implement, and does not require any a priori process knowledge except the system output response direction. For demonstrating the effectiveness and applicability of the learning control strategy, the control of a once-through boiler, as well as an open-loop unstable continuously stirred tank reactor (CSTR), were investigated. Furthermore, extensive comparisons of the proposed scheme with the conventional PI controller and with some existing model-free intelligent controllers were also performed. Due to significant features of simple structure, efficient algorithm and good performance, the proposed learning control strategy appears to be a promising and practical approach to the intelligent control of process systems subject to hard input constraints.     

On some idea of a neuro-fuzzy controller

The paper presents a neuro-fuzzy technique for the design of controllers. This technique can effectively deal with two main types of knowledge which usually describe the control strategy for complex systems, that is, a qualitative, linguistic, fuzzy knowledge usually expressed in the form of linguistic rules, and a quantitative, nonfuzzy information in the form of measurements and other numerical data. The proposed technique combines artificial neural networks with fuzzy logic yielding a structure that can be called a neuro-fuzzy controller or, broadly speaking, a fuzzy neural network. The paper presents a general structure of a neuro-fuzzy controller and two essential phases of its design, that is, a learning phase and a functioning phase. In turn, a numerical example which illustrates how the proposed controller works is presented. Finally, the paper describes an application of a neuro-fuzzy control to inverter drive systems for electric vehicles. The results of simulation and experimental investigations carried out on the laboratory model of an inverter drive system are also provided.     

Wavelet CMAC for MIMO uncertain nonlinear systems using a modified social ski-driver algorithm

This study uses a Mexican hat wavelet membership function for a cerebellar model articulation controller (CMAC) to develop a more efficient adaptive controller for multiple input multiple output (MIMO) uncertain nonlinear systems. The main controller is called the adaptive Mexican hat wavelet CMAC (MWCMAC), and an auxiliary controller is used to remove the residual error. For the MWCMAC, the online learning laws are derived from the gradient descent method. In addition, the learning rate values are very important and have a great impact on the performance of the control system; however, they are difficult to choose accurately. Therefore, a modified social ski driver (SSD) algorithm is proposed to find optimal learning rates for the control parameters. Finally, a magnetic ball levitation system and a nine-link biped robot are used to illustrate the effectiveness of the proposed SSD-based MWCMAC control system. The comparisons with other existing control algorithms have shown the superiority of the proposed control system.     

Designing neurofuzzy system based on ICART algorithm and its application for modeling jet fuel endpoint of hydrocracking process

In this paper, a neuro-fuzzy system based on improved CART algorithm (ICART) is presented, in which the ICART algorithm is used to design neuro-fuzzy system. It is worth noting that ICART algorithm partitions the input space into tree structure adaptively, which avoids the curse of dimensionality (number of rules goes up exponentially with number of input variables). Moreover, it adopts density function to construct the local model for every node in order to overcome the discontinuous boundaries existed in CART algorithm. In addition, a supervised scheme is used to adjust parameters to minimize the network output error and construct more accurate fuzzy model on the basis of the ICART algorithm. Finally, to illustrate the validity of the proposed method, a simulation research and a practical application are done. The results show that the proposed method can provide optimal model structure and parameters for fuzzy modeling, possesses high learning efficiency, and is smoother than CART algorithm. It can be successfully applied to modeling jet fuel endpoint of hydrocracking processing.     

Adaptive controller with fuzzy rules emulated structure and its applications

In this paper, the adaptive controller inspired by the neuro-fuzzy controller is proposed. Its structure, called fuzzy rules emulated network (FREN), is derived based on the fuzzy if–then rules. This structure not only emulates the fuzzy control rules but also allows the initial value of controller's parameters to be intuitively chosen. These parameters are further adjusted during system operation using a method similar to the steepest descent technique. The learning rate selection criteria based on Lyapunov's stability condition is also presented. FREN controller is applied to control various nonlinear systems, for examples, the single invert pendulum plant, the water bath temperature control, the high voltage direct current transmission system and the robotic system. Computer simulations results indicate that the proposed controller is able to control the target systems satisfactory.     

一种基于CMAC的自学习控制器

现有的基于CMAC的自学习控制器能够有效地减小跟踪误差,但是在跟踪连续变 化信号如正弦波时,由于累积误差的影响会产生过学习现象,进而导致系统的不稳定.为此, 提出一种新的基于CMAC的自学习控制器,它以系统的动态误差作为CMAC的激励信号, 从而避免了累积误差的影响.仿真结果表明,该控制器不仅是有效的,而且具有很强的鲁棒 性.此外,它可以使用较高的学习速率,实时性强.     

