Constrained charge-balanced minimum-power controls for spiking neuron oscillators

Dasanayake, Isuru; Li, Jr-Shin

doi:10.1016/j.sysconle.2014.09.011

Cited by 21 publications

(17 citation statements)

References 41 publications

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“…This figure illustrates the limits on possible spiking times of the Hodgkin-Huxley model, which is important to the design of practical control inputs. For example, the knowledge of the feasible spiking range is helpful in designing optimal controls with other objectives such as minimum power controls [13]. The optimal controls derived based on the Hodgkin-Huxley phase model, shown in Figure 4(b) and 4(c), are applied to the full Hodgkin-Huxley model, and a repeated application of such controls results in the desired spiking trains as displayed in Figure 7(a) and 7(b).…”

Section: Validation Of Phase Model Reduction To Full State-space Modelmentioning

confidence: 99%

“…Recently, controltheoretic approaches, including calculus of variations and the maximum principle, have been employed to design external stimuli for optimal manipulation of the dynamic behavior of neuron oscillators. These include the design of minimum-power controls for spiking a single neuron at specified time instances [11,12,13], optimal waveforms for entrainment of neuron ensembles [14,15,16], and open-loop controls for establishing and maintaining a desired phase configuration, such as anti-phase for two coupled neuron oscillators [17]. Work on considering stochastic effects to neuron systems such as the optimal control of neuronal spiking activity receiving a class of random synaptic inputs has also been investigated [18].…”

Section: Introductionmentioning

confidence: 99%

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Design of Charge-Balanced Time-Optimal Stimuli for Spiking Neuron Oscillators

Dasanayake

2014

Neural Computation

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Abstract. In this paper, we investigate the fundamental limits on how the interspike time of a neuron oscillator can be perturbed by the application of a bounded external control input (a current stimulus) with zero net electric charge accumulation. We use phase models to study the dynamics of neurons and derive charge-balanced controls that achieve the minimum and maximum inter-spike times for a given bound on the control amplitude. Our derivation is valid for any arbitrary shape of the phase response curve and for any value of the given control amplitude bound. In addition, we characterize the change in the structures of the charge-balanced time-optimal controls with the allowable control amplitude. We demonstrate the applicability of the derived optimal control laws by applying them to mathematically ideal and experimentally observed neuron phase models, including the widely-studied Hodgkin-Huxley phase model, and by verifying them with the corresponding original full state-space models. This work addresses a fundamental problem in the field of neural control and provides a theoretical investigation to the optimal control of oscillatory systems.

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Section: Validation Of Phase Model Reduction To Full State-space Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Design of Charge-Balanced Time-Optimal Stimuli for Spiking Neuron Oscillators

Dasanayake

2014

Neural Computation

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“…This means that there may be such ψ, the constants χ + and C that satisfy Eqs. (18), (19), and (20), but the waveform ψ is not optimal. In such cases nonoptimal waveforms need to be filtered out.…”

Section: Optimal Waveformmentioning

confidence: 99%

“…The shifted optimal envelope ψ * inv (τ − χ + ) will satisfy the condition Eqs. (18) and (19) with the constants χ + inv = 2π −χ + and C inv = −C. Since any optimal waveform ψ * 2 ∈ (1/2, 1] can be "inverted", we will focus only on the waveforms ψ * 2 ∈ [0, 1/2].…”

Section: Optimal Waveformmentioning

confidence: 99%

Optimal waveform for the entrainment of oscillators perturbed by an amplitude-modulated high-frequency force

Novičenko

Ratas

2016

Phys. Rev. E

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We analyze limit cycle oscillators under perturbation constructed as a product of two signals, namely, an envelope with a period close to natural period of an oscillator and a high-frequency carrier signal. A theory for obtaining an envelope waveform that achieves the maximal frequency interval of entrained oscillators is presented. The optimization problem for fixed power and maximal allowed amplitude is solved by employing the phase reduction method and the Pontryagin's maximum principle. We have shown that the optimal envelope waveform is a bang-bang-type solution. Also, we have found "inversion" symmetry that relates two signals with different powers but the same interval of entrained frequencies. The theoretical results are confirmed numerically on FitzHugh-Nagumo oscillators.

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“…It is also applicable to the treatment of subthalamic nucleus [7]. In these and many other neurological applications, considerations of optimal electrical stimulation, especially low-power electrical stimuli, are desired, since application of high power stimuli is harmful to the biological tissues and the reduction of power consumption in a neurological implant is essential in order to reduce its size and lengthen its lifetime [8].…”

Section: Introductionmentioning

confidence: 99%

A new approach to optimal control of conductance-based spiking neurons

Lou

Swamy

2017

Neural Networks

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This paper presents an algorithm for solving the minimum-energy optimal control problem of conductance-based spiking neurons. The basic procedure is (1) to construct a conductance-based spiking neuron oscillator as an affine nonlinear system, (2) to formulate the optimal control problem of the affine nonlinear system as a boundary value problem based on Pontryagin's maximum principle, and (3) to solve the boundary value problem using the homotopy perturbation method. The construction of the minimum-energy optimal control in the framework of the homotopy perturbation technique is novel and valid for a broad class of nonlinear conductance-based neuron models. The applicability of our method in the FitzHugh-Nagumo and Hindmarsh-Rose models is validated by simulations.

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Constrained charge-balanced minimum-power controls for spiking neuron oscillators

Cited by 21 publications

References 41 publications

Design of Charge-Balanced Time-Optimal Stimuli for Spiking Neuron Oscillators

Design of Charge-Balanced Time-Optimal Stimuli for Spiking Neuron Oscillators

Optimal waveform for the entrainment of oscillators perturbed by an amplitude-modulated high-frequency force

A new approach to optimal control of conductance-based spiking neurons

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