Optimal synchronization controller design for complex dynamical networks with unknown system dynamics

In this paper, the optimal synchronization controller design problem for complex dynamical networks with unknown system internal dynamics is studied. A necessary and sufficient condition on the existence of the optimal control minimizing a quadratic performance index is given. The optimal control law consists of a feedback control and a compensated feedforward control, and the feedback control gain can be obtained by solving the well-known Algebraic Riccati Equation (ARE). Especially, in the presence of unknown system dynamics, a novel adaptive iterative algorithm using the information of system states and inputs is proposed to solve the ARE to get the optimal feedback control gain. Finally, a simulation example shows the effectiveness of the theoretical results.     

Generalized lag synchronization of multiple weighted complex networks with and without time delay

The generalized lag synchronization of multiple weighted complex dynamical networks with fixed and adaptive couplings is investigated in this paper, respectively. By designing appropriate controller, several synchronization criteria are presented for multiple weighted complex dynamical networks with and without time delay based on the selected Lyapunov functional and inequality techniques. Moreover, an adaptive scheme to update the coupling weights is also developed for ensuring the generalized lag synchronization of multiple weighted complex dynamical networks with and without time delay. Finally, two numerical examples are provided in order to validate effectiveness of the proposed generalized lag synchronization criteria.     

Guaranteed cost synchronization for second-order wireless sensor networks with given cost budgets

The current paper addresses leader-following guaranteed cost synchronization with the cost budget given previously for the second-order wireless sensor networks. The published researches on guaranteed cost synchronization design criteria usually are based on the linear matrix inequality (LMI) techniques and cannot take the cost budget given previously into consideration. Firstly, the current paper proposes a guaranteed cost synchronization protocol, which can realize the tradeoff design between the battery power consumption and the synchronization regulation performance. Secondly, for the case without the given cost budget, sufficient conditions for leader-following guaranteed cost synchronization are presented and an upper bound of the cost function is shown. Thirdly, for the case that the cost budget is given previously, the criterion for leader-following guaranteed cost synchronization is proposed. Especially, the value ranges of control gains in these criteria are determined, which means that the existence of control gains in synchronization criteria can be guaranteed, but the LMI techniques can only determine the gain matrix and cannot give the value ranges of control gains. Moreover, these criteria are only associated with the minimum nonzero eigenvalue and the maximum eigenvalue, which can ensure the scalability of the wireless sensor networks. Finally, numerical simulations are given to illustrate theoretical results.     

Chaotification of a class of linear switching systems based on a Shilnikov criterion

This paper proposes an approach for constructing and generating chaos from a class of three-dimensional linear switching systems via a heteroclinic loop based on the Shilnikov criterion. First, the existence of a switching rule for the system is derived by utilizing the Shilnikov heteroclinic criterion. Then a general design philosophy and its procedure of switching rule are provided to ensure that the proposed approach is applicable to engineering. Two numerical examples are presented to validate the main principle and the implementability of the scheme. Theoretical analysis and numerical simulation are used to demonstrate the feasibility and effectiveness of developed techniques.     

Graph theory-based finite-time synchronization of fractional-order complex dynamical networks

This paper considers the finite-time synchronization problem for a class of fractional-order complex dynamical networks (FOCDNs). By utilizing the properties of fractional calculus and fractional-order comparison principle, we propose a new lemma. Base on the new lemma, some analysis techniques and algebraic graph theory method, some novel criteria are given to ensure finite-time synchronization of FOCDNs, and the upper bound of the setting time for synchronization is estimated. At last, numerical simulations are given to verify the effectiveness of the obtained results.     

Synergetic governing controller design for the hydraulic turbine governing system with complex conduit system

The hydraulic turbine governing system plays an indispensable role in maintaining the stability of electrical power system. In this paper, synergetic control theory is introduced to enhance the regulating ability of the hydraulic turbine governing system. For the purpose of describing the characteristics of objective system and deducing the synergetic control rule, a nonlinear mathematic model of a hydraulic turbine governing system with long tail race and two surge tanks is established. Furthermore, the nonlinear characteristic of the hydraulic turbine is described by six variable partial derivatives. For further investigation, the hydraulic turbine governing system is conducted to running under load condition when its coaxial generator connects to an infinite bus. Simulation experiments have been made under both load disturbance and three-phase short circuit fault conditions to compare the dynamic performances of proposed synergetic governing controller and classic PID controller. The results indicate that the proposed synergetic governing controller is an effective alternative in normal condition and a superior one in emergency. Moreover, the robustness of synergetic governing controller has also been discussed at the end of this paper.     

