Time optimal control of spiking neurons

Nabi, Ali; Moehlis, Jeff

doi:10.1007/s00285-011-0441-5

Cited by 43 publications

(21 citation statements)

References 31 publications

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“…In addition, controllability of an ensemble of uncoupled neurons was explored for various mathematically ideal phase models, where an effective computational optimal control method based on pseudospectral approximations was employed to construct optimal controls that elicit simultaneous spikes of a neuron ensemble [19,20]. The derivation of time-optimal and spike timing controls for spiking neurons has been attempted for limited classes of control functions [21,22], however, a complete characterization of the optimal solutions has not been provided, and an analytical and systematic approach for synthesizing the time-optimal controls has been missing.…”

Section: Introductionmentioning

confidence: 99%

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: Introductionmentioning

confidence: 99%

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

Dasanayake

2014

Neural Computation

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“…In the case of optimal convergence, considering (20) withū = α/T , we can easily see that there exists a value T cr > 0 such that φ(x * (T cr )) = 0. It follows that, for values T > T cr (ū < α/T cr ), the control pushes the trajectory onto the isostable |φ| = 0, thereby yielding an infinite time delay (8). Choosingū small and T large is therefore the optimal strategy.…”

Section: Magnitude and Duration Of The Control: Optimal Strategiesmentioning

confidence: 99%

“…The optimal control problem could be extended to other types of attractors, in which case the notion of isostables might need to be generalized. In the case of limit cycles, a similar problem using the so-called isochrons (instead of the isostables) could be investigated and related to existing results of time-optimal control [8].…”

Section: Magnitude and Duration Of The Control: Optimal Strategiesmentioning

confidence: 99%

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Converging to and escaping from the global equilibrium: Isostables and optimal control

Mauroy

2014

53rd IEEE Conference on Decision and Control

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Abstract-This paper studies the optimal control of trajectories converging to or escaping from a stable equilibrium. The control duration is assumed to be short. When the control is turned off, the trajectories have not reached the target and they subsequently evolve according to the free motion dynamics. In this context, we show that the problem can be formulated as a finite-horizon optimal control problem which relies on the notion of isostables. For linear and nonlinear systems, we solve this problem using Pontryagin's maximum principle and we study the relationship between the optimal solutions and the geometry of the isostables. Finally, optimal strategies for choosing the magnitude and duration of the control are considered.

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“…For instance, an optimal control scheme was performed in (Ahmadian, et al, 2011), where the control current I, consisted of the sequence of rectangular pulses, was limited in its amplitude. Alternative analysis (for a simplified 1-dimensional reduced model) was given in (Nabi & Moehlis, 2012). Adapted inverse control on spike train with delay was developed in (Li, et al, 2013).…”

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confidence: 99%