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, 2014-01-01)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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ItemDesign of observers implemented over FlexRay networks(IEEE, 2014-01-01)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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ItemExtremum seeking control: Convergence analysis(IEEE, 2014-03-26)This paper summarizes our recent work on dynamical properties for a class of extremum seeking (ES) controllers that have attracted a great deal of research attention in the past decade. Their local stability properties were already investigated, see [2]. We first show that semi-global practical convergence is possible if the controller parameters are carefully tuned and the objective function has a unique (global) extremum. An interesting tradeoff between the convergence rate and the size of the domain of attraction of the scheme is uncovered: the larger the domain of attraction, the slower the convergence of the algorithm. The amplitude, frequency and shape of the dither signal are important design parameters in the extremum seeking controller. In particular, we show that changing the amplitude of the dither adaptively can be used to deal with global extremum seeking in presence of local extrema. Moreover, we show that the convergence of the algorithm is proportional to the power of the dither signal. Consequently, the square-wave dither yields the fastest convergence among all dithers of the same frequency and amplitude. We consider extremum seeking of a class of bioprocesses to demonstrate our results and motivate some open research questions for multi-valued objective functions.
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ItemMulti-agent gradient climbing via extremum seeking control(IFAC - International Federation of Automatic Control, 2014)A unified framework based on discrete-time gradient-based extremum seeking control is proposed to localise an extremum of an unknown scalar field distribution using a group of equipped with sensors. The controller utilises estimates of gradients of the field from local dithering sensor measurements collected by the mobile agents. It is assumed that distributed coordination which ensures uniform asymptotic stability with respect to a prescribed formation of the agents is employed. The framework is useful in that a broad range of nonlinear programming algorithms can be combined with a wide class of cooperative control laws to perform extreme source seeking. Semi-global practical asymptotically stable convergence to local extrema is established in the presence of bounded field sampling noise.
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ItemImproving L₂ Gain Performance of Linear Systems by Reset Control(IFAC - International Federation of Automatic Control, 2014)In this paper, new Lyapunov-based reset rules are constructed to improve C2 gain performance of linear-time-invariant (LTI) systems. By using the hybrid system framework, sufficient conditions for exponential and finite gain C2 stability are presented. It is shown that the C2 gain of the closed loop system with resets can be improved compared with the base system. Numerical example supports our results.
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ItemControllability of Discrete-time Networked Control Systems with Try Once Discard Protocol(IFAC - International Federation of Automatic Control, 2014)This paper investigates controllability of discrete-time Networked Control Systems. The distinguishing feature is that the network imposes scheduling. The network is characterized by a dynamic protocol and different types of additional processing capabilities, as determined by available technology. For NCS with general nonlinear plants we present general controllability results. Finally, for NCS with linear plants we extend ideas motivated by NCS architectures with static protocols to state corresponding controllability results.
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ItemCo-design of output feedback laws and event-triggering conditions for linear systems(IEEE, 2014-01-01)We present a procedure to simultaneously design the output feedback law and the event-triggering condition to stabilize linear systems. The closed-loop system is shown to satisfy a global asymptotic stability property and the existence of a strictly positive minimum amount of time between two transmissions is guaranteed. The event-triggered controller is obtained by solving linear matrix inequalities (LMIs). We then exploit the flexibility of the method to maximize the guaranteed minimum amount of time between two transmissions. Finally, we provide a (heuristic) method to reduce the amount of transmissions, which is supported by numerical simulations.
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ItemEmulated controller design for networked control systems implemented on FlexRay(IEEE, 2014-01-01)We design stabilizing controllers for nonlinear networked control systems (NCS) whose transmissions are scheduled by FlexRay. FlexRay protocol has been developed by the automotive industry to provide high bandwidth and deterministic communications. It works with communication cycles which consist of a static segment and a dynamic segment during which different scheduling rules are employed. We generalize existing emulated controller designs to be applicable to NCS with FlexRay. We start from a feedback law which stabilizes the origin of the plant when there is no network. We then present a novel hybrid model of the closed-loop system when the controller is implemented over a network scheduled by FlexRay. Afterwards, we provide conditions on the network under which the stability of the NCS is ensured. In particular, we consider segments of arbitrary lengths and we provide segment-dependent maximal allowable transmission interval bounds. The analysis relies on the construction of a new hybrid Lyapunov function. We believe that this work demonstrates the flexibility of the emulation approach and that it can be used to investigate other control problems for NCS with switched protocols.