Lur’e Postnikov Lyapunov functional technique to global Mittag-Leffler stability of fractional-order neural networks with piecewise constant argument

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9 W average power, 150 kHz repetition rate diamond Raman laser at 1519 nm, pumped by a Yb fibre amplifier

Commercially available pulsed fibre lasers at ~1.5 μm have many uses in imaging, defense, communications and light radar (LIDAR) [1]. For 3D scanning LIDAR, higher signal-to-noise ratio requires lasers with high average power and high pulse repetition rate (ideally several MHz) for faster scanning rate, whereas to improve distance resolution requires pulse durations <10 ns [2,3]. One limitation of the pulsed fibre lasers at ~1.5 μm is scaling to high average powers [4]. Raman frequency conversion of high average power fibre master oscillator power amplifier (MOPA) systems at ~1 μm is a potential alternative. The large Raman shift and Raman gain of diamond allows two-stage Raman conversion to ~1.5 μm for ~1 μm pumping [5]. Excellent thermal properties make diamond suitable for high average powers [6]. Much work has been done on conversion of 1.064 μm lasers to 1.485 μm using diamond [7]; however, the “eye-safety” requirements for LIDAR typically call for wavelengths above 1.5 μm, due to the order of magnitude higher Maximum Permissible Exposure limit [8]. Developing such a diamond Raman laser (DRL) was the major motivation for this research

Distributed Adaptive Mittag&ndash;Leffler Formation Control for Second-Order Fractional Multi-Agent Systems via Event-Triggered Control Strategy

This brief investigates the Mittag&ndash;Leffler formation bounded control problem for second-order fractional multi-agent systems (FMASs), where the dynamical nodes of followers are modeled to satisfy quadratic (QUAD) condition. Firstly, under the undirected communication topology, for the considered second-order nonlinear FMASs, a distributed event-triggered control scheme (ETCS) is designed to realize the global Mittag&ndash;Leffler bounded formation control goal. Secondly, by introducing adaptive weights into triggering condition and control protocol, an adaptive event-triggered formation protocol is presented to achieve the global Mittag&ndash;Leffler bounded formation. Thirdly, a five-step algorithm is provided to describe protocol execution steps. Finally, two simulation examples are given to verify the effectiveness of the proposed schemes

Lur’e-Postnikov Lyapunov function approach to global robust Mittag-Leffler stability of fractional-order neural networks

Abstract In this paper, the global robust Mittag-Leffler stability analysis is preformed for fractional-order neural networks (FNNs) with parameter uncertainties. A new inequality with respect to the Caputo derivative of integer-order integral function with the variable upper limit is developed. By means of the properties of Brouwer degree and the matrix inequality analysis technique, the proof of the existence and uniqueness of equilibrium point is given. By using integer-order integral with the variable upper limit, Lur’e-Postnikov type Lyapunov functional candidate is constructed to address the global robust Mittag-Leffler stability condition in terms of linear matrix inequalities (LMIs). Finally, two examples are provided to illustrate the validity of the theoretical results

Distributed Adaptive Mittag–Leffler Formation Control for Second-Order Fractional Multi-Agent Systems via Event-Triggered Control Strategy

This brief investigates the Mittag–Leffler formation bounded control problem for second-order fractional multi-agent systems (FMASs), where the dynamical nodes of followers are modeled to satisfy quadratic (QUAD) condition. Firstly, under the undirected communication topology, for the considered second-order nonlinear FMASs, a distributed event-triggered control scheme (ETCS) is designed to realize the global Mittag–Leffler bounded formation control goal. Secondly, by introducing adaptive weights into triggering condition and control protocol, an adaptive event-triggered formation protocol is presented to achieve the global Mittag–Leffler bounded formation. Thirdly, a five-step algorithm is provided to describe protocol execution steps. Finally, two simulation examples are given to verify the effectiveness of the proposed schemes

Event-triggered H∞ anti-synchronisation for delayed neural networks with discontinuous neuron activations via non-fragile control strategy

This paper treats of the global event-triggered anti-synchronisation issue for discontinuous neural networks with the mixed time-varying delays and random feedback gain fluctuation via non-fragile control strategy. The random gain uncertainties are described by stochastic variables satisfying the Bernoulli distribution. Firstly, the novel hybrid controllers, which are composed of the non-fragile controller and the event-triggered controller, are designed. Then, based on Clarke's non-smooth analysis theory, general free-weighting matrix method, the Lyapunov-Krasovskii functional approach and Wirtinger-based multiple integral inequality analysis technology, the global event-triggered non-fragile anti-synchronisation conditions are established in terms of linear matrix inequalities (LMIs). In addition, under the considered external disturbance, the conditions with respect to the global event-triggered non-fragile $H_{\infty }$ anti-synchronisation are also addressed in forms of LMIs. Finally, two illustrative examples are provided to verify the effectiveness of the designed event-triggered non-fragile control scheme and the validity of theoretical results

Robust Almost Periodic Dynamics for Interval Neural Networks with Mixed Time-Varying Delays and Discontinuous Activation Functions

The robust almost periodic dynamical behavior is investigated for interval neural networks with mixed time-varying delays and discontinuous activation functions. Firstly, based on the definition of the solution in the sense of Filippov for differential equations with discontinuous right-hand sides and the differential inclusions theory, the existence and asymptotically almost periodicity of the solution of interval network system are proved. Secondly, by constructing appropriate generalized Lyapunov functional and employing linear matrix inequality (LMI) techniques, a delay-dependent criterion is achieved to guarantee the existence, uniqueness, and global robust exponential stability of almost periodic solution in terms of LMIs. Moreover, as special cases, the obtained results can be used to check the global robust exponential stability of a unique periodic solution/equilibrium for discontinuous interval neural networks with mixed time-varying delays and periodic/constant external inputs. Finally, an illustrative example is given to demonstrate the validity of the theoretical results

Complete Periodic Synchronization of Memristor-Based Neural Networks with Time-Varying Delays

This paper investigates the complete periodic synchronization of memristor-based neural networks with time-varying delays. Firstly, under the framework of Filippov solutions, by using M-matrix theory and the Mawhin-like coincidence theorem in set-valued analysis, the existence of the periodic solution for the network system is proved. Secondly, complete periodic synchronization is considered for memristor-based neural networks. According to the state-dependent switching feature of the memristor, the error system is divided into four cases. Adaptive controller is designed such that the considered model can realize global asymptotical synchronization. Finally, an illustrative example is given to demonstrate the validity of the theoretical results

Stability in Switched Cohen-Grossberg Neural Networks with Mixed Time Delays and Non-Lipschitz Activation Functions

The stability for the switched Cohen-Grossberg neural networks with mixed time delays and α-inverse Hölder activation functions is investigated under the switching rule with the average dwell time property. By applying multiple Lyapunov-Krasovskii functional approach and linear matrix inequality (LMI) technique, a delay-dependent sufficient criterion is achieved to ensure such switched neural networks to be globally exponentially stable in terms of LMIs, and the exponential decay estimation is explicitly developed for the states too. Two illustrative examples are given to demonstrate the validity of the theoretical results