Distributed coordination of multi-agent systems (MASs) has been widely studied in various emerging engineering applications, including connected vehicles, wireless networks, smart grids, and cyber-physical systems. In these contexts, agents make the decision locally, relying on the interaction with their immediate neighbors over the connected communication networks. The study of distributed coordination for the multi-agent system (MAS) with constraints is significant yet challenging, especially in terms of ubiquitous uncertainties, the heavy communication burden, and communication delays, to name a few. Hence, it is desirable to develop distributed algorithms for the constrained MAS with these practical issues. In this dissertation, we develop the theoretical results on robust distributed model predictive control (DMPC) algorithms for two types of control problems (i.e., formation stabilization problem and consensus problem) of the constrained and uncertain MAS and apply robust DMPC algorithms in applications of cooperative marine vehicles. More precisely, Chapter 1 provides a systematic literature review, where the state-of-the-art DMPC for formation stabilization and consensus, robust MPC, and MPC for motion control of marine vehicles are introduced. Chapter 2 introduces some notations, necessary definitions, and some preliminaries. In Chapter 3, we study the formation stabilization problem of the nonlinear constrained MAS with un- certainties and bounded time-varying communication delays. We develop a min-max DMPC algorithm with the self-triggered mechanism, which significantly reduces the communication burden while ensuring closed-loop stability and robustness. Chapter 4 investigates the consensus problem of the general linear MAS with input constraints and bounded time-varying delays. We design a robust DMPC-based consensus protocol that integrates a predesigned consensus protocol with online DMPC optimization techniques. Under mild technical assumptions, the estimation errors propagated over prediction due to delay-induced inaccurate neighboring information are proved bounded, based on which a robust DMPC strategy is deliberately designed to achieve robust consensus while satisfying control input constraints. Chapter 5 proposes a Lyapunov-based DMPC approach for the formation tracking control problem of co-operative autonomous underwater vehicles (AUVs) subject to environmental disturbances. A stability constraint leveraging the extended state observer-based auxiliary control law and the associated Lyapunov function is incorporated into the optimization problem to enforce the stability and enhance formation tracking performance. A collision-avoidance cost is designed and employed in the DMPC optimization problem to further guarantee the safety of AUVs. Chapter 6 presents a tube-based DMPC approach for the platoon control problem of a group of heterogeneous autonomous surface vehicles (ASVs) with input constraints and disturbances. In particular, a coupled inter-vehicle safety constraint is added to the DMPC optimization problem; it ensures that neighboring ASVs maintain the safe distance and avoid inter-vehicle collision. Finally, we summarize the main results of this dissertation and discuss some potential directions for future research in Chapter 7. / Graduate / 2023-04-19

Cette thèse regroupe nos résultats sur la prédiction de séries temporelles dépendantes. Le document comporte trois chapitres principaux où nous abordons des problèmes différents. Le premier concerne l’agrégation de prédicteurs de décalages de Bernoulli Causales, en adoptant une approche Bayésienne. Le deuxième traite de l’agrégation de prédicteurs de ce que nous définissions comme processus sous-linéaires. Une attention particulaire est portée aux processus autorégressifs localement stationnaires variables dans le temps, nous examinons un schéma de prédiction adaptative pour eux. Dans le dernier chapitre nous étudions le modèle de régression linéaire pour une classe générale de processus localement stationnaires. / This thesis regroups our results on dependent time series prediction. The work is divided into three main chapters where we tackle different problems. The first one is the aggregation of predictors of Causal Bernoulli Shifts using a Bayesian approach. The second one is the aggregation of predictors of what we define as sub-linear processes. Locally stationary time varying autoregressive processes receive a particular attention; we investigate an adaptive prediction scheme for them. In the last main chapter we study the linear regression problem for a general class of locally stationary processes.

