Synchronization in nonlinear complex networks with multiple time‐varying delays via adaptive aperiodically intermittent control

This article is concerned with the problem of synchronization in nonlinear complex networks with multiple time‐varying delays via adaptive aperiodically intermittent control. The couplings inside nodes are assumed to be nonlinear and subject to multiple time‐varying delays. Meanwhile, the connection topology among the nodes can be directed and weighted. Then, the adaptive aperiodically intermittent control method is employed to realize synchronization and automatic modification to compensate the changes in dynamic errors. In addition, several synchronization criteria are rigorously induced based on the Lyapunov stability theory. Finally, the proposed control method is evaluated by utilizing numerical simulation. The results can be also applied to linear complex networks with delays.     

Evaluation and comparison of GHz‐range LC oscillators using time‐varying root‐locus

This paper presents a comprehensive comparison between complementary metal‐oxide‐semiconductor (CMOS) LC‐oscillator topologies often used in GHz‐range transceivers. The comparison utilizes the time‐varying root‐locus (TVRL) method to add new insights into the operation of different oscillators. The paper focuses on the treatment of the TVRL trajectories obtained for different oscillators and establishes links between the trajectories and physical phenomena in oscillators. The evaluation of the root trajectories shows the advantages of the TVRL method for comparing oscillator topologies, which is also extended towards the analysis of voltage‐controlled oscillators. The necessary circuit simplifications required in closed‐form root‐locus analysis are avoided by the TVRL, which allows precise oscillator comparison and reveals details on the topology specifics. The derived conclusions have been verified by the Cadence Spectre‐RF simulator on 130‐nm CMOS process. Copyright © 2011 John Wiley & Sons, Ltd.     

Adaptive backstepping repetitive learning control design for nonlinear discrete‐time systems with periodic uncertainties

This paper addresses a tracking problem for uncertain nonlinear discrete‐time systems in which the uncertainties, including parametric uncertainty and external disturbance, are periodic with known periodicity. Repetitive learning control (RLC) is an effective tool to deal with periodic unknown components. By using the backstepping procedures, an adaptive RLC law with periodic parameter estimation is designed. The overparameterization problem is overcome by postponing the parameter estimation to the last backstepping step, which could not be easily solved in robust adaptive control. It is shown that the proposed adaptive RLC law without overparameterization can guarantee the perfect tracking and boundedness of the states of the whole closed‐loop systems in presence of periodic uncertainties. In addition, the effectiveness of the developed controller is demonstrated by an implementation example on a single‐link flexible‐joint robot. Copyright © 2014 John Wiley & Sons, Ltd.     

Floquet theory and non‐linear perturbation analysis for oscillators with differential‐algebraic equations

Oscillators are key components of electronic systems. In RF communication systems, they are used for frequency translation of information signals and for channel selection, and in digital electronic systems, they are used as a time reference, i.e. a clock signal, in order to synchronize operations. Undesired perturbations in practical electronic systems adversely affect the spectral and timing properties of oscillators, which is a key performance limiting factor, being a major contributor to bit‐error‐rate (BER) of RF communication systems, and creating synchronization problems in clocked and sampled‐data systems. Characterizing how perturbations affect oscillators is therefore crucial for practical applications. The traditional approach to analysing perturbed nonlinear systems (i.e. linearization) is not valid for oscillators. In this paper, we present a theory and efficient numerical methods, for non‐linear perturbation and noise analysis of oscillators described by a system of differential‐algebraic equations (DAEs). Our techniques can be used in characterizing phase noise and timing jitter due to intrinsic noise in IC devices, and evaluating the effect of substrate and supply noise on the timing properties of practical oscillators. In this paper, we also establish novel results for periodically time‐varying systems of linear DAEs, which we rely on in developing the above theory and the numerical methods. Copyright © 2000 John Wiley & Sons, Ltd.     

Nonlinear Lipschitz measure and adaptive control for stability and synchronization in delayed inertial Cohen‐Grossberg–type neural networks

In this paper, without transforming the original inertial neural networks into the first‐order differential equation by some variable substitutions, time‐varying delays are introduced into inertial Cohen‐Grossberg–type networks and the existence, the uniqueness, and the asymptotic stability and synchronisation for the neural networks are investigated. Firstly, the existence of a unique equilibrium point is proved by using nonlinear Lipschitz measure method. Second, by finding a new Lyapunov‐Krasovskii functional, some sufficient conditions are derived to ensure the asymptotic stability, the asymptotic synchronization, and the asymptotic adaptive synchronization. The results of this paper are new and they complete previously known results. We illustrate the effectiveness of the approach through a few examples.     

