Seddik M. Djouadi

Efficient Implementation of the Chan-Vese Models Without Solving PDEs

Efficient implementation methods are proposed for Chan-Vese models. The proposed methods do not require solutions of PDEs and are therefore fast. The advantages of level set methods, such as automatic handling of topological changes, are preserved. These methods utilize region information to guide the evolution of initial curves. Gaussian smoothing is applied to regularize the evolving curves. These algorithms are able to automatically and efficiently segment objects in complicated images. Experimental results show that the proposed methods work efficiently for images without strong noise. However, they still have initialization problems, as do the Chan-Vese models

Stochastic power control for wireless networks via SDEs: probabilistic QoS measures

The power control of wireless networks is formulated using a stochastic optimal control framework, in which the evolution of the channel is described by stochastic differential equations (SDEs). The latter capture the spatio-temporal variations of the communication link, as well as the randomness. This class of models is more realistic than the static models usually encountered in the literature. Under this scenario, average and probabilistic Quality of Service (QoS) measures are introduced to evaluate the performance of any control strategy by using Chernoff bounds. Moreover, the Chernoff bound is computed explicitly, while the solution of the stochastic optimal power control is obtained through pathwise optimization. The pathwise optimization can be solved using linear programming if predictable control strategies are introduced. Finally, if predictable control strategies do not hold, it is shown that the proposed power control problem reduces to particular convex optimizations.

Stochastic power control for time-varying long-term fading wireless networks

A new time-varying (TV) long-term fading (LTF) channel model which captures both the space and time variations of wireless systems is developed. The proposed TV LTF model is based on a stochastic differential equation driven by Brownian motion. This model is more realistic than the static models usually encountered in the literature. It allows viewing the wireless channel as a dynamical system, thus enabling well-developed tools of adaptive and nonadaptive estimation and identification techniques to be applied to this class of problems. In contrast with the traditional models, the statistics of the proposed model are shown to be TV, but converge in steady state to their static counterparts. Moreover, optimal power control algorithms (PCAs) based on the new model are proposed. A centralized PCA is shown to reduce to a simple linear programming problem if predictable power control strategies (PPCS) are used. In addition, an iterative distributed stochastic PCA is used to solve for the optimization problem using stochastic approximations. The latter solely requires each mobile to know its received signal-to-interference ratio. Generalizations of the power control problem based on convex optimization techniques are provided if PPCS are not assumed. Numerical results show that there are potentially large gains to be achieved by using TV stochastic models, and the distributed stochastic PCA provides better power stability and consumption than the distributed deterministic PCA.

Robust Stabilization Over Communication Channels in the Presence of Unstructured Uncertainty

This paper is concerned with the problem of controlling plants over communication channels, where the plant is subject to two types of unstructured uncertainty: additive uncertainty and stable coprime factor uncertainty. Necessary lower bounds on the rate of transmission (or channel capacity) C, for robust stabilization, are computed explicitly. In particular, it is shown that the lower bound in the additive uncertainty case corresponds to a fixed point of a particular function. In the stable coprime factor uncertainty case, the derivation relies on linear fractional transformation concepts. The results are important in determining the minimum channel capacity needed in order to stabilize plants subject to unstructured uncertainty over communication channels. For instance, the bounds obtained can be used to analyze the effect of uncertainty on the channel capacity in control over communication channels. Finally, an illustrative example is provided

Position and Velocity Tracking in Mobile Networks Using Particle and Kalman Filtering With Comparison

This paper presents several methods based on signal strength and wave scattering models for tracking a user. The received-signal level method is first used in combination with maximum likelihood (ML) estimation and triangulation to obtain an estimate of the location of the mobile. Due to nonline-of-sight conditions and multipath propagation environments, this estimate lacks acceptable accuracy for demanding services, as the numerical results reveal. The 3-D wave scattering multipath channel model of Aulin is employed, together with the recursive nonlinear Bayesian estimation algorithms to obtain improved location estimates with high accuracy. Several Bayesian estimation algorithms are considered, such as the extended Kalman filter (EKF), the particle filter (PF), and the unscented PF (UPF). These algorithms cope with nonlinearities in order to estimate mobile location and velocity. Since the EKF is very sensitive to the initial state, we propose the use of the ML estimate as the initial state of the EKF. In contrast to the EKF tracking approach, the PF and UPF approaches do not rely on linearized motion models, measurement relations, and Gaussian assumptions. Numerical results are presented to evaluate the performance of the proposed algorithms when the measurement data do not correspond to the ones generated by the model. This shows the robustness of the algorithm based on modeling inaccuracies.

