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The increased adoption and deployment of cyber-physical systems in critical infrastructure in recent years have led to challenging questions about safety and reliability. These systems usually operate in uncertain environments and are required to satisfy a broad spectrum of specifications. Thus, automated tools are necessary to alleviate the need for manual design and proof of their correct behaviors. This thesis studies mathematical and computational frameworks to design correct and optimal control strategies for discrete-time and continuous-time systems with temporal and spatial specifications. Signal Temporal Logic (STL) is employed as a rich and expressive language to impose temporal constraints and deadlines on system performance. The first part of the thesis introduces a novel quantitative semantics for STL that improves the evaluation of temporal logic specifications. Furthermore, an extension of STL, called Weighted Signal Temporal Logic (wSTL), is defined in order to formalize satisfaction priorities of multiple specifications and time preferences in a high-level specification. Learning-based frameworks are proposed to infer quantitative semantics, and satisfaction priorities and preferences from data. The second part develops optimization frameworks to determine control strategies enforcing the satisfaction of wSTL specifications by different classes of systems. Mixed-integer programming and gradient-based optimization techniques are studied to solve the control synthesis problem. Further evaluation and optimization algorithms are presented based on Control Barrier Functions to guarantee continuous-time satisfaction of safety-critical specifications in a system. The third part of this thesis focuses on utilizing STL to express spatio-temporal specifications that are widely used in networks of locally interacting dynamical systems. Machine learning techniques are used to derive spatio-temporal quantitative semantics, which is employed in automated frameworks for evaluation and synthesis of complex spatial and temporal properties. Case studies illustrating the synthesis of spatio-temporal patterns in biological cell networks are presented.

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This thesis investigates Bicoprime Factorisations (BCFs) and their possible uses in robust control theory. BCFs are a generalisation of coprime factorisations, which have been well known and widely used by the control community over the last few decades. Though they were introduced at roughly the same time as coprime factorisations, they have been largely ignored, with only a very small number of results derived in the literature. BCFs are first introduced and the fundamental theory behind them is developed. This includes results such as internal stability in terms of BCFs, parametrisation of the BCFs of a plant and state space constructions of BCFs. Subsequently, a BCF uncertainty structure is proposed, that encompasses both left and right coprime factor uncertainty. A robust control synthesis procedure is then developed with respect to this BCF uncertainty structure. The proposed synthesis method is shown to be advantageous in the following two aspects: (1) the standard assumptions associated with H-infinity control synthesis are directly fulfilled without the need of loop shifting or normalisation of the generalised plant and (2) any or all of the plant's unstable dynamics can be ignored, thus leading to a reduction in the dimensions of the Algebraic Riccati Equations (AREs) that need to be solved to achieve robust stabilisation. Normalised BCFs are then defined, which are shown to provide many advantages, especially in the context of robust control synthesis. When using a normalised BCF of the plant, lower bounds on the achievable BCF robust stability margin can be easily and directly computed a priori, as is the case for normalised coprime factors. Although the need for an iterative procedure is not completely avoided when designing an optimal controller, it is greatly simplified with the iteration variable being scalar. Unlike coprime factorisations where a single ARE needs to be solved to achieve normalisation, two coupled AREs must be satisfied for a BCF to be normalised. Two recursive methods are proposed to solve this problem. Lastly, an example is presented where the theory developed is used in a practical scenario. A quadrotor Unmanned Aerial Vehicle (UAV) is considered and a normalised BCF controller is designed which in combination with feedback linearisation is used to control both the attitude and position of the vehicle.

