A Switching Fluid Limit of a Stochastic Network Under a State-Space-Collapse Inducing Control with Chattering

Routing mechanisms for stochastic networks are often designed to produce state space collapse (SSC) in a heavy-traffic limit, i.e., to confine the limiting process to a lower-dimensional subset of its full state space. In a fluid limit, a control producing asymptotic SSC corresponds to an ideal sliding mode control that forces the fluid trajectories to a lower-dimensional sliding manifold. Within deterministic dynamical systems theory, it is well known that sliding-mode controls can cause the system to chatter back and forth along the sliding manifold due to delays in activation of the control. For the prelimit stochastic system, chattering implies fluid-scaled fluctuations that are larger than typical stochastic fluctuations. In this paper we show that chattering can occur in the fluid limit of a controlled stochastic network when inappropriate control parameters are used. The model has two large service pools operating under the fixed-queue-ratio with activation and release thresholds (FQR-ART) overload control which we proposed in a recent paper. We now show that, if the control parameters are not chosen properly, then delays in activating and releasing the control can cause chattering with large oscillations in the fluid limit. In turn, these fluid-scaled fluctuations lead to severe congestion, even when the arrival rates are smaller than the potential total service rate in the system, a phenomenon referred to as congestion collapse. We show that the fluid limit can be a bi-stable switching system possessing a unique nontrivial periodic equilibrium, in addition to a unique stationary point

Self-Control of Traffic Lights and Vehicle Flows in Urban Road Networks

Based on fluid-dynamic and many-particle (car-following) simulations of traffic flows in (urban) networks, we study the problem of coordinating incompatible traffic flows at intersections. Inspired by the observation of self-organized oscillations of pedestrian flows at bottlenecks [D. Helbing and P. Moln\'ar, Phys. Eev. E 51 (1995) 4282--4286], we propose a self-organization approach to traffic light control. The problem can be treated as multi-agent problem with interactions between vehicles and traffic lights. Specifically, our approach assumes a priority-based control of traffic lights by the vehicle flows themselves, taking into account short-sighted anticipation of vehicle flows and platoons. The considered local interactions lead to emergent coordination patterns such as ``green waves'' and achieve an efficient, decentralized traffic light control. While the proposed self-control adapts flexibly to local flow conditions and often leads to non-cyclical switching patterns with changing service sequences of different traffic flows, an almost periodic service may evolve under certain conditions and suggests the existence of a spontaneous synchronization of traffic lights despite the varying delays due to variable vehicle queues and travel times. The self-organized traffic light control is based on an optimization and a stabilization rule, each of which performs poorly at high utilizations of the road network, while their proper combination reaches a superior performance. The result is a considerable reduction not only in the average travel times, but also of their variation. Similar control approaches could be applied to the coordination of logistic and production processes

Actualización de semaforización en Santa Marta Magdalena

En el presente informe estará desarrollado bajo la modalidad de auxiliar de investigación el cual consta del proyecto de investigación. ACTIALIZACION DE LOS SISTEMAS DE SEMAFORIZACION DE LA CIUDAD DE SANTA MARTA EMPLEANDO NUEVAS TECNOLOGIAS. llevado a cabo por el semillero de investigación de la universidad cooperativa de Colombia seccional Santa Marta, donde presentaremos los análisis y estudios necesarios para cumplir con el objetivo general que se ha planteado dentro de este, el cual consta de la caracterización de sistemas tecnológicos implementados en redes de semaforización en países seleccionados a nivel mundial. Con fin de estudiar y analizar cada una de las opciones escogidas y poder implementarlas en la actualización de las redes de semaforización de la ciudad de Santa Marta en pro a mejorar la fluidez y garantizar una seguridad optima en el tráfico principalmente enhoras picos. Este proyecto está compuesto por la introducción donde se establecerá la importancia de este tipo de investigaciones y los beneficios que han tenido en forma general. Tendremos un planteamiento del problema donde se identifica el problema y se delimita el espacio geográfico, así como su espacio temporal a través de la investigación del problema para una posterior formulación de este. Lo que nos lleva a plantar un objetivo general descrito anteriormente y unos objetivos específicos que nos brindan la posibilidad de llegar a una solución óptima. Dentro del informe se establecerá los métodos de investigación utilizados, marco conceptual, métodos de análisis de literatura. Registro de dichos análisis, análisis de resultados, conclusiones.This report will be developed under the modality of research assistant which consists of the research project. UPDATE OF THE SEMPHORIZATION SYSTEMS OF THE CITY OF SANTA MARTA USING NEW TECHNOLOGIES. carried out by the research seedbed of the Santa Marta sectional cooperative university of Colombia, where we will present the analyzes and studies necessary to fulfill the general objective that has been proposed within this, which consists of the characterization of technological systems implemented in traffic light networks in selected countries worldwide. In order to study and analyze each of the chosen options and to be able to implement them in updating the traffic light networks of the city of Santa Marta in order to improve fluidity and guarantee optimal traffic safety, mainly during peak hours. This project consists of the introduction where the importance of this type of research and the benefits they have had in general will be established. We will have an approach to the problem where the problem is identified and the geographical space is delimited, as well as its temporal space through the investigation of the problem for a later formulation of it. Which leads us to plant a general objective described above and specificobjectives that give us the possibility of reaching an optimal solution. The report will establish the research methods used, the conceptual framework, and the literature analysis methods. Record of said analyzes, analysis of results, conclusions.Resumen. -- Abstract. -- Introduccion. -- Planteamiento del problema. -- Formulación del problema. -- Objetivos. -- Objetivo general. -- Objetivos específicos. -- Justificación. -- Marco conceptual. -- De-limitación de la investigación. -- Linea de investigación. -- Delimitaciòn espacial. -- Delimitaciòn temporal. -- Metodología. -- Tipo de investigación. -- Diseño de la investigación. -- Técnica para la recolección de información. -- Análisis de literatura. -- Resultados. -- Conclusiones. -- Recomendaciones. -- Bibliográfica. -