Event-triggered synchronization of delayed neural networks with actuator saturation using quantized measurements

This paper studies event-triggered synchronization control problem for delayed neural networks with quantization and actuator saturation. Firstly, in order to reduce the load of network meanwhile retain required performance of system, the event-triggered scheme is adopted to determine if the sampled signal will be transmitted to the quantizer. Secondly, a synchronization error model is constructed to describe the master-slave synchronization system with event-triggered scheme, quantization and input saturation in a unified framework. Thirdly, on the basis of Lyapunov–Krasovskii functional, sufficient conditions for stabilization are derived which can ensure synchronization of the master system and slave system; particularly, a co-designed parameters of controller and the corresponding event-triggered parameters are obtained under the above stability condition. Lastly, two numerical examples are employed to illustrate the effectiveness of the proposed approach.     

Finite-time stabilization of memristor-based inertial neural networks with discontinuous activations and distributed delays

In this paper, the finite-time stabilization problem for memristor-based inertial neural networks (MINNs) with discontinuous activations (DAs) and distributed delays is investigated. To deal with the discontinuous property of the MINNs, the nonsmooth analysis theory is invoked. Furthermore, to simplify the MINNs with second-order state derivative, an order-reduced method is adopted. Then the second-order MINNs is transformed into a simpler first-order differential system. Moreover, the verifiable algebraic criteria are derived for the finite-time stabilization of MINNs with DAs and distributed delays under the designed control approach. Finally, the effectiveness of the obtained results are illustrated via numerical simulations.     

A new Lyapunov functional approach to sampled-data synchronization control for delayed neural networks

This paper discusses the problem of synchronization for delayed neural networks using sampled-data control. We introduce a new Lyapunov functional, called complete sampling-interval-dependent discontinuous Lyapunov functional, which can adequately capture sampling information on both intervals from $r(t?\overline{\tau })$ to $r(t_k?\overline{\tau })$ and from $r(t?\overline{\tau })$ to $r(t_{k+1}?\overline{\tau })$. Based on this Lyapunov functional and an improved integral inequality, less conservative conditions are derived to ensure the stability of the synchronization error system, leading to the fact that the drive neural network is synchronized with the response neural network. The desired sampled-data controller is designed in terms of solutions to linear matrix inequalities. A numerical example is provided to demonstrate that the proposed approaches are effective and superior to some existing ones in the literature.     

State and unknown input estimations for discrete-time switched linear systems with average dwell time

In this paper, the problem of state and unknown input estimations for a class of discrete-time switched linear systems with average dwell time switching is investigated. First, a proportional integral observer with an exponential H_∞ performance is constructed to estimate the system state and unknown input simultaneously. Second, both of the observability and the stability of the estimation error system are analyzed, then the derivation of the observer gain matrices is transformed into the calculation of linear matrix inequalities. Third, the obtained results are extended to the systems with output disturbances. Finally, two simulation examples are provided to show the validity and effectiveness of the proposed methods.     

Static group synchronization of second-order multi-agent systems via pinning control

This paper investigates the expected static group synchronization problem of the second-order multi-agent systems via pinning control. For directed communication topology with spanning tree, based on Gershgorin disk theorem and the matrix property, a static pinning control protocol with fixed gains is first introduced and some sufficient and necessary static group synchronization criteria are also established. It is worth mentioning that a rigorous proof is also given that only one pinning node is needed to guarantee static group synchronization, which could be inferred that our protocol might be more economical and effective in large scale of multi-agent systems. Then, for weakly connected directed communication topology with nodes of zero in-degree, an adaptive pinning control applied to the node with zero in-degree is also proposed to achieve static group synchronization. Finally, the efficiency of the proposed protocols is verified by two simulation examples.     

Solving future equation systems using integral-type error function and using twice ZNN formula with disturbances suppressed

In this paper, for solving future equation systems, two novel discrete-time advanced zeroing neural network models are proposed, analyzed and investigated. First of all, by using integral-type error function and twice zeroing neural network (or termed, Zhang neural network) formula, as the preliminaries and bases of future problems solving, two continuous-time advanced zeroing neural network models are presented for solving continuous time-variant equation systems. Secondly, a one-step-ahead numerical differentiation rule termed 5-instant discretization formula is presented for the first-order derivative approximation with higher computational precision. By exploiting the presented 5-instant discretization formula to discretize the continuous-time advanced zeroing neural network models, two novel discrete-time advanced zeroing neural network models are proposed. Theoretical analyses on the convergence and precision of the discrete-time advanced zeroing neural network models are proposed. In addition, in the presence of disturbance, the proposed discrete-time advanced zeroing neural network models still possess excellent performance. Comparative numerical experimental results further substantiate the efficacy and superiority of the proposed discrete-time advanced zeroing neural network models for solving the future equation systems.     

