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This paper explores event-based feedback schemes for controlling spike timing in phase models of neurons with the constraint of a charge- balanced stimulus over a period of stimulation. We present an energy-optimal control system based on variational methods. We also present a biologically- inspired quasi-impulsive control system that, mimicking the signaling behavior of real neurons, can achieve reference phase tracking. Applied to a pacemaker- driven ensemble, this control can achieve desynchronization using a set of charge-balanced stimuli.

Objective. To demonstrate the applicability of optimal control theory for designing minimum energy charge-balanced input waveforms for single periodically-firing in vitro neurons from brain slices of Long-Evans rats. Approach. The method of control uses the phase model of a neuron and does not require prior knowledge of the neuron’s biological details. The phase model of a neuron is a one-dimensional model that is characterized by the neuron’s phase response curve (PRC), a sensitivity measure of the neuron to a stimulus applied at different points in its firing cycle. The PRC for each neuron is experimentally obtained by measuring the shift in phase due to a short-duration pulse injected into the periodically-firing neuron at various phase values. Based on the measured PRC, continuous-time, charge-balanced, minimum energy control waveforms have been designed to regulate the next firing time of the neuron upon application at the onset of an action potential. Main result. The designed waveforms can achieve the inter-spike-interval regulation for in vitro neurons with energy levels that are lower than those of conventional monophasic pulsatile inputs of past studies by at least an order of magnitude. They also provide the advantage of being charge-balanced. The energy efficiency of these waveforms is also shown by performing several supporting simulations that compare the performance of the designed waveforms against that of phase shuffled surrogate inputs, variants of the minimum energy waveforms obtained from suboptimal PRCs, as well as pulsatile stimuli that are applied at the point of maximum PRC. It was found that the minimum energy waveforms perform better than all other stimuli both in terms of control and in the amount of energy used. Specifically, it was seen that these charge-balanced waveforms use at least an order of magnitude less energy than conventional monophasic pulsatile stimuli. Significance. The significance of this work is that it uses concepts from the theory of optimal control and introduces a novel approach in designing minimum energy charge-balanced input waveforms for neurons that are robust to noise and implementable in electrophysiological experiments. (Some figures may appear in colour only in the online journal)

With inspiration from Arthur Winfree's idea of randomizing the phase of an oscillator by driving its state to a set in which the phase is not defined, i.e., the phaseless set, we employ a Hamilton-Jacobi-Bellman approach to design a minimum energy control law that effectively randomizes the next spiking time for a two-dimensional conductance-based model of noisy oscillatory neurons. The control is initially designed for the deterministic system through the numerical solution of the Hamilton-Jacobi-Bellman partial differential equation for the cost-to-go function, from which the minimum energy stimulus can be found; then its performance is investigated in the presence of noise. It is shown that such control causes a considerable amount of randomization in the timing of the neuron's next spike.

We employ optimal control theory to design an event-based, minimum energy, desynchronizing control stimulus for a network of pathologically synchronized, heterogeneously coupled neurons. This works by optimally driving the neurons to their phaseless sets, switching the control off, and letting the phases of the neurons randomize under intrinsic background noise. An event-based minimum energy input may be clinically desirable for deep brain stimulation treatment of neurological diseases, like Parkinson's disease. The event-based nature of the input results in its administration only when it is necessary, which, in general, amounts to fewer applications, and hence, less charge transfer to and from the tissue. The minimum energy nature of the input may also help prolong battery life for implanted stimulus generators. For the example considered, it is shown that the proposed control causes a considerable amount of randomization in the timing of each neuron's next spike, leading to desynchronization for the network.

We consider the problem of desynchronizing a network of synchronized, globally (all-to-all) coupled neurons using an input to a single neuron. This is done by applying the discrete time dynamic programming method to reduced phase models for neural populations. This technique numerically minimizes a certain cost function over the whole state space, and is applied to a Kuramoto model and a reduced phase model for Hodgkin-Huxley neurons with electrotonic coupling. We evaluate the effectiveness of control inputs obtained by averaging over results obtained for different coupling strengths. We also investigate the applicability of this method to Hodgkin-Huxley models driven by multiplicative stimuli.

By injecting an electrical current control stimulus into a neuron, one can change its inter-spike intervals. In this paper, we investigate the time optimal control problem for periodically firing neurons, represented by different one-dimensional phase models, and find analytical expressions for the minimum and maximum values of inter-spike intervals achievable with small bounded control stimuli. We consider two cases: with a charge-balance constraint on the input, and without it. The analytical calculations are supported with numerical results for examples of qualitatively different neuron models.

