This work focuses on the robustness issues related to distributed model predictive control (DMPC) strategies in the presence of model uncertainty. The robustness of DMPC with respect to model uncertainty has been identified by researchers as a key factor in the successful application of DMPC. A first task towards the formulation of robust DMPC strategy was to propose a new systematic methodology for the selection of a control structure in the context of DMPC. The methodology is based on the trade-off between performance and simplicity of structure (e.g., a centralized versus decentralized structure) and is formulated as a multi-objective mixed-integer nonlinear program (MINLP). The multi-objective function is composed of the contribution of two indices: 1) closed-loop performance index computed as an upper bound on the variability of the closed-loop system due to the effect on the output error of either set-point or disturbance input, and 2) a connectivity index used as a measure of the simplicity of the control structure. The parametric uncertainty in the models of the process is also considered in the methodology and it is described by a polytopic representation whereby the actual process’s states are assumed to evolve within a polytope whose vertices are defined by linear models that can be obtained from either linearizing a nonlinear model or from their identification in the neighborhood of different operating conditions. The system’s closed-loop performance and stability are formulated as Linear Matrix Inequalities (LMI) problems so that efficient interior-point methods can be exploited. To solve the MINLP a multi-start approach is adopted in which many starting points are generated in an attempt to obtain global optima. The efficiency of the proposed methodology is shown through its application to benchmark simulation examples. The simulation results are consistent with the conclusions obtained from the analysis. The proposed methodology can be applied at the design stage to select the best control configuration in the presence of model errors. A second goal accomplished in this research was the development of a novel online algorithm for robust DMPC that explicitly accounts for parametric uncertainty in the model. This algorithm requires the decomposition of the entire system’s model into N subsystems and the solution of N convex corresponding optimization problems in parallel. The objective of this parallel optimizations is to minimize an upper bound on a robust performance objective by using a time-varying state-feedback controller for each subsystem. Model uncertainty is explicitly considered through the use of polytopic description of the model. The algorithm employs an LMI approach, in which the solutions are convex and obtained in polynomial time. An observer is designed and embedded within each controller to perform state estimations and the stability of the observer integrated with the controller is tested online via LMI conditions. An iterative design method is also proposed for computing the observer gain. This algorithm has many practical advantages, the first of which is the fact that it can be implemented in real-time control applications and thus has the benefit of enabling the use of a decentralized structure while maintaining overall stability and improving the performance of the system. It has been shown that the proposed algorithm can achieve the theoretical performance of centralized control. Furthermore, the proposed algorithm can be formulated using a variety of objectives, such as Nash equilibrium, involving interacting processing units with local objective functions or fully decentralized control in the case of communication failure. Such cases are commonly encountered in the process industry. Simulations examples are considered to illustrate the application of the proposed method. Finally, a third goal was the formulation of a new algorithm to improve the online computational efficiency of DMPC algorithms. The closed-loop dual-mode paradigm was employed in order to perform most of the heavy computations offline using convex optimization to enlarge invariant sets thus rendering the iterative online solution more efficient. The solution requires the satisfaction of only relatively simple constraints and the solution of problems each involving a small number of decision variables. The algorithm requires solving N convex LMI problems in parallel when cooperative scheme is implemented. The option of using Nash scheme formulation is also available for this algorithm. A relaxation method was incorporated with the algorithm to satisfy initial feasibility by introducing slack variables that converge to zero quickly after a small number of early iterations. Simulation case studies have illustrated the applicability of this approach and have demonstrated that significant improvement can be achieved with respect to computation times. Extensions of the current work in the future should address issues of communication loss, delays and actuator failure and their impact on the robustness of DMPC algorithms. In addition, integration of the proposed DMPC algorithms with other layers in automation hierarchy can be an interesting topic for future work.