一种自适应CMAC在交流励磁水轮发电系统中仿真研究

在分析常规CMAC结构的基础上,针对一类非线性、参数时变和不确定的控制系统,提出了一种自适应CMAC神经网络的控制器．该控制器以系统动态误差和给定信号量作为CMAC的激励信号,并与自适应线性神经元网络相结合构成系统的复合控制．为了验证其有效性,将其应用到交流励磁水轮发电机系统的多变量非线性控制中,并与常规的PID控制效果进行了比较．仿真结果表明,该控制器具有较强鲁棒性和自适应能力,控制品质优良。     

Direct adaptive iterative learning control of nonlinear systems using an output-recurrent fuzzy neural network

In this paper, a direct adaptive iterative learning control (DAILC) based on a new output-recurrent fuzzy neural network (ORFNN) is presented for a class of repeatable nonlinear systems with unknown nonlinearities and variable initial resetting errors. In order to overcome the design difficulty due to initial state errors at the beginning of each iteration, a concept of time-varying boundary layer is employed to construct an error equation. The learning controller is then designed by using the given ORFNN to approximate an optimal equivalent controller. Some auxiliary control components are applied to eliminate approximation error and ensure learning convergence. Since the optimal ORFNN parameters for a best approximation are generally unavailable, an adaptive algorithm with projection mechanism is derived to update all the consequent, premise, and recurrent parameters during iteration processes. Only one network is required to design the ORFNN-based DAILC and the plant nonlinearities, especially the nonlinear input gain, are allowed to be totally unknown. Based on a Lyapunov-like analysis, we show that all adjustable parameters and internal signals remain bounded for all iterations. Furthermore, the norm of state tracking error vector will asymptotically converge to a tunable residual set as iteration goes to infinity. Finally, iterative learning control of two nonlinear systems, inverted pendulum system and Chua's chaotic circuit, are performed to verify the tracking performance of the proposed learning scheme.     

Adaptive CMAC neural control of chaotic systems with a PI-type learning algorithm

The cerebellar model articulation controller (CMAC) has the advantages such as fast learning property, good generalization capability and information storing ability. Based on these advantages, this paper proposes an adaptive CMAC neural control (ACNC) system with a PI-type learning algorithm and applies it to control the chaotic systems. The ACNC system is composed of an adaptive CMAC and a compensation controller. Adaptive CMAC is used to mimic an ideal controller and the compensation controller is designed to dispel the approximation error between adaptive CMAC and ideal controller. Based on the Lyapunov stability theorems, the designed ACNC feedback control system is guaranteed to be uniformly ultimately bounded. Finally, the ACNC system is applied to control two chaotic systems, a Genesio chaotic system and a Duffing–Holmes chaotic system. Simulation results verify that the proposed ACNC system with a PI-type learning algorithm can achieve better control performance than other control methods.     

Hybrid adaptive fuzzy identification and control of nonlinearsystems

We present a combined direct and indirect adaptive control scheme for adjusting an adaptive fuzzy controller, and adaptive fuzzy identification model parameters. First, using adaptive fuzzy building blocks, with a common set of parameters, we design and study an adaptive controller and an adaptive identification model that have been proposed for a general class of uncertain structure nonlinear dynamic systems. We then propose a hybrid adaptive (HA) law for adjusting the parameters. The HA law utilizes two types of errors in the adaptive system, the tracking error and the modeling error. Performance analysis using a Lyapunov synthesis approach proves the superiority of the HA law over the direct adaptive (DA) method in terms of faster and improved tracking and parameter convergence. Furthermore, this is achieved at negligible increased implementation cost or computational complexity. We prove a theorem that shows the properties of this hybrid adaptive fuzzy control system, i.e., bounds for the integral of the squared errors, and the conditions under which these errors converge asymptotically to zero are obtained. Finally, we apply the hybrid adaptive fuzzy controller to control a chaotic system, and the inverted pendulum system     

Modeling and control of carbon monoxide concentration using aneuro-fuzzy technique

Modeling and control of carbon monoxide (CO) concentration using a neuro-fuzzy technique are discussed. A self-organizing fuzzy identification algorithm (SOFIA) for identifying complex systems such as CO concentration is proposed. The main purpose of SOFIA is to reduce the computational requirement for identifying a fuzzy model. In particular, the authors simplify a procedure for finding the optimal structure of fuzzy partition. The δ rule, which is a basic learning method in neural networks, is used for parameter identification of a fuzzy model. SOFIA consists of four stages which effectively realize structure identification and parameter identification. The procedure of SOFIA is concretely demonstrated by a simple example which has been used in some modeling exercises. The identification result shows effectiveness of SOFIA. Next, the authors apply SOFIA to a prediction problem for CO concentration in the air at the busiest traffic intersection in a large city of Japan. Prediction results show that the fuzzy model is much better than a linear model. Furthermore, the authors simulate a control system for keeping CO concentration at a constant level by using the identified fuzzy model. A self-learning method for adaptively modifying controller parameters by δ rule is introduced because the dynamics of real CO concentration system changes gradually over a long period of time. Two self-learning controllers are designed in this simulation. One is a self-learning linear PI controller. The other is a self-learning fuzzy PI controller. The authors investigate robustness and adaptability of this control system for disturbance and parameter perturbation of the CO concentration model. Simulation results show that the self-learning fuzzy controller is more robust and adaptive