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.     

Fuzzy-identification-based adaptive backstepping control using a self-organizing fuzzy system

In this paper, a fuzzy-identification-based adaptive backstepping control (FABC) scheme is proposed. The FABC system is composed of a backstepping controller and a robust controller. The backstepping controller, which uses a self-organizing fuzzy system (SFS) with the structure and parameter learning phases to on-line estimate the controlled system dynamics, is the principal controller, and the robust controller is designed to dispel the effect of approximation error introduced by the SFS. The developed SFS automatically generates and prunes the fuzzy rules by the proposed structure adaptation algorithm and the parameters of the fuzzy rules and membership functions tunes on-line in the Lyapunov sense. Thus, the overall closed-loop FABC system can guarantee that the tracking error and parameter estimation error are uniformly ultimately bounded; and the tracking error converges to a desired small neighborhood around zero. Finally, the proposed FABC system is applied to a chaotic dynamic system to show its effectiveness. The simulation results verify that the proposed FABC system can achieve favorable tracking performance even with unknown controlled system dynamics.     

Intelligent complementary sliding-mode control with dead-zone parameter modification

This paper proposes an intelligent complementary sliding-mode control (ICSMC) system which is composed of a computed controller and a robust controller. The computed controller includes a neural dynamics estimator and the robust compensator is designed to prove a finite L₂-gain property. The neural dynamics estimator uses a recurrent neural fuzzy inference network (RNFIN) to approximate the unknown system term in the sense of the Lyapunov function. In traditional neural network learning process, an over-trained neural network would force the parameters to drift and the system may become unstable eventually. To resolve this problem, a dead-zone parameter modification is proposed for the parameter tuning process to stop when tracking performance index is smaller than performance threshold. To investigate the capabilities of the proposed ICSMC approach, the ICSMC system is applied to a one-link robotic manipulator and a DC motor driver. The simulation and experimental results show that favorable control performance can be achieved in the sense of the L₂-gain robust control approach by the proposed ICSMC scheme.     

Robust adaptive fuzzy tracking control for a class of strict-feedback nonlinear systems based on backstepping technique

In this paper, the robust adaptive fuzzy tracking control problem is discussed for a class of perturbed strict-feedback nonlinear systems. The fuzzy logic systems in Mamdani type are used to approximate unknown nonlinear functions. A design scheme of the robust adaptive fuzzy controller is proposed by use of the backstepping technique. The proposed controller guarantees semi-global uniform ultimate boundedness of all the signals in the derived closed-loop system and achieves the good tracking performance. The possible controller singularity problem which may occur in some existing adaptive control schemes with feedback linearization techniques can be avoided. In addition, the number of the on-line adaptive parameters is not more than the order of the designed system. Finally, two simulation examples are used to demonstrate the effectiveness of the proposed control scheme.     

Design of intelligent power controller for DC–DC converters using CMAC neural network

DC–DC converters are the devices which can convert a certain electrical voltage to another level of electrical voltage. They are very popularly used because of the high efficiency and small size. This paper proposes an intelligent power controller for the DC–DC converters via cerebella model articulation controller (CMAC) neural network approach. The proposed intelligent power controller is composed of a CMAC neural controller and a robust controller. The CMAC neural controller uses a CMAC neural network to online mimic an ideal controller, and the robust controller is designed to achieve L ₂ tracking performance with desired attenuation level. Finally, a comparison among a PI control, adaptive neural control and the proposed intelligent power control is made. The experimental results are provided to demonstrate the proposed intelligent power controller can cope with the input voltage and load resistance variations to ensure the stability while providing fast transient response and simple computation.     

Reliable control design for composite‐driven scheme based on delay networked T‐S fuzzy system

This paper is focused on reliable controller design for a composite‐driven scheme of networked control systems via Takagi‐Sugeno fuzzy model with probabilistic actuator fault under time‐varying delay. The proposed scheme is distinguished from the other schemes as mentioned in this paper. Aims of this article are to solve the control problem by considering the H_∞, dissipative, and L₂?L_∞ constraints in a unified way. Firstly, to improve the efficient utilization of bandwidth, the adaptive composite‐driven scheme is introduced. In such a scenario, the channel transmission mechanism can be adjusted between adaptive event‐triggered generator scheme and time‐driven scheme. In this study, the threshold is dependent on a new adaptive law, which can be obtained online rather than a predefined constant. With a constant threshold, it is difficult to get the variation of the system. Secondly, a novel fuzzy Lyapunov‐Krasovskii functional is constructed to design the fuzzy controller, and delay‐dependent conditions for stability and performance analysis of the control system are obtained. Then, LMI‐based conditions for the existence of the desired fuzzy controller are presented. Finally, an inverted pendulum that is controlled through the channel is provided to illustrate the effectiveness of the proposed method.     

