Finite-time synchronization of Markovian neural networks with proportional delays and discontinuous activations

In this paper, finite-time synchronization of neural networks (NNs) with discontinuous activation functions (DAFs), Markovian switching, and proportional delays is studied in the framework of Filippov solution. Since proportional delay is unbounded and different from infinite-time distributed delay and classical finite-time analytical techniques are not applicable anymore, new 1-norm analytical techniques are developed. Controllers with and without the sign function are designed to overcome the effects of the uncertainties induced by Filippov solutions and further synchronize the considered NNs in a finite time. By designing new Lyapunov functionals and using M-matrix method, sufficient conditions are derived to guarantee that the considered NNs realize synchronization in a settling time without introducing any free parameters. It is shown that, though the proportional delay can be unbounded, complete synchronization can still be realized, and the settling time can be explicitly estimated. Moreover, it is discovered that controllers with sign function can reduce the control gains, while controllers without the sign function can overcome chattering phenomenon. Finally, numerical simulations are given to show the effectiveness of theoretical results

Synchronization of Discontinuous Neural Networks with Delays via Adaptive Control

The drive-response synchronization of delayed neural networks with discontinuous activation functions is investigated via adaptive control. The synchronization of this paper means that the synchronization error approaches to zero for almost all time as time goes to infinity. The discontinuous activation functions are assumed to be monotone increasing which can be unbounded. Due to the mild condition on the discontinuous activations, adaptive control technique is utilized to control the response system. Under the framework of Filippov solution, by using Lyapunov function and chain rule of differential inclusion, rigorous proofs are given to show that adaptive control can realize complete synchronization of the considered model. The results of this paper are also applicable to continuous neural networks, since continuous function is a special case of discontinuous function. Numerical simulations verify the effectiveness of the theoretical results. Moreover, when there are parameter mismatches between drive and response neural networks with discontinuous activations, numerical example is also presented to demonstrate the complete synchronization by using discontinuous adaptive control

Fixed-time control of delayed neural networks with impulsive perturbations

This paper is concerned with the fixed-time stability of delayed neural networks with impulsive perturbations. By means of inequality analysis technique and Lyapunov function method, some novel fixed-time stability criteria for the addressed neural networks are derived in terms of linear matrix inequalities (LMIs). The settling time can be estimated without depending on any initial conditions but only on the designed controllers. In addition, two different controllers are designed for the impulsive delayed neural networks. Moreover, each controller involves three parts, in which each part has different role in the stabilization of the addressed neural networks. Finally, two numerical examples are provided to illustrate the effectiveness of the theoretical analysis

Robust generalized Mittag-Leffler synchronization of fractional order neural networks with discontinuous activation and impulses.

Fractional order system is playing an increasingly important role in terms of both theory and applications. In this paper we investigate the global existence of Filippov solutions and the robust generalized Mittag-Leffler synchronization of fractional order neural networks with discontinuous activation and impulses. By means of growth conditions, differential inclusions and generalized Gronwall inequality, a sufficient condition for the existence of Filippov solution is obtained. Then, sufficient criteria are given for the robust generalized Mittag-Leffler synchronization between discontinuous activation function of impulsive fractional order neural network systems with (or without) parameter uncertainties, via a delayed feedback controller and M-Matrix theory. Finally, four numerical simulations demonstrate the effectiveness of our main results.N/

Exponential Lag Synchronization of Cohen-Grossberg Neural Networks with Discrete and Distributed Delays on Time Scales

In this article, we investigate exponential lag synchronization results for the Cohen-Grossberg neural networks (C-GNNs) with discrete and distributed delays on an arbitrary time domain by applying feedback control. We formulate the problem by using the time scales theory so that the results can be applied to any uniform or non-uniform time domains. Also, we provide a comparison of results that shows that obtained results are unified and generalize the existing results. Mainly, we use the unified matrix-measure theory and Halanay inequality to establish these results. In the last section, we provide two simulated examples for different time domains to show the effectiveness and generality of the obtained analytical results.Comment: 20 pages, 18 figure

Comparative evaluation of approaches in T.4.1-4.3 and working definition of adaptive module

The goal of this deliverable is two-fold: (1) to present and compare different approaches towards learning and encoding movements us- ing dynamical systems that have been developed by the AMARSi partners (in the past during the first 6 months of the project), and (2) to analyze their suitability to be used as adaptive modules, i.e. as building blocks for the complete architecture that will be devel- oped in the project. The document presents a total of eight approaches, in two groups: modules for discrete movements (i.e. with a clear goal where the movement stops) and for rhythmic movements (i.e. which exhibit periodicity). The basic formulation of each approach is presented together with some illustrative simulation results. Key character- istics such as the type of dynamical behavior, learning algorithm, generalization properties, stability analysis are then discussed for each approach. We then make a comparative analysis of the different approaches by comparing these characteristics and discussing their suitability for the AMARSi project

Timing, kinematics, and the cerebellum: Tapping into differences between musicians and non-musicians