Mathematical models of physical systems are pervasive in engineering. These models can be used to analyze properties of the system, to simulate the system, or synthesize controllers. However, many of these models are too complex or too large for standard analysis and synthesis methods to be applicable. Hence, there is a need to reduce the complexity of models. In this thesis, techniques for reducing complexity of large linear time-invariant (lti) state-space models and linear parameter-varying (lpv) models are presented. Additionally, a method for synthesizing controllers is also presented. The methods in this thesis all revolve around a system theoretical measure called the H2-norm, and the minimization of this norm using nonlinear optimization. Since the optimization problems rapidly grow large, significant effort is spent on understanding and exploiting the inherent structures available in the problems to reduce the computational complexity when performing the optimization. The first part of the thesis addresses the classical model-reduction problem of lti state-space models. Various H2 problems are formulated and solved using the proposed structure-exploiting nonlinear optimization technique. The standard problem formulation is extended to incorporate also frequency-weighted problems and norms defined on finite frequency intervals, both for continuous and discrete-time models. Additionally, a regularization-based method to account for uncertainty in data is explored. Several examples reveal that the method is highly competitive with alternative approaches. Techniques for finding lpv models from data, and reducing the complexity of lpv models are presented. The basic ideas introduced in the first part of the thesis are extended to the lpv case, once again covering a range of different setups. lpv models are commonly used for analysis and synthesis of controllers, but the efficiency of these methods depends highly on a particular algebraic structure in the lpv models. A method to account for and derive models suitable for controller synthesis is proposed. Many of the methods are thoroughly tested on a realistic modeling problem arising in the design and flight clearance of an Airbus aircraft model. Finally, output-feedback H2 controller synthesis for lpv models is addressed by generalizing the ideas and methods used for modeling. One of the ideas here is to skip the lpv modeling phase before creating the controller, and instead synthesize the controller directly from the data, which classically would have been used to generate a model to be used in the controller synthesis problem. The method specializes to standard output-feedback H2 controller synthesis in the lti case, and favorable comparisons with alternative state-of-the-art implementations are presented.

With the increase of robotic presence in our homes and work environment, it has become imperative to consider human-in-the-loop systems when designing robotic controllers. This includes both a physical presence of humans as well as interaction on a decision and control level. One important aspect of this is to design controllers which are guaranteed to satisfy specified safety constraints. At the same time we must minimize the risk of not finding solutions, which would force the system to stop. This require some room for relaxation to be put on the specifications. Another aspect is to design the system to be adaptive to the human and its environment. In this thesis we approach the problem by considering control synthesis for multi-agent systems under hard and soft constraints, where the human has direct impact on how the soft constraint is violated. To handle the multi-agent structure we consider both a classical centralized automata based framework and a decentralized approach with collision avoidance. To handle soft constraints we introduce a novel metric; hybrid distance, which quantify the violation. The hybrid distance consists of two types of violation; continuous distance or missing deadlines, and discrete distance or spacial violation. These distances are weighed against each other with a weight constant we will denote as the human preference constant. For the human impact we consider two types of feedback; direct feedback on the violation in the form of determining the human preference constant, and direct control input through mixed-initiative control where the human preference constant is determined through an inverse reinforcement learning algorithm based on the suggested and followed paths. The methods are validated through simulations. / I takt med att robotar blir allt vanligare i våra hem och i våra arbetsmiljöer, har det blivit allt viktigare att ta hänsyn till människan plats i systemen när regulatorerna för robotorna designas. Detta innefattar både människans fysiska närvaro och interaktion på besluts- och reglernivå. En viktig aspekt i detta är att designa regulatorer som garanterat uppfyller givna villkor. Samtidigt måste vi minimera risken att ingen lösning hittas, eftersom det skulle tvinga systemet till ett stopp. För att uppnå detta krävs det att det finns rum för att mjuka upp villkoren. En annan aspekt är att designa systemet så att det är anpassningsbart till människan och miljön. I den här uppsatsen närmar vi oss problemet genom att använda regulator syntes för multi-agent system under hårda och mjuka villkor där människan har direkt påverkan på hur det svaga villkoret överträds. För att hantera multi-agent strukturen undersöker vi både det klassiska centraliserade automata-baserade ramverket och ett icke-centraliserat tillvägagångsätt med krockundvikning. För att hantera mjuka villkor introducerar vi en metrik; hybrida avståndet, som kvantifierar överträdelsen. Det hybrida avståndet består av två typer av överträdelse (kontinuerligt avstånd eller missandet av deadlines, och diskret avstånd eller rumsliga överträdelser) som vägs mot varandra med en vikt konstant som vi kommer att kalla den mänskliga preferens kontanten. Som mänsklig påverkan överväger vi direkt feedback på överträdelsen genom att hon bestämmer värdet på den mänskliga preferens kontanten, och direkt påverkan på regulatorn där den mänskliga preferens konstanten bestäms genom en inverserad förstärkt inlärnings algoritm baserad på de föreslagna och följda vägarna. Metoderna valideras genom simuleringar. / <p>QC20190517</p>

