Generalized Hopfield Neural Network Research Articles

Application of generalized hopfield neural network for the steady state analysis of self-excited induction generators

This study proposes a generalized Hopfield neural network (GHNN) for solving the non-linear equations involved in the steady state analysis of Self-Excited Induction Generators (SEIGs). Unlike other neural network architectures, the generalized Hopfield neural network can convert a non-linear equation solving problem into an optimization problem. Moreover, the weights and bias of GHNN can easily be obtained from the coefficients of the non-linear equations to be solved without additional training dataset. Motivated by its simplicity, faster convergence, and global stability properties, this study proposes a GHNN for solving the non-linear equations involved in the steady state analysis of Self-Excited Induction Generators (SEIGs). Moreover, unlike the heuristic algorithms, this approach does not require the boundary values for the unknown parameters (per unit frequency, magnetizing reactance Xm and core loss resistance Rm) of the SEIG to be given as inputs, for initiating the optimization process and it ensures guaranteed convergence. Symbolic programming technique has been employed to form the non-linear equations required for the analysis, thereby eliminating the lengthy derivations involved. The formulated equations are then used to form an energy function and a set of differential equations describing the dynamic behavior of the Hopfield network is obtained from this function. These equations are then solved until the energy function minimizes to zero to arrive at the unknown parameters of the SEIG. Using the energy function equation, the stability analysis of the proposed network has been carried out according to the Lyapunov’s second method of stability, which assures the convergence of the proposed method leading to the solutions. The proposed method has been found to be more efficient than other conventional optimization techniques, in terms of accuracy, number of iterations required and computation time. Experiments have been conducted on a 3.5 kW, 415 V SEIG and the results are shown to be in close agreement with the values predetermined using GHNN. It is also concluded that wind driven SEIGS, will find increased deployment in hybrid renewable energy sources, being applied in several emerging areas.

Hopfield Neural Network-Based Average Current Mode Control of Synchronous SEPIC Converter

ABSTRACT Average Current Mode (ACM) controlled synchronous DC–DC converters are increasingly required for computer power supplies and electric vehicle battery chargers. In this study, Generalized Hopfield Neural Network (GHNN) tuned PI controllers has been proposed for ACM control of synchronous single ended primary inductance converter (SEPIC). The dynamic converter model, required for designing the controllers, is derived using the state-space averaging technique considering all the converter non-idealities. In addition, modified Hankel matrix method is applied to reduce the derived converter model to its first-order equivalent to minimize the design complexity. Using the reduced-order model, the control loop errors are formulated as objective functions in terms of their PI controller parameters. These objective functions are then solved using GHNN to obtain the optimal PI controller parameters. The transient and steady-state performance of the converter with the proposed controller is studied and compared with controllers tuned using Zeigler Nicholas (ZN) method, Genetic Algorithm (GA), Particle Swarm Optimization (PSO), and Reduced-Order Linear Quadratic Regulator (ROLQR) control scheme for variations in the input voltage, reference voltage and load using MATLAB/ Simulink R2015b software tool. Results revealed that the proposed GHNN based controller has fast dynamic performance with less settling time, % overshoot, and steady-state error than existing control methods. A 100W converter prototype is also constructed and tested using TMS320C2000TM microcontroller to verify the effectiveness of the GHNN control algorithm.

A hybrid MFO‐GHNN tuned self‐adaptive FOPID controller for ALFC of renewable energy integrated hybrid power system

This paper proposes a hybrid moth flame optimization–generalized Hopfield neural network (MFO-GHNN) optimized self-adaptive fractional order proportional integral derivative (FOPID) controller for automatic load frequency control of multi-area hybrid power system (HPS). The control problem is formulated with an objective function of area control error associated with unknown parameters such as Kp, Ki, Kd, λ and μ of FOPID controller. The fractional order of differentiator and integrator terms, and the initial values of Kp, Ki and Kd, are drawn from MFO algorithm. Then, the Kp, Ki and Kd are fine-tuned by solving the dynamic equations governing the behaviour of GHNN under system uncertainties. To test the practicability and effectiveness of the proposed controller, the multi-area HPS is studied with uncertain change in load demand, system parameters, solar and wind power generation. The proposed method is modelled using MATLAB/Simulink. The results showed that the steady state and transient performance indices of proposed FOPID controller are significantly enhanced than the PID, MFO-FOPID and GHNN-PID controllers. In addition, the stability of non-linear dynamic HPS is analysed using Matignon's theorem of stability. Further, the performance of controller is validated using real time digital simulator run in hardware-in-the loop environment.

