STRICT LYAPUNOV FUNCTIONS AND FEEDBACK CONTROLS FOR SIR MODELS WITH QUARANTINE AND VACCINATION

We provide a new global strict Lyapunov function construction for a susceptible, infected, and recovered (or SIR) disease dynamics that includes quarantine of infected individuals and mass vaccination. We use the Lyapunov function to design feedback controls to asymptotically stabilize a desired endemic equilibrium, and to prove input-to-state stability for the dynamics with a suitable restriction on the disturbances. Our simulations illustrate the potential of our feedback controls to reduce peak levels of infected individuals

Discrete-time optimal preview control

There are many situations in which one can preview future reference signals, or future disturbances. Optimal Preview Control is concerned with designing controllers which use this preview to improve closed-loop performance. In this thesis a general preview control problem is presented which includes previewable disturbances, dynamic weighting functions, output feedback and nonpreviewable disturbances. It is then shown how a variety of problems may be cast as special cases of this general problem; of particular interest is the robust preview tracking problem and the problem of disturbance rejection with uncertainty in the previewed signal. . (', The general preview problem is solved in both the Fh and Beo settings. The H2 solution is a relatively straightforward extension ofpreviously known results, however, our contribution is to provide a single framework that may be used as a reference work when tackling a variety of preview problems. We also provide some new analysis concerning the maximum possible reduction in closed-loop H2 norm which accrues from the addition of preview action. / Name of candidate: Title of thesis: I DESCRIPTION OF THESIS Andrew Hazell Discrete-Time Optimal Preview Control The solution to the Hoo problem involves a completely new approach to Hoo preview control, in which the structure of the associated Riccati equation is exploited in order to find an efficient algorithm for computing the optimal controller. The problem tackled here is also more generic than those previously appearing in the literature. The above theory finds obvious applications in the design of controllers for autonomous vehicles, however, a particular class of nonlinearities found in typical vehicle models presents additional problems. The final chapters are concerned with a generic framework for implementing vehicle preview controllers, and also a'case study on preview control of a bicycle.Imperial Users onl

Development of U-model enhansed nonlinear systems

Nonlinear control system design has been widely recognised as a challenging issue where the key objective is to develop a general model prototype with conciseness, flexibility and manipulability, so that the designed control system can best match the required performance or specifications. As a generic systematic approach, U-model concept appeared in Prof. Quanmin Zhu’s Doctoral thesis, and U-model approach was firstly published in the journal paper titled with ‘U-model based pole placement for nonlinear plants’ in 2002.The U-model polynomial prototype precisely describes a wide range of smooth nonlinear polynomial models, defined as a controller output u(t-1) based time-varying polynomial models converted from the original nonlinear model. Within this equivalent U-model expression, the first study of U-model based pole placement controller design for nonlinear plants is a simple mapping exercise from ordinary linear and nonlinear difference equations to time-varying polynomials in terms of the plant input u(t-1). The U-model framework realised the concise and applicable design for nonlinear control system by using such linear polynomial control system design approaches.Since the first publication, the U-model methodology has progressed and evolved over the course of a decade. By using the U-model technique, researchers have proposed many different linear algorithms for the design of control systems for the nonlinear polynomial model including; adaptive control, internal control, sliding mode control, predictive control and neural network control. However, limited research has been concerned with the design and analysis of robust stability and performance of U-model based control systems.This project firstly proposes a suitable method to analyse the robust stability of the developed U-model based pole placement control systems against uncertainty. The parameter variation is bounded, thus the robust stability margin of the closed loop system can be determined by using LMI (Linear Matrix Inequality) based robust stability analysis procedure. U-block model is defined as an input output linear closed loop model with pole assignor converted from the U-model based control system. With the bridge of U-model approach, it connects the linear state space design approach with the nonlinear polynomial model. Therefore, LMI based linear robust controller design approaches are able to design enhanced robust control system within the U-block model structure.With such development, the first stage U-model methodology provides concise and flexible solutions for complex problems, where linear controller design methodologies are directly applied to nonlinear polynomial plant-based control system design. The next milestone work expands the U-model technique into state space control systems to establish the new framework, defined as the U-state space model, providing a generic prototype for the simplification of nonlinear state space design approaches.The U-state space model is first described as a controller output u(t-1) based time-varying state equations, which is equivalent to the original linear/nonlinear state space models after conversion. Then, a basic idea of corresponding U-state feedback control system design method is proposed based on the U-model principle. The linear state space feedback control design approach is employed to nonlinear plants described in state space realisation under U-state space structure. The desired state vectors defined as xd(t), are determined by closed loop performance (such as pole placement) or designer specifications (such as LQR). Then the desired state vectors substitute the desired state vectors into original state space equations (regarded as next time state variable xd(t) = x(t) ). Therefore, the controller output u(t-1) can be obtained from one of the roots of a root-solving iterative algorithm.A quad-rotor rotorcraft dynamic model and inverted pendulum system are introduced to verify the U-state space control system design approach for MIMO/SIMO system. The linear design approach is used to determine the closed loop state equation, then the controller output can be obtained from root solver. Numerical examples and case studies are employed in this study to demonstrate the effectiveness of the proposed methods

