Control of robots using radial basis function neural networks with dead‐zone

In this paper, we examine the control of robot manipulators utilizing a Radial Basis Function (RBF) neural network. We are able to remove the typical requirement of Persistence of Excitation (PE) for the desired trajectory by introducing an error minimizing dead‐zone in the learning dynamics of the neural network. The dead‐zone freezes the evolution of the RBF weights when the performance error is within a bounded region about the origin. This guarantees that the weights do not go unbounded even if the PE condition is not imposed. Utilizing protection ellipsoids we derive conditions on the feedback gain matrices that guarantee that the origin of the closed loop system is semi‐globally uniformly bounded. Simulations are provided illustrating the techniques. Copyright © 2011 John Wiley & Sons, Ltd.     

Indirect adaptive control of nonlinear system via dynamic multilayer neural networks with multi‐time scales

This paper deals with adaptive nonlinear identification and trajectory tracking problem via dynamic multilayer neural network with different time scales. By means of a Lyapunov‐like analysis, we determine stability conditions for the on‐line identification. Then, a sliding mode controller is designed for trajectory tracking with consideration of the modeling error and disturbance. The main contributions of the paper lie in the following aspects. First, we extend our prior identification results of single‐layer dynamic neural networks with multi‐time scales to those of multilayer case. Second, the e‐modification in standard use in adaptive control is introduced in the on‐line update laws to guarantee bounded weights and bounded identification errors. Third, the potential singularity problem in controller design is solved by using new update laws for the NN weights so that the control signal is guaranteed bounded. The stability of proposed controller is proved by using Lyapunov function. Simulation results demonstrate the effectiveness of the proposed algorithm. Copyright © 2014 John Wiley & Sons, Ltd.     

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.     

Adaptive neural control for nonstrict‐feedback stochastic nonlinear time‐delay systems with input and output constraints

This paper investigates an adaptive neural tracking control for a class of nonstrict‐feedback stochastic nonlinear time‐delay systems with input saturation and output constraint. First, the Gaussian error function is used to represent a continuous differentiable asymmetric saturation model. Second, the appropriate Lyapunov‐Krasovskii functional and the property of hyperbolic tangent functions are used to compensate the time‐delay effects, the neural network is used to approximate the unknown nonlinearities, and a barrier Lyapunov function is designed to ensure that the output parameters are restricted. At last, based on Lyapunov stability theory, a robust adaptive neural control method is proposed, and the designed controller decreases the number of learning parameters and thus reduces the computational burden. It is shown that the designed neural controller can ensure that all the signals in the closed‐loop system are 4‐Moment (or 2 Moment) semi‐globally uniformly ultimately bounded and the tracking error converges to a small neighborhood of the origin. Two examples are given to further verify the effectiveness of the proposed approach.     

Adaptive TS‐FNN control for a class of uncertain multi‐time‐delay systems: The exponentially stable sliding mode‐based approach

This paper presents an adaptive Takagi–Sugeno fuzzy neural network (TS‐FNN) control for a class of multiple time‐delay uncertain nonlinear systems. First, we develop a sliding surface guaranteed to achieve exponential stability while considering mismatched uncertainty and unknown delays. This exponential stability result based on a novel Lyapunov–Krasovskii method is an improvement when compared with traditional schemes where only asymptotic stability is achieved. The stability analysis is transformed into a linear matrix inequalities problem independent of time delays. Then, a sliding mode control‐based TS‐FNN control scheme is proposed to achieve asymptotic stability for the controlled system. Since the TS‐FNN combines TS fuzzy rules and a neural network structure, fewer numbers of fuzzy rules and tuning parameters are used compared with the traditional pure TS fuzzy approach. Moreover, all the fuzzy membership functions are tuned on‐line even in the presence of input uncertainty. Finally, simulation results show the control performance of the proposed scheme. Copyright © 2008 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.     

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.     

A genetic‐based neuro‐fuzzy controller for blind equalization of time‐varying channels

This paper presents a neuro‐fuzzy network (NFN) where all its parameters can be tuned simultaneously using genetic algorithms (GAs). The approach combines the merits of fuzzy logic theory, neural networks and GAs. The proposed NFN does not require a priori knowledge about the system and eliminates the need for complicated design steps such as manual tuning of input–output membership functions, and selection of fuzzy rule base. Although, only conventional GAs have been used, convergence results are very encouraging. A well‐known numerical example derived from literature is used to evaluate and compare the performance of the network with other equalizing approaches. Simulation results show that the proposed neuro‐fuzzy controller, all parameters of which have been tuned simultaneously using GAs, offers advantages over existing equalizers and has improved performance. From the perspective of application and implementation, this paper is very interesting as it provides a new method for performing blind equalization. The main contribution of this paper is the use of learning algorithms to train a feed‐forward neural network for M‐ary QAM and PSK signals. This paper also provides a platform for researchers of the area for further development. Copyright © 2008 John Wiley & Sons, Ltd.     