We present a new approach to the problem of desynchronization of a population of all-to-all coupled oscillators. Motivated by Deep Brain Stimulation treatment of Parkinson's Disease, the objective is to break this synchrony in the fullest measure by means of a control input only applied to one of the oscillators. Specifically, nonlinear hybrid control is proposed as a novel method for robust global asymptotic stabilization of the splay state. The problem setup is presented in a general way, and a simple example is solved that gives an idea of how this method might be applied in practice.

The optimal input current for a reduced neuron model and a specific target spiking time is obtained. The objective of optimization is to minimize the total input energy to the system subject to a zero net input integral over the time horizon. This “charge-balance constraint” ensures that no net external charge is injected into the neuron. The results are compared to optimal currents for which the charge-balance constraint is not imposed.

In this paper, a fuzzy based controller is developed in order to control the braking action of the rear axle of a series hybrid city bus. The controller's target is to recapture the kinetic energy of the bus as much as possible during braking, while still maintaining its stability. The bus under study is one of the Iran-Khodro Company's productions called O457 which is currently undergoing a procedure of hybridization. The hybrid type used is a series hybrid configuration in which an internal combustion engine and a battery pack supply its electric traction motors in order to propel the bus. The implemented fuzzy controller takes the bus speed, batteries SOC level and the brake-pedal displacement as its three input variables. The developed controller is adopted to analyze the O457 energy regeneration performance on three different drive cycles, each repeated four times on three different ground grades. Simulation results show higher energy regeneration compared to the ADvanced VehIcle SimulatOR, ADVISOR results in all cases.

In this paper a fuzzy power controller for a parallel hybrid passenger car is developed in order to minimize its fuel consumption and optimize its components efficiencies. This is done by controlling the engine operating points in its optimal region and maintaining the SoC of batteries and electric motor operating point at the highest possible efficiency. Of course the designed control strategy must be able to obey the driver’s commands and achieve the PNGV regulations. The controller implemented in this paper is a Mamdani fuzzy logic controller which takes the batteries SoC, electric motor’s speed, ICE speed and the total demanded torque as its input variables and gives the ICE torque as its output. This controller has been simulated using the ADvanced VehIcle SimulatOR (ADVISOR) and its results have been compared to the default fuel mode fuzzy controller of ADVISOR. Simulation results show considerable improvement in the efficiency of the ICE and consequently, fuel consumption and acceleration performances.Copyright © 2006 by ASME

Objective. To demonstrate the applicability of optimal control theory for designing minimum energy charge-balanced input waveforms for single periodically-firing in vitro neurons from brain slices of Long-Evans rats. Approach. The method of control uses the phase model of a neuron and does not require prior knowledge of the neuron’s biological details. The phase model of a neuron is a one-dimensional model that is characterized by the neuron’s phase response curve (PRC), a sensitivity measure of the neuron to a stimulus applied at different points in its firing cycle. The PRC for each neuron is experimentally obtained by measuring the shift in phase due to a short-duration pulse injected into the periodically-firing neuron at various phase values. Based on the measured PRC, continuous-time, charge-balanced, minimum energy control waveforms have been designed to regulate the next firing time of the neuron upon application at the onset of an action potential. Main result. The designed waveforms can achieve the inter-spike-interval regulation for in vitro neurons with energy levels that are lower than those of conventional monophasic pulsatile inputs of past studies by at least an order of magnitude. They also provide the advantage of being charge-balanced. The energy efficiency of these waveforms is also shown by performing several supporting simulations that compare the performance of the designed waveforms against that of phase shuffled surrogate inputs, variants of the minimum energy waveforms obtained from suboptimal PRCs, as well as pulsatile stimuli that are applied at the point of maximum PRC. It was found that the minimum energy waveforms perform better than all other stimuli both in terms of control and in the amount of energy used. Specifically, it was seen that these charge-balanced waveforms use at least an order of magnitude less energy than conventional monophasic pulsatile stimuli. Significance. The significance of this work is that it uses concepts from the theory of optimal control and introduces a novel approach in designing minimum energy charge-balanced input waveforms for neurons that are robust to noise and implementable in electrophysiological experiments. (Some figures may appear in colour only in the online journal)