Cette thèse étudie le problème d'identification de la topologie d'un réseau de systèmes complexes dynamiques, dont les sous-systèmes sont décrits par des équations différentielles ordinaires (EDO) et/ou par des équations différentielles à retard (EDR). La première partie de ce travail porte sur l’identification des paramètres du réseau de systèmes linéaires. Ainsi, différentes classes de systèmes linéaires ont été traitées, à savoir les systèmes sans retard, les systèmes à retard commensurable et les systèmes à entrées inconnues. Un observateur impulsif est proposé afin d'identifier à la fois les états et les paramètres inconnus de la classe de système dynamique considérée en temps fini. Afin de garantir l'existence de l'observateur impulsif proposé, des conditions suffisantes sont déduites. Des exemples illustratifs sont donnés afin de montrer l'efficacité de l'observateur en temps fini proposé.La deuxième partie de ce travail traite le problème de l'identification de la topologie d'un réseau de systèmes dynamiques non linéaires. Dans nos considérations, les coefficients interconnexions de la topologie du réseau sont considérés comme des paramètres constants. Par conséquent, l'identification de la topologie est équivalente à l'identification des paramètres inconnus. Tout d’abord, nous avons déduit des conditions suffisantes sur l’identifiabilité des paramètres, puis nous avons proposé un différenciateur uniforme avec convergence en temps fini pour estimer les paramètres inconnus / This thesis investigates the topology identification problem for network of dynamical complex systems, whose subsystems are described by ordinary differential equations (ODE) and/or delay differential equations (DDE). The first part of this work focuses on the parameters identification of the network of linear systems. Thus, different classes of linear systems have been treated namely systems without delay, systems with commensurable delay and systems with unknown inputs. An impulsive observer is proposed in order to identify both the states and the unknown parameters of the considered class of dynamic system in finite time. In order to guarantee the existence of the proposed impulsive observer, sufficient conditions are deduced. An illustrative example is given in order to show the efficiency of the proposed finite-time observer.The second part of this work treats the topology identification of the network of nonlinear dynamic systems. In our considerations, the topology connections are represented as constant parameters, therefore the topology identification is equivalent to identify the unknown parameters. A sufficient condition on parameter identifiability is firstly deduced, and then a uniform differentiator with finite-time convergence is proposed to estimate the unknown parameters

In recent years, there has been increasing interest in studying time-delayed coupled networks of oscillators since these occur in many real life applications. In many cases symmetry, patterns can emerge in these networks; as a consequence, a part of the system might repeat itself, and properties of this symmetric subsystem represent the whole dynamics. In this thesis, an analysis of a second order N-node time-delay fully connected network is made. This study is carried out using symmetry groups. The existence of multiple eigenvalues forced by symmetry is shown, as well as the possibility of uncoupling the linearization at equilibria, into irreducible representations due to the symmetry. The existence of steady-state and Hopf bifurcations in each irreducible representation is also proved. Three different models are used to analyze the network dynamics, namely, the full-phase, the phase, and the phase-difference model. A finite set of frequencies ω is also determined, which might correspond to Hopf bifurcations in each case for critical values of the delay. Although we restrict our attention to second order nodes, the results could be extended to higher order networks provided the time-delay in the connections between nodes remains equal. / Nos últimos anos, tem havido um crescente interesse em estudar redes de osciladores acopladas com retardo de tempo uma vez que estes ocorrem em muitas aplicações da vida real. Em muitos casos, simetria e padrões podem surgir nessas redes; em consequência, uma parte do sistema pode repetir-se, e as propriedades deste subsistema simétrico representam a dinâmica da rede toda. Nesta tese é feita uma análise de uma rede de N nós de segunda ordem totalmente conectada com atraso de tempo. Este estudo é realizado utilizando grupos de simetria. É mostrada a existência de múltiplos valores próprios forçados por simetria, bem como a possibilidade de desacoplamento da linearização no equilíbrio, em representações irredutíveis. É também provada a existência de bifurcações de estado estacionário e Hopf em cada representação irredutível. São usados três modelos diferentes para analisar a dinâmica da rede: o modelo de fase completa, o modelo de fase, e o modelo de diferença de fase. É também determinado um conjunto finito de frequências ω, que pode corresponder a bifurcações de Hopf em cada caso, para valores críticos do atraso. Apesar de restringir a nossa atenção para nós de segunda ordem, os resultados podem ser estendido para redes de ordem superior, desde que o tempo de atraso nas conexões entre nós permanece igual.

