Parkinsonian oscillations and their suppression by closed-loop deep brain stimulation based on fuzzy concept

This paper provides an adaptive closed-loop strategy for suppressing the pathological oscillations of the basal ganglia based on a variable universe fuzzy algorithm. The pathological basal ganglia oscillations in the theta (4-9 Hz) and beta (12-35 Hz) frequency bands have been demonstrated to be associated with the tremor and rigidity/bradykinesia symptoms in Parkinson's disease (PD). Although the clinical application of open-loop deep brain stimulation (DBS) is effective, the stimulation waveform with the fixed parameters cannot be self-adjusted as the disease progresses, and thus the stimulation effects go poor. To deal with this difficult problem, a variable universe fuzzy closed-loop strategy is proposed to modulate different PD states. We establish a cortico-basal ganglia-thalamocortical network model to simulate pathological oscillations and test the control effect. The results suggest that the proposed closed-loop control strategy can accommodate the variation of brain states and symptoms, which may become an alternative method to administrate the symptoms in PD.     

Robustness of the bistable behavior of a biological signaling feedback loop

Biological signaling networks comprised of cellular components including signaling proteins and small molecule messengers control the many cell function in responses to various extracellular and intracellular signals including hormone and neurotransmitter inputs, and genetic events. Many signaling pathways have motifs familiar to electronics and control theory design. Feedback loops are among the most common of these. Using experimentally derived parameters, we modeled a positive feedback loop in signaling pathways used by growth factors to trigger cell proliferation. This feedback loop is bistable under physiological conditions, although the system can move to a monostable state as well. We find that bistability persists under a wide range of regulatory conditions, even when core enzymes in the feedback loop deviate from physiological values. We did not observe any other phenomena in the core feedback loop, but the addition of a delayed inhibitory feedback was able to generate oscillations under rather extreme parameter conditions. Such oscillations may not be of physiological relevance. We propose that the kinetic properties of this feedback loop have evolved to support bistability and flexibility in going between bistable and monostable modes, while simultaneously being very refractory to oscillatory states. (c) 2001 American Institute of Physics.     

Square-wave self-modulation in diode lasers with polarization-rotated optical feedback

The square-wave response of edge-emitting diode lasers subject to a delayed polarization-rotated optical feedback is studied in detail. Specifically, the polarization state of the feedback is rotated such that the natural laser mode is coupled into the orthogonal, unsupported mode. Square-wave self-modulated polarization intensities oscillating in antiphase are observed experimentally. We find numerically that these oscillations naturally appear for a broad range of values of parameters, provided that the feedback is sufficiently strong and the differential losses in the normally unsupported polarization mode are small. We then investigate the laser equations analytically and find that the square-wave oscillations are the result of a bifurcation phenomenon.     

Coherence and stochastic resonance in threshold crossing detectors with delayed feedback

We consider the dynamical behavior of threshold systems driven by external periodic and stochastic signals and internal delayed feedback. Specifically, the effect of positive delayed feedback on the sensitivity of a threshold crossing detector (TCD) to periodic forcing embedded in noise is investigated. The system has an intrinsic ability to oscillate in the presence of positive feedback. We first show conditions under which such reverberatory behavior is enhanced by noise, which is a form of coherence resonance (CR) for this system. Further, for input signals that are subthreshold in the absence of feedback, the open-loop stochastic resonance (SR) characteristic can be sharply enhanced by positive delayed feedback. This enhancement is shown to depend on the stimulus period, and is maximal when this period is matched to an integer multiple of the delay. Reverberatory oscillations, which are particularly prominent after the offset of periodic forcing, are shown to be eliminated by a summing network of such TCDs with local delayed feedback. Theoretical analysis of the crossing rate dynamics qualitatively accounts for the existence of CR and the resonant behavior of the SR effect as a function of delay and forcing frequency.     

Information and maximum power in a feedback controlled Brownian ratchet

Closed-loop or feedback controlled ratchets are Brownian motors that operate using information about the state of the system. For these ratchets, we compute the power output and we investigate its relation with the information used in the feedback control. We get analytical expressions for one-particle and few-particle flashing ratchets, and we find that the maximum power output has an upper bound proportional to the information. In addition, we show that the increase of the power output that results from changing the optimal open-loop ratchet to a closed-loop ratchet also has an upper bound that is linear in the information.     

Mutual synchronization in a system of two bistable oscillators executing regular and chaotic oscillations

A numerical analysis of a new model describing two coupled modified Chua??s oscillators is conducted. Equations of a partial oscillator differ from classical equations in that the former contain additional delayed feedback in another writing of dimensionless time. Changeover from regular oscillations in the absence of additional feedback to additional-feedback-induced (switchable) chaotic oscillations is studied. It is shown that, when normal regular oscillations, as well as additional-feedback-induced chaotic oscillations, are synchronized, difference oscillations are left. They are absent only when the control parameters of partial oscillators are identical. The application of a harmonic signal allows one to control the oscillations of a chaotic system of coupled modified bistable oscillators.     