Event triggered reliable synchronization of semi-Markovian jumping complex dynamical networks via generalized integral inequalities

This paper focuses on the synchronization problem of semi-Markovian jumping complex dynamical networks with time-varying coupling delays against actuator failures. In an aim to shrink the treatment of network resources event triggered control strategy is proposed to achieve the synchronization criteria. By constructing Lyapunov–Krasovski functional, some delay dependent criteria that assures the synchronization of CDN are derived with the help of the general integral inequalities. It should be noted that the general integral inequality used here is general than that of Jensen inequality, the Wirtinger-based inequality, the Bessel-Legendre inequality, the Wirtinger-based double integral inequality, and the auxiliary function-based integral inequalities. The resulting LMIs can be easily verified with the help of the available softwares. Finally, simulation results are proposed to verify the effectiveness of the general integral inequality and designed control law.     

Stability and synchronization criteria for fractional order competitive neural networks with time delays: An asymptotic expansion of Mittag Leffler function

Competitive neural networks(CNNs) has not been well developed in nonlinear fractional order dynamical system, which is developed first time in this paper. Then, by means of a proper Lyapunov functional, asymptotic expansion of Mittag-Leffler function properties, together with some Caputo derivative properties, the testable novel sufficient conditions are given to guarantee the existence, uniqueness of the equilibrium point as well as global asymptotic stability for a class of fractional order competitive neural networks (FOCNNs) are all derived in the form of matrix elements. Furthermore, the boundedness for the solution of FOCNN is presented by employing Cauchy–Schwartz inequality and Gronwall inequality. Besides, a linear feedback control and adaptive feedback control are designed to achieve the global asymptotic synchronization criterion for FOCNNs with time delay and these explored consequences are extended from some previous integer order CNNs output. At last, two numerical simulations are performed to illustrate the effectiveness of our proposed theoretical results.     

Multi-lagged-input iterative dynamic linearization based data-driven adaptive iterative learning control

This article presents a multi-lagged-input based data-driven adaptive iterative learning control (M-DDAILC) method for nonlinear multiple-input-multiple-output (MIMO) systems by virtue of multi-lagged-input iterative dynamic linearization (IDL). The original nonlinear and non-affine MIMO system is equivalently transformed into a linear input-output incremental counterpart without loss of dynamics. The proposed learning law utilizes the desired trajectory to cancel the influence from iteration-by-iteration variations, as well as additional multi-lagged inputs to improve control performance. The developed iterative estimation law is more effective and also makes estimation of the unknown parameters easier because the dynamics for each parameter to represent are decreased by dividing the system into multiple components in the multi-lagged-input IDL formulation. Moreover, the proposed M-DDAILC does not need an explicit and accurate model. It is proved to be iteratively convergent with rigorous analysis. Both a numerical example and a practical application to a permanent magnet linear motor are provided to verify the validity and applicability of the proposed method.     

Event-triggered decentralized output-feedback control for interconnected nonlinear systems with input quantization

In this paper, the event-triggered decentralized control problem for interconnected nonlinear systems with input quantization is investigated. A state observer is constructed to estimate the unmeasurable states, and the state-dependent interconnections are accommodated by presenting some smooth functions. Then by employing backstepping technique and neural networks (NNs) approximation capability, a novel decentralized output feedback control strategy and an event-triggered mechanism are designed simultaneously. It is proved through Lyapunov theory that the closed-loop system is stable and the tracking property of all subsystems is guaranteed. Finally, the effectiveness of the proposed scheme is illustrated by an example.     

General synchronization criteria for nonlinear Markovian systems with random delays

It is well known that control of Markovian systems is a difficult problem. This paper considers synchronization control of Markovian coupled nonlinear systems with random delays. A new control scheme is proposed. Sufficient conditions in terms of linear matrix inequalities (LMIs) are obtained such that the coupled system can be asymptotically synchronized onto an isolated system. The synchronization criteria include classical mode-dependent and mode-independent results as special cases. The design method of the control gains is also given. Compared with mode-dependent and mode-independent control methods, our results are more practical and have lower conservatism, respectively. Numerical simulations are given to verify the effectiveness of the theoretical results.     

Mechanical analysis and ultimate boundary estimation of the chaotic permanent magnet synchronous motor

In this paper, we present the dimensionless form of a chaotic permanent magnet synchronous motor (PMSM). Its Kolmogorov formalism, which can be used to describe dissipative-forced dynamical systems, shows that there exist four types of torques, i.e., inertial torque, internal torque, dissipative torque and external torque. The mechanical analysis of the dimensionless PMSM is given for five different combinations of these torques. Numerical simulations show that the occurrence of chaos depends on these four types of torques. Moreover, the ultimate boundary estimation of the dimensionless chaotic PMSM is also investigated theoretically and numerically.