Les principales contributions de cette thèse concernent le développement de méthodes pour la synthèse de contrôleurs et pour l'analyse de la stabilité des systèmes linéaires, soit variant ou invariant dans le temps. Concernant les systèmes invariant dans le temps, le but est la synthèse de contrôleurs robustes d'ordre réduit pour les systèmes en temps continu qui présentent des paramètres incertains. La méthode présentée pour la synthèse est basée sur une technique en deux étapes, où un gain de retour d'état est construit dans la première étape, et appliqué à la deuxième, fournissant le contrôleur robuste souhaité. Chaque étape consiste à la résolution de conditions sous la forme d'inégalités matricielles linéaires.Dans le cas des systèmes variant dans le temps, en général, en fonction des informations disponibles, deux modèles mathématiques peuvent être utilisés. D'un côté, pour des systèmes dont les éléments variant dans le temps sont bornés mais pas complètement connus, on peut utiliser des modèles dépendant de paramètres variants, ce qui donne une représentation polytopique. Dans ce cas là, la technique de stabilisation proposée est basée sur la méthode en deux étapes, pour générer des contrôleurs dépendants des paramètres. On suppose que les paramètres sont mesurables en ligne, et les contrôleurs sont synthétisés pour qu'ils soient robustes à des bruits de mesures. De l'autre côté, si les dynamiques variantes dans le temps sont connues, on peut traiter directement le système sans utiliser aucune paramétrisation. Deux techniques de synthèse sont proposées pour ce cas: la construction des gains stabilisants en utilisant directement la matrice de transition d'état, et une technique de synthèse conçue à partir d'un nouveau critère de vérification de la stabilité du système. La validité des méthodes proposées est illustrée par plusieurs exemples numériques, qui montrent la qualité des résultats qui peuvent être obtenus / The main contributions of this thesis concern the development of methods for the stability analysis and the synthesis of controllers for linear systems, either time-varying or time-invariant. Concerning time-invariant systems, the objective is the synthesis of reduced-order robust controllers for continuous-time systems presenting uncertain parameters. The method presented for the synthesis is based on a two-stages technique, in which a stabilizing state-feedback gain is constructed in the first stage and then applied on the second stage to search for the desired controller. Each stage consists in the resolution of conditions based on linear matrix inequalities. In the case of time-varying systems, depending on the amount of available information, twomathematical models may be used. On one hand, if the time-varying elements of the system are not entirely known, one can model the system as function of time-varying parameters, resulting on a polytopic representation. In this case, the stabilization method proposed is based on the two-stages technique, which yields parameter-dependent controllers. The parameters are supposed to be real-time measurable, and the controllers are robust with respect to noises and uncertainties on the measures. On the other hand, if the time-varying dynamics are known, the system may be directly handled without using any parameterization. Two synthesis techniques are proposed in this case: the construction of stabilizing gains by using the state transition matrix, and a synthesis technique derived from a new stability criterion for time-varying systems. The validity of the proposed methods is illustrated through numerical examples, that show the efficiency of the results that can be obtained

[pt] Os modelos orientados por score, também conhecidos como modelos generalizados de score autorregressivo (GAS), representam uma classe de modelos de séries temporais orientados por observação. Eles possuem propriedades desejáveis para modelagem de séries temporais, como a capacidade de modelar diferentes distribuições condicionais e considerar parâmetros variantes no tempo dentro de uma estrutura flexível. Neste trabalho, apresentamos ScoreDrivenModels.jl, um pacote Julia de código aberto para modelagem, previsão e simulação de séries temporais usando a estrutura de modelos baseados em score. O pacote é flexível no que diz respeito à definição do modelo, permitindo ao usuário especificar a estrutura de atraso e quais parâmetros são variantes no tempo ou constantes. Também é possível considerar várias distribuições, incluindo Beta, Exponencial, Gama, Lognormal, Normal, Poisson, Student s t e Weibull. A interface fornecida é flexível, permitindo aos usuários interessados implementar qualquer distribuição e parametrização desejada. / [en] Score-driven models, also known as generalized autoregressive score (GAS) models, represent a class of observation-driven time series models. They possess desirable properties for time series modeling, such as the ability to model different conditional distributions and to consider time-varying parameters within a flexible framework. In this dissertation, we present ScoreDrivenModels.jl, an open-source Julia package for modeling, forecasting, and simulating time series using the framework of score-driven models. The package is flexible with respect to model definition, allowing the user to specify the lag structure and which parameters are time-varying or constant. It is also possible to consider several distributions, including Beta, Exponential, Gamma, Lognormal, Normal, Poisson, Student s t, and Weibull. The provided interface is flexible, allowing interested users to implement any desired distribution and parametrization.