Diseño de controladores continuos convergentes por un tiempo fijo para sistemas dinámicos con incertidumbre

Este documento presenta controladores no lineales que proveen convergencia en tiempo fijo al origen (o a una vecindad del origen) para sistemas dinámicos de alto orden sujetos a incertidumbres (disturbios deterministicos no desvanescentes y disturbios estocásticos desvanescentes dependientes de los estados y el tiempo). Dos de los tres controladores diseñados incluyen un diferenciador convergente en tiempo fijo, un observador de disturbios convergente en tiempo fijo, y un regulador convergente en tiempo fijo. El diferenciador se da en el caso que el ´único estado medible del sistema dinámico es el de mayor grado relativo. El observador de disturbios convergente en tiempo fijo se emplea para estimar variaciones de disturbios no desvanecentes y no acotados. En caso de que las cotas para los disturbios sean desconocidas se incluye un observador adaptable convergente en tiempo fijo caracterizado por no incrementar de manera excesiva las ganancias del controlador. En cuanto a la presencia simultanea de disturbios determinísticos no desvanescentes y disturbios estocásticos desvanescentes dependientes de los estados y el tiempo, se presenta un algoritmo Super-twisting estocástico convergente en tiempo fijo. El problema de estimación del tiempo de convergencia de los controladores se resuelve calculando una cota superior uniforme del tiempo fijo de convergencia. Finalmente, los algoritmos diseñados se verifican en dos casos de estudio: Un motor DC con armadura y un problema de gestión de stocks. Resultados de las simulaciones confirman convergencia en tiempo fijo y robustez de los controladores diseñados

Observability studies for spacecraft attitude determination based on temperature data