This work focuses on the robustness issues related to distributed model predictive control (DMPC) strategies in the presence of model uncertainty. The robustness of DMPC with respect to model uncertainty has been identified by researchers as a key factor in the successful application of DMPC. A first task towards the formulation of robust DMPC strategy was to propose a new systematic methodology for the selection of a control structure in the context of DMPC. The methodology is based on the trade-off between performance and simplicity of structure (e.g., a centralized versus decentralized structure) and is formulated as a multi-objective mixed-integer nonlinear program (MINLP). The multi-objective function is composed of the contribution of two indices: 1) closed-loop performance index computed as an upper bound on the variability of the closed-loop system due to the effect on the output error of either set-point or disturbance input, and 2) a connectivity index used as a measure of the simplicity of the control structure. The parametric uncertainty in the models of the process is also considered in the methodology and it is described by a polytopic representation whereby the actual process’s states are assumed to evolve within a polytope whose vertices are defined by linear models that can be obtained from either linearizing a nonlinear model or from their identification in the neighborhood of different operating conditions. The system’s closed-loop performance and stability are formulated as Linear Matrix Inequalities (LMI) problems so that efficient interior-point methods can be exploited. To solve the MINLP a multi-start approach is adopted in which many starting points are generated in an attempt to obtain global optima. The efficiency of the proposed methodology is shown through its application to benchmark simulation examples. The simulation results are consistent with the conclusions obtained from the analysis. The proposed methodology can be applied at the design stage to select the best control configuration in the presence of model errors. A second goal accomplished in this research was the development of a novel online algorithm for robust DMPC that explicitly accounts for parametric uncertainty in the model. This algorithm requires the decomposition of the entire system’s model into N subsystems and the solution of N convex corresponding optimization problems in parallel. The objective of this parallel optimizations is to minimize an upper bound on a robust performance objective by using a time-varying state-feedback controller for each subsystem. Model uncertainty is explicitly considered through the use of polytopic description of the model. The algorithm employs an LMI approach, in which the solutions are convex and obtained in polynomial time. An observer is designed and embedded within each controller to perform state estimations and the stability of the observer integrated with the controller is tested online via LMI conditions. An iterative design method is also proposed for computing the observer gain. This algorithm has many practical advantages, the first of which is the fact that it can be implemented in real-time control applications and thus has the benefit of enabling the use of a decentralized structure while maintaining overall stability and improving the performance of the system. It has been shown that the proposed algorithm can achieve the theoretical performance of centralized control. Furthermore, the proposed algorithm can be formulated using a variety of objectives, such as Nash equilibrium, involving interacting processing units with local objective functions or fully decentralized control in the case of communication failure. Such cases are commonly encountered in the process industry. Simulations examples are considered to illustrate the application of the proposed method. Finally, a third goal was the formulation of a new algorithm to improve the online computational efficiency of DMPC algorithms. The closed-loop dual-mode paradigm was employed in order to perform most of the heavy computations offline using convex optimization to enlarge invariant sets thus rendering the iterative online solution more efficient. The solution requires the satisfaction of only relatively simple constraints and the solution of problems each involving a small number of decision variables. The algorithm requires solving N convex LMI problems in parallel when cooperative scheme is implemented. The option of using Nash scheme formulation is also available for this algorithm. A relaxation method was incorporated with the algorithm to satisfy initial feasibility by introducing slack variables that converge to zero quickly after a small number of early iterations. Simulation case studies have illustrated the applicability of this approach and have demonstrated that significant improvement can be achieved with respect to computation times. Extensions of the current work in the future should address issues of communication loss, delays and actuator failure and their impact on the robustness of DMPC algorithms. In addition, integration of the proposed DMPC algorithms with other layers in automation hierarchy can be an interesting topic for future work.