Eso‐Based Adaptive Robust Control of Dual Motor Driving Servo System

Based on extended state observer (ESO), we propose an adaptive robust control (ARC) for a dual motor driving servo system, in which there exist nonlinearities affecting control performance. To apply ESO and estimate the lumped uncertainty online, backlash and friction are analyzed and the nonlinear model of the plant is derived. We achieve several control objectives. First, the bias torque is considered in order to eliminate the effect of backlash. Second, the speed feedback is used to maintain the speed synchronization of motors. Then, to achieve feedforward control, finite‐time ESO is designed to estimate the unknown nonlinearities online. Furthermore, the ESO‐based adaptive robust controller is designed to guarantee L_∞ of tracking error by an initialization method, maintaining the transient performance of tracking behavior. Finally, extensive experimental results on a practical test rig validate the effectiveness of our proposed method.     

非仿射非线性系统的自主构架模糊控制器

针对SISO非仿射非线性系统,提出一种新型自主构架模糊控制器.此控制器由鲁棒控制器与自主构架模糊系统构成.模糊系统初始只含有一条规则,根据系统误差和ε完备性2条准则自主增加规则及隶属函数,从而完善模糊系统结构,逼近非线性系统不确定量.模糊系统利用"伪模糊输出"法对新增规则后件初始化,考虑到实际计算能力,采用替换隶属函数机制限制规则数目.通过理论推导证明了系统的稳定性,理论和半实物仿真实验验证了所提出方法的有效性.     

Robust neural network control system design for linear ultrasonic motor

Linear ultrasonic motor (LUSM) has much merit, such as high precision, fast control dynamics and large driving force, etc.; however, the dynamic characteristic of LUSM is nonlinear and the precise dynamic model of LUSM is difficult to obtain. To tackle this problem, this study presents a robust neural network control (RNNC) system for LUSM to track a reference trajectory with L ₂ robust tracking performance. The developed RNNC system is composed of a neural network controller and a robust controller. The neural network controller is the principal controller used to mimic an ideal controller and the robust controller is adopted to achieve L ₂ robust tracking performance. The developed RNNC system is then applied to control an LUSM. Experimental results show that the developed RNNC system can achieve favorable tracking performance with unknown of LUSM model.     

Adaptive event-triggered robust H∞ control for Takagi–Sugeno fuzzy networked Markov jump systems with time-varying delay

This paper considers an adaptive event-triggered robust H_∞ control for the Takagi–Sugeno (T-S) fuzzy under the networked Markov jump systems (NMJSs) with time-varying delay. First, a new adaptive event-triggered scheme is developed to guarantee the T-S fuzzy NMJSs, and as a result, communication energy consumption reduced while device efficiency is maintained. Besides, an asynchronous operation method is adopted to deal with the mismatched premise variables between the fuzzy system and the fuzzy controller. One of the main objectives of this article is to construct the fuzzy state-feedback controller (mode-dependent) in a closed-loop form for stochastic stability for all admissible parameter uncertainties with an H_∞ performance index. Different from the conventional triggering mechanism, in this paper, the parameters of the triggering function are based on a new adaptive law that is obtained online rather than a predefined constant. To achieve the less conservative control design, a new type of stochastic Lyapunov–Krasovskii functional is designed by decomposing method, in which the delay interval transforms into various equidistant subintervals in terms of linear matrix inequalities. An example of a truck-trailer application is used to demonstrate the effectively of the proposed algorithms.     