Nonlinear systems occur in industrial processes, economical systems, biotechnology and in many other areas. The thesis treats methods for system identification and control of such nonlinear systems, and applies the proposed methods to a solar heating/cooling plant. Two applications, an anaerobic digestion process and a domestic solar heating system are first used to illustrate properties of an existing nonlinear recursive prediction error identification algorithm. In both cases, the accuracy of the obtained nonlinear black-box models are comparable to the results of application specific grey-box models. Next a convergence analysis is performed, where conditions for convergence are formulated. The results, together with the examples, indicate the need of a method for providing initial parameters for the nonlinear prediction error algorithm. Such a method is then suggested and shown to increase the usefulness of the prediction error algorithm, significantly decreasing the risk for convergence to suboptimal minimum points. Next, the thesis treats model based control of systems with input signal dependent time delays. The approach taken is to develop a controller for systems with constant time delays, and embed it by input signal dependent resampling; the resampling acting as an interface between the system and the controller. Finally a solar collector field for combined cooling and heating of office buildings is used to illustrate the system identification and control strategies discussed earlier in the thesis, the control objective being to control the solar collector output temperature. The system has nonlinear dynamic behavior and large flow dependent time delays. The simulated evaluation using measured disturbances confirm that the controller works as intended. A significant reduction of the impact of variations in solar radiation on the collector outlet temperature is achieved, though the limited control range of the system itself prevents full exploitation of the proposed feedforward control. The methods and results contribute to a better utilization of solar power.

The main interest of the present thesis is the constrained control of time-delay system, more specifically taking into consideration the discretization problem (due to, for example, a communication network) and the presence of constraints in the system's trajectories and control inputs. The effects of data-sampling and modeling problem are studied in detail, where an uncertainty is added into the system due to additional effect of the discretization and delay. The delay variation with respect to the sampling instants is characterized by a polytopic supra-approximation of the discretization/delay induced uncertainty. Some stabilizing techniques, based on Lyapunov's theory, are then derived for the unconstrained case. Lyapunov-Krasovskii candidates were also used to obtain LMI conditions for a state feedback, in the ''original" state-space of the system. For the constrained control purposes, the set invariance theory is used intensively, in order to obtain a region where the system is ''well-behaviored", despite the presence of constraints and (time-varying) delay. Due to the high complexity of the maximal delayed state admissible set obtained in the augmented state-space approach, in the present manuscript we proposed the concept of set invariance in the ''original" state-space of the system, called D-invariance. Finally, in the las part of the thesis, the MPC scheme is presented, in order to take into account the constraints and the optimality of the control solution.

Genes encode proteins, some of which in turn regulate other genes. Such interactions make up gene regulatory relationships or (dynamic) gene regulatory networks. With advances in the measurement technology for gene expression and in genome sequencing, it has become possible to measure the expression level of thousands of genes simultaneously in a cell at a series of time points over a specific biological process. Such time-course gene expression data may provide a snapshot of most (if not all) of the interesting genes and may lead to a better understanding gene regulatory relationships and networks. However, inferring either gene regulatory relationships or networks puts a high demand on powerful computational methods that are capable of sufficiently mining the large quantities of time-course gene expression data, while reducing the complexity of the data to make them comprehensible. This dissertation presents several computational methods for inferring gene regulatory relationships and gene regulatory networks from time-course gene expression. These methods are the result of the authors doctoral study. Cluster analysis plays an important role for inferring gene regulatory relationships, for example, uncovering new regulons (sets of co-regulated genes) and their putative cis-regulatory elements. Two dynamic model-based clustering methods, namely the Markov chain model (MCM)-based clustering and the autoregressive model (ARM)-based clustering, are developed for time-course gene expression data. However, gene regulatory relationships based on cluster analysis are static and thus do not describe the dynamic evolution of gene expression over an observation period. The gene regulatory network is believed to be a time-varying system. Consequently, a state-space model for dynamic gene regulatory networks from time-course gene expression data is developed. To account for the complex time-delayed relationships in gene regulatory networks, the state space model is extended to be the one with time delays. Finally, a method based on genetic algorithms is developed to infer the time-delayed relationships in gene regulatory networks. Validations of all these developed methods are based on the experimental data available from well-cited public databases.

