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Taous-Meriem Laleg-Kirati

Publications and source records attributed to Taous-Meriem Laleg-Kirati.

35 records · Page 2Linked to original sources
arXiv2021

Model-free LQR based PID controller for trajectory tracking of 2-DoF helicopter: comparison and experimental results

This paper studies the performance of a model-free LQR based PID (i-LQR-PID) controller designed for tracking control problem of a 2-DoF laboratory helicopter. The control problem addressed in 2-DoF helicopter system aims to track the desired pitch and yaw axes trajectories despite disturbed operating conditions. In addition to the unpredictable variations, the 2-DoF helicopter dynamic is highly nonlinear with having strong cross-couplings in their models as well as being open loop unstable system. Thus, we propose a model-free LQR based PID control strategy in order to achieve better trajectory tracking control objectives. Robustness tests are performed experimentally to show the effectiveness of the model-free control.

eess.SY↗
arXiv2021

Fish Growth Trajectory Tracking via Reinforcement Learning in Precision Aquaculture

This paper studies the fish growth trajectory tracking via reinforcement learning under a representative bioenergetic growth model. Due to the complex aquaculture condition and uncertain environmental factors such as temperature, dissolved oxygen, un-ionized ammonia, and strong nonlinear couplings, including multi-inputs of the fish growth model, the growth trajectory tracking problem can not be efficiently solved by the model-based control approaches in precision aquaculture. To this purpose, we formulate the growth trajectory tracking problem as sampled-data optimal control using discrete state-action pairs Markov decision process. We propose two Q-learning algorithms that learn the optimal control policy from the sampled data of the fish growth trajectories at every stage of the fish life cycle from juveniles to the desired market weight in the aquaculture environment. The Q-learning scheme learns the optimal feeding control policy to fish growth rate cultured in cages and the optimal feeding rate control policy with an optimal temperature profile for the aquaculture fish growth rate in tanks. The simulation results demonstrate that both Q-learning strategies achieve high trajectory tracking performance with less amount feeding rates.

eess.SY↗
arXiv2021

Establishing and Maintaining a Reliable Optical Wireless Communication in Underwater Environment

This paper proposes the trajectory tracking problem between an autonomous underwater vehicle (AUV) and a mobile surface ship, both equipped with optical communication transceivers. The challenging issue is to maintain stable connectivity between the two autonomous vehicles within an optical communication range. We define a directed optical line-of-sight (LoS) link between the two-vehicle systems. The transmitter is mounted on the AUV while the surface ship is equipped with an optical receiver. However, this optical communication channel needs to preserve a stable transmitter-receiver position to reinforce service quality, which typically includes a bit rate and bit error rates. A cone-shaped beam region of the optical receiver is approximated based on the channel model; then, a minimum bit rate is ensured if the AUV transmitter remains inside of this region. Additionally, we design two control algorithms for the transmitter to drive the AUV and maintain it in the cone-shaped beam region under an uncertain oceanic environment. Lyapunov function-based analysis that ensures asymptotic stability of the resulting closed-loop tracking error is used to design the proposed NLPD controller. Numerical simulations are performed using MATLAB/Simulink to show the controllers' ability to achieve favorable tracking in the presence of the solar background noise within competitive times. Finally, results demonstrate the proposed NLPD controller improves the tracking error performance more than $70\%$ under nominal conditions and $35\%$ with model uncertainties and disturbances compared to the original PD strategy.

eess.SY↗
arXiv2021

Model Predictive Control Paradigms for Fish Growth Reference Tracking in Precision Aquaculture

In precision aquaculture, the primary goal is to maximize biomass production while minimizing production costs. This objective can be achieved by optimizing factors that have a strong influence on fish growth, such as the feeding rate, temperature, and dissolved oxygen. This paper provides a comparative study of three model predictive control (MPC) strategies for fish growth reference tracking under a representative bioenergetic growth model in precision aquaculture. We propose to evaluate three candidate MPC formulations for fish growth reference tracking based on the receding horizon. The first MPC formulation tracks a desired fish growth trajectory while penalizing the feed ration, temperature, and dissolved oxygen. The second MPC optimization strategy directly penalizes the feed conversion ratio (FCR), which is the ratio between food quantity and fish weight gain while minimizing the actual growth state's deviation from the given reference growth trajectory. The third MPC formulation includes a tradeoff between the growth rate trajectory tracking, the dynamic energy and the cost of food. Numerical simulations that integrate a realistic bioenergetic fish growth model of Nile tilapia (Oreochromis niloticus) are illustrated to examine the comparative performance of the three proposed optimal control strategies.