An increasing number of applications ranging from multi-vehicle systems, large-scale process control systems, transportation systems to smart grids call for the development of cooperative control theory. Meanwhile, when designing the cooperative controller, the state and control constraints, ubiquitously existing in the physical system, have to be respected. Model predictive control (MPC) is one of a few techniques that can explicitly and systematically handle the state and control constraints. This dissertation studies the robust MPC and distributed MPC strategies, respectively. Specifically, the problems we investigate are: the robust MPC for linear or nonlinear systems, distributed MPC for constrained decoupled systems and distributed MPC for constrained nonlinear systems with coupled system dynamics. In the robust MPC controller design, three sub-problems are considered. Firstly, a computationally efficient multi-stage suboptimal MPC strategy is designed by exploiting the j-step admissible sets, where the j-step admissible set is the set of system states that can be steered to the maximum positively invariant set in j control steps. Secondly, for nonlinear systems with control constraints and external disturbances, a novel robust constrained MPC strategy is designed, where the cost function is in a non-squared form. Sufficient conditions for the recursive feasibility and robust stability are established, respectively. Finally, by exploiting the contracting dynamics of a certain type of nonlinear systems, a less conservative robust constrained MPC method is designed. Compared to robust MPC strategies based on Lipschitz continuity, the strategy employed has the following advantages: 1) it can tolerate larger disturbances; and 2) it is feasible for a larger prediction horizon and enlarges the feasible region accordingly. For the distributed MPC of constrained continuous-time nonlinear decoupled systems, the cooperation among each subsystems is realized by incorporating a coupling term in the cost function. To handle the effect of the disturbances, a robust control strategy is designed based on the two-layer invariant set. Provided that the initial state is feasible and the disturbance is bounded by a certain level, the recursive feasibility of the optimization is guaranteed by appropriately tuning the design parameters. Sufficient conditions are given ensuring that the states of each subsystem converge to the robust positively invariant set. Furthermore, a conceptually less conservative algorithm is proposed by exploiting the controllability set instead of the positively invariant set, which allows the adoption of a shorter prediction horizon and tolerates a larger disturbance level. For the distributed MPC of a large-scale system that consists of several dynamically coupled nonlinear systems with decoupled control constraints and disturbances, the dynamic couplings and the disturbances are accommodated through imposing new robustness constraints in the local optimizations. Relationships among, and design procedures for the parameters involved in the proposed distributed MPC are derived to guarantee the recursive feasibility and the robust stability of the overall system. It is shown that, for a given bound on the disturbances, the recursive feasibility is guaranteed if the sampling interval is properly chosen. / Graduate / 0548 / 0544 / 0546 / liuxiaotao1982@gmail.com

Une vallée hydroélectrique est constituée d'un nombre important de centrales interconnectées du fait de l'utilisation de la même ressource en eau. Pour pouvoir optimiser en temps réel sa production, il a été proposé dans cette thèse d'utiliser les méthodes associées aux systèmes à grande échelle pour développer les outils nécessaires. Cette étude de la commande globale du système a été orientée vers l'utilisation des méthodes de décomposition-coordination. Ces méthodes ont été examinées et appliquées à un cas d'étude simplifié (une partie de la vallée hydraulique) mis à disposition par EDF. Plus particulièrement, les méthodes de décomposition-coordination par les prix, ou encore par les prédictions des interactions, s'appuyant sur des commandes MPC, ont été considérées et comparées avec une commande centralisée. En vue d'une implémentation temps-réel, nous nous sommes intéressés à exprimer les problèmes d'optimisation comme des problèmes QP, pour ensuite obtenir des solutions explicites en utilisant une méthodologie de caractérisation géométrique. Nous avons proposé des formulations complètement explicites (niveau coordinateur et sous-systèmes) pour les deux méthodes. Des résultats de simulation avec des données réelles mises à disposition par EDF sont présentés. Afin de valider les méthodes conçues, une première phase d'implantation sur la plate-forme Supervision NG d'EDF permettant la communication avec un modèle de la vallée hydroélectrique (basé sur les équations de Saint Venant et la bathymétrie de la rivière), est enfin incluse dans ce mémoire. / This study is mainly about the hydroelectric production problem. What we aim to do, is to develop optimization tools for a chain of hydroelectric plants, using appropriate control methodologies. A hydroelectric valley is a large scale system, made up of interconnected plants. The study of the global control system has been focused to the use of decomposition-coordination methods. Those methods have been examined and applied to a simplified case study (a part of a hydroelectric valley) given by EDF. To be more specific, the price decomposition - coordination method and the interactions prediction method, based on MPC controls, have been considered and compared to a centralized control. Because of the need of implementation in real time, we have expressed the optimization problems as QP problems, so as to obtain explicit solutions using the geometric characterization methodology. We have proposed a completely explicit formulation (both at the coordinator level and at the subsystems level) for both methods. Simulation results with real data information given by EDF are also presented. To verify and validate the designed methods, a first step of implementation on the supervision platform NG by EDF, that allows the communication with a model of the hydroelectric valley (based on the equations of Saint Venant and on the river bathymetry) is finally also included in this thesis.

