Electrical and Electronic Engineering - Research Publications
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ItemElectrical Stimulation of Neural Tissue Modeled as a Cellular Composite: Point Source Electrode in an Isotropic Tissue(IEEE, 2014)Standard volume conductor models of neural electrical stimulation assume that the electrical properties of the tissue are well described by a conductivity that is smooth and homogeneous at a microscopic scale. However, neural tissue is composed of tightly packed cells whose membranes have markedly different electrical properties to either the intra- or extracellular space. Consequently, the electrical properties of tissue are highly heterogeneous at the microscopic scale: a fact not accounted for in standard volume conductor models. Here we apply a recently developed framework for volume conductor models that accounts for the cellular composition of tissue. We consider the case of a point source electrode in tissue comprised of neural fibers crossing each other equally in all directions. We derive the tissue admittivity (that replaces the standard tissue conductivity) from single cell properties, and then calculate the extracellular potential. Our findings indicate that the cellular composition of tissue affects the spatiotemporal profile of the extracellular potential. In particular, the full solution asymptotically approaches a near-field limit close to the electrode and a far-field limit far from the electrode. The near-field and far-field approximations are solutions to standard volume conductor models, but differ from each other by nearly an order or magnitude. Consequently the full solution is expected to provide a more accurate estimate of electrical potentials over the full range of electrode-neurite separations.
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ItemAveraging for nonlinear systems on Riemannian manifolds(IEEE, 2013)This paper provides a derivation of the averaging methods for nonlinear time-varying dynamical systems defined on Riemannian manifolds. We extend the results on ℝ n to Riemannian manifolds by employing the language of differential geometry.
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ItemExtremum seeking control for nonlinear systems on compact Riemannian manifolds(IEEE Press, 2014)This paper formulates the extremum seeking control problem for nonlinear dynamical systems which evolve on Riemannian manifolds and presents stability results for a class of numerical algorithms defined in this context. The results are obtained based upon an extension of extremum seeking algorithms in Euclidean spaces and a generalization of Lyapunov stability theory for dynamical systems defined on Rimannian manifolds. We employ local properties of Lyapunov functions to extend the singular perturbation analysis on Riemannian manifolds. Consequently, the results of the singular perturbation on manifolds are used to obtain the convergence of extremum seeking algorithms for dynamical systems on Riemannian manifolds.
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ItemCloseness of solutions and averaging for nonlinear systems on Riemannian manifolds(IEEE, 2013)An averaging result for periodic dynamical systems evolving on Euclidean spaces is extended to those evolving on (differentiable) Riemannian manifolds. Using standard tools from differential geometry, a perturbation result for time-varying dynamical systems is developed that measures closeness of trajectories via a suitable metric on a finite time horizon. This perturbation result is then extended to bound excursions in the trajectories of periodic dynamical systems from those of their respective averages, on an infinite time horizon, yielding the specified averaging result. Some simple examples further illustrating this result are also presented.
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ItemA UNIFYING FRAMEWORK FOR ANALYSIS AND DESIGN OF EXTREMUM SEEKING CONTROLLERS(IEEE, 2012-01-01)We summarize a unifying design approach to continuous-time extremum seeking that was recently reported by the authors. This approach is based on a feedback control paradigm that was to the best of our knowledge explicitly summarized for the first time in this form in our recent work. This paradigm covers some existing extremum seeking schemes, provides a direct link to off-line optimization and can be used as a unifying framework for design of novel extremum seeking schemes. Moreover, we show that other extremum seeking problem formulations can be interpreted using this unifying viewpoint. We believe that this unifying view will be invaluable to systematically design and analyze extremum seeking controllers in various settings.
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ItemTrajectory-based proofs for sampled-data extremum seeking control(IEEE, 2013)Extremum seeking of nonlinear systems based on a sampled-data control law is revisited. It is established that under some generic assumptions, semi-global practical asymptotically stable convergence to an extremum can be achieved. To this end, trajectory-based arguments are employed, by contrast with Lyapunov-function-type approaches in the existing literature. The proof is simpler and more straightforward; it is based on assumptions that are in general easier to verify. The proposed extremum seeking framework may encompass more general optimisation algorithms, such as those which do not admit a state-update realisation and/or Lyapunov functions. Multi-unit extremum seeking is also investigated within the context of accelerating the speed of convergence.
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ItemOn a Shubert Algorithm-Based Global Extremum Seeking Scheme(IEEE, 2012)This paper adapts the so-called Shubert algorithm for Extremum Seeking Control (ESC) to seek the global extremum (in presence of local extrema) of general dynamic plants. Different from derivative based methods that are widely used in ESC, the Shubert algorithm is a good representative of sampling optimization methods. With knowledge of the Lipschitz constant of an unknown static mapping, this deterministic algorithm seeks the global extremum. By introducing “waiting time” the proposed Shubert algorithm-based global extremum seeking guarantees the semi-global practical convergence (in the initial states) to the global extremum if compact sets of inputs are considered. Several numerical examples demonstrate how proposed method may be successfully deployed.
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ItemSmall-gain theorems of LaSalle type for hybrid systems(IEEE, 2012)We study stability of hybrid systems described as feedback interconnections of smaller subsystems, within a Lyapunov-based ISS small-gain analysis framework. We focus on constructing a weak (nonstrictly decreasing) Lyapunov function for the overall hybrid system from weak ISS-Lyapunov functions for the subsystems in the interconnection. Asymptotic stability of the hybrid system is then concluded by applying results of LaSalle type. The utility of this approach is illustrated on feedback systems arising in event-triggered control and quantized control.
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ItemA Neural Mass Model of Spontaneous Burst Suppression and Epileptic Seizures(IEEE, 2013)The paper presents a neural mass model that is capable of simulating the transition to and from various forms of paroxysmal activity such as burst suppression and epileptic seizure-like waveforms. These events occur without changing parameters in the model. The model is based on existing neural mass models, with the addition of feedback of fast dynamics to create slowly time varying parameters, or slow states. The goal of this research is to establish a link between system properties that modulate neural activity and the fast changing dynamics, such as membrane potentials and firing rates that can be manipulated using electrical stimulation. Establishing this link is likely to be a necessary component of a closed-loop system for feedback control of pathological neural activity.
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ItemAveraging in singularly perturbed hybrid systems with hybrid boundary layer systems(IEEE, 2012-01-01)We analyze a class of singularly perturbed hybrid systems based on two auxiliary hybrid systems: the averaged system, which approximates the slow dynamics, and the boundary layer system, which approximates the fast dynamics. The average system is generated by averaging the solutions of the boundary layer system. The novelty of this work is that the boundary layer system is a hybrid system rather than a continuous-time system. This extends available results to cover new classes of hybrid systems. We illustrate how to apply our results through an example that is a power converter system under hybrid feedbacks implemented by pulse-width modulation (PWM).