Quasi‐ARX neural network based adaptive predictive control for nonlinear systems

In this paper, a new switching mechanism is proposed based on the state of dynamic tracking error so that more information will be provided –not only the error but also a one up to pth differential error will be available as the switching variable. The switching index is based on the Lyapunov stability theory. Thus the switching mechanism can work more effectively and efficiently. A simplified quasi‐ARX neural‐network (QARXNN) model presented by a state‐dependent parameter estimation (SDPE) is used to derive the controller formulation to deal with its computational complexity. The switching works inside the model by utilizing the linear and nonlinear parts of an SDPE. First, a QARXNN is used as an estimator to estimate an SDPE. Second, by using SDPE, the state of dynamic tracking error is calculated to derive the switching index. Additionally, the switching formula can use an SDPE as the switching variable more easily. Finally, numerical simulations reveal that the proposed control gives satisfactory tracking and disturbance‐rejection performances. Experimental results demonstrate its effectiveness. © 2015 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

Adaptive control of discrete‐time nonlinear systems by recurrent neural networks in quasi‐sliding mode like regime

The aim of this study was to design an adaptive control strategy based on recurrent neural networks (RNNs). This neural network was designed to obtain a non‐parametric approximation (identification) of discrete‐time uncertain nonlinear systems. A discrete‐time Lyapunov candidate function was proposed to prove the convergence of the identification error. The adaptation laws to adjust the free parameters in the RNN were obtained in the same stability analysis. The control scheme used the states of the identifier, and it was developed fulfilling the necessary conditions to establish a behavior comparable with a quasi‐sliding mode regime. This controller does not use the regular form of the switching function that commonly appears in the sliding mode control designs. The Lyapunov candidate function to design the controller and the identifier simultaneously requires the existence of positive definite solutions of two different matrix inequalities. As consequence, a class of separation principle was proven when the RNN‐based identifier and the controller were designed by the same analysis. Simulations results were designed to show the behavior of the proposed controller solving the tracking problem for the trajectories of a direct current (DC) motor. The performance of the proposed controller was compared with the solution obtained when a classical proportional derivative controller and an adaptive first‐order sliding mode controller assuming poor knowledge of the plant. In both cases, the proposed controller showed superior performance when the relation between the tracking error convergence and the energy used to reach it was evaluated. Copyright © 2016 John Wiley & Sons, Ltd.     

Modular‐based adaptive control of uncertain nonlinear time‐varying systems with piecewise jumping parameters

Nonlinear time‐varying systems exist widely in practice. Therefore, it is of great theoretical importance and practical value to investigate the problem of controlling such systems. However, the results available in developing adaptive control to address such a problem are still limited. Especially a majority of them are restricted to be slowly time‐varying linear systems. This paper presents a modular‐based adaptive control scheme for parametric strict feedback nonlinear time‐varying systems. The parameters considered include both continuous and piecewise time‐varying parameters, and they are not necessarily restricted to be slowly time‐varying or infrequent jumping. The technique of adaptive backstepping with nonlinear damping is employed in the control design module, while the parameter projection algorithm is performed on the parameter estimation module. It is proved that the uniform boundedness of all closed‐loop system signals can be guaranteed with the proposed control scheme. The performance of the tracking error in the mean square sense with respect to the parameter variation rate is also established. Furthermore, perfect asymptotically tracking can be achieved when the varying rates of unknown parameters are in the space. Copyright © 2013 John Wiley & Sons, Ltd.     

Observer‐based adaptive neural control of uncertain MIMO nonlinear systems with unknown control direction

This paper investigates adaptive neural network output feedback control for a class of uncertain multi‐input multi‐output (MIMO) nonlinear systems with an unknown sign of control gain matrix. Because the system states are not required to be available for measurement, an observer is designed to estimate the system states. In order to deal with the unknown sign of control gain matrix, the Nussbaum‐type function is utilized. By using neural network, we approximated the unknown nonlinear functions and perfectly avoided the controller singularity problem. The stability of the closed‐loop system is analyzed by using Lyapunov method. Theoretical results are illustrated through a simulation example. Copyright © 2012 John Wiley & Sons, Ltd.     

Finite‐time synchronization and adaptive synchronization of memristive recurrent neural networks with delays

This paper solves the finite‐time synchronization and adaptive synchronization problems of drive‐response memristive recurrent neural networks with delays under two control methods. First, the state‐feedback control rule containing delays and the adaptive control rule are designed for realizing synchronization of drive‐response memristive recurrent neural networks in finite time. Then, on the basis of the Lyapunov stability theory, many algebraic sufficient conditions are obtained to guarantee finite‐time synchronization and adaptive synchronization of drive‐response memristive recurrent neural networks via two control methods, which are easily verified. In addition, the estimation of the upper bounds of the settling time of finite‐time synchronization is obtained. Lastly, to illustrate the effectiveness of the obtained theoretical results, two examples are given.     

