Showing papers by "Hassan K. Khalil published in 2011"

Robust Stabilization of Non-Minimum Phase Nonlinear Systems Using Extended High-Gain Observers

Abstract: A robust, stabilizing output feedback controller for systems in the normal form, which could potentially include unstable zero dynamics, is presented. The control scheme adopted herein incorporates continuously-implemented sliding mode control-chosen for its robustness properties as well as its ability to prescribe or constrain the motion of trajectories in the sliding phase-and an extended high gain observer to estimate the derivatives of the output and one of the unknown functions. Stabilization in the case of an unknown control coefficient and uncertain constant parameters is shown.

Model-based analysis and control of a network of basal ganglia spiking neurons in the normal and parkinsonian states.

Abstract: Controlling the spatiotemporal firing pattern of an intricately connected network of neurons through microstimulation is highly desirable in many applications. We investigated in this paper the feasibility of using a model-based approach to the analysis and control of a basal ganglia (BG) network model of Hodgkin-Huxley (HH) spiking neurons through microstimulation. Detailed analysis of this network model suggests that it can reproduce the experimentally observed characteristics of BG neurons under a normal and a pathological Parkinsonian state. A simplified neuronal firing rate model, identified from the detailed HH network model, is shown to capture the essential network dynamics. Mathematical analysis of the simplified model reveals the presence of a systematic relationship between the network's structure and its dynamic response to spatiotemporally patterned microstimulation. We show that both the network synaptic organization and the local mechanism of microstimulation can impose tight constraints on the possible spatiotemporal firing patterns that can be generated by the microstimulated network, which may hinder the effectiveness of microstimulation to achieve a desired objective under certain conditions. Finally, we demonstrate that the feedback control design aided by the mathematical analysis of the simplified model is indeed effective in driving the BG network in the normal and Parskinsonian states to follow a prescribed spatiotemporal firing pattern. We further show that the rhythmic/oscillatory patterns that characterize a dopamine-depleted BG network can be suppressed as a direct consequence of controlling the spatiotemporal pattern of a subpopulation of the output Globus Pallidus internalis (GPi) neurons in the network. This work may provide plausible explanations for the mechanisms underlying the therapeutic effects of deep brain stimulation (DBS) in Parkinson's disease and pave the way towards a model-based, network level analysis and closed-loop control and optimization of DBS parameters, among many other applications.

Neural Feedback for Instantaneous Spatiotemporal Modulation of Afferent Pathways in Bi-Directional Brain–Machine Interfaces

Abstract: In bi-directional brain-machine interfaces (BMIs), precisely controlling the delivery of microstimulation, both in space and in time, is critical to continuously modulate the neural activity patterns that carry information about the state of the brain-actuated device to sensory areas in the brain. In this paper, we investigate the use of neural feedback to control the spatiotemporal firing patterns of neural ensembles in a model of the thalamocortical pathway. Control of pyramidal (PY) cells in the primary somatosensory cortex (S1) is achieved based on microstimulation of thalamic relay cells through multiple-input multiple-output (MIMO) feedback controllers. This closed loop feedback control mechanism is achieved by simultaneously varying the stimulation parameters across multiple stimulation electrodes in the thalamic circuit based on continuous monitoring of the difference between reference patterns and the evoked responses of the cortical PY cells. We demonstrate that it is feasible to achieve a desired level of performance by controlling the firing activity pattern of a few “key” neural elements in the network. Our results suggest that neural feedback could be an effective method to facilitate the delivery of information to the cortex to substitute lost sensory inputs in cortically controlled BMIs.

Analysis of a nonlinear high-gain observer in the presence of measurement noise

Abstract: Motivated by the sensitivity of high-gain observers to measurement noise, this paper presents a high-gain observer with a nonlinear gain that takes the form of a piecewise linear function. The piecewise function is designed to have three linear regions, with the two outermost sectors chosen to elicit the desired behavior in the transient and steady-state responses, respectively. In order to overcome the tradeoff between fast state reconstruction and measurement noise attenuation, a larger observer gain is generated during the transient response than in the steady-state response. Thus, by reducing the observer gain after achieving satisfactory state estimates, the effect of noise on the steady-state performance is reduced. Moreover, the observer presented in this paper is shown to surpass the system performance achieved when using comparable observers. The proof argues boundedness and ultimate boundedness of the closed-loop system under the proposed output feedback.

Model-based spatiotemporal analysis and control of a network of spiking Basal Ganglia neurons

Abstract: Precise spatiotemporal control of the output of a network of intricately connected neurons through microstimulation is highly desirable in many neural prosthetic applications. This control, however, is challenging, in part due to the large number of unobserved variables in the system under consideration, the complexity underlying the local mechanisms of microstimulation, and the interplay between the intrinsic network structure and its dynamic response to external stimulation. In this work we use a simplified firing rate model, identified from a network of Hodgkin-Huxley (HH) type spiking Basal Ganglia (BG) neurons, to study the response of the network to patterned microstimulation, and to design effective feedback control laws to approximate a desired spatiotemporal pattern. Mathematical analysis of the simplified model using Singular Value Decomposition (SVD) suggests that the BG neural circuit under study exhibits strong spatiotemporal selectivity and only responds strongly to a range of specific spatiotemporal stimulation patterns. We use the concept of functional controllability based on SVD to evaluate the effectiveness of various combinations of stimulation sites for a given set of neurons to be controlled. The results suggest that the functional controllability is largely decided by the network connectivity and the connection strength. Finally, we demonstrate that the controller design based on the simplified model is indeed effective in driving the output neurons to follow a prescribed spatiotemporal firing pattern in the network output.

Regulation under disturbances with multiple harmonics of unknown frequency

Abstract: In this paper, we address the regulation problem for a linear plant driven by a neutrally stable exosystem. It is assumed that the plant is subjected to an exogenous disturbance, and that this signal is formed of known harmonics of a sinusoidal reference signal whose frequency is unknown. Such an exosystem is motivated by the case where the system possesses an input nonlinearity like hysteresis. We propose an adaptive servocompensator requiring estimation of only the primary frequency. Using two-time-scale analysis, we establish the semi-global convergence of the parameter error to an arbitrarily small neighborhood of zero, when the adaptation gain is small enough and when the disturbance is sufficiently small comparing to the reference signal. The proposed control scheme involves far fewer adaptation variables than existing methods, and its performance is verified in both simulation and experiments conducted on a nanopositioning stage.

Performance of an optimal receiver in the presence of alpha-stable and Gaussian noises

Abstract: This paper deals with the optimal (in the maximum likelihood sense) detection performance of binary transmission in a mixture of a Gaussian noise and an impulsive interference modeled as an alpha-stable process. The main contribution is in the Monte Carlo simulation that shows that the Gaussianity assumption for the test statistic as reported in earlier works is not valid unless a very large number of repetitions is used.

Tracking an unknown two-frequency reference using a frequency estimator-based servocompensator

Abstract: In this work, we address the tracking problem for an unknown reference comprised of two sinusoids. We propose an adaptive servocompensator based on a pair of frequency estimators. Slow adaptation is used to create three time scales within the closed-loop system, corresponding to the controller and plant dynamics, fast frequency estimate, and slow frequency estimate. Stability of the boundary-layer system, comprised of the servocompensator and plant dynamics, is achieved with a stabilizing controller. Novel nonlinear analysis is then performed on the average system to show global asymptotic stability. The algorithm's performance is verified by experiments conducted on a commercial nanopositioner, and its performance is shown to be comparable to that of iterative learning control.