eess.SY↗
arXiv2019

QuPWM: Feature Extraction Method for MEG Epileptic Spike Detection

Epilepsy is a neurological disorder classified as the second most serious neurological disease known to humanity, after stroke. Localization of the epileptogenic zone is an important step for epileptic patient treatment, which starts with epileptic spike detection. The common practice for spike detection of brain signals is via visual scanning of the recordings, which is a subjective and a very time-consuming task. Motivated by that, this paper focuses on using machine learning for automatic detection of epileptic spikes in magnetoencephalography (MEG) signals. First, we used the Position Weight Matrix (PWM) method combined with a uniform quantizer to generate useful features. Second, the extracted features are classified using a Support Vector Machine (SVM) for the purpose of epileptic spikes detection. The proposed technique shows great potential in improving the spike detection accuracy and reducing the feature vector size. Specifically, the proposed technique achieved average accuracy up to 98\% in using 5-folds cross-validation applied to a balanced dataset of 3104 samples. These samples are extracted from 16 subjects where eight are healthy and eight are epileptic subjects using a sliding frame of size of 100 samples-points with a step-size of 2 sample-points

eess.SP↗
arXiv2015

Modulating Functions-Based Method for Parameters and Source Estimation in One-Dimensional Partial Differential Equations

In this paper, modulating functions-based method is proposed for estimating space-time dependent unknowns in one-dimensional partial differential equations. The proposed method simplified the problem into a system of algebraic equations linear in unknown parameters. The well-posedness of modulating functions-based solution is proven. The wave and the fifth order KdV equations are used as examples to show the effectiveness of the proposed method in both noise-free and noisy cases.

math.NA↗
arXiv2014

Image representation and denoising using squared eigenfunctions of Schrodinger operator

This paper extends to two dimensions the recent signal analysis method based on the semi-classical analysis of the Schrodinger operator. The generalization uses the separation of variables technique when writing the eigenfunctions of the Schrodinger operator. The algorithm is described and the effect of some parameters on the convergence of this method are numerically studied. Some examples on image reconstruction and denosing are illustrated.

math.SP↗
arXiv2014

A Novel Approach for Parameter and Differentiation Order Estimation for a Space Fractional Advection Dispersion Equation

In this paper, we propose a new approach, based on the so-called modulating functions to estimate the average velocity, the dispersion coefficient and the differentiation order in a space fractional advection dispersion equation. First, the average velocity and the dispersion coefficient are estimated by applying the modulating functions method, where the problem is transferred into solving a system of algebraic equations. Then, the modulating functions method combined with Newton's method is applied to estimate all three parameters simultaneously. Numerical results are presented with noisy measurements to show the effectiveness and the robustness of the proposed method.

math.OC↗
arXiv2014

An adaptive observer for wave equation's source estimation

Observers are well known in control theory. Originally designed to estimate the hidden states of dynamical systems given some measurements, the observers scope has been recently extended to the estimation of some unknowns, for systems governed by partial differential equations. In this paper, observers are used to solve inverse source problem for a one-dimensional wave equation. An adaptive observer is designed to estimate the state and source components for a fully discretized system. The effectiveness of the method is emphasized in noise-free and noisy cases and an insight on the impact of measurements' size and location is provided.

math.OC↗
arXiv2014

Direct and Inverse Source Problem for a Space Fractional Advection Dispersion Equation

In this paper, direct and inverse problems for a space fractional advection dispersion equation on a finite domain are studied. The inverse problem consists in determining the source term from a final observation. We first drive the fundamental solution to the direct problem and we show that the relation between source and the final observation is linear. Moreover, we study the well-posedness of both problems: existence, uniqueness and stability. Finally, we illustrate the results with a numerical example.