Predictor‐based iterative neural dynamic surface control for three‐phase voltage source PWM rectifier

This paper addresses the control problem of a three‐phase voltage source pulse width modulation rectifier in the presence of parametric uncertainties and external time‐varying disturbances. An adaptive controller is designed by combining a modified dynamic surface control method and a predictor‐based iterative neural network control algorithm. Especially, neural networks with iterative update laws based on prediction errors are employed to identify the lumped uncertainties. Besides, a finite‐time‐convergent differentiator, instead of a first‐order filter, is used to obtain the time derivative of the virtual control law. Using a Lyapunov–Krasovskii functional, it is proved that all signals in the closed‐loop system are ultimately uniformly bounded. Both simulation and experimental studies are provided to show the effectiveness of the proposed approach. © 2017 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

Adaptive B‐spline neural network‐based vector control for a grid side converter in wind turbine‐DFIG systems

This paper presents a novel control system design for the grid‐side converter of doubly fed induction generator wind power generation systems. The control method proposed in this work is a vector control based on adaptive B‐spline neural network by using a simple fixed‐gain stabilizing control topology. The adaptive control is designed both for inner current loops and an outer DC‐link voltage loop of the grid side converter control system. To guarantee the control stability, the weights updating rule for the B‐spline neural network is synthesized by utilizing Lyapunov's direct method. To verify the effectiveness of the proposed control system, extensive simulations are performed using MATLAB/Simulink. Based on the simulation results, it is concluded that the proposed controller has improved performance compared to an optimum proportional integral control system. It is also relatively robust against external disturbances and variations of the control parameters. © 2015 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

Compact CMOS implementation of a low‐power,current‐mode programmable cellular neural network

We report on the design and characterization of a full‐analog programmable current‐mode cellular neural network (CNN) in CMOS technology. In the proposed CNN, a novel cell‐core topology, which allows for an easy programming of both feedback and control templates over a wide range of values, including all those required for many signal processing tasks, is employed. The CMOS implementation of this network features both low‐power consumption and small‐area occupation, making it suitable for the realization of large cell‐grid sizes. Device level and Monte Carlo simulations of the network proved that the proposed CNN can be successfully adopted for several applications in both grey‐scale and binary image processing tasks. Results from the characterization of a preliminary CNN test‐chip (8×1 array), intended as a simple demonstrator of the proposed circuit technique, are also reported and discussed. Copyright © 2001 John Wiley & Sons, Ltd.     

Direct adaptive neural control of nonlinear strict‐feedback systems with unmodeled dynamics using small‐gain approach

In this paper, a novel direct adaptive neural control approach is presented for a class of single‐input and single‐output strict‐feedback nonlinear systems with nonlinear uncertainties, unmodeled dynamics, and dynamic disturbances. Radial basis function neural networks are used to approximate the unknown and desired control signals, and a direct adaptive neural controller is constructed by combining the backstepping technique and the property of hyperbolic tangent function. It is shown that the proposed control scheme can guarantee that all signals in the closed‐loop system are semi‐globally uniformly ultimately bounded in mean square. The main advantage of this paper is that a novel adaptive neural control scheme with only one adaptive law is developed for uncertain strict‐feedback nonlinear systems with unmodeled dynamics. Simulation results are provided to illustrate the effectiveness of the proposed scheme. Copyright © 2015 John Wiley & Sons, Ltd.     

On‐line parameter estimation for a class of time‐varying continuous systems with bounded disturbances

In this paper, we proposed an on‐line parameter estimation algorithm for a class of time‐varying continuous systems with bounded disturbance. In this method, a novel polynomial approximator with a bounded regressor vector is constructed and utilized to approximate the time‐varying parameters. The direct least‐squares algorithm is employed to acquire the on‐line estimates, so that several useful properties of the direct estimation, such as fast convergence and robustness to the bounded disturbance, are reflected in our method. We have proved that the estimation error of this method is bounded. Furthermore, the bound on the Euclidean norm of the estimation error is derived. The simulation results demonstrate that this method can provide accurate estimates of time‐varying parameters even under the influence of bounded disturbance. Copyright © 2010 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 finite‐time H∞ control for extended Markov jump nonlinear systems

This paper presents a neural‐network‐based finite‐time H_∞ control design technique for a class of extended Markov jump nonlinear systems. The considered stochastic character is described by a Markov process, but with only partially known transition jump rates. The sufficient conditions for the existence of the desired controller are derived in terms of linear matrix inequalities such that the closed‐loop system trajectory stays within a prescribed bound in a fixed time interval and has a guaranteed H_∞ noise attenuation performance for all admissible uncertainties and approximation errors of the neural networks. A numerical example is used to illustrate the effectiveness of the developed theoretic results. Copyright © 2009 John Wiley & Sons, Ltd.     

