Second-order Neural Networks Research Articles

Event-triggered-based fixed/preassigned-time synchronization control of second-order neural networks with distributed delays

In this article, a kind of second-order neural networks with variable coefficients and distributed delays are discussed. At first, new lemmas about fixed/preassigned-time synchronization for such system are respectively constructed. Then, some novel criteria are given to get fixed/preassigned-time synchronization for such delayed system based on the these lemmas. Unlike feedback controllers are used in previous works, two effective event-triggered controllers are, respectively, proposed here to investigate the second-order neural networks. In addition, event-triggered control and non-reduced order way are combined use to realize fixed/preassigned-time synchronization for such delayed system at the first time, which has advantages from both efficiency of control and brevity of criterion. Finally, two examples are presented to show validity of the proposed criteria.

Quasi‐bipartite synchronisation of multiple inertial signed delayed neural networks under distributed event‐triggered impulsive control strategy

The central concern of this paper is to study leader-following quasi-bipartite synchronisation of a multiple inertial signed neural networks with varying time-delay by utilising distributed event-triggered impulsive control scheme, where connections between adjacent nodes of the neural networks either positive or negative. The second-order neural networks, called inertial neural networks, can be transformed into differential equations of first-order by implementing suitable variable substitution. Under certain hypothesis about the node dynamics, signed graph theory and balanced topology of networks, some conditions are derived in terms of lower-dimensional linear matrix inequalities (LMIs) to achieve leader-following quasi-bipartite synchronisation. In addition, a basic algebraic condition is derived to estimate the theoretical upper bound for the error node. Finally, some numerical simulations are provided to illustrate the correctness of the theoretical results.

Super-twisting-based continuous neural networks modelling of second-order interconnected systems

ABSTRACTThe aim of this work was to design a non-parametric model of interconnected systems represented by uncertain second-order systems with incomplete information (only the generalized position vector is measurable). Artificial neural networks appeared to be a plausible alternative to get a non-parametric representation of the aforementioned interconnected systems. The modelling strategy used a set of spatial distributed second-order continuous neural networks (CNN). Each node in the interconnected system was represented as a second-order continuous neural network added by the super-twisting discontinuous sliding mode algorithm. The non-parametric modelling problem was reduced to design a feasible expression for the CNN weights in order to reproduce the states (including the generalized derivative of position vector) of all the nodes dynamics together and simultaneously. The adaptive laws for the CNN weights ensured the convergence of the CNN trajectories to the states of the uncertain interconnected system. To investigate the qualitative behaviour of the suggested methodology, two numerical examples were proposed. The first one represents the interconnection of three mass–spring–damper mechanical systems. The second example considers the problem of the non-parametric modelling problem for a wave partial differential equation. A set of three-dimensional graphic representations were used to demonstrate the identification abilities achieved by the CNN designed in this study for the second case.

Discussion of “Evapotranspiration Modeling Using Second-Order Neural Networks” by Sirisha Adamala, N. S. Raghuwanshi, Ashok Mishra, and Mukesh K. Tiwari

Discussion of “Evapotranspiration Modeling Using Second-Order Neural Networks” by Sirisha Adamala, N. S. Raghuwanshi, Ashok Mishra, and Mukesh K. Tiwari

Discussion of “Evapotranspiration Modeling Using Second-Order Neural Networks” by Sirisha Adamala, N. S. Raghuwanshi, Ashok Mishra, and Mukesh K. Tiwari

Discussion of “Evapotranspiration Modeling Using Second-Order Neural Networks” by Sirisha Adamala, N. S. Raghuwanshi, Ashok Mishra, and Mukesh K. Tiwari

Closure to “Evapotranspiration Modeling Using Second-Order Neural Networks” by Sirisha Adamala, N. S. Raghuwanshi, Ashok Mishra, and Mukesh K. Tiwari

Closure to “Evapotranspiration Modeling Using Second-Order Neural Networks” by Sirisha Adamala, N. S. Raghuwanshi, Ashok Mishra, and Mukesh K. Tiwari

Multistable learning dynamics in second-order neural networks with time-varying delays

In this paper, we present new results on multistability and attractivity of second-order networks with unsupervised Hebbian-type learning component and time-varying delays. By using the properties of activation functions, we divide state space into invariant sets and establish new criteria of coexistence of equilibrium points which are exponentially stable. The attained results show that second-order synaptic interactions and learning behaviour have an important effect on the multistable convergence of the networks. Finally, numerical simulations will illustrate multistable learning dynamics of second-order networks.

Unsupervised learning in second-order neural networks for motion analysis

This paper demonstrates how unsupervised learning based on Hebb-like mechanisms is sufficient for training second-order neural networks to perform different types of motion analysis. The paper studies the convergence properties of the network in several conditions, including different levels of noise and motion coherence and different network configurations. We demonstrate the effectiveness of a novel variability dependent learning mechanism, which allows the network to learn under conditions of large feature similarity thresholds, which is crucial for noise robustness. The paper demonstrates the particular relevance of second-order neural networks and therefore correlation based approaches as contributing mechanisms for directional selectivity in the retina.

Goal Directed Adaptive Behavior in Second-Order Neural Networks: The MAXSON family of architectures

The paper presents a neural network architecture (MAXSON) based on second-order connections that can learn a multiple goal approach/avoid task using reinforcement from the environment. It also enables an agent to learn vicariously, from the successes and failures of other agents. The paper shows that MAXSON can learn certain spatial navigation tasks much faster than traditional Q-learning, as well as learn goal directed behavior, increasing the agent's chances of long-term sur vival. The paper shows that an extension of MAXSON (V-MAXSON) enables agents to learn vicariously, and this improves the overall survivability of the agent population.

Associative memory design using discrete-time second-order neural networks with local interconnections

In this brief a design method for associative memories using a new model of discrete-time high-order neural networks which includes local interconnections among neurons is illustrated. The synthesis approach, which exploits the properties of pseudoinverse matrices, is flexible as it enables one to choose the complexity of the associative memory to be designed; that is, it can generate networks for associative memories with first-order and/or higher order interactions among neurons. The suggested technique preserves local interconnections among neurons, making feasible an implementation of such networks. Simulation results and comparisons among different neural architectures are reported to show the applicability of the proposed method.

Optical implementation of a translation-invariant second-order neural network for multiple-pattern classification

A novel approach to the optical implementation of second-order neural networks that can recognize multiple patterns is reported. The systems issues, especially the accuracy required for the weighted interconnections, are discussed for numeric character (0-9) recognition. It is shown that the accuracy of the weighted interconnections has a far greater influence on the network performance during training than on classification. To lessen the problem, we introduce an adaptive learning rule, whereby the optical power is adjusted during training. Finally, numeric character recognition using an experimental system with a liquid-crystal display is demonstrated.