Decentralized adaptive control of nonlinear large‐scale pure‐feedback interconnected systems with time‐varying delays

In this paper, an adaptive decentralized neural control problem is addressed for a class of pure‐feedback interconnected system with unknown time‐varying delays in outputs interconnections. By taking advantage of implicit function theorem and the mean‐value theorem, the difficulty from the pure‐feedback form is overcome. Under a wild assumption that the nonlinear interconnections are assumed to be bounded by unknown nonlinear functions with outputs, the difficulties from unknown interconnections are dealt with, by introducing continuous packaged functions and hyperbolic tangent functions, and the time‐varying delays in interconnections are compensated by Lyapunov–Krasovskii functional. Radial basis function neural network is used to approximate the unknown nonlinearities. Dynamic surface control is successfully extended to eliminate ‘the explosion of complexity’ problem in backstepping procedure. To reduce the computational burden, minimal learning parameters technique is successfully incorporated into this novel control design. A delay‐independent decentralized control scheme is proposed. With the adaptive neural decentralized control, only one estimated parameter need to be updated online for each subsystem. Therefore, the controller is more simplified than the existing results. Also, semiglobal uniform ultimate boundedness of all of the signals in the closed‐loop system is guaranteed. Finally, simulation studies are given to demonstrate the effectiveness of the proposed design scheme. Copyright © 2013 John Wiley & Sons, Ltd.     

Observer‐based nonlinear feedback decentralized neural adaptive dynamic surface control for large‐scale nonlinear systems

This paper presents a nonlinear gain feedback technique for observer‐based decentralized neural adaptive dynamic surface control of a class of large‐scale nonlinear systems with immeasurable states and uncertain interconnections among subsystems. Neural networks are used in the observer design to estimate the immeasurable states and thus facilitate the control design. Besides avoiding the complexity problem in traditional backstepping, the new nonlinear feedback gain method endows an automatic regulation ability into the pioneering dynamic surface control design and improvement in dynamic performance. Novel Lyapunov function is designed and rigorous stability analysis is given to show that all the closed‐loop signals are kept semiglobally uniformly ultimately bounded, and the output tracking errors can be guaranteed to converge to sufficient area around zero, with the bound values characterized by design parameters in an explicit manner. Simulation and comparative results are shown to verify effectiveness.     

Cooperative adaptive neural partial tracking errors constrained control for nonlinear multi‐agent systems

This paper considers the problem of partial tracking errors constrained for high‐order nonlinear multi‐agent systems in strict‐feedback form. In the control design, radial‐based function neural networks are utilized to identify uncertain nonlinear functions, and a cooperative adaptive dynamic surface control is proposed to avoid the explosion of complexity in the backstepping technique. Based on the minimal learning parameter technique and the predefined performance approach, a novel cooperative adaptive neural network control method is developed. The proposed controller is able to guarantee that all the closed‐loop network signals are cooperative semi‐globally uniformly ultimately bounded, and partial tracking errors confine all times within the predefined bounds. Finally, simulation example and comparative example with previous methods are given to verify and clarify the effectiveness of the new design procedure. Copyright © 2016 John Wiley & Sons, Ltd.     

Adaptive backstepping neural control of state‐delayed nonlinear systems with full‐state constraints and unmodeled dynamics

In this paper, the problem of adaptive neural control is discussed for a class of strict‐feedback time‐varying delays nonlinear systems with full‐state constraints and unmodeled dynamics, as well as distributed time‐varying delays. The considered nonlinear system with full‐state constraints is transformed into a nonlinear system without state constraints by introducing a one‐to‐one asymmetric nonlinear mapping. Based on modified backstepping design and using radial basis function neural networks to approximate the unknown smooth nonlinear function and using a dynamic signal to handle dynamic uncertainties, a novel adaptive backstepping control is developed for the transformed system without state constraints. The uncertain terms produced by state time delays and distributed time delays are compensated for by constructing appropriate Lyapunov‐Krasovskii functionals. All signals in the closed‐loop system are proved to be semiglobally uniformly ultimately bounded. A numerical example is provided to illustrate the effectiveness of the proposed design scheme.     

