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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ItemPWM hybrid control systems: averaging tools for analysis and design(IEEE, 2010)We consider averaging for a class of hybrid systems that are motivated by Pulse Width Modulated (PWM) implementation of hybrid control laws for general nonlinear plants. Rapid time variations in the flow map of a hybrid system generate solutions that are also solutions of a time-invariant average hybrid system that is slightly perturbed. Results relating solutions of the time-varying system to solutions of the average system ensue. In the absence of finite escape times for the average system, on compact time domains each solution of the time-varying system is close to a solution of the average system. In the presence of asymptotic stability for the average system, the time-varying system exhibits semi-global, practical asymptotic stability. These results rely on mild regularity properties for the average system. In particular, the average system is not required to exhibit unique solutions. Both periodic and non-periodic flow maps are considered.
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ItemLyapunov functions for L-2 and input-to-state stability in a class of quantized control systems(IEEE, 2011-01-01)ℒ 2 and input-to-state stability (ISS) properties of a class of linear quantized control systems are considered. The quantized control system differs slightly from the ones considered in the literature previously. A recently proposed hybrid modeling framework and corresponding Lyapunov analysis tools are used to calculate the finite gains of the closed loop system.
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ItemIdle speed control using linear time varying model predictive control and discrete time approximations(IEEE, 2010-01-01)This paper addresses the problem of idle speed control of hydrogen fueled internal combustion engine (H2ICE) using model predictive control (MPC) and sampled data control (SDC) theories. In the first step, results from SDC theory and a version of MPC are collectively employed to obtain a rigorously developed new generic control strategy. Here, a controller, based on a family of approximate discrete time models, is designed within a previously proposed framework to have guaranteed practical asymptotic stability of the exact (unknown) discrete time model. Controller design, accomplished using MPC theory, is facilitated by successive online linearizations of the nonlinear discrete time model at each sampling instant. In the second step, the technique is implemented in the idle speed control of hydrogen internal combustion engine (H2ICE). Various conditions under which this theory can be implemented are presented and their validity for idle speed control problem are discussed. Simulations are presented to illustrate the effectiveness of the control scheme.
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