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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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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ItemCoordination of blind agents on Lie groups(IEEE, 2015)This paper presents an algorithm for the synchronization of blind agents evolving on a connected Lie group. We employ the method of extremum seeking control for nonlinear dynamical systems defined on connected Riemannian manifolds to achieve the synchronization among the agents. This approach is independent of the underlying graph of the system and each agent updates its position on the connected Lie group by only receiving the synchronization cost function.
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ItemDesign of observers implemented over FlexRay networks(IEEE, 2014)We investigate the observer design for nonlinear systems whose measurements are sent over a network governed by FlexRay. FlexRay is a communication protocol used in the automotive industry which has the feature to switch between two scheduling rules associated with the two segments of its communication cycles. The objective of this paper is to generalize existing works on emulated observers for networked control systems (NCS) to be applicable to NCS with FlexRay. We propose for that purpose a novel hybrid model and guarantee the observer convergence provided that, for each segment, the scheduling rules are uniformly globally exponentially stable and the maximal allowable transmission intervals satisfy given explicit bounds. The analysis relies on the use of an hybrid Lyapunov function we recently constructed to investigate the stabilization of NCS with FlexRay. We finally apply the approach to a class of globally Lipschitz systems, which includes linear time-invariant systems as a particular case.
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ItemNetworked control systems with communication constraints: Tradeoffs between transmission intervals and delays(IEEE, 2014-03-26)There are many communication imperfections in networked control systems (NCSs) such as varying delays, varying transmission intervals, packet loss, communication constraints and quantization effects. Most of the available literature on NCSs focuses on only one of these aspects, while ignoring the others. In this paper we present a general framework that incorporates both communication constraints (only one node accessing the network per transmission), varying delays and varying transmission intervals. Based on a newly developed NCS model including these three network phenomena, we will provide an explicit (Lyapunov-based) procedure to compute bounds on the maximally allowable transmission interval (MATI) and the maximally allowable delay (MAD) that guarantee stability of the NCS. The developed results lead to tradeoff curves between MATI and MAD as will be illustrated using a benchmark example.
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ItemFlexible Nash seeking using stochastic difference inclusions(IEEE, 2015)We present a novel algorithm designed to achieve robust convergence to Nash equilibria in non-cooperative games, where players are not required to participate in the game for all time, neither to know the exact mathematical form of their cost function. In this algorithm each player employs stochastic probing dynamics that only require measurements of its own cost function, together with a dynamic time-ratio mechanism that enforces its frequency of participation in the game to satisfy a time-ratio constraint. The algorithm is modeled by a constrained stochastic difference inclusion with non-unique solutions that encompass a complete set of admissible behaviors for each player. To characterize the convergence and stability properties of the system we introduce the notion of mean-square practical exponential stability for constrained stochastic difference inclusions, as well as sufficient Lyapunov conditions that certify this property. Simulation examples are used to demonstrate the results.