Neural network‐based adaptive control of piezoelectric actuators with unknown hysteresis

This paper proposes a neural network (NN)‐based adaptive control of piezoelectric actuators with unknown hysteresis. Based on the classical Duhem model described by a differential equation, the explicit solution to the equation is explored and a new hysteresis model is constructed as a linear model in series with a piecewise continuous nonlinear function. An NN‐based dynamic pre‐inversion compensator is designed to cancel out the effect of the hysteresis. With the incorporation of the pre‐inversion compensator, an adaptive control scheme is proposed to have the position of the piezoelectric actuator track the desired trajectory. This paper has three distinct features. First, it applies the NN to online approximate complicated piecewise continuous unknown nonlinear functions in the explicit solution to Duhem model. Second, an observer is designed to estimate the output of hysteresis of piezoelectric actuator based on the system input and output. Third, the stability of the controlled piezoelectric actuator with the observer is guaranteed. Simulation results for a practical system validate the effectiveness of the proposed method in this paper. Copyright © 2008 John Wiley & Sons, Ltd.     

Adaptive neural dynamic surface control of MIMO nonlinear time delay systems with time‐varying actuator failures

In this paper, an adaptive dynamic surface control approach is developed for a class of multi‐input multi‐output nonlinear systems with unknown nonlinearities, bounded time‐varying state delays, and in the presence of time‐varying actuator failures. The type of the considered actuator failure is that some unknown inputs may be stuck at some time‐varying values where the values, times, and patterns of the failures are unknown. The considered actuator failure can cover most failures that may occur in actuators of the systems. With the help of neural networks to approximate the unknown nonlinear functions and combining the dynamic surface control approach with the backstepping design method, a novel control approach is constructed. The proposed design method does not require a priori knowledge of the bounds of the unknown time delays and actuator failures. The boundedness of all the closed‐loop signals is guaranteed, and the tracking errors are proved to converge to a small neighborhood of the origin. The proposed approach is employed for a double inverted pendulums benchmark as well as a chemical reactor system. The simulation results show the effectiveness of the proposed method. Copyright © 2016 John Wiley & Sons, Ltd.     

Neural network‐based adaptive attitude tracking control for flexible spacecraft with unknown high‐frequency gain

Adaptive control design using neural networks (a) is investigated for attitude tracking and vibration stabilization of a flexible spacecraft, which is operated at highly nonlinear dynamic regimes. The spacecraft considered consists of a rigid body and two flexible appendages, and it is assumed that the system parameters are unknown and the truncated model of the spacecraft has finite but arbitrary dimension as well, for the purpose of design. Based on this nonlinear model, the derivation of an adaptive control law using neural networks (NNs) is treated, when the dynamics of unstructured and state‐dependent nonlinear function are completely unknown. A radial basis function network that is used here for synthesizing the controller and adaptive mechanisms is derived for adjusting the parameters of the network and estimating the unknown parameters. In this derivation, the Nussbaum gain technique is also employed to relax the sign assumption for the high‐frequency gain for the neural adaptive control. Moreover, systematic design procedure is developed for the synthesis of adaptive NN tracking control with L₂ ‐gain performance. The resulting closed‐loop system is proven to be globally stable by Lyapunov's theory and the effect of the external disturbances and elastic vibrations on the tracking error can be attenuated to the prescribed level by appropriately choosing the design parameters. Numerical simulations are performed to show that attitude tracking control and vibration suppression are accomplished in spite of the presence of disturbance torque/parameter uncertainty. Copyright © 2009 John Wiley & Sons, Ltd.     

基于神经网络的一类非线性系统自适应滑模控制

针对可以分解为标称系统和不确定系统两部分的SISO非线性系统,提出了一种基于神经网络的自适应滑模控制方案。控制器由标称控制律和补偿控制律组成,标称控制律用来控制标称系统,补偿控制律是基于Lyapunov稳定性理论设计的自适应神经滑模控制律,用来控制不确定系统,而神经网络用来逼近系统的不确定性。理论分析和计算机仿真都证明,本文提出的控制策略不但能解决这类系统的轨迹跟踪控制问题,而且可以保证闭环系统的渐近稳定性。     

基于差分进化小波神经网络的多维非线性系统辨识

提出一种基于差分进化小波神经网络(DE-WNN)的多维非线性系统辨识方法。利用差分进化算法同时优化小波神经网络的结构和参数,简化网络结构,提高小波神经网络的学习精度和收敛速度。将该方法应用于多维非线性系统的辨识,并与RBF神经网络和遗传小波神经网络的辨识结果进行了比较,实验结果表明,差分进化算法优化的小波神经网络隐层节点为6,迭代次数为30,网络训练时间为0.58s,辨识均方误差达到1.02×10?4,所提出的方法具有更高的辨识精度和收敛速度,能够更好的辨识出多维非线性系统。     

Neural network based terminal iterative learning control for uncertain nonlinear non‐affine systems

In this paper, a novel neural network based terminal iterative learning control method is proposed for a class of uncertain nonlinear non‐affine systems to track run‐varying reference point with initial state variance. In this new control scheme, the non‐affine terminal dynamics are converted affine, and the unrealisable recurrent network is simplified into realisable static network. As a result, the effect of initial state and control signal on terminal output can be estimated by neural network. With this estimation, the proposed control scheme can drive nonlinear non‐affine systems to track run‐varying reference point in the presence of initial state variance. Stability and convergence of this approach are proven, and numerical simulation results are provided to verify its effectiveness.     