À l’heure actuelle, les stratégies de gestion de l’énergie pour les bâtiments sontprincipalement basées sur une concaténation de règles logiques. Bien que cette approcheoffre des avantages certains, particulièrement lors de sa mise en oeuvre sur des automatesprogrammables, elle peine à traiter la diversité de situations complexes quipeuvent être rencontrées (prix de l’énergie variable, limitations de puissance, capacitéde stockage d’énergie, bâtiments de grandes dimension).Cette thèse porte sur le développement et l’évaluation d’une commande prédictivepour la gestion de l’énergie dans le bâtiment ainsi que l’étude de l’embarcabilité del’algorithme de contrôle sur une cible temps-réel (Roombox - Schneider-Electric).La commande prédictive est basée sur l’utilisation d’un modèle du bâtiment ainsique des prévisions météorologiques et d’occupation afin de déterminer la séquencede commande optimale à mettre en oeuvre sur un horizon de prédiction glissant.Seul le premier élément de cette séquence est en réalité appliqué au bâtiment. Cetteséquence de commande optimale est obtenue par la résolution en ligne d’un problèmed’optimisation. La capacité de la commande prédictive à gérer des systèmes multivariablescontraints ainsi que des objectifs économiques, la rend particulièrementadaptée à la problématique de la gestion de l’énergie dans le bâtiment.Cette thèse propose l’élaboration d’un schéma de commande distribué pour contrôlerles conditions climatiques dans chaque zone du bâtiment. L’objectif est de contrôlersimultanément: la température intérieure, le taux de CO2 ainsi que le niveaud’éclairement dans chaque zone en agissant sur les équipements présents (CVC, éclairage,volets roulants). Par ailleurs, le cas des bâtiments multi-sources (par exemple:réseau électrique + production locale solaire), dans lequel chaque source d’énergie estcaractérisée par son propre prix et une limitation de puissance, est pris en compte.Dans ce contexte, les décisions relatives à chaque zone ne peuvent plus être effectuéesde façon indépendante. Pour résoudre ce problème, un mécanisme de coordinationbasé sur une décomposition du problème d’optimisation centralisé est proposé. Cettethèse CIFRE 1 a été préparée au sein du laboratoire Gipsa-lab en partenariat avecSchneider-Electric dans le cadre du programme HOMES (www.homesprogramme.com). / Currently, energy management strategies for buildings are mostly based on a concatenationof logical rules. Despite the fact that such rule based strategy can be easilyimplemented, it suffers from some limitations particularly when dealing with complexsituations. This thesis is concerned with the development and assessment ofModel Predictive Control (MPC) algorithms for energy management in buildings. Inthis work, a study of implementability of the control algorithm on a real-time hardwaretarget is conducted beside yearly simulations showing a substantial energy savingpotential. The thesis explores also the ability of MPC to deal with the diversity ofcomplex situations that could be encountered (varying energy price, power limitations,local storage capability, large scale buildings).MPC is based on the use of a model of the building as well as weather forecasts andoccupany predictions in order to find the optimal control sequence to be implementedin the future. Only the first element of the sequence is actually applied to the building.The best control sequence is found by solving, at each decision instant, an on lineoptimization problem. MPC’s ability to handle constrained multivariable systems aswell as economic objectives makes this paradigm particularly well suited for the issueof energy management in buildings.This thesis proposes the design of a distributed predictive control scheme to controlthe indoor conditions in each zone of the building. The goal is to control thefollowing simultaneously in each zone of the building: indoor temperature, indoorCO2 level and indoor illuminance by acting on all the actuators of the zone (HVAC,lighting, shading). Moreover, the case of multi-source buildings is also explored, (e.g.power from grid + local solar production), in which each power source is characterizedby its own dynamic tariff and upper limit. In this context, zone decisions can nolonger be performed independently. To tackle this issue, a coordination mechanismis proposed. A particular attention is paid to computational effectiveness of the proposedalgorithms. This CIFRE2 Ph.D. thesis was prepared within the Gipsa-lab laboratoryin partnership with Schneider-Electric in the scope of the HOMES program(www.homesprogramme.com).

