Washout Filter Control Research Articles

Bifurcation anti‐control technique in a fractional‐order stable finance model

AbstractSetting up differential models to give a description of the object economical phenomenon in the world today is very essential in economics and mathematics. In this current study, we are committed to the study on the anti‐control of Hopf bifurcation for a fractional‐order stable finance model. By virtue of a suitable washout filter controller involving time delay, we obtain a fractional‐order controlled finance model. Selecting the time delay as bifurcation parameter, we derive a new delay‐independent stability and bifurcation condition to assure that the involved fractional‐order controlled finance model is locally asymptotically stable and generates Hopf bifurcation around the equilibrium point. The investigation clearly manifests that the designed washout filter controller is a very effective means of bifurcation anti‐control. Ultimately, the obtained simulation figures and bifurcation diagrams are sufficiently presented to verify effectiveness for the proposed control technique. The established theoretical fruits have great significance in maintaining financial balance. Up to the present, the report on anti‐control technique of Hopf bifurcation for fractional‐order dynamical systems is quite rare. The research idea can also be applied to probe into the control issue of bifurcation and chaos for numerous other fractional‐order dynamical models in many areas.

Washout filter control technique for a fractional-order chaotic finance model

On the basis of the previous publications, we set up a new fractional-order chaotic finance model. Taking advantage of washout filter controller, we are committed to the study on the chaotic control for the considered fractional-order chaotic finance model. Applying the stability criterion and Hopf bifurcation knowledge of fractional order differential dynamical system, a series of delay-independent stability and bifurcation conditions are established to assure the stability and the occurrence of Hopf bifurcation of the fractional-order controlled chaotic finance model. The investigation indicates that the role of delay in controlling the stability and Hopf bifurcation for the fractional-order controlled chaotic finance model is fully reflected. In the end, numerical simulation figures and bifurcation plots are presented to sustain the established primary conclusions. Our work supplements the earlier studies and enriches the chaos control theory of fractional-order dynamical system.

Control of Hopf Bifurcation Type of a Neuron Model Using Washout Filter

A quantitative mathematical model of neurons should not only include enough details to consider the dynamics of single neurons but also minimize the complexity of the model so that the model calculation is convenient. The two-dimensional Prescott model provides a good compromise between the authenticity and computational efficiency of a neuron. The dynamic characteristics of the Prescott model under external electrical stimulation are studied by combining analytical and numerical methods in this paper. Through the analysis of the equilibrium point distribution, the influence of model parameters and external stimulus on the dynamic characteristics is described. The occurrence conditions and the type of Hopf bifurcation in the Prescott model are analyzed, and the analytical determination formula of the Hopf bifurcation type in the neuron model is obtained. Washout filter control is used to change the Hopf bifurcation type, so that the subcritical Hopf bifurcation transforms to supercritical Hopf bifurcation, so as to realize the change of the dynamic characteristics of the model.

Bifurcation Patterns of Bursting within pre-Bötzinger Complex and Their Control

A variety of firing rhythms can be generated spontaneously in the pre-Bötzinger complex. External stimuli can cause changes in the pattern of the firing rhythm, which may cause different physiological effects in the body. In this study, by the fast and slow time scale dynamics, with one- and two-parameter bifurcation analysis, we study the bursting patterns and their transition mechanisms of the pre-Bötzinger complex under washout filter controller. The results may help us understand the relationship between different firing patterns of neurons and external stimuli, and further reveal the mechanisms of disease due to external stimuli.

Control strategies for Hopf bifurcation in a chaotic associative memory

Abstract This paper presents a set of control approaches that can deal with unwanted dynamics such as the Hopf Bifurcation in a Chaotic Associative Memory (CAM) for two distinct goals: the bifurcation critical point shift to anticipate or to postpone the start of a Hopf bifurcation; or to extinguish it. A Washout Filter Control, a Polynomial Control, and an adaptive control for data-driven called the Model-Free Adaptive Control were used in this study. We present the results of numerical simulations in a CAM with three neurons (a system with six dimensions), which were trained classically to retrieve a set of memories. Our analysis includes the dynamics of the bifurcated system, the ability of the network to recover the memories learned and how it is affected by the control strategies. The generality of the proposed control approaches was tested to control a different system and for a different behavior (chaotic dynamics).