Robust adaptive fuzzy tracking control for a class of strict-feedback nonlinear systems based on backstepping technique

In this paper, the robust adaptive fuzzy tracking control problem is discussed for a class of perturbed strict-feedback nonlinear systems. The fuzzy logic systems in Mamdani type are used to approximate unknown nonlinear functions. A design scheme of the robust adaptive fuzzy controller is proposed by use of the backstepping technique. The proposed controller guarantees semi-global uniform ultimate boundedness of all the signals in the derived closed-loop system and achieves the good tracking performance. The possible controller singularity problem which may occur in some existing adaptive control schemes with feedback linearization techniques can be avoided. In addition, the number of the on-line adaptive parameters is not more than the order of the designed system. Finally, two simulation examples are used to demonstrate the effectiveness of the proposed control scheme.     

ADAPTIVE FUZZY‐BASED MIXED H2/H∞ TRACKING CONTROL DESIGN IN UNCERTAIN ROBOTIC SYSTEMS

In this study, an adaptive fuzzy‐based mixed H₂/H_∞ tracking control design is developed in robotic systems under unknown or uncertain plant parameters and external disturbances. The mixed H₂/H_∞ control design has the advantage of both H₂ optimal control performance and H_∞ robust control performance and the fuzzy adaptive control scheme is used to compensate for the plant uncertainties. By virtue of the skew‐symmetric property in the robotic systems and adequate choice of state variable transformation, sufficient conditions are developed for the adaptive fuzzy‐based mixed H₂/H_∞ tracking control problems in terms of a pair of coupled algebraic equations instead of a pair of coupled differential equations. The proposed methods are simple and the coupled algebraic equations can be solved analytically. Simulation results indicate that the desired performance of the proposed adaptive fuzzy‐based mixed H₂/H_∞ tracking control schemes for the uncertain robotic systems can be achieved.     

Robust L1 output tracking control for uncertain networked control systems described by T-S fuzzy model with distributed delays

This paper concentrates on investigating the robust L₁ output tracking control problem for the networked control systems described by Takagi–Sugeno fuzzy model with distributed delays and uncertainties. First, according to the parallel distributed compensation and Lyapunov theory, a fuzzy delay-dependent and basis-dependent Lyapunov–Krasovskii function that contributes to reducing the conservatism is constructed. Second, the L₁ performance criterion guaranteeing the asymptotic stability of the corresponding tracking control system and satisfying the prescribed tracking performance is derived. Furthermore, the output tracking control problem is converted into a convex optimisation problem. Finally, the results from simulation certify the effectiveness of the designed controller.     

Robust H ∞ and adaptive tracking control against actuator faults with a linearised aircraft application

This article studies the problem of designing adaptive fault-tolerant H _∞ tracking controllers for a class of aircraft flight systems against general actuator faults and bounded perturbations. A robust adaptive state-feedback controller is constructed by a stabilising controller gain and an adaptive control gain function. Using mode-dependent Lyapunov functions, linear matrix inequality-based conditions are developed to find the controller gain such that disturbance attenuation performance is optimised. Adaptive control schemes are proposed to estimate the unknown controller parameters on-line for unparametrisable stuck faults and perturbation compensations. Based on Lyapunov stability theory, it is shown that the resulting closed-loop systems can guarantee asymptotic tracking with H _∞ performances in the presence of faults on actuators and perturbations. An application to a decoupled linearised dynamic aircraft system and its simulation results are given.     

Adaptive dynamic CMAC neural control of nonlinear chaotic systems with L2 tracking performance

The advantage of using cerebellar model articulation control (CMAC) network has been well documented in many applications. However, the structure of a CMAC network which will influence the learning performance is difficult to select. This paper proposes a dynamic structure CMAC network (DSCN) which the network structure can grow or prune systematically and their parameters can be adjusted automatically. Then, an adaptive dynamic CMAC neural control (ADCNC) system which is composed of a computation controller and a robust compensator is proposed via second-order sliding-mode approach. The computation controller containing a DSCN identifier is the principal controller and the robust compensator is designed to achieve L₂ tracking performance with a desired attenuation level. Moreover, a proportional–integral (PI)-type adaptation learning algorithm is derived to speed up the convergence of the tracking error in the sense of Lyapunov function and Barbalat’s lemma, thus the system stability can be guaranteed. Finally, the proposed ADCNC system is applied to control a chaotic system. The simulation results are demonstrated that the proposed ADCNC scheme can achieve a favorable control performance even under the variations of system parameters and initial point.     