Support for this work from Praxair; the McMaster Advanced Control Consortium; and the Natural Sciences and Engineering Research Council of Canada (NSERC), Grant CRDPJ 445717, is gratefully acknowledged. / In the air separation industry, cryogenic distillation is the dominant technology for separating large quantities of air into individual high purity component products. Due to the complexity of the process, in addition to significant energy input, air separation units (ASUs) also have high degrees of material and thermal integration and low process agility. As markets become more competitive and dynamic, especially after electricity market deregulation, ASUs can no longer practice mostly stationary operations, and are in need for design and control strategies to achieve high adaptability. In this study, we address such issues through a dynamic optimization framework. The use of rigorous dynamic models is important for developing economically beneficial designs and operating practices. The first part of this study focuses on the modeling aspect. For the column section of the plant, a full-order stage-wise model and a collocation based reduced order model are proposed. Model size, simulation time and predication accuracy are compared. For the primary heat exchanger, a novel moving boundary model is derived to handle the phase change in such a multi-stream heat exchanger. Simulation results demonstrate the capability of the proposed model in tracking the boundary points of the phase change occurrence, as well as the potential pinch point, along the length of the heat exchanger. The second part of the study addresses the operation aspects of ASUs through conducting dynamic optimization studies with collocation based dynamic models. We first performed a comprehensive analysis for a storage-then-utilization strategy on a nitrogen plant, following a two-tier multi-period formulation. As the parameter varies with time, the plant collects liquid, either directly from liquid product or by liquefaction of overproduced gas product, and then redistributes it for meeting gas product demand or as additional reflux. Effects of electricity price and demand profiles, additional operation costs, as well as product specifications are explored. Then we investigated the economic incentive for employing preemptive actions on a super-staged argon system, which allows the plant to take actions before external changes arrive. In the evaluation, changes are in the gas oxygen product demand. During the preemptive period, the plant takes either a single set or multiple sets of control actions. In the demand increase case, operation degrees of freedom are introduced to or removed from the set of decision variables. The demand decrease scenarios are explored with an under-supplied or saturated liquid oxygen market. / Dissertation / Doctor of Philosophy (PhD)

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In the past decade, the integration of spatiotemporal constraints into control systems has emerged as a crucial necessity, driven by the demand for enhanced performance, guaranteed safety, and the execution of complex tasks. Spatiotemporal constraints involve criteria that are dependent on both space and time, which can be represented by time-varying constraints in nonlinear control systems. Funnel-based control methods provide computationally tractable and robust feedback control laws to enforce time-varying constraints in uncertain nonlinear systems. This thesis begins by exploring the application of funnel-based control designs to address performance specifications in coordinate-free formation control of multi-agent systems. Moreover, we develop new robust feedback control schemes dealing with coupled spatiotemporal constraints in uncertain nonlinear systems that cannot be directly addressed by conventional funnel-based control methods. In the first part of the thesis, we present a novel coordinate-free formation control scheme for directed leader-follower multi-agent systems, exhibiting almost global convergence to the desired shape. The synthesis of fully decentralized robust controllers for agents is achieved through the application of the Prescribed Performance Control (PPC) method. This method imposes spatiotemporal funnel constraints on each agent's formation errors, ensuring a predefined transient and steady-state performance while maintaining robustness to system uncertainties. The core idea in this work is the utilization of bipolar coordinates to achieve orthogonal (decoupled) formation errors for each follower agent. This approach not only ensures the global convergence to the desired shape but also facilitates the effective application of the PPC method. In the second part of the thesis, first, we introduce a novel approach that extends funnel-based control schemes to deal with a specific class of time-varying hard and soft constraints. In this work, we employ an online Constraint Consistent Funnel (CCF) planning scheme to tackle couplings between hard and soft constraints. By satisfying these CCF constraints, we ensure adherence to hard (safety) constraints, while soft (performance) constraints are met only when they do not conflict with the hard constraints. Subsequently, we directly employ the PPC design method to craft a robust, low-complexity control law, ensuring that the system's outputs consistently stay within the online planned CCF constraints. In subsequent work, we tackle the challenge of satisfying a generalized class of potentially coupled time-varying output constraints. We show that addressing multiple constraints effectively boils down to formulating a single consolidating constraint. Ensuring the fulfillment of