Improved Droop Control with Washout Filter

In this paper, a droop washout filter controller (DWC), composed of a conventional droop controller and a washout filter controller, is proposed. The droop controller is used to ensure the “plug-and-play” capability, and the droop gain is set small. The washout filter is introduced to compensate the active power dynamic performance (APDP). Compared to the droop controller, the DWC can achieve accurate active power sharing and smaller frequency difference without losing the APDP. Additionally, a novel modeling technology is proposed, using which a small-signal model for an island microgrid (MG) is constructed as a singular system. The system’s stability is analyzed and the DWC is verified using real-time (RT-LAB) simulation with hardware in the loop (HIL).

Analysis of Washout Filter-Based Power Sharing Strategy—An Equivalent Secondary Controller for Islanded Microgrid Without LBC Lines

As a supplement of the droop control, the concept of secondary controlled microgrid (MG) has been extensively studied for voltage and frequency restoration. However, the low band-width communication (LBC) channels are needed to exchange information between the primary and secondary controllers, and the performance of the secondary controller degrades due to the uncertain communication delay and data drop-out in the LBC lines. Recently, a washout filter-based power sharing method was presented without communication lines and additional control loops. In this paper, the equivalence between secondary control and washout filter-based power sharing strategy for islanded MG is demonstrated, and the generalized washout filter control scheme has been obtained. Additionally, the physical meaning of control parameters of secondary controllers is also presented. Besides, a complete small-signal model of the generalized washout filter-based control method for islanded MG system is built, which can be utilized to design the control parameters and analyze the stability of MG system. Finally, extensive simulation and experimental results are provided to confirm the validity and effectiveness of the derived equivalent control scheme for islanded MG.

Hopf bifurcation control of the Rössler system based on Washout filter controller

The Washout filter is adopted to control Hopf bifurcation in Rössler system. The effect of its parameters on the position of bifurcation point, the bifurcation type, and the amplitude of periodic solution is discussed in detail. Based on Routh criterion, the stability region in parameter space is found out firstly. Then the influence of the filter’s time constant and the linear gain on the location of bifurcation point is analyzed. By using the Direct Normal Form method, the normal form of the controlled Rössler system is deduced and the coefficient of resonant term is expressed as a function of the nonlinear gain. It is revealed that, by changing the sign and the absolute value of the real part of the coefficient, the nonlinear gain can modify the periodic solution’s amplitude and Hopf bifurcation type. All the results obtained are verified by numerical simulation.

Action potential initial dynamical control and analysis of a minimum neuron model

Neuron is a basic unit of information transmission in the nervous system . Neuron encodes the information input from the dendrites by generating action potential sequences of different firing patterns. The different firing patterns result from different action potential initial dynamic mechanisms for neurons to generate spikes. The result of competition between neuron ion currents with different dynamic features in the sub threshold potential determines the action potential initial dynamic mechanism. In this paper, we adopt a minimum neuron model to design the wash-out filter from a physiological view for achieving the transition between different action potential initial dynamic mechanisms and for verifying that the wash-out filter control changes the action potential initial dynamic mechanism of neuron by affecting the result of competition between currents with different dynamic features in the sub-threshold potential.

Chaotic synchronization of a fractional-order system based on washout filter control

In this paper, chaos in a fractional-order neural network system with varying time delays is presented, and chaotic synchronization system with varying time delays is constructed. The stability of constructed synchronization system is analyzed by Laplace transformation theory. In addition, the bifurcation graph of the chaotic system is illustrated. The study results show that the chaos in such fractional-order neural networks with varying time delay can be synchronized, and Washout filter control can be used to reduce the range of coupled parameter.

Flutter Control of a Two-dimensional Airfoil Using Wash-out Filter Technique

The wash-out filter (WF) technique is used to control the flutter of a two dimensional air-foil with cubic non-linearity in incompressible flow. Firstly, Hopf bifurcation theory is used to determine the point at which the nonlinear controller is introduced. The system is then transformed into Jordan canonical form, based on analysis of linearized eigenvalues of the system. Secondly, for the introduced WF controller, the linear control gain is determined according to Hopf bifurcation condition. The symbolic computing program of normal form direct method (NFDM) is also used to obtain the normal form of the controlled system. The non-linear control gain can be determined based on the relation of the type of bifurcation and the parameters of the normal form, to transform sub-critical Hopf bifurcation to be super critical one Lastly, numerical simulations are used to certify the validity of theoretical analysis, in which the amplitude of flutter or limit cycle of the controlled system is reduced greatly, comparing to the original system.