Self‐tuning PID control of a brushless DC motor by adaptive interaction

In this paper, a self‐tuning algorithm for proportional integral derivative (PID) control based on the adaptive interaction (AI) approach theory efficiently used in artificial neural networks (ANNs) is proposed. In this approach, a system is decomposed into interconnected subsystems, and adaptation occurs in the interaction weights among these subsystems. The principle behind the adaptation algorithm is mathematically equivalent to a gradient descent algorithm. The same adaptation as the well‐known backpropagation algorithm (BPA) can be achieved without the need of a feedback network, which would propagate the errors, by applying adaptive interaction. Thereby, the ANN controller can be adapted directly without wasting calculation time in order to increase the frequency response of the controller. The velocity control of a brushless DC motor (BLDCM) under slowly and rapidly changing load conditions is simulated to demonstrate the effectiveness of the algorithm. The AI tuning algorithm was used to tune up the PID gains, and the simulation results with PID adaptation process are presented by comparing the obtained results with the adaptive PID controller based on BPNN and a conventional PID controller. © 2014 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

Robust adaptive dynamic surface control for linear time‐varying systems

In this paper, robust output‐feedback tracking control is considered for a class of linear time‐varying plants whose time‐varying parameters are unknown bounded with bounded derivatives and output is affected by unknown bounded additive disturbances. Using adaptive dynamic surface control technique, the proposed scheme possesses the following advantages: (1) the design procedure is simple and the control law is easy to be implemented, and (2) by introducing an initialization technique, together with adjusting some design parameters, the performance of system tracking error can be guaranteed regardless of the time variation. It is proved that with the proposed scheme, all the closed‐loop signals are semi‐globally uniformly ultimately bounded. Simulation results are presented to demonstrate the effectiveness of the proposed scheme. Copyright © 2013 John Wiley & Sons, Ltd.     

Direct adaptive neural tracking control for a class of stochastic pure‐feedback nonlinear systems with unknown dead‐zone

This paper considers the problem of adaptive neural tracking control for a class of nonlinear stochastic pure‐feedback systems with unknown dead zone. Based on the radial basis function neural networks' online approximation capability, a novel adaptive neural controller is presented via backstepping technique. It is shown that the proposed controller guarantees that all the signals of the closed‐loop system are semi‐globally, uniformly bounded in probability, and the tracking error converges to an arbitrarily small neighborhood around the origin in the sense of mean quartic value. Simulation results further illustrate the effectiveness of the suggested control scheme. Copyright © 2012 John Wiley & Sons, Ltd.     

Robust adaptive estimation of nonlinear system with time‐varying parameters

The vast majority of available parameter estimation methods assume that the parameters to be estimated are constant or slowly time‐varying and mainly depend on a predictor or observer design so that a large adaptive gain must be used to achieve fast adaptation; this may result in high‐frequency oscillations when the system subjects to a large source of uncertainties or disturbances. This paper is concerned with adaptive online estimation of time‐varying parameters for two kinds of linearly parameterized nonlinear systems. By dividing the time into small intervals, the time‐varying parameters are approximated in terms of polynomials with unknown coefficients. Then a novel adaptive law design methodology is developed to estimate those constant coefficients, for which the parameter estimation error information is explicitly derived and used to drive the adaptations. To guarantee the continuity of the parameter estimation for all time, a parameter resetting scheme is introduced at the beginning of each interval. Finite‐time estimation convergence and the robustness against disturbances are all proved. Extensive simulation examples are provided to demonstrate the efficacy of the proposed algorithms for estimating time‐varying parameters. Copyright © 2014 John Wiley & Sons, Ltd.     

A new model reference adaptive control for linear time‐varying systems

Recent results on the adaptive control of linear time‐varying systems have considered mostly the case in which the range or rate of parameter variations is small. In this paper, a new state feed‐back model reference adaptive control is developed for systems with bounded arbitrary parameter variations. The important feature of the proposed adaptive control is an uncertainty estimation algorithm, which guarantees almost zero tracking error. Note that the conventional parameter estimation algorithm in the adaptive control guarantees only bounded tracking error. Copyright © 2000 John Wiley & Sons, Ltd.