Remerging Feigenbaum Trees, Coexisting Behaviors and Bursting Oscillations in a Novel 3D Generalized Hopfield Neural Network

This paper, a novel 3D generalized Hopfield neural network is proposed and investigated in order to generate and highlight some unknown behaviors related to such type of neural network. This generalized model is constructed by exploiting the effect of an external stimulus on the dynamics of a simplest 3D autonomous Hopfield neural network reported to date. The stability of the model around its ac-equilibrium point is studied. We note that the model has three types of stability depending on the value of the external stimulus. The stable node-focus, the unstable saddle focus, and the stable node characterize the stability of the equilibrium point of the model. Traditional nonlinear analyses tools are used to highlight and support several complex phenomena such as remerging Feigenbaum trees, the coexistence of up to two, four and six disconnected stable states when the amplitude of the external stimulus is set to zero. Furthermore, for some values of the frequency and amplitudes of the external stimulus, bursting oscillations occur. This latter behavior is characterized by the fact that oscillations switch between quiescent states and spiking states, repetitively. The transformed phase portraits are used to support the bursting mode of oscillations found. Finally, PSpice simulations enable to support the results of the theoretical studies.

A new mechanical approach to handle generalized Hopfield neural networks

We propose a modification of the cost function of the Hopfield model whose salient features shine in its Taylor expansion and result in more than pairwise interactions with alternate signs, suggesting a unified framework for handling both with deep learning and network pruning. In our analysis, we heavily rely on the Hamilton–Jacobi correspondence relating the statistical model with a mechanical system. In this picture, our model is nothing but the relativistic extension of the original Hopfield model (whose cost function is a quadratic form in the Mattis magnetization and mimics the non-relativistic counterpart, the so-called classical limit). We focus on the low-storage regime and solve the model analytically by taking advantage of the mechanical analogy, thus obtaining a complete characterization of the free energy and the associated self-consistency equations in the thermodynamic limit. Further, on the numerical side, we test the performances of our proposal with extensive Monte Carlo simulations, showing that the stability of spurious states (limiting the capabilities of the standard Hebbian construction) is sensibly reduced due to presence of unlearning contributions that prune them massively.

An improved immune algorithm for optimizing the pulse width modulation control sequence of inverters

ABSTRACTIn this article, an improved immune algorithm (IIA), based on the fundamental principles of the biological immune system, is proposed for optimizing the pulse width modulation (PWM) control sequence of a single-phase full-bridge inverter. The IIA takes advantage of the receptor editing and adaptive mutation mechanisms of the immune system to develop two operations that enhance the population diversity and convergence of the proposed algorithm. To verify the effectiveness and examine the performance of the IIA, 17 cases are considered, including fixed and disturbed resistances. Simulation results show that the IIA is able to obtain an effective PWM control sequence. Furthermore, when compared with existing immune algorithms (IAs), genetic algorithms (GAs), a non-traditional GA, simplified simulated annealing, and a generalized Hopfield neural network method, the IIA can achieve small total harmonic distortion (THD) and large magnitude. Meanwhile, a non-parametric test indicates that the IIA is significantly better than most comparison algorithms. Supplemental data for this article can be accessed athttp://dx.doi.org/10.1080/0305215X.2016.1250894.