Hysteresis-based switching observers for linear systems using quadratic boundedness

Switched-gain observers are investigated for the purpose of estimating the state of linear systems affected by bounded noises. Under mild assumptions, hybrid observers with switching gains are proposed and provided with stability analysis based on quadratic boundedness for the estimation error. Such observers are designed by solving optimization problems aimed at minimizing upper bounds on the estimation error in such a way as to get the smallest invariant set. The effectiveness of the proposed approach is evaluated with some numerical case studies

해밀턴 구조와 외란 관측기 기법을 이용한 라그랑주 점 궤도 주변에서의 경계 상대 운동 및 궤도유지

학위논문 (박사) -- 서울대학교 대학원 : 공과대학 기계항공공학부, 2020. 8. 김유단.In this dissertation, a novel strategy for station-keeping and formation flight of spacecraft in the vicinity of unstable libration point orbits is presented, and its performance and stability are analyzed. The presented control strategy leverages the Hamiltonian nature of the equations of motion, rather than simply applying the control theory from the perspective of ``signal processing". A filtered extended high-gain observer, a kind of disturbance observer, is designed to mitigate the performance degradation of the control strategy due to model uncertainties and external disturbances. Canonical coordinates are adopted to design a controller that exploits the mathematical structure of Hamiltonian system inherent in orbital mechanics, and then the equations of motion of spacecraft are represented in the form of Hamilton's equation with generalized coordinates and momenta. The baseline controller, utilizing the canonical form of the Hamiltonian system, is divided into two parts: i) a Hamiltonian structure-preserving control, and ii) an energy dissipation control. Hamiltonian structure-preserving control can be designed in accordance with the Lagrange-Dirichlet criterion, i.e., a sufficient condition for the nonlinear stability of Hamiltonian system. Because the Hamiltonian structure-preserving control makes the system marginally stable instead of asymptotically stable, the resultant motion of the Hamiltonian structure-preserving control yields a bounded trajectory. Through the frequency analysis of bounded relative motion, a circular motion can be achieved for particular initial conditions. By appropriately switching the gain of the Hamiltonian structure-preserving control, the radius of bounded motion can be adjusted systematically, which is envisioned that this approach can be applied to spacecraft formation flight. Furthermore, the energy dissipation control can be activated to make the spacecraft's bounded relative motion converge to the nominal orbit. On the other hand, a filtered extended high-gain observer is designed for the robust station-keeping and formation flight even under highly uncertain deep-space environment. The filtered extended high-gain observer estimates the velocity state of the spacecraft and disturbance acting on the spacecraft by measuring only the position of the spacecraft. The filtered extended high-gain observer includes an integral state feedback to attenuate navigation error amplification due to the high gain of the observer. The global convergence of the observer is shown, and it is also shown that the tracking error is ultimately bounded to the nominal libration point orbit by applying the Hamiltonian structure-based controller. Numerical simulations demonstrate the performance of the designed control strategy. Halo orbit around the L2 point of the Earth-Moon system is considered as an illustrative example, and various perturbations are taken into account.