Nonstationary chaotic oscillations in lasers with frequency-shifted feedback

The nonlinear dynamics of lasers with frequency-shifted delayed feedback are investigated. Resonant excitation of sustained relaxation oscillations by harmonic resonance is demonstrated. Self-induced switching between sustained relaxation oscillation and spiking oscillation is observed as the feedback coefficient is increased. Observed instabilities are well reproduced by numerical simulations of proposed model equations. A statistical analysis of this switching phenomenon is carried out numerically, and the results indicate that an inverse-power relation with the feedback coefficient determines the periods over which the system dwells in its relaxation-oscillation state.     

随机参数Duffing系统中的随机混沌及其延迟反馈控制

研究了谐和激励下含有界随机参数Duffing系统(简称随机Duffing系统)中的随机混沌及其延迟反馈控制问题.借助Gegenbauer多项式逼近理论，将随机Duffing系统转化为与其等效的确定性非线性系统.这样，随机Duffing系统在谐和激励下的混沌响应及其控制问题就可借等效的确定性非线性系统来研究.分析阐明了随机混沌的主要特点，并采用Wolf算法计算等效确定性非线性系统的最大Lyapunov指数，以判别随机Duffing系统的动力学行为.数值计算表明，恰当选取不同的反馈强度和延迟时间，可分别达到抑制或诱发系统混沌的目的，说明延迟反馈技术对随机混沌控制也是十分有效的. 关键词： 随机Duffing系统 延迟反馈控制 随机混沌 Gegenbauer多项式     

Resurgence of oscillation in coupled oscillators under delayed cyclic interaction

This paper investigates the emergence of amplitude death and revival of oscillations from the suppression states in a system of coupled dynamical units interacting through delayed cyclic mode. In order to resurrect the oscillation from amplitude death state, we introduce asymmetry and feedback parameter in the cyclic coupling forms as a result of which the death region shrinks due to higher asymmetry and lower feedback parameter values for coupled oscillatory systems. Some analytical conditions are derived for amplitude death and revival of oscillations in two coupled limit cycle oscillators and corresponding numerical simulations confirm the obtained theoretical results. We also report that the death state and revival of oscillations from quenched state are possible in the network of identical coupled oscillators. The proposed mechanism has also been examined using chaotic Lorenz oscillator.     

Phase switching in Hindmarsh-Rose relay neurons

A system of Hindmarsh-Rose relay neurons with time delay coupling is considered in which the relay (central) neuron has an additional feedback term that represents the interaction activity with a local environment. The strength of environmental coupling with the central neuron plays an important role in inducing synchronization and de-synchronization between the outer neurons. The strength of feedback developed from the environmental coupling has created a gradual quenching in the oscillations of the central neuron. At a higher feedback coupling strength, oscillation of the central neuron is suppressed drastically and a transition from a regime of synchronization to out-of-phase synchronization take place between the oscillations of the two outer neurons.     

Feedback control of flow resonances using balanced reduced-order models

This paper investigates the use of balanced reduced-order models for the feedback control of flow resonances. Specifically, the Eigensystem Realization Algorithm is used to find balanced reduced-order models of the linear dynamics of such flow resonances. The method is applied first to a computational problem in direct numerical simulations of cavity resonances, and then to a lab-scale experiment of combustion oscillations. Although the resulting reduced-order models both have fewer than 10 degrees of freedom, the feedback controllers that are based on them perform very well, with closed-loop stability achieved over a wide range of operating conditions.     

Transport reversal in a delayed feedback ratchet

Feedback flashing ratchets are thermal rectifiers that use information on the state of the system to operate the switching on and off of a periodic potential. They can induce directed transport even with symmetric potentials thanks to the asymmetry of the feedback protocol. We investigate here the dynamics of a feedback flashing ratchet when the asymmetry of the ratchet potential and of the feedback protocol favor transport in opposite directions. The introduction of a time delay in the control strategy allows one to nontrivially tune the relative relevance of the competing asymmetries leading to an interesting dynamics. We show that the competition between the asymmetries leads to a current reversal for large delays. For small ensembles of particles current reversal appears as the consequence of the emergence of an open-loop like dynamical regime, while for large ensembles of particles it can be understood as a consequence of the stabilization of quasiperiodic solutions. We also comment on the experimental feasibility of these feedback ratchets and their potential applications.     

Chaotic breathers in delayed electro-optical systems

We show that in integro-differential delayed dynamical systems, a hybrid state of simultaneous fast-scale chaos and slow-scale periodicity can emerge subsequently to a sequence of Hopf bifurcations. The resulting time trace thereby consists in chaotic oscillations "breathing" periodically at a significantly lower frequency. Experimental evidence of this type of dynamics in delayed dynamical systems is achieved with a Mach-Zehnder modulator optically fed by a semiconductor laser and is subjected to a delayed nonlinear electro-optical feedback. We also propose a theoretical understanding of the phenomenon.     