Real‐time identification of nonlinear multiple‐input–multiple‐output systems with unknown input time delay using Wiener model with Neuro‐Laguerre structure

In this article, a real‐time block‐oriented identification method for nonlinear multiple‐input–multiple‐output systems with input time delay is proposed. The proposed method uses the Wiener structure, which consists of a linear dynamic block (LDB) followed by a nonlinear static block (NSB). The LDB is described by the Laguerre filter lattice, whereas the NSB is characterized using the neural networks. Due to the online adaptation of the parameters, the proposed method can cope with the changes in the system parameters. Moreover, the convergence and bounded modeling error are shown using the Lyapunov direct method. Four practical case studies show the effectiveness of the proposed algorithm in the open‐loop and closed‐loop identification scenarios. The proposed method is compared with the recently published methods in the literature in terms of the modeling accuracy, parameter initialization, and required information from the system.     

Discrete‐time periodic adaptive control for parametric systems with non‐sector nonlinearities

In this paper, a periodic adaptive control approach is proposed for a class of discrete‐time parametric systems with non‐sector nonlinearities. The proposed periodic adaptive control law is characterized by either one‐period delayed parametric updating or two‐period delayed parametric updating when input gain contains periodic unknowns. Logarithmic‐type discrete Lyapunov function is employed to handle the difficulties caused by the uncertainties that do not satisfy the linear growth condition. Some extensions to nonlinear systems with multiple unknown parameters and time‐varying input gain, tracking tasks, as well as higher‐order systems in canonical form, are also discussed. Copyright © 2013 John Wiley & Sons, Ltd.     

Synchronous and asynchronous operation in dual‐band VCOs

We present a comprehensive analysis of the asynchronous and synchronous operations of fourth‐order oscillators underlying dual‐band voltage‐controlled oscillators. We analyze the occurrence of the self‐synchronization phenomenon (internal resonance) if the ratio of normal frequencies is nearly a ratio of integers, which is 1:3 in the cubic approximation of the nonlinear oscillator characteristic. In this case, we have the simultaneous presence of 2 oscillations with a frequency ratio 1:3, which was demonstrated to be very effective in generating high‐frequency signals in mm‐wave range. The analysis is carried out by developing an analytical approach relying on the averaging principle, as it follows the van der Pol method. The averaging equations, derived simply by a quadrature, allow us to analyze easily the stationary and transient oscillations, and their stability, both in asynchronous and synchronous operations. Expressions for the amplitudes and phases were derived for a cubic nonlinearity and verified by Spice simulations.     

Adaptive finite‐time control for high‐order nonlinear systems with mismatched disturbances

In this paper, adaptive finite‐time control is addressed for a class of high‐order nonlinear systems with mismatched disturbances. An adaptive finite‐time controller is designed in which variable gains are adjusted to ensure finite‐time stabilization for the closed‐loop system. Chattering is reduced by a designed adaptive sliding mode observer which is also used to deal with the mismatched disturbances in finite time. The proposed adaptive finite‐time control method avoids calculating derivative repeatedly of traditional backstepping methods and reduces computational burden effectively. Three numerical examples are given to illustrate the effectiveness of the proposed method.     

Observer design for neutral‐type neural networks with discrete and distributed time‐varying delays

This paper is concerned with the problem of state estimation for a class of neural networks with discrete and distributed interval time‐varying delays. We propose a new approach of nonlinear estimator design for the class of neutral‐type neural networks. By constructing a newly augmented Lyapunov‐Krasovskii functional, we establish sufficient conditions to guarantee the estimation error dynamics to be globally exponentially stable. The obtained results are formulated in terms of linear matrix inequalities (LMIs), which can be easily verified by the MATLAB LMI control toolbox. Then, the desired estimators gain matrix is characterized in terms of the solution to these LMIs. Three numerical examples are given to show the effectiveness of the proposed design method.     

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.     

T‐S fuzzy model–based adaptive repetitive learning consensus control of high‐order multiagent systems with imprecise communication topology structure

This paper addresses the consensus problem for high‐order nonlinear multiagent systems with imprecise communication topology structure (ICTS) and unknown periodic time‐varying parameters. Takagi‐Sugeno fuzzy models are used to portray the ICTS. By using the reparameterization technique, the repetitive learning control protocol is presented to guarantee that all the followers can track the leader asymptotically under the condition that the ICTS is fuzzy union connected. The information of the leader is known to a small portion of following agents; an auxiliary control term is presented for each follower agent to handle leader's dynamics. The consensus performance is analyzed via Lyapunov stability theory. Furthermore, the proposed protocol is further promoted to solve the formation control problem. Finally, the validity of the proposed methods are verified by two simulation examples.     

Adaptive synchronization of fractional‐order complex networks via pinning control

Adaptive synchronization of a class of fractional‐order complex networks is investigated in this paper. On the basis of the fractional‐order system stability theory, adaptive synchronization criteria of fractional‐order complex networks with 0 < q < 1 is achieved. Furthermore, pinning control method is then suggested to control the networks, and adaptive strategy is employed to tune the control gains and coupling strength. Because the nodes with high degree may not be the center of the networks, a new attempt to choose the pinned nodes on the basis of the closeness centrality scheme is proposed. Finally, numerical simulations are given to verify the effectiveness of the proposed approach based on the closeness centrality scheme. Copyright © 2012 John Wiley & Sons, Ltd.     