this consolidating constraint guarantees both convergence to and invariance of the time-varying output-constrained set within a user-defined finite time. Building on the PPC design method, we introduce a novel, robust low-complexity feedback control framework to handle this issue in uncertain high-order MIMO nonlinear control systems. Additionally, we present a mechanism for online modification of the consolidating constraint to secure a least-violating solution when constraint infeasibilities occur for an unknown time interval. / Under det senaste decenniet har integrationen av bivillkor i tid och rum för reglersystem framstått som en nödvändighet, driven av efterfrågan på förbättrad prestanda, garanterad säkerhet och utförandet av komplexa uppgifter. Bivillkor i tid och rum för icke-linjära reglersystem kan representeras av tidsvarierande bivillkor. Trattbaserade reglermetoder ("funnel-based control") tillhandahåller beräkningsmässigt hanterbara och robusta återkopplingslagar för att garantera tidsvarier-ande bivillkor i osäkra icke-linjära system. Denna avhandling börjar med att utforska tillämpningen av trattbaserade kontrollmetoder för att hantera prestanda-specifikationer i koordinatfri formationskontroll av multiagentsystem. Dessutom utvecklar vi nya robusta återkopplingslagar som hanterar kopplade bivillkor i tid och rum för osäkra icke-linjära system som inte direkt kan hanteras av konventionella trattbaserade kontrollmetoder. I den första delen av avhandlingen presenterar vi en ny koordinatfri formationskontrollmetod för riktade ledare-följare multiagentsystem, vilken uppvisar nästan global konvergens till den önskade formen. Syntesen av helt decentraliserade robusta regulatorer för agenter uppnås genom tillämpning av Prescribed Performance Control (PPC)-metoden. Denna metod lägger på trattbivillkor i tid och rum på varje agents formationsfel och säkerställer en fördefinierad transient och stationär prestanda samtidigt som robusthet mot systemosäkerheter bibehålls. Kärnan i detta arbete är användningen av bipolära koordinater för att uppnå ortogonala (frikopplade) formationsfel för varje följande agent. Detta tillvägagångssätt säkerställer inte bara global konvergens till den önskade formen utan underlättar också en effektiva tillämpning av PPC-metoden. I den andra delen av avhandlingen introducerar vi först ett nytt tillvägagångssätt som utökar trattbaserade kontrollmetoder för att hantera en specifik klass av tidsvar-ierande hårda och mjuka bivillkor. I detta arbete använder vi en online Constraint Consistent Funnel (CCF)-planeringsmetod för att tackla sammankopplingar mellan hårda och mjuka bivillkor. Genom att uppfylla dessa CCF-bivillkor säkerställer vi efterlevnad av hårda (säkerhets-) bivillkor, medan mjuka (prestanda-) bivillkor uppfylls endast när de inte strider mot de hårda bivillkoren. Därefter tillämpar vi direkt PPC-designmetoden för att utforma en robust reglerlag med låg komplexitet som säkerställer att systemets utsignal konsekvent håller sig inom de online planerade CCF-bivillkoren. Därefter hanterar vi utmaningen med att uppfylla en generaliserad klass av potentiellt kopplade tidsvarierande utsignals-bivillkor. Vi visar att effektiv hantering av flera bivillkor i grund och botten handlar om att formulera ett sammanfattande bivillkor. Uppfyllandet av detta sammanfattande bivillkor garanterar både konvergens till och invarians av den tidsvarierande mängden som uppfyller utsignalsbivillkoren, inom en användardefinierad begränsad tid. Baserat på PPC-designmetoden introducerar vi en ny, robust återkopplingsregulatorstruktur för att hantera detta problem i osäkra högordnings MIMO icke-linjära reglersystem. Dessutom presenterar vi en mekanism för online-modifiering av det sammanfattande bivillkoret för att säkra en lösning med minsta möjliga kränkning då bivillkoren blir omöjliga att uppfylla under en okänd tidsperiod. / <p>QC 20231229</p>

[pt] Este trabalho tem como finalidade analisar diferentes estratégias de detecção passíveis de aplicação em sistemas de transmissão OFDM (Orthogonal Frequency Division Multiplexing) operando em canais que variam rapidamente no tempo. Além dos métodos clássicos de detecção lineares tais como filtro casado, Zero Forcing e MMSE (Minimum Mean-Square Error), outras duas técnicas são estudadas, abrangendo também combinações entre elas. A primeira é a técnica de cancelamento paralelo de interferência (PIC - Parallel Interference Cancellation), a segunda é a detecção por busca por verossimilhança ascendente (LAS – Likelihood Ascent Search), ambas empregadas em conjunção com o filtro casado. Esse trabalho apresenta também um estudo dos efeitos de uma estimativa imperfeita do canal, no desempenho dos esquemas de detecção aqui enfocados. Os resultados dos experimentos são analisados em termos da taxa de erro de bit (BER) e custo computacional (complexidade)associado a estes esquemas. / [en] This work analyzing different detection strategies that can be applied in OFDM (Orthogonal Frequency Division Multiplexing) transmission systems over fast time-varying channels. In addition to classical linear methods of detection such as a Matched Filter, Zero Forcing and MMSE, two other techniques are studied, also encompassing combinations of them. The first is the Parallel Interference Cancellation (PIC) technique, the second is Likelihood Ascent Search (LAS), both used in conjunction with the Matched Filter. This work also presents a study of the effects of imperfect channel estimation on the performance of the detection schemes studied here. The results of the experiments are analyzed in terms of bit error rate (BER) and computational cost (complexity) associated with these schemes.