Networked control systems (NCSs) present many advantages such as easy installation and maintenance, flexible layouts and structures of components, and efficient allocation and distribution of resources. Consequently, they find potential applications in a variety of emerging industrial systems including multi-agent systems, power grids, tele-operations and cyber-physical systems. The study of NCSs with nonlinear dynamics (i.e., nonlinear NCSs) is a very significant yet challenging topic, and it not only widens application areas of NCSs in practice, but also extends the theoretical framework of NCSs with linear dynamics (i.e., linear NCSs). Numerous issues are required to be resolved towards a fully-fledged theory of industrial nonlinear NCS design. In this dissertation, three important problems of nonlinear NCSs are investigated: The robust filtering problem, the robust model predictive control (MPC) problem and the robust distributed MPC problem of large-scale nonlinear systems. In the robust filtering problem of nonlinear NCSs, the nonlinear system model is subject to uncertainties and external disturbances, and the measurements suffer from time delays governed by a Markov process. Utilizing the Lyapunov theory, the algebraic Hamilton-Jacobi inequality (HJI)-based sufficient conditions are established for designing the H_infty nonlinear filter. Moreover, the developed results are specialized for a special type of nonlinear systems, by presenting the HJI in terms of matrix inequalities. For the robust MPC problem of NCSs, three aspects are considered. Firstly, to reduce the computation and communication load, the networked MPC scheme with an efficient transmission and compensation strategy is proposed, for constrained nonlinear NCSs with disturbances and two-channel packet dropouts. A novel Lyapunov function is constructed to ensure the input-to-state practical stability (ISpS) of the closed-loop system. Secondly, to improve robustness, a networked min-max MPC scheme are developed, for constrained nonlinear NCSs subject to external disturbances, input and state constraints, and network-induced constraints. The ISpS of the resulting nonlinear NCS is established by constructing a new Lyapunov function. Finally, to deal with the issue of unavailability of system state, a robust output feedback MPC scheme is designed for constrained linear systems subject to periodical measurement losses and external disturbances. The rigorous feasibility and stability conditions are established. For the robust distributed MPC problem of large-scale nonlinear systems, three steps are taken to conduct the studies. In the first step, the issue of external disturbances is addressed. A robustness constraint is proposed to handle the external disturbances, based on which a novel robust distributed MPC algorithm is designed. The conditions for guaranteeing feasibility and stability are established, respectively. In the second step, the issue of communication delays are dealt with. By designing the waiting mechanism, a distributed MPC scheme is proposed, and the feasibility and stability conditions are established. In the third step, the robust distributed MPC problem for large-scale nonlinear systems subject to control input constraints, communication delays and external disturbances are studied. A dual-mode robust distributed MPC strategy is designed to deal with the communication delays and the external disturbances simultaneously, and the feasibility and the stability conditions are developed, accordingly. / Graduate / 0548 / 0544

The operation of groups of heavy-duty vehicles at small inter-vehicular distances, known as platoons, lowers the overall aerodynamic drag and, therefore, reduces fuel consumption and greenhouse gas emissions. Experimental tests conducted on a flat road and without traffic have shown that platooning has the potential to reduce the fuel consumption up to 10%. However, platoons are expected to drive on public highways with varying topography and traffic. Due to the large mass and limited engine power of heavy-duty vehicles, road slopes can have a significant impact on feasible and optimal speed profiles. Therefore, maintaining a short inter-vehicular distance without coordination can result in inefficient or even infeasible speed trajectories. Furthermore, external traffic can interfere by affecting fuel-efficiency and threatening the safety of the platooning vehicles. This thesis addresses the