We develop a novel autonomous control synthesis strategy called Phase Space Navigator for the automatic synthesis of nonlinear control systems. The Phase Space Navigator generates global control laws by synthesizing flow shapes of dynamical systems and planning and navigating system trajectories in the phase spaces. Parsing phase spaces into trajectory flow pipes provide a way to efficiently reason about the phase space structures and search for global control paths. The strategy is particularly suitable for synthesizing high-performance control systems that do not lend themselves to traditional design and analysis techniques.

Multi-agent systems are employed for a group of agents to achieve coordinated tasks, in which distributed sensing, computing, communication and control are usually integrated with shared resources. Efficient usage of these resources is therefore an important issue. In addition, in applications such as robotics, a group of agents may encounter the request of a sequence of tasks and deadline constraint on the completion of each task is a common requirement. Thus, the integration of multi-agent task scheduling and control synthesis is of great practical interest. In this thesis, we study control of multi-agent systems under a networked control system framework. The first purpose is to design resource-efficient communication and control strategies to solve consensus problem for multi-agent systems.The second purpose is to jointly schedule task sequence and design controllers for multiagent systems that are subject to a sequence of deadline-constrained tasks. In the first part, a distributed asynchronous event-triggered communication and control strategy is proposed to tackle multi-agent consensus. It is shown that the proposed event-triggered communication and control strategy fulfils the reduction of both the rates of sensor-controller communication and controller-actuator communication as well as excluding Zeno behavior. To further relax the requirement of continuous sensing and computing, a periodic event-triggered communication and control strategy is proposed in the second part. In addition, an observer-based encoder-decoder with finite-level quantizeris designed to deal with the constraint of limited data rate. An explicit formula for the maximum allowable sampling period is derived first. Then, it is proven that exponential consensus can be achieved in the presence of data rate constraint. Finally, in the third part, the problem of deadline-constrained multi-agent task scheduling and control synthesis is addressed. A dynamic scheduling strategy is proposed and a distributed hybrid control law is designed for each agent that guarantees the completion and deadline satisfaction of each task. The effectiveness of the theoretical results in the thesis is verified by several simulation examples. / <p>QC 20180918</p>

Dans le présent travail de thèse, nous souhaitons approfondir l’étude des systèmes à commutation pour des problèmes aux dérivées partielles en explorant de nouvelles pistes d’investigation, incluant notamment la question de la synthèse de contrôle garanti par décomposition de l’espace des états, la synthèse de contrôle nécessitant la réduction de modèle, le contrôle des différentes sources d’erreur sur des quantités d’intérêt, et la mesure des incertitudes sur les états et les paramètres du modèle. Nous envisageons l’utilisation de méthodes de calcul ensemblistes associées à des méthodes de réduction de modèle, ainsi que l’utilisation d’observateurs d’état pour l’estimation en ligne du système. / In this thesis, we focus on switched control systems described by partial differential equations, and investigate the issues of guaranteed control of such systems using state-space decomposition methods. The use of state-space decomposition methods requires model order reduction, control of the different sources of error for quantities of interest, and measure of uncertainties on the states and parameters of the system. We are considering using set-based computation methods, in association with model order reduction techniques, along with the use of state-observers for on-line estimation of the system.