Real-Time Quantum Feedback Control: ManipulatingQuantum State in Non-Markovian System

In this paper, we propose a closed-loop real-time feedback design for manipulating a quantum state to a target eigenstate via sequential measurements. To this end, based on the Lyapunov stability theorem, considering the controllability and convergence of the system, we select one measured observable and two control channels, which feedback part of the output signal to the input end, forming a closed-loop control. By dynamical programming, we find the optimal parameters to achieve state transfer with a high probability by real-time feedback control. Numerical simulation experiments show that, in a stochastic quantum system with non-Markovian noise, the real-time control strategy moves the system from initial state to the target eigenstate with fast convergence.

     

Experimental validation of a collocated PVDF volume velocity sensor/actuator pair

The active control of sound transmission through a rectangular panel is experimentally verified. The control system is based on a collocated volume velocity sensor/actuator pair which measures and excites the first radiation mode of the panel. Suppression of the first radiation mode is an efficient strategy to control the low frequency sound radiation from the panel. This configuration leads to a simple single-input single-output control system, to which feedback control can be applied.Two implementations of the volume velocity sensor/actuator pair are tested. First, a polyvinyledene fluoride polymer (PVDF) volume velocity actuator foil with shaped electrodes is used in combination with an identical PVDF volume velocity sensor foil. Due to the mechanical coupling between the PVDF sensor and actuator foil, it is shown that a direct velocity feedback control scheme is not feasible because higher order structural modes will be destabilized. Instead integral force feedback is applied, such that the open-loop transfer function has a roll-off towards higher frequencies. Experiments show that this control strategy results in a reduction of the sound pressure in the receiving room of 10 dB at the first structural resonance without spillover to higher order modes. Due to the roll-off towards high frequencies, the control over higher order modes remains limited. Second, a discrete volume velocity sensor is constructed by summing the signals from 12 point sensors placed on the panel. The volume velocity actuator consists of two PVDF foils, glued on each side of the panel and driven in opposite phase. Direct volume velocity feedback is applied to this system, which is minimum phase. This control system is capable of reducing the sound pressure in the receiving room below 300 Hz by 10-15 dB without spillover to higher order modes.     

Markov Quantum Feedback Control Based on Homodyne Measurement of a Two-Qubit System

We consider the system consisting of two qubits collectively damped,with the output being unit-efficiency measured and subsequently fedback to control the system state. Our primary goal in this paper is (i) to solve the feedback-modified master equation, (ii) to demonstrate the ability of feedback control based on the solutions, and (iii) to pick out different steady states by choosing different driving strengths and feedback strengths tocounteract the effects of both damping and the measurement back-action on the system. We further investigate some properties of the equilibrium steady state, its distribution probability and entanglement vs. the driving and feedback amplitudes. We find that in our feedback model feedback plays a negative role in producing entanglement.     

Noise-induced optical bistability and state transitions in spin-crossover solids with delayed feedback

Considering the time-delayed feedback and environmental perturbations in spin-crossover system, we construct a stochastic delayed differential equation to study the state transitions from the low spin (LS) state to the high spin (HS) state in spin-crossover solids. It is shown that the delayed feedback and noise can induce optical bistability and state transitions. The mean first-passage time (MFPT) of the transition from the LS state to the HS state as the function of the noise intensity exhibits a maximum, and the noise-enhanced stability is observed. However the MFPT decreases with increase of the delayed feedback intensity, thus the delayed feedback accelerates the conversion from the LS state to the HS state.     

统一混沌系统的时延模糊控制

在将统一混沌系统表达为T-S模型的基础上, 利用泛函微分方程的Lyapunov-Krasovskii稳定性理论和线性矩阵不等式(LMIs)方法,设计出一个新的带时延状态反馈模糊控制器.仿真结果显示,所设计的控制器能有效地控制统一混沌系统的混沌时间轨迹到其平衡点,且控制简单可靠.     

Comparison of decentralized velocity feedback control for thin homogeneous and stiff sandwich panels using electrodynamic proof-mass actuators

Theoretical and experimental work is presented to compare the effect of decentralised velocity feedback control on thin homogeneous and sandwich panels. The decentralised control system consists of five control units, which are composed of a proof-mass electrodynamic actuator with an accelerometer underneath its footprint and an analogue controller. The stability of the feedback loops is analysed by considering the sensor-actuator open-loop frequency response function of each control unit and the eigenvalues of the fully populated matrix of open-loop frequency response functions between the five sensors and five actuators. The control performance is then analysed in terms of the time-averaged total kinetic energy and total sound power radiated by the two panels. The results show that for a stiff sandwich panel higher stable feedback gains can be implemented than on a thin homogeneous panel of comparable weight per unit area. Moreover the implementation of decentralised velocity feedback can offset some of the undesirable sound transmission properties of lightweight sandwich structures by efficiently reducing structural vibration and sound power radiation in the mid audio frequency range.