Global Lagged Finite-Time Synchronization of Two Chaotic Lur’e Systems Subject to Time Delay

In this paper, the energy method is employed to analytically investigate the influence of time delay in signal transmission on synchronization between two coupled FitzHugh-Nagumo (FHN) neurons. Unlike pre-existing methods that deal with synchronization problems, our major idea is to consider the change rate of the energy of the synchronization error system, since the original system’s synchronization is equivalent to the disappearance of the energy of the error system. In rewriting the original coupled system in the corresponding energy coordinates based on the energy method, we find that the change rate of energy of the error system can be divided into two parts (periodic and non-periodic). The synchronization criterion for the original system can then be obtained by letting the non-periodic part of the change rate of the energy be less than zero. The correctness of the analysis is illustrated with numerical simulations. Our analytical results show that time delay in signal transmission has very significant effects on the synchronization between two FHN neurons. If the time delay in signal transmission is not taken into account in the two coupled FHN neurons, synchronous spikes cannot be achieved in the system for any given coupling strength. By adjusting the value of the time delay in signal transmission, the neural system can freely switch between neural rest and synchronous spikes. This means that time delay in signal transmission is crucial for the occurrence of synchronous spikes in the FHN neural system, which contributes to our understanding of the interaction between neurons. We analytically show the influence of the time delay on the synchronization between two FHN neurons, which was seldom considered by other researchers.

Influence of the time delay of signal transmission on synchronization conditions in drive-response systems

As an important part of the smart grid, a wide-area measurement system (WAMS) provides the key technical support for power system monitoring, protection and control. But 20 uncertainties in system parameters and signal transmission time delay could worsen the damping effect and deteriorate the system stability. In the presented study, the subspace system identification technique (SIT) is used to firstly derive a low-order linear model of a power system from the measurements. Then, a novel adaptive wide-area damping control scheme for online tuning of the wide-area damping controller (WADC) parameters using the residue method is proposed. In order to eliminate the effects of the time delay to the signal transmission, a simple and practical time delay compensation algorithm is proposed to compensate the time delay in each wide-area control signal. Detailed examples, inspired by the IEEE test system under various disturbance scenarios, have been used to verify the effectiveness of the proposed adaptive wide-area damping control scheme.

In this paper, approximate lag synchronization (LS) and anticipating synchronization (AS) between two unidirectionally coupled hyperchaotic Chen systems without time-delay coupling are analytically investigated. Firstly, the synchronization condition for exact LS in two unidirectionally coupled hyperchaotic Chen systems with time delay in signal transmission is analytically obtained. Under such conditions, approximate LS and AS are discussed by replacing the true time-delay terms with their Taylor expansions up to the third order.Differently from other research studies, the condition for exact LS is derived by regarding LS as a special type of generalized synchronization (GS), which has nothing to do with the value of the time delay. It is convenient to individually change the value of the lag and anticipation time of approximate LS and AS without considering the synchronization condition. Our study shows the power of a new method for recreating the past signals or predicting the future signals of a hyperchaotic Chen system by using its current signals. The results provide a simple way to eliminate the negative effects of time delay in the signal transmission between two hyperchaotic systems.

In this paper, the tracking control of relative motion of two spacecraft in a leader-follower form is investigated. The time delay of signal transmission between the two spacecraft and external disturbances are explicitly considered. For time delay, we model the relative motion in a linear form and utilize the Lyapunov-Krasovskii functional combining with free-weighting matrix method to complete the stability analysis. The external disturbances are then attenuated in the H ∞ sense. Besides, we take the integral quadratic of the tracking error and control input as the tracking performance index, which is in the H 2 sense. A set of linear matrix inequalities (LMIs) is then derived incorporating all the design requirements and cone complementarity linearization technique is used to solve the LMIs. The theoretical analysis is completed based on the general motion model of circular reference orbit for leader spacecraft and numerical simulation results demonstrate the validity of the designed controller.

Integrated motor-transmission (IMT) powertrain systems are widely used in future electric vehicles due to the advantages of their simple structure configuration and high controllability. In electric vehicles, precise speed tracking control is critical to ensure good gear shifting quality of an IMT powertrain system. However, the speed tracking control design becomes challenging due to the inevitable time delay of signal transmission introduced by the in-vehicle network and unknown road slope variation. Moreover, the system parameter uncertainties and signal measurement noise also increase the difficulty for the control algorithm. To address these issues, in this paper a robust speed tracking control strategy for electric vehicles with an IMT powertrain system is proposed. A disturbance observer and low-pass filter are developed to decrease the side effect from the unknown road slope variation and measurement noise and reduce the estimation error of the external load torque. Then, the network-induced delay speed tracking model is developed and is upgraded considering the damping coefficient uncertainties of the IMT powertrain system, which can be described through the norm-bounded uncertainty reduction method. To handle the network-induced delay and parameter uncertainties, a novel and less-conservative Lyapunov function is proposed to design the robust speed tracking controller by the linear matrix inequality (LMI) algorithm. Meanwhile, the estimation error and measurement noise are considered as the external disturbances in the controller design to promote robustness. Finally, the results demonstrate that the proposed controller has the advantages of strong robustness, excellent speed tracking performance, and ride comfort over the current existing controllers.

