Stochastic Event-Based Control and Estimation

Digital controllers are traditionally implemented using periodic sampling, computation, and actuation events. As more control systems are implemented to share limited network and CPU bandwidth with other tasks, it is becoming increasingly attractive to use some form of event-based control instead, where precious events are used only when needed. Forms of event-based control have been used in practice for a very long time, but mostly in an ad-hoc way. Though optimal solutions to most event-based control problems are unknown, it should still be viable to compare performance between suggested approaches in a reasonable manner. This thesis investigates an event-based variation on the stochastic linear-quadratic (LQ) control problem, with a fixed cost per control event. The sporadic constraint of an enforced minimum inter-event time is introduced, yielding a mixed continuous-/discrete-time formulation. The quantitative trade-off between event rate and control performance is compared between periodic and sporadic control. Example problems for first-order plants are investigated, for a single control loop and for multiple loops closed over a shared medium. Path constraints are introduced to model and analyze higher-order event-based control systems. This component-based approach to stochastic hybrid systems allows to express continuous- and discrete-time dynamics, state and switching constraints, control laws, and stochastic disturbances in the same model. Sum-of-squares techniques are then used to find bounds on control objectives using convex semidefinite programming. The thesis also considers state estimation for discrete time linear stochastic systems from measurements with convex set uncertainty. The Bayesian observer is considered given log-concave process disturbances and measurement likelihoods. Strong log-concavity is introduced, and it is shown that the observer preserves log-concavity, and propagates strong log-concavity like inverse covariance in a Kalman filter. A recursive state estimator is developed for systems with both stochastic and set-bounded process and measurement noise terms. A time-varying linear filter gain is optimized using convex semidefinite programming and ellipsoidal over-approximation, given a relative weight on the two kinds of error