problem of safe and fuel-efficient control for heavy-duty vehicle platooning. We propose a hierarchical control architecture that splits this complex control problem into two layers. The layers are responsible for the fuel-optimal control based on look-ahead information on road topography and the real-time vehicle control, respectively. The top layer, denoted the platoon coordinator, relies on a dynamic programming framework that computes the fuel-optimal speed profile for the entire platoon. The bottom layer, denoted the vehicle control layer, uses a distributed model predictive controller to track the optimal speed profile and the desired inter-vehicular spacing policy. Within this layer, constraints on the vehicles' states guarantee the safety of the platoon. The effectiveness of the proposed controller is analyzed by means of simulations of several realistic scenarios. They suggest a possible fuel saving of up to 12% for the follower vehicles compared to the use of existing platoon controllers. Analysis of the simulation results shows how the majority of the fuel saving comes from a reduced usage of vehicles brakes. A second problem addressed in the thesis is model predictive control for obstacle avoidance and lane keeping for a passenger car. We propose a control framework that allows to control the nonlinear vehicle dynamics with linear model predictive control. The controller decouples the longitudinal and lateral vehicle dynamics into two successive stages. First, plausible braking and throttle profiles are generated. Second, for each profile, linear time-varying models of the lateral dynamics are derived and used to formulate a collection of linear model predictive control problems. Their solution provides the optimal control input for the steering and braking actuators. The performance of the proposed controller has been evaluated by means of simulations and real experiments. / <p>QC 20150911</p>

No description available.

In this thesis, we develop methods leading towards the distributed control of spatio-temporally constrained systems. Overall, we focus on two different approaches: a model predictive control approach and an approach based on ensuring set-invariance via control barrier functions. Developing a distributed control framework for spatio-temporally constrained systems is challenging since multiple subsystems are interconnected via time-varying state constraints. Often, such constraints are only implicitly given as logic formulas, for example in Signal Temporal Logic (STL). Our approach to dealing with spatio-temporal constraints is as follows. We aim at combining the computational efficiency of low-level feedback controllers with planning algorithms. Low-level feedback controllers shall ensure the satisfaction of parts of spatio-temporal constraints such as coupling state constraints or short term time-constraints. In contrast, planning algorithms account for those parts that require computationally intense planning operations. Powerful low-level controllers can simplify the planning task significantly. For this reason, the focus of this thesis is on the development of low level feedback controllers.  In the first part, we focus on handling coupling state constraints using a model predictive control (MPC) approach. Commonly, the distributed handling of coupling state constraints requires a sequential or iterative MPC scheme which however is computationally time-intense. We address this issue by employing consistency constraints to develop a parallelized distributed model predictive controller (DMPC). By using consistency constraints, each subsystem guarantees to its neighbors that its states stay within a particular neighborhood around a reference trajectory. Furthermore, we propose extensions to robust and iterative schemes. Building up on this, also systems with bounded dynamic couplings can be controlled. In the second part, we focus on methods for ensuring set-invariance. In particular, we focus on control barrier functions (CBF). We show how spatio-temporal constraints that comprise disjunctions (logic OR) can be encoded in non-smooth time-varying control barrier functions and how subgradients can be used to synthesize an efficient gradient-based controller. For these results, controllability assumptions must be invoked. To extend the results to systems with weaker controllability properties, we investigate the connection between controllability properties and the construction