Neural‐hybrid control of systems with sandwiched dead‐zones

The control of systems that have sandwiched nonsmooth nonlinearities, such as a dead‐zone sandwiched between two dynamic blocks, is addressed. An adaptive inverse control scheme using a hybrid controller structure and a neural network based inverse compensator, is proposed for such systems with unknown sandwiched dead‐zone. This neural‐hybrid controller consists of an inner loop discrete‐time feedback structure incorporated with an adaptive inverse using a neural network for the unknown dead‐zone, and an outer‐loop continuous‐time feedback control law for achieving desired output tracking. The dead‐zone compensator consists of two neural networks, one used as an estimator of the sandwiched dead‐zone function and the other for the compensation itself. The compensator neural network has neurons that can approximate jump functions such as a dead‐zone inverse. The weights of the two neural networks are tuned using a modified gradient algorithm. Simulation results are given to illustrate the performance of the proposed neural‐hybrid controller. Copyright © 2002 John Wiley & Sons, Ltd.     

Maximum power extraction on wind turbine systems using block‐backstepping with gradient dynamics control

In this work, a novel adaptive control scheme that allows driving a stand‐alone variable‐speed wind turbine system to its maximum power point is presented. The scheme is based on the regulation of the optimal rotor speed point of the wind turbine. In order to compute the rotor speed reference, a model‐based extremum‐seeking algorithm is derived. The wind speed signal is necessary to calculate this reference, and a novel artificial neural network is derived to approximate this signal. The neural network does not need off‐line learning stage, because a nonlinear dynamics for the weight vector is proposed. A block‐backstepping controller is derived to stabilize and to drive the system to the optimal power point; to avoid singularities, the gradient dynamics technique is applied to this controller. Numerical simulations are carried out to show the performance of the controller and the estimator. Copyright © 2016 John Wiley & Sons, Ltd.     

Robust hybrid estimation and rejection of multi‐frequency signals

We consider the problem of output regulation for LTI systems in the presence of unknown exosystems. The knowledge about the multi‐frequency signals exosystem consists in the maximum number of frequencies and their maximal value. The control scheme relies on two main components: an estimation algorithm, to reconstruct the signal generated by the exosystem, and a controller, to enforce the output regulation property to the closed‐loop system. To tackle the first task, we propose a hybrid observer for the estimation of the (possibly piece‐wise continuous) number and values of the frequencies contained in the exogenous signal. The hybrid observer is particularly appealing for numerical implementations, and it is combined with a self‐tuning algorithm of the free parameters (gains), thus improving its performance even in case of noisy measurements. Semi‐global exponential convergence of the estimation error is provided. As far as the second task is concerned, a robust hybrid regulator is designed for practical rejection of the multi‐frequency disturbance signal acting on the plant. The result is achieved by exploiting the frequencies estimated by the hybrid observer. The effectiveness of the proposed control scheme is shown by means of numerical simulations. Copyright © 2016 John Wiley & Sons, Ltd.     

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.     

M‐matrices and global convergence of discontinuous neural networks

The paper considers a general class of neural networks possessing discontinuous neuron activations and neuron interconnection matrices belonging to the class of M‐matrices or H‐matrices. A number of results are established on global exponential convergence of the state and output solutions towards a unique equilibrium point. Moreover, by exploiting the presence of sliding modes, conditions are given under which convergence in finite time is guaranteed. In all cases, the exponential convergence rate, or the finite convergence time, can be quantitatively estimated on the basis of the parameters defining the neural network. As a by‐product, it is proved that the considered neural networks, although they are described by a system of differential equations with discontinuous right‐hand side, enjoy the property of uniqueness of the solution starting at a given initial condition. The results are proved by a generalized Lyapunov‐like approach and by using tools from the theory of differential equations with discontinuous right‐hand side. At the core of the approach is a basic lemma, which holds under the assumption of M‐matrices or H‐matrices, and enables to study the limiting behaviour of a suitably defined distance between any pair of solutions to the neural network. Copyright © 2006 John Wiley & Sons, Ltd.