Networked system state estimation in smart grid over cognitive radio infrastructures

Cognitive radio system is an intensively studied area in that it saves money and bandwidth by sensing the available licensed spectrum for unlicensed users. This advantage provides a promising future for the application of cognitive radio in smart grid. In this paper, we propose to communicate through a cognitive radio link between the sensors at the consumer side and the control center of smart grid. In this way, the state estimator needs to adjust to this new communication link as the link is affected by primary users. This link is governed by multiple semi-Markov processes each of which can capture and model one channel of the cognitive radio system. State estimation algorithms under this structure are developed for two cases: one with arrival acknowledge and the other without. Numerical examples are given to illustrate the performance of the proposed estimation algorithm.

Stochastic differential equations for modeling, estimation and identification of mobile-to-mobile communication channels

Mobile-to-mobile networks are characterized by node mobility that makes the propagation environment time varying and subject to fading. As a consequence, the statistical characteristics of the received signal vary continuously, giving rise to a Doppler power spectral density (DPSD) which varies from one observation instant to the next. The current models do not capture and track the time varying characteristics. This paper is concerned with dynamical modeling of time varying mobile-to-mobile channels, parameter estimation and identification from received signal measurements. The evolution of the propagation environment is described by stochastic differential equations, whose parameters can be determined by approximating the band-limited DPSD using the Gauss-Newton method. However, since the DPSD is not available online, we propose to use a filter-based expectation maximization algorithm and Kalman filter to estimate the channel parameters and states, respectively. The scheme results in a finite dimensional filter which only uses the first and second order statistics. The algorithm is recursive allowing the inphase and quadrature components and parameters to be estimated online from received signal measurements. The algorithms are tested using experimental data collected from moving sensor nodes in indoor and outdoor environments demonstrating the methods viability.

State Estimation over a Semi-Markov Model Based Cognitive Radio System

Cognitive radio is a very popular research area in the communication community as cost and bandwidth can be saved by sensing the available licensed spectrum for unlicensed users. This paves the way for the application of cognitive radio in control systems over wireless communication links. A typical control system comprises a sensor interconnected with an actuator, a plant and controller. In this paper, it is assumed that the sensor and estimator communicate through a cognitive radio link. The state estimator needs to adjust to this new communication media as it is affected by interruptions from primary users, resulting in packet losses. The cognitive radio link is modeled as multiple semi-Markov processes each of which can capture the channel dynamics. Two different cases are considered. The first case assumes that acknowledgement of packet arrivals is available at the estimator while the second case does not. For the first case, sufficient conditions are derived for the stability of the peak covariance process which guarantees the stability of the estimator covariance. For the second case, an estimator is designed. Numerical examples are given to show the performance of the proposed estimators. Several applications of the proposed work are also discussed.

Spectrum sensing in low SNR regime via stochastic resonance

Spectrum sensing is essential in cognitive radio to enable dynamic spectrum access. In many scenarios, primary user signal must be detected reliably in low signal-to-noise ratio (SNR) regime under required sensing time. We propose to use stochastic resonance, a nonlinear filter having certain resonance frequency, to detect primary users when the SNR is very low. Both block and sequential detection schemes are studied. Simulation results show that, under the required false alarm rate, both detection probability and average detection delay can be substantially improved. A few implementation issues are also discussed.

Dynamic Control Allocation for Damping of Inter-Area Oscillations

Use of actuator redundancy to achieve higher reliability is a widely accepted engineering design technique and is used in this study to build resiliency and ensure power system stability in the presence of high levels of renewables. This paper presents a new design method for fault-tolerant wide-area damping controllers (WADCs) using modal-based control allocation (MB-CA), which coordinates a set of actuators to contribute to damping of inter-area oscillations. In our proposed method, when an actuator fails or is unavailable (e.g., due to communication failure), the supervisory MB-CA distributes the control signals to the remaining healthy actuators based on effects on the modal system, desired control actions, and actuator constraints. Our proposed block offers the benefits of modular design where it is independent of the nominal WADC. The proposed method consists of mainly two design steps. The first step is to design a WADC based on a fault-free model using robust control methods. The second step is to design an MB-CA to manage actuator availability and constraints. To validate the feasibility and demonstrate the design principles, a set of comprehensive case studies are conducted on a modified 192-bus Western Electricity Coordinating Council system. Numerical results verify the effectiveness of the proposed approach in ensuring resiliency to different actuator failures and actuator availability.