 Electrical and Electronic Engineering  Research Publications
Electrical and Electronic Engineering  Research Publications
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ItemEstimating the unmeasured membrane potential of neuronal populations from the EEG using a class of deterministic nonlinear filtersChong, M ; Postoyan, R ; Nesic, D ; Kuhlmann, L ; Varsavsky, A (IOP PUBLISHING LTD, 201204)We present a modelbased estimation method to reconstruct the unmeasured membrane potential of neuronal populations from a singlechannel electroencephalographic (EEG) measurement. We consider a class of neural mass models that share a general structure, specifically the models by Stam et al (1999 Clin. Neurophysiol. 110 180113), Jansen and Rit (1995 Biol. Cybern. 73 35766) and Wendling et al (2005 J. Clin. Neurophysiol. 22 343). Under idealized assumptions, we prove the global exponential convergence of our filter. Then, under more realistic assumptions, we investigate the robustness of our filter against model uncertainties and disturbances. Analytic proofs are provided for all results and our analyses are further illustrated via simulations.

ItemNonlinear automatic target tracking in clutter using dynamic Gaussian mixtureMusicki, D ; Song, TL ; Kim, WC ; Nesic, D (Institution of Engineering and Technology, 20121201)This study presents a complete algorithm for single target tracking in clutter, which addresses simultaneously: nonlinear measurements; uncertain target detections; presence of random clutter measurements; and uncertain target existence. Proposed algorithm generalises the integrated track splitting (ITS) filter by extending the ITS functionality to highly nonlinear measurements. The nonlinear target tracking and estimation problems may also be solved by application of particle filters, albeit incurring a significant computational expense relative to proposed solution. In an environment without data association uncertainties proposed filter becomes a nonlinear estimator.

ItemInputtostate stability for a class of hybrid dynamical systems via averagingWang, W ; Nesic, D ; Teel, AR (Springer, 201202)Inputtostate stability (ISS) properties for a class of timevarying hybrid dynamical systems via averaging method are considered. Two definitions of averages, strong average and weak average, are used to approximate the timevarying hybrid systems with timeinvariant hybrid systems. Closeness of solutions between the timevarying system and solutions of its weak or strong average on compact time domains is given under the assumption of forward completeness for the average system. We also show that ISS of the strong average implies semiglobal practical (SGP)ISS of the actual system. In a similar fashion, ISS of the weak average implies semiglobal practical derivative ISS (SGPDISS) of the actual system. Through a power converter example, we show that the main results can be used in a framework for a systematic design of hybrid feedbacks for pulsewidth modulated control systems.

ItemRobust stability of packetized predictive control of nonlinear systems with disturbances and Markovian packet lossesQuevedo, DE ; Nesic, D (PERGAMONELSEVIER SCIENCE LTD, 20120801)We study a predictive control formulation for uncertain discretetime nonlinear uniformly continuous plant models where controller output data is transmitted over an unreliable communication channel. The channel introduces Markovian dataloss and does not provide acknowledgments of receipt. To achieve robustness with respect to dropouts, at every sampling instant the controller transmits packets of data. These contain possible control inputs for a finite number of future time instants, and minimize a finite horizon cost function. At the actuator side, received packets are buffered, providing the plant inputs. Within this context, we adopt a stochastic Lyapunov function approach to establish stability results of the networked control system. A distinguishing aspect of this work is that it considers situations where the maximum number of consecutive packet dropouts has unbounded support.

ItemAnalysis for a class of singularly perturbed hybrid systems via averagingWang, W ; Teel, AR ; Nesic, D (PERGAMONELSEVIER SCIENCE LTD, 20120601)A class of singularly perturbed hybrid dynamical systems is analyzed. The fast states are restricted to a compact set a priori. The continuoustime boundary layer dynamics produce solutions that are assumed to generate a welldefined average vector field for the slow dynamics. This average, the projection of the jump map in the direction of the slow states, and flow and jump sets from the original dynamics define the reduced, or average, hybrid dynamical system. Assumptions about the average system lead to conclusions about the original, higherdimensional system. For example, forward precompleteness for the average system leads to a result on closeness of solutions between the original and average system on compact time domains. In addition, global asymptotic stability for the average system implies semiglobal, practical asymptotic stability for the original system. We give examples to illustrate the averaging concept and to relate it to classical singular perturbation results as well as to other singular perturbation results that have appeared recently for hybrid systems. We also use an example to show that our results can be used as an analysis tool to design hybrid feedbacks for continuoustime plants implemented by fast but continuous actuators.