Synchronization and tracking control for multi‐motor driving servo systems with backlash and friction

This paper presents a novel switching controller incorporated with backlash and friction compensations, which is utilized to achieve speed synchronization among multi‐motor and load position tracking. The proposed controller consists of two parts: synchronization and tracking control in contact mode and robust control in backlash mode, where a function characterizing whether backlash occurs is used for switching between two modes. Using the proposed switching controller, several control objectives are achieved. Firstly, the coupling problem of speed synchronization and load tracking in contact mode is addressed by introducing a switching plane. Secondly, based on the switching plane, an improved prescribed performance function is introduced to attain load tracking with prescribed performances, and L_∞ performance of speed synchronization is guaranteed by initialization method, maintaining the transient performance of synchronization behavior. Thirdly, the lumped uncertain nonlinearity including friction and other uncertain functions is compensated by Chebyshev neural network in contact mode. Furthermore, a robust control is adopted in backlash mode to make system traverse backlash at an exponential rate and simultaneously eliminate low‐speed crawling phenomenon of LuGre friction. Finally, comparative simulations on four‐motor driving servo system are provided to verify the effectiveness and reliability. Copyright © 2015 John Wiley & Sons, Ltd.     

Decentralised indirect adaptive output feedback fuzzy H ∞ tracking design for a class of large-scale nonlinear systems

A novel decentralised indirect adaptive output feedback fuzzy controller with a compensation controller and an H _∞ tracking controller is presented for a class of uncertain large-scale nonlinear systems in this article. The compensator adaptively compensates for interconnections between subsystems as well as mismatched errors, while the H _∞ controller suppresses the effect of external disturbances. Based upon the combination of fuzzy inference systems, a state observer, H _∞ tracking technique and the strictly positive real condition, the proposed overall observer-based decentralised algorithm guarantees not only asymptotical tracking of reference trajectories but also an arbitrary small attenuation level of the unmodelled error dynamics including the disturbances on the tracking control. Simulation results substantiate the effectiveness of the proposed scheme.     

H α tracking of uncertain SISO nonlinear systems: an observer-based adaptive fuzzy approach

Observer-based adaptive fuzzy H _∞ control is proposed to achieve H _∞ tracking performance for a class of nonlinear systems, which are subject to model uncertainty and external disturbances and in which only a measurement of the output is available. The control scheme is tested in the cart-pole balancing problem.     

Adaptive output feedback tracking controller for a class of uncertain strict feedback nonlinear systems in the absence of state measurements

In this article, design of an adaptive control scheme for a class of uncertain single-input single-output systems in strict feedback form via a backstepping technique has been proposed. It is assumed that system output and its derivatives are available. By virtue of the observability concept, it is shown that for this class of systems there exists a one-to-one map, which maps output and its derivatives to system states. By means of this mapping and using linearly parametrised approximators, such as fuzzy logic systems or neural networks, the uncertain nonlinear dynamics and unavailable states are estimated. The proposed adaptive controller guarantees that the closed-loop system is uniformly ultimately bounded and the influence of minimum approximation error on the L ₂-norm of the output tracking error is attenuated arbitrarily. The effectiveness of the proposed scheme has been demonstrated through simulation results.     

MIXED H2/H∞ ADAPTIVE TRACKING CONTROL DESIGN FOR UNCERTAIN CONSTRAINED ROBOTS

In this study, a PID‐type controller incorporating an adaptive learning scheme for the mixed H₂/H_∞ tracking performance is developed for constrained robots under unknown or uncertain plant parameters and external disturbances. The mixed H₂/H_∞ control design has the advantage of both H₂ optimal control performance and H_∞ robust control performance and the adaptive control scheme is used to compensate the plant uncertainties. By virtue of the skew‐symmetric property of the constrained robotic systems and an adequate choice of state variable transformation, sufficient conditions are developed for the adaptive mixed H₂/H_∞ tracking control problems in terms of a pair of coupled algebraic equations instead of a pair of coupled nonlinear differential equations. The proposed methods are simple and the coupled algebraic equations can be solved analytically. Simulation results indicate that the desired performance of the proposed adaptive mixed H₂/H_∞ tracking control schemes for the uncertain constrained robotic systems can be achieved.