Die Schätzung und Steuerung der Fluglage ist elementar für jede Raumfahrzeugmission. Die erforderliche Genauigkeit hängt von der jeweiligen Mission und ihren Nutzlasten ab. Ein funktionierendes Lageregelungssystem ist jedoch immer unverzichtbar, um die Zielgenauigkeit und Stabilität der Nutzlasten zu gewährleisten, die für den Erfolg der Mission entscheidend sind. Daher ist es sinnvoll, redundante Methoden zur Schätzung und Regelung der aktuellen Fluglage einzusetzen. Diese Arbeit fokussiert sich primär auf die Lageschätzung. Hierbei wird untersucht ob und wie Temperaturmessungen für die Lagebestimmung genutzt werden können. Diese Untersuchung wird durchgeführt, indem die zugrundeliegenden mathematischen Beschreibungen der Fluglage sowie der Temperaturdynamik betrachtet werden. Auf deren Grundlage wird dann ein Beobachter zur Lageschätzung entwickelt, der sich hauptsächlich auf die Temperaturdaten von zwei verschiedenen Sensorkonfigurationen stützt. In der ersten Konfiguration wird nur ein einziger Temperatursensor verwendet, dessen Informationen mit Gyroskopmessungen fusioniert werden, um die Lage zu bestimmen. Dies wird durch eine Transformation in Normalform und eine neuartige Lagebeschreibung erreicht. Auftretende Mehrdeutigkeiten bei der Lagebestimmung sowie alternative Beobachterdesigns werden vorgestellt. Die Analyse zeigt, dass mit dem vorgeschlagenen Beobachter lokale Aussagen zur Lageschätzung getroffen werden können - vorausgesetzt, die verwendeten Modelle und Messungen sind ausreichend genau und es steht genügend Rechenleistung zur Verfügung. In der zweiten Konfiguration werden sechs Paare von Temperatursensoren betrachtet. Jedes Paar besteht aus zwei Sensoren mit unterschiedlichen physikalischen Eigenschaften und zeigt in Richtung einer anderen Raumfahrzeugachse. Diese Sensorsignale enthalten genügend Informationen, um die Fluglage zu rekonstruieren, ohne dass die Verwendung von Ableitungen höherer Ordnung erforderlich ist. Es wird ein Algorithmus vorgeschlagen, der die Position der Sonne und der Erde schätzt und diese zur Bestimmung der Lage verwendet. Die Beobachter für beide Konfigurationen verwenden eine Transformation in eine kanonische Form, um ihre Schätzungen zu erhalten. Die resultierenden Beobachter sind daher sowohl in den transformierten als auch in den ursprünglichen Koordinaten formuliert. Während diese Beobachter unter Annahmen die häufig in der Literatur verwendeten werden äquivalent sind, kann es, sobald diese Annahmen fallengelassen werden, zu einer Reihe interessanter Phänomene wie Mehrdeutigkeit der Lösungen und sogar Instabilität kommen. Diese Phänomene werden an unserem vorgestellten System veranschaulicht und es werden Methoden vorgeschlagen, um sie zu bewältigen. Die für die zweite Konfiguration entworfenen Beobachter werden auf die von der Raumsondenmission GRACE erhaltenen Daten angewandt. Dabei hat sich gezeigt, dass die vorgeschlagenen Modelle für die Temperaturschätzung mit einem R2-Wert zwischen 78,8 % und 99,9 % gut geeignet sind. Die vorgeschlagenen Algorithmen erlauben eine Genauigkeit mit einem mittleren Fehler über eine Umlaufbahn von weniger als fünf Grad und lassen sich nachweislich leicht durch zusätzliche Messungen ergänzen.Attitude estimation and control is fundamental for every spacecraft mission. Accuracy requirements are strongly dependant on mission level goals and the respective payloads and experiments. However, it is always essential for the mission success to have a functioning attitude control system to allow a high pointing accuracy and stability of the payloads. Therefore, it is useful to employ redundant means to estimate and control the current attitude. The estimation of the attitude is the main topic of this work in which the information contained in temperature measurements for attitude estimation is investigated. This investigation is carried out by providing the underlying mathematical descriptions of the attitude as well as temperature dynamics. Different observer designs are considered based on these models to estimate the attitude relying mostly on the temperature data obtained from two different sensor configurations. In the first configuration, only a single temperature sensor is employed and the information is fused with gyroscope measurements to determine the attitude. This is achieved based on a transformation into normal form and a novel attitude description. Arising ambiguities in the attitude estimation, as well as alternative observer designs are presented. The analysis shows that with the proposed observer, it is possible to estimate the attitude provided that the employed models and measurements are sufficiently accurate and that enough computational power is available. The second configuration considers six pairs of temperature sensors. Each pair consists of two sensors with different physical properties and every pair points into a different body axis. These sensor signals contain enough information to reconstruct the attitude without requiring the usage of higher-order derivatives. An algorithm is proposed that estimates the position of the Sun and Earth and uses these to estimate the attitude. The observers for both configurations use a transformation of the system dynamics into canonical form to obtain a formulation of the problem that allows for estimation. The resulting observers are therefore formulated in transformed and original coordinates. While these observers are equivalent under assumptions widely used in literature, the moment these assumptions are dropped, a number of interesting phenomena such as ambiguity of the solutions and even instability can occur. These phenomena are illustrated by the system of interest and methods are proposed to deal with them. The designed observers for the second configuration are applied to the data obtained from the spacecraft mission GRACE. The results indicate that the proposed models are well suited for the temperature estimation with a R2 value between 78.8% and 99.9%. The proposed algorithms admit an accuracy with a mean error over an orbit of less than five degrees and are shown to be easily augmented with additional measurements

Programming Languages and Systems

This open access book constitutes the proceedings of the 29th European Symposium on Programming, ESOP 2020, which was planned to take place in Dublin, Ireland, in April 2020, as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2020. The actual ETAPS 2020 meeting was postponed due to the Corona pandemic. The papers deal with fundamental issues in the specification, design, analysis, and implementation of programming languages and systems