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.     

A wave‐front‐time dependent corona model for transmission‐line surge calculations

For transmission‐line surge studies, the inclusion of corona discharge due to high voltage surges is important as well as the inclusion of frequency‐dependent effects. Because the charge‐voltage (q‐v) curve of a lightning surge is different from that of a switching surge, a corona model should reproduce different q‐v curves for different wave‐front times. The present paper proposes a wave‐front time dependent corona model which can express the dependence by a simple calculation procedure as accurately as a rigorous finite‐difference method which requires an enormous calculation time. The simplicity enhances the incorporation of the corona model into a line model, because a large number of models are to be inserted into the line model by discretization. The q‐v curves calculated by the proposed method agrees well with field tests. This paper also proposes an efficient method to deal with nonlinear corona branches in distributed‐parameter line model using the trapezoidal rule of integration and the predictor‐corrector method. © 1999 Scripta Technica, Electr Eng Jpn, 129(1): 29–38, 1999     

A new false‐root identification method based on two‐terminal fault location algorithm for double‐circuit transmission lines

A fault location algorithm without synchronization for double‐circuit transmission lines does not require sampling synchronization, reduces the cost, and has a higher engineering value, but the algorithm still needs to be improved in the false‐root identification. This paper conducts further studies on this issue. First, the false‐root problem of the fault location algorithm without synchronization is analyzed, and then a new false‐root identification method is proposed, which is based on the difference of the existence of the false root in the calculation of the voltage amplitude along the line with different electrical moduli. It can solve the problem of the traditional method, which cannot distinguish between voltage amplitudes when they are close. Second, considering the shortcoming of the existing phase‐mode transformation matrix, a new phase‐mode transformation matrix applied to double‐circuit lines is deduced, which is based on the six‐sequence component method; it can be combined with the new false‐root identification method, thereby realizing false‐root identification under various types of faults. Finally, fault location is realized by using the moduli in the mold domain. The principle does not need to synchronize data in two terminals and is not affected by the fault types, fault resistances, and other factors. As is shown in a large number of Alternative Transients Program version of Electro‐Magnetic Transients Program (ATP‐EMTP) simulation results, the fault location has a higher accuracy © 2017 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

A novel adaptive Gauss pseudospectral method for nonlinear optimal control of constrained hypersonic re‐entry vehicle problem

Optimal control of constrained hypersonic re‐entry vehicle is difficult due to the complex nonlinear dynamics and nonlinear constraints. A novel adaptive Gauss pseudospectral method with some new strategies is therefore proposed to deal with the optimal control problem of hypersonic re‐entry vehicle to ensure that the complex constraints are satisfied all the way. First, state transformation is applied to make the variables more uniform in quantities. Second, some extreme points are applied in designing appropriate subintervals to track the control profiles effectively and the collocation points are adaptively redistributed based on the evaluated approximation errors. Third, a detection procedure is proposed to ensure that the constraints are satisfied all the way during the whole re‐entry process. The proposed method is illustrated by testing a hypersonic re‐entry vehicle problem. The results reveal that path constraints and terminal conditions are well satisfied. The research results, including the comparison with other methods, such as the classical Gauss pseudospectral method and the control vector parameterization method, show the effectiveness of the proposed adaptive approach.     

Decentralized output feedback controller design for nonlinear interconnected systems with unknown control direction and time‐varying delays

The decentralized output feedback control problem is considered for a class of large‐scale systems with unknown time‐varying delays. The uncertain interconnections are bounded by general nonlinear functions with unknown coefficients. The control direction parameters are unknown for each subsystem, which brings a challenging issue for decentralized controller design. To deal with this problem, we propose a new decentralized control scheme with the help of Nussbaum function. The decentralized filter is designed at first. By constructing Lyapunov–Krasovskii functional, we design the dynamic output feedback controller. It is rigorously proved that the closed‐loop system is asymptotically stable. Finally, the simulation is performed, and the results verify the effectiveness of the proposed method. Copyright © 2013 John Wiley & Sons, Ltd.     

Fast computation of Q‐value‐based dynamic programming on road networks

One of the essential components of vehicle navigation systems is route planning. The single shortest path problem and multiple shortest path problem have been widely studied for route planning. This paper introduces a Q‐value‐based dynamic programming using the division concept for solving both single and multiple shortest path problems on road networks. The proposed algorithm divides the whole network into different divisions, and the updating of Q values in each division is one stage for searching the optimal routes on road networks. The proposed algorithm can greatly save the computational time without any preprocessing on the road networks. The proposed algorithm is also systematically studied in various sizes of road networks. The simulation results show the efficiency and effectiveness of the proposed algorithm on large‐scale road networks. © 2012 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.