ItemOn emulated nonlinear reducedorder observers for networked control systemsPostoyan, R ; Nesic, D (PERGAMONELSEVIER SCIENCE LTD, 201204)We consider a general class of nonlinear reducedorder observers and show that the global asymptotic convergence of the observation error in the absence of networkinduced constraints is maintained for the emulated observer semiglobally and practically (with respect to the maximum allowable transmission interval) when system measurements are sent through a communication channel. Networks governed by a Lyapunov uniformly globally asymptotically stable protocol are investigated. Our results can be used to synthesize various observers for networked control systems for a range of network configurations, as we illustrate it by considering classes of immersion and invariance observers which include the circlecriterion observers.

ItemA robust circle criterion observer with application to neural mass modelsChong, M ; Postoyan, R ; Nesic, D ; Kuhlmann, L ; Varsavsky, A (PERGAMONELSEVIER SCIENCE LTD, 20121101)A robust circle criterion observer is designed and applied to neural mass models. At present, no existing circle criterion observers apply to the considered models, i.e. the required linear matrix inequality is infeasible. Therefore, we generalise available results to derive a suitable estimation algorithm. Additionally, the design also takes into account input uncertainty and measurement noise. We show how to apply the observer to estimate the mean membrane potential of neuronal populations of a popular single cortical column model from the literature.

ItemA discretetime framework for stability analysis of nonlinear networked control systemsvan de Wouw, N ; Nesic, D ; Heemels, WPMH (PERGAMONELSEVIER SCIENCE LTD, 20120601)In this paper we develop a prescriptive framework for the stabilising controller design based on approximate discretetime models for nonlinear Networked Control Systems (NCSs) with timevarying sampling intervals, large timevarying delays and packet dropouts. As opposed to emulationbased approaches where the effects of samplingandhold and delays are ignored in the phase of controller design, we propose an approach in which the controller design is based on approximate discretetime models constructed for a set of nominal (nonzero) sampling intervals and nominal delays while taking into account samplingandhold effects. Subsequently, sufficient conditions for the global exponential stability of the closedloop NCS are provided.

ItemMultivariable Newtonbased extremum seekingGhaffari, A ; Krstic, M ; Nesic, D (PERGAMONELSEVIER SCIENCE LTD, 20120801)We present a Newtonbased extremum seeking algorithm for the multivariable case. The design extends the recent Newtonbased extremum seeking algorithms for the scalar case and introduces a dynamic estimator of the inverse of the Hessian matrix that removes the difficulty with the possible singularity of a possible direct estimate of the Hessian matrix. The estimator of the inverse of the Hessian has the form of a differential Riccati equation. We prove local stability of the new algorithm for general nonlinear dynamic systems using averaging and singular perturbations. In comparison with the standard gradientbased multivariable extremum seeking, the proposed algorithm removes the dependence of the convergence rate on the unknown Hessian matrix and makes the convergence rate, of both the parameter estimates and of the estimates of the Hessian inverse, userassignable. In particular, the new algorithm allows all the parameters to converge with the same speed, yielding straight trajectories to the extremum even with maps that have highly elongated level sets, in contrast to curved "steepest descent" trajectories of the gradient algorithm. Simulation results show the advantage of the proposed approach over gradientbased extremum seeking, by assigning equal, desired convergence rates to all the parameters using Newton's approach.

ItemPractical stability of approximating discretetime filters with respect to model mismatchTechakesari, O ; Ford, JJ ; Nesic, D (PERGAMONELSEVIER SCIENCE LTD, 20121101)This paper establishes practical stability results for an important range of approximate discretetime filtering problems involving mismatch between the true system and the approximating filter model. Practical stability is established in the sense of an asymptotic bound on the amount of bias introduced by the model approximation. Our analysis applies to a wide range of estimation problems and justifies the common practice of approximating intractable infinite dimensional nonlinear filters by simpler computationally tractable filters.