of CBFs. As a result, we propose a construction method for CBFs based on finite horizon predictions. The constructed CBF exhibits favorable properties for the extension of the previous results on encoding spatio-temporal constraints in CBFs to systems with weaker controllability properties. At last, we investigate with a case study how set-invariance methods can be used to implicitly coordinate systems subject to coupled state constraints. Our proposed method is fully decentralized and subsystems coordinate themselves purely via their actions and the adjustment of their individual constraints. In the end, we draw a conclusion and outline how the presented results contribute to the development of a distributed control framework for spatio-temporally constrained systems. / I den här avhandlingen utvecklar vi metoder som leder till distribuerad styrning av tillstånds-temporalt begränsade system. Vi följer två olika tillvägagångssätt: å ena sidan en modellprediktiv styrning och å andra sidan ett tillvägagångssätt som bygger på att säkerställa invarians i mängden via kontrollbarriärfunktioner. Det är en utmaning att utveckla ett ramverk för distribuerad styrning för tillstånds-temporalt begränsade system, eftersom flera delsystem är sammankopplade via sina tillståndsbegränsningar som varierar över tiden. Ofta ges sådana begränsningar endast implicit som logiska formler, till exempel i Signal Temporal Logic (STL).  Vår metod för att hantera tillstånds- och tidsmässiga begränsningar är följande. Vi strävar efter att kombinera beräkningseffektiviteten hos återkopplingsregulatorer på låg nivå med planeringsalgoritmer. Återkopplingsregulatorer på låg nivå skall säkerställa att delar av de tillstånds- och tidsmässiga begränsningarna uppfylls, t.ex. sammankopplande tillståndsbegränsningar eller kortsiktiga tidsbegränsningar, medan planeringsalgoritmerna tar hänsyn till de delar som kräver beräkningsintensiva planeringsoperationer. Kraftfulla styrsystem på låg nivå kan förenkla planeringsuppgiften avsevärt. Därför fokuserar vi i denna avhandlingen på utvecklingen av återkopplingsregulatorer på låg nivå.  I den första delen fokuserar vi på att hantera sammankopplande tillståndsbegränsningar för distribuerade system med hjälp av en modell prediktiv styrning (MPC). Vanligtvis kräver den distribuerade hanteringen av kopplingsbegränsningar ett sekventiellt eller iterativt MPC-system som dock är tidskrävande. Därför utvecklar vi en parallelliserad distribuerad modell prediktiv styrning (DMPC) baserad på konsistensbegränsningar. Därigenom garanterar ett delsystem till sina grannar att det håller sig inom ett visst område runt en referensbana. Den generiska formuleringen av vårt DMPC-system möjliggör flera realiseringar. En särskild realisering föreslås. Dessutom utvecklas utvidgningar till ett robust och iterativt system samt ett DMPC-system för system med begränsade dynamiska kopplingar. I den andra delen fokuserar vi på metoder för att säkerställa invariansen av mängder. Vi fokuserar särskilt på kontrollbarriärfunktioner (CBF). Vi visar hur tillstånds- och tidsmässiga begränsningar kan inkodas i icke-glatta tidsvarierande kontrollbarriärfunktioner och hur subgradienter kan användas för att konstruera en effektiv gradientbaserad styrning. För dessa resultat måste antaganden om kontrollerbarhet åberopas. För att utvidga detta resultat till system med svagare kontrollerbarhetsegenskaper undersöker vi kopplingen mellan dynamiska systems kontrollerbarhetsegenskaper och konstruktionen av en CBF. Som ett resultat av detta föreslår vi en konstruktionsmetod för CBF:er som bygger på förutsägelser för ändliga horisonter. Den konstruerade CBF:n uppvisar gynnsamma egenskaper för att utvidga det tidigare resultatet om kodning av rums-temporala begränsningar i CBF:er till system med svagare kontrollerbarhetsegenskaper. Slutligen undersöker vi med hjälp av en fallstudie hur metoder för att säkerställa invariansen av mängder kan användas för att implicit samordna system som är kopplade via tillståndsbegränsningar. Vår föreslagna metod är helt decentraliserad och delsystemen samordnar sig själva endast via sina handlingar och justeringen av sina individuella begränsningar. Slutligen drar vi en slutsats och beskriver hur de presenterade resultaten bidrar till utvecklingen av ett ramverk för distribuerad styrning av tillstånds- och tidsmässigt begränsade system. / <p>QC 20230520</p>

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