본 논문에서는 불안정한 동적특성을 갖는 라그랑주 점 궤도 주변에서 위성의 궤도유지 및 편대비행을 위한 제어기와 관측기를 설계하였으며, 설계된 제어기와 관측기의 안정성 그리고 전체 시스템의 안정성을 분석하였다. 설계한 기준 제어 전략은 신호처리 관점의 제어이론을 기반으로 하지 않고, 라그랑주 점 궤도의 자연적인 수학적 구조를 활용하였다. 모델 불확실성과 외부 외란으로 인한 기준 제어 전략의 성능저하를 완화하기 위해 외란관측기의 일종인 확장 고이득 관측기를 설계하였다. 본 논문에서는 궤도역학에 내재되어 있는 해밀턴 시스템의 구조를 활용하는 제어기를 설계하기 위해 정준좌표를 도입하였으며, 좌표변환을 통해 위성의 운동방정식을 해밀턴 시스템의 정준형식으로 나타내었다. 해밀턴 시스템의 정준형식으로 표현된 운동방정식을 이용해 설계한 기준 제어기는 해밀턴-구조 보존제어와 에너지 소산제어로 분리 설계된다. Lagrange-Dirichlet 기준은 정준형식으로 나타낸 해밀턴 시스템의 비선형 안정성을 판별하는 충분조건으로, 해밀턴-구조 보존제어 설계의 기준이 된다. 기준 라그랑주 점 궤도 주위에서 해밀턴-구조 보존 제어를 적용한 결과, 위성은 기준궤도로 수렴하지 않고 기준궤도와 유한한 거리를 유지하는 경계운동을 하였다. 경계운동의 주파수 분석을 통하여 특정한 초기조건 하에서는 원형 경계운동이 가능하였으며, 더 나아가 해밀턴-구조 보존제어의 제어이득 값을 적절히 설정함으로 원형 경계운동의 크기를 체계적으로 조절할 수 있고 이를 위성 편대비행에 응용할 수 있음을 보였다. 추가적으로 에너지 소산제어 입력을 설계하여 위성이 기준 라그랑주 점 궤도로 점근 수렴하는 운동도 가능함을 수학적으로 증명하였다. 한편, 심우주상의 예측하기 어려운 섭동력 및 불확실성 하에서도 강건한 궤도유지와 편대비행을 수행하기 위해 확장 고이득 관측기를 설계하였다. 확장 고이득 관측기는 위성의 위치 정보만을 이용하여 위성의 속도와 위성에 작용하는 외란을 동시에 추정하며, 추정된 상태변수를 이용하여 기준이 되는 피드백 제어입력을 생성한다. 추정된 외란은 피드포워드 형태의 제어입력으로 구성되어 제어기의 성능을 강건하게 만든다. 심우주 공간상의 위성의 궤도결정 결과로 얻어지는 위치정보는 상대적으로 큰 오차를 갖는데, 확장 고이득 관측기는 위치 오차를 증폭시킨다는 단점이 있다. 본 연구에서는 이러한 단점을 완화하고자 적분 관측기 형태로 개선된 필터링된 확장 고이득 관측기를 설계하고 수렴성을 분석하였다. 그리고 필터링된 확장 고이득 관측기와 시스템의 해밀턴 구조를 활용하는 제어기를 적용한 전체 시스템의 안정성을 분석하였다. 불안정한 라그랑주 점 궤도 주변에서 위성의 궤도유지와 편대비행을 위해 설계된 제어기법의 성능을 확인하고자 수치 시뮬레이션을 수행하였다. 수치 시뮬레이션을 위해 지구-달 시스템의 L2 주변 헤일로 궤도를 기준궤도로 설정하였으며, 심우주 공간에서의 다양한 섭동력 및 모델 불확실성을 고려하였다. 궤도결정 오차로 인한 위성의 위치 및 속도 불확실성이 존재 하더라도 제안한 제어기법을 통해 위성이 궤도유지와 편대비행을 만족스럽게 수행함을 보였다.1 Introduction 1 1.1 Background and Motivation 1 1.2 Literature Review 3 1.2.1 Spacecraft Station-Keeping in the Vicinity of the Libration Point Orbits 3 1.2.2 Spacecraft Formation Flight in the Vicinity of the Libration Point Orbits 5 1.3 Contributions 7 1.4 Dissertation Outline 10 2 Background 13 2.1 Circular Restricted Three-Body Problem 14 2.1.1 Equilibrium Solutions and Periodic Orbits 16 2.1.2 Stability of Periodic Orbits 20 2.2 Hamiltonian Mechanics 21 2.2.1 Hamiltonian Approach to CR3BP 21 2.2.2 Hamiltonian Approach to LPO Tracking Problem 22 3 Hamiltonian Structure-Based Control 25 3.1 Classical Linear Hamiltonian Structure-Preserving Control 27 3.2 Switching Hamiltonian Structure-Preserving Control 29 3.2.1 Orbital Properties of Spacecraft 33 3.2.2 Switching Point 1: From a Circular Orbit to an Elliptical Orbit 34 3.2.3 Switching Point 2: From an Elliptical Orbit to a Circular Orbit 37 3.3 Hamiltonian Structure-Based Control 39 3.3.1 Potential Shaping Control 39 3.3.2 Energy Dissipation Control 45 4 Filtered Extended High-Gain Observer and Closed-Loop Stability 49 4.1 Filtered Extended High-Gain Observer and Its Convergence 51 4.2 Closed-Loop Stability Analysis 56 5 Numerical Simulations 67 5.1 Disturbance Model 67 5.2 Navigation Error Model 68 5.3 Simulation Results 69 5.3.1 Simulation 1 71 5.3.2 Simulation 2 77 5.3.3 Simulation 3 81 5.3.4 Simulation 4 93 5.3.5 Simulation 5 98 6 Conclusion 101 6.1 Concluding Remarks 101 6.2 Further Work 103 Bibliography 105 국문초록 127Docto