Adaptive finite-time synchronization control for fractional-order complex-valued dynamical networks with multiple weights

Tunnel personnel positioning method based on TOA and modified location-fingerprint positioning

The time delay of signal transmission in the bilateral teleoperation system remains to be a severe problem for stability and transparency, despite that various methods have been proposed for alleviating the effects. Among those approaches, the neural networks (NN) based method is model-free and adaptable for system uncertainties and disturbances, which have shown great potential for teleoperation signal prediction. In this study, firstly, the concept of Passive Prediction and Active Prediction is clarified, i.e., Passive Predictor makes prediction given the delayed signals, while Active Predictor gives prediction based on raw signals before transmission. Secondly, a new Long Short-Term Memory (LSTM) based Bilateral Active Estimation Model (BAEM) is proposed for estimating the time delay in both directions of the teleoperation system, and the condition and proof of the model stability are provided. Based on the proposed model, another LSTM-based Active predictor is used thereafter, to predict the teleoperation signals with as long time in advance as the estimated time delay provided in its transmission direction. The proposed prediction method is independent of dynamic systems, hence it is applicable for general teleoperation scenarios. Moreover, any predictive methods other than LSTM can be embedded in the model, showing great extensibility.

With the development of network technology and automation control technology, the analysis and design of network automation control system has become one of the research hotspots in the field of control theory and application, and it will also become an inevitable trend in the development of industrial control technology. Due to the introduction of communication networks, the time delay of signal transmission in the control system has become one of the main factors that affect the control effect. It will reduce the performance of the system and even cause system instability. Traditional control methods cannot effectively solve this problem. Artificial intelligence the method provides new ideas. The purpose of this paper is to study the automation control system based on artificial intelligence technology. Aiming at the random and time-varying characteristics of network automation control latency, this paper examines two artificial intelligence control algorithms, namely the Smith controller with fuzzy PID and generalized prediction control based on dynamic network error correction in BP automation and implementation network. In the control system, reduce the effect of time delay on the control system performance. Aiming at the problem of time delay compensation and PID controller parameter tuning in network control systems, this paper proposes a type of PID network control method based on fast BP network. Experimental research shows that the control system designed by the GPC dynamic network correction algorithm used in this document has a faster response time and less overrun, and the test result is about 20% better than the traditional GPC algorithm.

Global synchronization in finite time for fractional-order neural networks with discontinuous activations and time delays

A theory of decision making with perception through parallel information channels is presented. Decision making is considered a parallel competitive process. Every channel can provide confirmation or rejection of a decision concept. Different channels provide different impact on the specific concepts caused by the goals and individual cognitive features. All concepts are divided into semantic clusters due to the goals and the system defaults. The clusters can be alternative or complimentary. The 'winner-take-all' concept nodes firing takes place within the alternative cluster. Concepts can be independently activated in the complimentary cluster. A cognitive channel affects a decision concept by sending an activating or inhibitory signal. The complimentary clusters serve for building up complex concepts by superimposing activation received from various channels. The decision making is provided by the alternative clusters. Every active concept in the alternative cluster tends to suppress the competitive concepts in the cluster by sending inhibitory signals to the other nodes of the cluster. The model accounts for a time delay in signal transmission between the nodes and explains decreasing of the reaction time if information is confirmed by different channels and increasing of the reaction time if deceiving information received from the channels.

The second part of the analytical review considers in detail an adaptive filtering application in the systems of adaptive optical systems (AOS) from the perspective of the airborne laser platforms. Herein the AOS operates under aero-optical distortions and vibrations, which further complicate the propagation of the laser beam. Adaptive filtering is considered as a way to improve the efficiency of the control system of adaptive optical systems, allowing to improve running an adaptive optics control loop: by 1.5-2 times with compensation for only the aero-optical disturbances, by 1.5 times with compensation only for the free-stream turbulence, and by 2.5-3.5 times for the combination of aero-optics and free-stream turbulence.The article discusses implementation of a new type of the controller, which uses intellectual algorithms to predict (through an artificial neural network) a short-term horizon of evolution of aberrations due to aero-optical effect. This controller allows us to deal with a large time delay in signal transmission (up to 5 time steps of sampling).The application of two deformable mirrors in the adaptive optical system to provide control at the spaced frequencies is especially considered. A low-frequency mirror is used to correct the lower-order aberrations (tip-tilt, defocusing, astigmatism, coma) requiring large strokes of executive mechanisms (actuators) in the deformable mirror. A high-frequency mirror is used to correct the higher-order aberrations requiring small strokes of drives. Various control algorithms to control the system from two adaptive mirrors are briefly reviewed.The obtained results, conclusions, and recommendations are supposedly to be used in development of specification of requirements for systems of adaptive optics.

Simple zero singularity analysis in a coupled FitzHugh–Nagumo neural system with delay

In this paper, we analyse the characteristics of one type of circuit structure that is extended from simplified Lorenz system by taking a memristor as feedback. Considering the transmission time delay between master system and slave system, we used a compound finite-time synchronisation signal controller, which consists of a general feedback control signal and a fine adjustment signal, to ensure the synchronisation of two memristive hyperchaotic circuits based on Lorenz system. Based on Lyapunov stability theory, finite-time control, matrix inequality, and considering the transmission time delay, the finite-time synchronisation condition for this type of memristive hyperchaotic circuit based on Lorenz system with transmission time delay via finite-time controller is given. Finally, simulation results are used to verify the feasibility and effectiveness of this method.