Router-based network traffic observation by terminal sliding mode control theory

Since the early days of the Internet, network traffic monitoring (NTM) has always played a strategic role in understanding and characterizing users’ activities. Nowadays, with the increased complexity of the Internet infrastructure, applications, and services, this role has become more crucial than ever. The aims of NTM are mainly focused on the three improvements, which include the quality of service (QoS) of the network, optimization of resource usage, and enhancement of security in computer networks. Specifically speaking, firstly, network conditions can be recognized by the network manager with NTM scheme. It provides the complete details about the QoS of networks, such as bandwidth, throughput, propagation delay, link availability, jitter, server memory, database space and etc. Secondly, with NTM being implemented at network nodes, i.e., network gateways, such as routers, or network links, the network traffic that is traversing the network is under online observation. Thereby, the network utilization can be improved by optimizing the resource usage to avoid the network congestions. Thirdly, unauthenticated service or approaches to the server will be identified by regularly monitoring the traffic. The network convention and statistics about the traffic will be known easily which helps to troubleshoot the network. Security events will also be investigated and the entry of the user will be maintained for responsibility. The work in this thesis focuses on the development of an intelligent real-time dynamic router-based network traffic observation (RNTO) by using the terminal sliding-mode theory. The RNTO technique is applied at network gateways, i.e., routers, to estimate the status of the traffic flows at the router level. The aims of the proposed RNTO technique is to estimate the traffic states, such as queue length (QL)in router buffer, average congestion window size (ACwnd), and the queuing dynamics of the additional traffic flows (ATF). The main contributions of the work can be broadly categorized into four parts. First, the problem of router-based network traffic monitoring is formulated as an observer design by using TSM theory for RNTO applications. The proposed TSM observer in the research is a network-based monitoring, which is implemented into the network gateways, i.e., network routers. Different from the static network traffic monitoring methods, the TSM observer is designed by using control methods based on the fluid-flow mathematical model, which represents the traffic dynamics of the interactions in a set of TCP traffic flows through network routers. By considering the time delay and stochastic properties in the data transmission network, the sliding-mode observation strategy is proposed with its high robustness with system parameter uncertainties as well as the external disturbance rejection. Given the natural weakness of chattering in sliding mode control signal, which can affect the system state, the chattering avoiding technique of the proposed TSM observation was utilized by using a smooth control signal for estimating the abnormal dynamics. It does not need any low-pass filler, which will lead to a phase leg. In addition, for the stochastic dynamics of the network traffics, fast transient convergence at a distance from and within a close range of the equilibrium of the traffic dynamics is essential to quickly capture traffic dynamics in network systems. Thus, a fractional term has been considered in the TSM for faster convergence in system states to efficiently estimate the traffic behaviors. Second, the issue of internal dynamics in network observation system is studied by proposing a novel full-order TSM strategy to speed up the convergence rate of the estimation error. In the RNTO scheme, the precise estimation for ACwnd is needed to estimate the queuing dynamics of ATF. However, the estimation error for ACwnd is not available and it converges to origin asymptotically, which results in a long response time in estimation. The proposed novel TSM observer has been designed to drive the estimation error for ACwnd to a defined known area in the finite-time, which can be calculated. Thereby, the estimation error of ACwnd can converge to origin asymptotically within the defined area. This strategy has shortened the response time and improves the estimation accuracy. This further improves the estimation accuracy for ATF. The comparative studies are conducted to evaluate the performance. Third, the issue of algorithm-efficient RNTO is investigated by considering an event triggered sliding-mode observer to reduce the computational load and the communication burden. Instead of the time-driven observation scheme, the control of the sliding mode observer is formulated under the event triggered scheme. The control of the observer is designed to be smooth and is directly applied to estimate the dynamics of the additional traffic flows. The event triggered observation algorithms is developed to reduce the computational load of the network router and the communication resource of output link in the network. Fourth, the problem of global RNTO is addressed by developing a fuzzy TSM observer by using fuzzy theory to achieve global operation under network uncertainties. The existing RNTO schemes are based on the linearization of a certain network conditions, i.e., a fixed number of TCP connections, which is a constant value N. Given the network suffers from time-varying fading, shadowing and interference and the data rate changes over time, the current methods proposed so far might not effectively and accurately monitor and estimate the traffic dynamics under network uncertainties. The T-S fuzzy models are used to model the traffic dynamics of the time-varying data changes in network link resources, i.e. the time-varying number of TCP sections, N(t) in a mathematical model. Based on the T-S fuzzy models, the fuzzy terminal sliding mode observer is established by using the fuzzy logic theory to estimate the states of the network traffic to achieve the global observation performance under the network uncertainties. In the fuzzy terminal sliding mode observer, the control signal is designed to be continuous for application of estimating the additional traffic flows without the low-pass filter. To evaluate the proposed RNTO technique, the networking simulator tool Network Simulator II (NS-II) has been used. The proposed RNTO algorithms are coded and implemented into network routers in NS-II. Numerous simulation scenarios are considered and performed. The comparative studies are also conducted by analyzing the NS-2 results. The results have demonstrated the effectiveness and efficiency of the proposed RNTO algorithms

Guaranteed Distributed Observers for Networked Systems

[ES] En este artículo se propone un observador distribuido garantista para sistemas en red, considerando de forma explícita el problema de los retardos variables en las comunicaciones. Se asume que la información intercambiada entre agentes llega siempre a su destino, si bien las comunicaciones están sujetas a retardos variables, cuyo valor máximo se supone conocido. Cada observador trabaja con información parcial, y necesita comunicarse con observadores vecinos para llevar a cabo una estimación del estado completo del sistema. Para representar a los conjuntos garantistas, cuya función es acotar en tiempo real la región en la que se encuentra el estado del sistema, se ha optado por la utilización de zonotopos. Esto permite integrar de forma sencilla la información recibida por cada agente. Finalmente se presentan resultados de simulación para validar el algoritmo propuesto.[EN] This paper proposes a guaranteed distributed observer for networked systems, taking into account the problem of the variable delays in communications. We assume that the information exchanged among the agents always arrives to its destination, although the communication are subject to variable delays, whose maximum value is known. Each observer works with partial information, and needs to communicate with neighbouring observers to carry out an estimation of the complete state of the system. The guaranteed sets, whose function is to delimit in real time the region in which the state of the system belong to, are represented by zonotopes. This kind of sets allows a simple integration of the information received by each agent. 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