Genes encode proteins, some of which in turn regulate other genes. Such interactions make up gene regulatory relationships or (dynamic) gene regulatory networks. With advances in the measurement technology for gene expression and in genome sequencing, it has become possible to measure the expression level of thousands of genes simultaneously in a cell at a series of time points over a specific biological process. Such time-course gene expression data may provide a snapshot of most (if not all) of the interesting genes and may lead to a better understanding gene regulatory relationships and networks. However, inferring either gene regulatory relationships or networks puts a high demand on powerful computational methods that are capable of sufficiently mining the large quantities of time-course gene expression data, while reducing the complexity of the data to make them comprehensible. This dissertation presents several computational methods for inferring gene regulatory relationships and gene regulatory networks from time-course gene expression. These methods are the result of the authors doctoral study. Cluster analysis plays an important role for inferring gene regulatory relationships, for example, uncovering new regulons (sets of co-regulated genes) and their putative cis-regulatory elements. Two dynamic model-based clustering methods, namely the Markov chain model (MCM)-based clustering and the autoregressive model (ARM)-based clustering, are developed for time-course gene expression data. However, gene regulatory relationships based on cluster analysis are static and thus do not describe the dynamic evolution of gene expression over an observation period. The gene regulatory network is believed to be a time-varying system. Consequently, a state-space model for dynamic gene regulatory networks from time-course gene expression data is developed. To account for the complex time-delayed relationships in gene regulatory networks, the state space model is extended to be the one with time delays. Finally, a method based on genetic algorithms is developed to infer the time-delayed relationships in gene regulatory networks. Validations of all these developed methods are based on the experimental data available from well-cited public databases.

¡@¡@Pseudo-noise (PN) code synchronizer is an essential element of direct-sequence code division multiple access (DS-CDMA) system because data transmission is possible only after the receiver accurately synchronizes the locally generated PN code with the incoming PN code. The code synchronization is processed in two steps, acquisition and tracking, to estimate the delay offset between the two codes. Recently, the adaptive LMS filtering scheme has been proposed for performing both code acquisition and tracking with the identical structure, where the LMS algorithm is used to adjust the FIR filter taps to search for the value of delay-offset adaptively. A decision device is employed in the adaptive LMS filtering scheme as a decision variable to indicate code synchronization, hence it plays an important role for the performance of mean acquisition time (MAT). In this thesis, only code acquisition is considered. ¡@¡@In this thesis, a new decision device, referred to as the weight vector square norm (WVSN) test method, is devised associated with the adaptive LMS filtering scheme for code acquisition in DS-CDMA system. The system probabilities of the proposed scheme are derived for evaluating MAT. Numerical analyses and simulation results verify that the performance of the proposed scheme, in terms of detection probability and MAT, is superior to the conventional scheme with mean-squared error (MSE) test method, especially when the signal-to-interference-plus-noise ratio (SINR) is relatively low. ¡@¡@Furthermore, an efficient and joint-adaptation code acquisition scheme, i.e., a smart antenna coupled with the proposed adaptive LMS filtering scheme with the WVSN test method, is devised for applying to a base station, where all antenna elements are employed during PN code acquisition. This new scheme is a process of PN code acquisition and the weight coefficients of smart antenna jointly and adaptively. Numerical analyses and simulation results demonstrate that the performance of the proposed scheme with five antenna elements, in terms of the output SINR, the detection probability and the MAT, can be improved by around 7 dB, compared to the one with single antenna case.