Musical performance relies on basic processes such as timing, and the synchronization of motor responses with environmental stimuli. The study of the effects of musical training on behaviour and the brain provides an opportunity to understand these processes and their neural correlates, particularly in relation to the cerebellum, a brain region implicated in timing. The first study presented here compared musicians and non-musicians on the standard sensorimotor synchronization task of finger tapping to a metronome, with and without tactile feedback. The results indicated that musicians differed from non-musicians in their use of kinematics and sensory information for synchronization. The second study focused on how musical training affects event-based and emergent timing in repetitive rhythmic tapping and drawing. Event-based timing has been shown to rely on an internal clock-like process that is independent of the motor response. Conversely, emergent timing establishes regular rhythmic movement by stabilizing kinematic parameters without reference to an explicit internal representation of time intervals. Musical training was associated with improved precision in event-based timing but not in emergent timing. For musicians only, the kinematic parameter of movement jerk was decoupled from timing variability in both event-based and emergent timing. These results support the dissociability of the two timing modes, highlight the limits of musical training, and show that the relationship between kinematics and timing is affected by musical expertise. The third study examined differences between musicians and non-musicians in a finger-tapping task, and in regional cerebellar volumes measured from magnetic resonance imaging data. Smaller volumes were associated with an earlier age of start of musical training, and with better timing performance. These findings are evidence for a sensitive period, before seven years, for initiation of musical training. Timing variability was associated with the volume of right Lobule VI, indicating localization of event-based timing to this region. The overall pattern of results suggests that musicians may be using sensory information to maintain timing in a more efficient and parsimonious manner compared to non-musicians. This is interpreted as evidence that musicians are using a top-down approach for many music-related tasks, in contrast to the bottom-up approach of non-musicians

Timing, kinematics, and the cerebellum: Tapping into differences between musicians and non-musicians

Musical performance relies on basic processes such as timing, and the synchronization of motor responses with environmental stimuli. The study of the effects of musical training on behaviour and the brain provides an opportunity to understand these processes and their neural correlates, particularly in relation to the cerebellum, a brain region implicated in timing. The first study presented here compared musicians and non-musicians on the standard sensorimotor synchronization task of finger tapping to a metronome, with and without tactile feedback. The results indicated that musicians differed from non-musicians in their use of kinematics and sensory information for synchronization. The second study focused on how musical training affects event-based and emergent timing in repetitive rhythmic tapping and drawing. Event-based timing has been shown to rely on an internal clock-like process that is independent of the motor response. Conversely, emergent timing establishes regular rhythmic movement by stabilizing kinematic parameters without reference to an explicit internal representation of time intervals. Musical training was associated with improved precision in event-based timing but not in emergent timing. For musicians only, the kinematic parameter of movement jerk was decoupled from timing variability in both event-based and emergent timing. These results support the dissociability of the two timing modes, highlight the limits of musical training, and show that the relationship between kinematics and timing is affected by musical expertise. The third study examined differences between musicians and non-musicians in a finger-tapping task, and in regional cerebellar volumes measured from magnetic resonance imaging data. Smaller volumes were associated with an earlier age of start of musical training, and with better timing performance. These findings are evidence for a sensitive period, before seven years, for initiation of musical training. Timing variability was associated with the volume of right Lobule VI, indicating localization of event-based timing to this region. The overall pattern of results suggests that musicians may be using sensory information to maintain timing in a more efficient and parsimonious manner compared to non-musicians. This is interpreted as evidence that musicians are using a top-down approach for many music-related tasks, in contrast to the bottom-up approach of non-musicians

Synchronization of Complex-Valued Dynamical Networks

Dynamical networks (DNs) have been broadly applied to describe natural and human systems consisting of a large number of interactive individuals. Common examples include Internet, food webs, social networks, neural networks, etc. One of the crucial and significant collective behaviors of DNs is known as synchronization. In reality, synchronization phenomena may occur either inside a network or between two or more networks, which are called “inner synchronization” and “outer synchronization”, respectively. On the other hand, many real systems are more suitably characterized by complex-valued dynamical systems, such as quantum systems, complex Lorenz system, and complex-valued neural networks. The main focus of this thesis is on synchronization of complex-valued dynamical networks (CVDNs). In this thesis, we firstly design a delay-dependent pinning impulsive controller to study synchronization of time-delay CVDNs. By taking advantage of the Lyapunov function in the complex field, some delay-independent synchronization criteria of CVDNs are established, which generalizes some existing synchronization results. Then, by employing the Lyapunov functional in the complex field, several delay-dependent sufficient conditions on synchronization of CVDNs with various sizes of delays are constructed. Moreover, we study synchronization of CVDNs with time-varying delays under distributed impulsive controllers. By taking advantage of time-varying Lyapunov function/ functional in the complex domain, several synchronization criteria for CVDNs with time-varying delays are derived in terms of complex-valued linear matrix inequalities (LMIs). Then, we propose a memory-based event-triggered impulsive control (ETIC) scheme with three levels of events in the complex field to investigate the synchronization problem of CVDNs with both discrete and distributed time delays, and we further consider an event-triggered pinning impulsive control (ETPIC) scheme combining the proposed ETIC and a pinning algorithm to study synchronization of time-delay CVDNs. Results show that the proposed ETIC scheme and ETPIC scheme can effectively synchronize CVDNs with the desired trajectory. Secondly, we study generalized outer synchronization of drive-response time-delayed CVDNs via hybrid control. A hybrid controller is proposed in the complex domain to construct response complex-valued networks. Some generalized outer synchronization criteria for drive-response CVDNs are established, which extend the existing generalized outer synchronization results to the complex field. Thirdly, we study the average-consensus problem of potential complex-valued multi-agent systems. A complex-variable hybrid consensus protocol is proposed, and time delays are taken into account in both the continuous-time protocol and the discrete-time protocol. Delay-dependent sufficient conditions are established to guarantee the proposed complex-variable hybrid consensus protocol can solve the average-consensus problem. Lastly, as a practical application for complex-valued networked systems, the synchronization problem of master-slave complex-valued neural networks (CVNNs) is studied via hybrid control and delayed ETPIC, respectively. We also investigate the state estimation problem of CVNNs by designing the adaptive impulsive observer in the complex field