Design and Real-Time Implementation of SHEPWM in Single-Phase Inverter Using Generalized Hopfield Neural Network

In this paper, a real-time implementation of selective harmonic elimination pulsewidth modulation (SHEPWM) using generalized Hopfield neural network (GHNN) as applied to the single-phase inverter is designed and discussed. Finding the location of the switching instants in the case of SHEPWM involves the solution of a set of nonlinear algebraic transcendental equations. The problem is redrafted as an optimization problem, and it is solved by using GHNN. Though, in principle, then number of harmonics can be eliminated using the presented methodology, this paper tries for the case of the elimination of the 5th-, 7th-, 11th-, and 13th-order harmonics while retaining the desired fundamental. An energy function is formulated for this problem and the set of ordinary differential equations (ODEs) describing the behavior of GHNN is obtained. A program in KEIL C was developed to solve these systems of ODEs by the Runge-Kutta fourth-order method to give the switching instants for continuously varying modulation indexes (M). A MATLAB simulation was carried out, and an experimental setup was also constructed in order to validate the simulated results. The fast Fourier transform analysis of the simulated output voltage waveform and the experimental output voltage waveform confirms the effectiveness of the proposed method. Hence, the proposed method proves that it is much applicable in the industrial applications by virtue of its suitability in real-time applications.

Stability analysis for the generalized Hopfield neural networks with multi-level activation functions

Using the continuity property of neuron state variables and Lyapunov functional, this paper religiously gives sufficient conditions ensuring the equilibrium number, local stable state number, global stability and complete stability of the Hopfield neural networks with multi-level activation functions. Compared with the known relevant literatures, the obtained results are more precise. Finally, three examples are employed to illustrate the obtained criteria.

On the almost periodic solution of generalized Hopfield neural networks with time-varying delays

This paper presents several sufficient conditions about existence, uniqueness and stability of the almost periodic solution of general Hopfield neural networks with time-varying delays using exponential dichotomy, several fixed point theorems, Halanay inequality, Lyapunov functional and some inequality techniques. These results extend and improve some known relevant works, e.g. the restrictions to the connection weight matrices are slacker, and it is not required that the activation functions are globally Lipschitzian. Most importantly, these conditions are easy to check and apply. Finally, one example is employed to illustrate the conclusions, and the simulated results show the validity. Particularly, the right assertion about the existence, uniqueness and stability of the almost periodic solution of the specific generalized Hopfield neural networks is given only by our criteria, and the relevant criteria provided by a recent reference fail.

A bifurcation analysis of the four dimensional generalized Hopfield neural network

Abstract A four neuron Hopfield neural network with asymmetric weights and self-connection is analyzed. Its stable steady state and periodic attractors are identified and a complete bifurcation diagram is constructed. A center manifold reduction is undertaken and by means of normal form theory, the characteristics of the limit cycles are obtained. The network is seen to have a large memory storage capacity with both fixed point and periodic memories coexisting. The onset of chaos as reported previously is considered.

Existence and stability of global solution for generalized Hopfield neural network system

Existence and stability of global solution for generalized Hopfield neural network system

Generalized Hopfield neural network for concurrent testing

The use of generalized Hopfield neural networks in designing the checking circuitry of a concurrent testable circuit is discussed. The aliasing probability, a measure for evaluating the performance of the checking circuitry, is provided. It is shown how, by using spectral techniques based on the Reed-Muller transform, the aliasing probability can be expressed as a function of the Reed-Muller coefficients. Therefore, obtaining the checking circuitry means selecting a set of Reed-Muller spectral coefficients, with fewer elements than a given bound, that minimizes the aliasing probability. To apply the neural networks to design the checking circuitry for concurrent testing, the aliasing probability has been used as an energy function, and the Hopfield neural network has been modified to have an associated energy function with any type of polynomial dependence on the processor states.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The semi-discrete solution for generalized hopfield neural network systems with transmission

In this article, we consider a class of generalized Hopfield neural network systems with transmission. We obtain the numerical solution for the systems by using the semi-discrete method. Making use of the estimation method, we prove the existence, the uniqueness, and the convergence of the numerical solution strictly.

Stability analysis of artificial neural networks under random perturbation

Based on the theory of stochastic differential equation, the stability of a kind of continuous-time generalized Hopfield neural networks with white noise perturbation is studied in the paper, and the related stability criteria and design requirements of neural networks are established.