This dissertation is focused on developing a new passband behavioral model in order to account for asymmetric intermodulation distortion resulted from memory effect. First, a measurement setup is prepared to measure the AM/AM, AM/PM distortion, magnitudes and the phases of intermodulation (IMD) and fundamental (FUND) components which are created by the amplifier where phase is calculated only by measuring magnitudes. Then, responses of a sample amplifier are measured for different excitation situations (center frequency and tone spacing are swept). A new modeling technique, namely Odd Order Modeling (OOM), is proposed which has unequal time delay terms. The reason of unequal time delay addition is the change of effective channel length according to the average power passing through that channel. These unequal delays create asymmetry in the IMD components. General Power Series Expansion (GPSE) model is also extracted, OOM and GPSE model performances are compared by using NMSE metric. In order to improve model performance, even order terms with envelope of input are added. It is mathematically proven that even order terms with envelope of the input have contribution to IMD and FUND components&rsquo / . This improved version of modeling is named as Even Order modeling (EOM). EOM model performance is compared with the others&rsquo / performance for two-tone excitation measurement results. It is shown that EOM gives the most accurate result. Model performance is checked for unequal four-tone signal as well. EOM model is applied to baseband DPD circuit after making some modifications. Model linearization performance is compared with the performances of the other memory polynomial modeling techniques.

In this thesis, a sliding mode controller employing a new sliding surface for antilock brake system (ABS) is proposed, its stability is proven formally and its performance is compared with existing sliding mode controllers. The new sliding mode controller uses the integral-derivative surface, which includes error, its derivative and its integral, all at the same time. This and the already existing derivative surface, which includes error and its derivative only, are named zerothorder sliding surfaces. Their stability analysis is done using first-order auxiliary surfaces. Auxiliary surfaces equal the sliding surfaces when derivative of the error becomes zero. The first-order error surface, which includes only the error, and the integral surface, which includes error and its integral, were also designed for comparison. During design, tire brake force response is modelled as an uncertainty. Controllers are simulated on a road with an abrupt change in road coefficient of adhesion. Controller parameters used are optimized, which results in comparable stopping distances while braking on a constant coefficient of adhesion road. Effect of first order actuator dynamics with varying time constants and actuator absolute time delay were considered. Reaching and sliding properties of controllers were also investigated, using results on a constant coefficient of adhesion road. It is observed that zeroth-order sliding surfaces give smoother response for both derivative and integral-derivative cases. As the controllers employing error and derivative surfaces get unstable in the presence of actuator time delay, the integral-derivative surface, proposed in this study, stands as the best controller.

With the rapid development of optical communications and the increasing amount of data exchanged, it has become utterly important to provide effective ar- chitectures to protect sensitive data. The use of chaotic optoelectronic devices has already demonstrated great potential in terms of additional computational security at the physical layer of the optical network. However, the determination of the security level and the lack of a multi-user framework are two hurdles which have prevented their deployment on a large scale. In this thesis, we propose to address these two issues. First, we investigate the security of a widely used chaotic generator, the external cavity semiconductor laser (ECSL). This is a time-delay system known for providing complex and high-dimensional chaos, but with a low level of security regarding the identification of its most critical parameter, the time delay. We perform a detailed analysis of the influence of the ECSL parameters to devise how higher levels of security can be achieved and provide a physical interpretation of their origin. Second, we devise new architectures to multiplex optical chaotic signals and realize multi-user communications at high bit rates. We propose two different approaches exploiting known chaotic optoelectronic devices. The first one uses mutually cou- pled ECSL and extends typical chaos-based encryption strategies, such as chaos-shift keying (CSK) and chaos modulation (CMo). The second one uses an electro-optical oscillator (EOO) with multiple delayed feedback loops and aims first at transpos- ing coded-division multiple access (CDMA) and then at developing novel strategies of encryption and decryption, when the time-delays of each feedback loop are time- dependent.