math.AP↗
arXiv2013

Identification of fractional order systems using modulating functions method

The modulating functions method has been used for the identification of linear and nonlinear systems. In this paper, we generalize this method to the on-line identification of fractional order systems based on the Riemann-Liouville fractional derivatives. First, a new fractional integration by parts formula involving the fractional derivative of a modulating function is given. Then, we apply this formula to a fractional order system, for which the fractional derivatives of the input and the output can be transferred into the ones of the modulating functions. By choosing a set of modulating functions, a linear system of algebraic equations is obtained. Hence, the unknown parameters of a fractional order system can be estimated by solving a linear system. Using this method, we do not need any initial values which are usually unknown and not equal to zero. Also we do not need to estimate the fractional derivatives of noisy output. Moreover, it is shown that the proposed estimators are robust against high frequency sinusoidal noises and the ones due to a class of stochastic processes. Finally, the efficiency and the stability of the proposed method is confirmed by some numerical simulations.

math.NA↗
arXiv2012

Fractional order differentiation by integration with Jacobi polynomials

The differentiation by integration method with Jacobi polynomials was originally introduced by Mboup, Join and Fliess. This paper generalizes this method from the integer order to the fractional order for estimating the fractional order derivatives of noisy signals. The proposed fractional order differentiator is deduced from the Jacobi orthogonal polynomial filter and the Riemann-Liouville fractional order derivative definition. Exact and simple formula for this differentiator is given where an integral formula involving Jacobi polynomials and the noisy signal is used without complex mathematical deduction. Hence, it can be used both for continuous-time and discrete-time models. The comparison between our differentiator and the recently introduced digital fractional order Savitzky-Golay differentiator is given in numerical simulations so as to show its accuracy and robustness with respect to corrupting noises.

math.NA↗
arXiv2012

Mathematical properties of a semi-classical signal analysis method: noisy signal case

Recently, a new signal analysis method based on a semi-classical approach has been proposed [1]. The main idea in this method is to interpret a signal as a potential of a Schrodinger operator and then to use the discrete spectrum of this operator to analyze the signal. In this paper, we are interested in a mathematical analysis of this method in discrete case considering noisy signals.

math.NA↗
arXiv2010

On semi-Classical Questions Related to Signal Analysis

This study explores the reconstruction of a signal using spectral quantities associated with some self-adjoint realization of an h-dependent Schrödinger operator when the parameter h tends to 0. Theoretical results in semi-classical analysis are proved. Some numerical results are also presented. We first consider as a toy model the sech^2 function. Then we study a real signal given by arterial blood pressure measurements. This approach seems to be very promising in signal analysis. Indeed it provides new spectral quantities that can give relevant information on some signals as it is the case for arterial blood pressure signal.

math.AP↗
arXiv2010

Semi-classical signal analysis

This study introduces a new signal analysis method called SCSA, based on a semi-classical approach. The main idea in the SCSA is to interpret a pulse-shaped signal as a potential of a Schrödinger operator and then to use the discrete spectrum of this operator for the analysis of the signal. We present some numerical examples and the first results obtained with this method on the analysis of arterial blood pressure waveforms.

math-ph↗
arXiv2010

Validation of a New Method for Stroke Volume Variation Assessment: a Comparaison with the PiCCO Technique

This paper proposes a novel, simple and minimally invasive method for stroke volume variation assessment using arterial blood pressure measurements. The arterial blood pressure signal is reconstructed using a semi-classical signal analysis method allowing the computation of a parameter, called the first systolic invariant INVS1. We show that INVS1 is linearly related to stroke volume. To validate this approach, a statistical comparaison between INVS1 and stroke volume measured with the PiCCO technique was performed during a 15-mn recording in 21 mechanically ventilated patients in intensive care. In 94% of the whole recordings, a strong correlation was estimated by cross-correlation analysis (mean coefficient=0.9) and linear regression (mean coefficient=0.89). Once the linear relation had been verified, a Bland-Altman test showed the very good agreement between the two approaches and their interchangeability. For the remaining 6%, INVS1 and the PiCCO stroke volume were not correlated at all, and this discrepancy, interpreted with the help of mean pressure, heart rate and peripheral vascular resistances, was in favor of INVS1.

physics.med-ph↗