Advances in state estimation, diagnosis and control of complex systems

This dissertation intends to provide theoretical and practical contributions on estimation, diagnosis and control of complex systems, especially in the mathematical form of descriptor systems. The research is motivated by real applications, such as water networks and power systems, which require a control system to provide a proper management able to take into account their specific features and operating limits in presence of uncertainties related to their operation and failures from component malfunctions. Such a control system is expected to provide an optimal operation to obtain efficient and reliable performance. State estimation is an essential tool, which can be used not only for fault diagnosis but also for the controller design. To achieve a satisfactory robust performance, set theory is chosen to build a general framework for descriptor systems subject to uncertainties. Under certain assumptions, these uncertainties are propagated and bounded by deterministic sets that can be explicitly characterized at each iteration step. Moreover, set-invariance characterizations for descriptor systems are also of interest to describe the steady performance, which can also be used for active mode detection. For the controller design for complex systems, new developments of economic model predictive control (EMPC) are studied taking into account the case of underlying periodic behaviors. The EMPC controller is designed to be recursively feasible even with sudden changes in the economic cost function and the closed-loop convergence is guaranteed. Besides, a robust technique is plugged into the EMPC controller design to maintain these closed-loop properties in presence of uncertainties. Engineering applications modeled as descriptor systems are presented to illustrate these control strategies. From the real applications, some additional difficulties are solved, such as using a two-layer control strategy to avoid binary variables in real-time optimizations and using nonlinear constraint relaxation to deal with nonlinear algebraic equations in the descriptor model. Furthermore, the fault-tolerant capability is also included in the controller design for descriptor systems by means of the designed virtual actuator and virtual sensor together with an observer-based delayed controller.Esta tesis propone contribuciones de carácter teórico y aplicado para la estimación del estado, el diagnóstico y el control óptimo de sistemas dinámicos complejos en particular, para los sistemas descriptores, incluyendo la capacidad de tolerancia a fallos. La motivación de la tesis proviene de aplicaciones reales, como redes de agua y sistemas de energía, cuya naturaleza crítica requiere necesariamente un sistema de control para una gestión capaz de tener en cuenta sus características específicas y límites operativos en presencia de incertidumbres relacionadas con su funcionamiento, así como fallos de funcionamiento de los componentes. El objetivo es conseguir controladores que mejoren tanto la eficiencia como la fiabilidad de dichos sistemas. La estimación del estado es una herramienta esencial que puede usarse no solo para el diagnóstico de fallos sino también para el diseño del control. Con este fin, se ha decidido utilizar metodologías intervalares, o basadas en conjuntos, para construir un marco general para los sistemas de descriptores sujetos a incertidumbres desconocidas pero acotadas. Estas incertidumbres se propagan y delimitan mediante conjuntos que se pueden caracterizar explícitamente en cada instante. Por otra parte, también se proponen caracterizaciones basadas en conjuntos invariantes para sistemas de descriptores que permiten describir comportamientos estacionarios y resultan útiles para la detección de modos activos. Se estudian también nuevos desarrollos del control predictivo económico basado en modelos (EMPC) para tener en cuenta posibles comportamientos periódicos en la variación de parámetros o en las perturbaciones que afectan a estos sistemas. Además, se demuestra que el control EMPC propuesto garantiza la factibilidad recursiva, incluso frente a cambios repentinos en la función de coste económico y se garantiza la convergencia en lazo cerrado. Por otra parte, se utilizan técnicas de control robusto pata garantizar que las estrategias de control predictivo económico mantengan las prestaciones en lazo cerrado, incluso en presencia de incertidumbre. Los desarrollos de la tesis se ilustran con casos de estudio realistas. Para algunas de aplicaciones reales, se resuelven dificultades adicionales, como el uso de una estrategia de control de dos niveles para evitar incluir variables binarias en la optimización y el uso de la relajación de restricciones no lineales para tratar las ecuaciones algebraicas no lineales en el modelo descriptor en las redes de agua. Finalmente, se incluye también una contribución al diseño de estrategias de control con tolerancia a fallos para sistemas descriptores