245 research outputs found

    Analysis and synthesis of randomly switched systems with known sojourn probabilities

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    In this paper, a new approach is proposed and investigated for the stability analysis and stabilizing controller design of randomly switched linear discrete systems. The approach is based on sojourn probabilities and it is assumed that these probabilities are known a prior. A new Lyapunov functional is constructed and two main theorems are proved in this paper. Theorem 1 gives a sufficient condition for a switched system with known sojourn probabilities to be mean square stable. Theorem 2 gives a sufficient condition for the design of a stabilizing controller. The applications of these theorems and the corresponding corollary and lemma are demonstrated by three numerical examples. Finally, some future research is proposed

    Stability Analysis of Continuous-Time Switched Systems with a Random Switching Signal

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    This paper is concerned with the stability analysis of continuous-time switched systems with a random switching signal. The switching signal manifests its characteristics with that the dwell time in each subsystem consists of a fixed part and a random part. The stochastic stability of such switched systems is studied using a Lyapunov approach. A necessary and sufficient condition is established in terms of linear matrix inequalities. The effect of the random switching signal on system stability is illustrated by a numerical example and the results coincide with our intuition.Comment: 6 pages, 6 figures, accepted by IEEE-TA

    Stability Analysis of A Class of Hybrid Stochastic Retarded Systems Under Asynchronous Switching

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    Modeling and Stability Analysis of Nonlinear Sampled-Data Systems with Embedded Recovery Algorithms

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    Computer control systems for safety critical systems are designed to be fault tolerant and reliable, however, soft errors triggered by harsh environments can affect the performance of these control systems. The soft errors of interest which occur randomly, are nondestructive and introduce a failure that lasts a random duration. To minimize the effect of these errors, safety critical systems with error recovery mechanisms are being investigated. The main goals of this dissertation are to develop modeling and analysis tools for sampled-data control systems that are implemented with such error recovery mechanisms. First, the mathematical model and the well-posedness of the stochastic model of the sampled-data system are presented. Then this mathematical model and the recovery logic are modeled as a dynamically colored Petri net (DCPN). For stability analysis, these systems are then converted into piecewise deterministic Markov processes (PDP). Using properties of a PDP and its relationship to discrete-time Markov chains, a stability theory is developed. In particular, mean square equivalence between the sampled-data and its associated discrete-time system is proved. Also conditions are given for stability in distribution to the delta Dirac measure and mean square stability for a linear sampled-data system with recovery logic

    Behavior Trees in Robotics and AI: An Introduction

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    A Behavior Tree (BT) is a way to structure the switching between different tasks in an autonomous agent, such as a robot or a virtual entity in a computer game. BTs are a very efficient way of creating complex systems that are both modular and reactive. These properties are crucial in many applications, which has led to the spread of BT from computer game programming to many branches of AI and Robotics. In this book, we will first give an introduction to BTs, then we describe how BTs relate to, and in many cases generalize, earlier switching structures. These ideas are then used as a foundation for a set of efficient and easy to use design principles. Properties such as safety, robustness, and efficiency are important for an autonomous system, and we describe a set of tools for formally analyzing these using a state space description of BTs. With the new analysis tools, we can formalize the descriptions of how BTs generalize earlier approaches. We also show the use of BTs in automated planning and machine learning. Finally, we describe an extended set of tools to capture the behavior of Stochastic BTs, where the outcomes of actions are described by probabilities. These tools enable the computation of both success probabilities and time to completion

    Self-similar traffic and network dynamics

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    Copyright © 2002 IEEEOne of the most significant findings of traffic measurement studies over the last decade has been the observed self-similarity in packet network traffic. Subsequent research has focused on the origins of this self-similarity, and the network engineering significance of this phenomenon. This paper reviews what is currently known about network traffic self-similarity and its significance. We then consider a matter of current research, namely, the manner in which network dynamics (specifically, the dynamics of transmission control protocol (TCP), the predominant transport protocol used in today's Internet) can affect the observed self-similarity. To this end, we first discuss some of the pitfalls associated with applying traditional performance evaluation techniques to highly-interacting, large-scale networks such as the Internet. We then present one promising approach based on chaotic maps to capture and model the dynamics of TCP-type feedback control in such networks. Not only can appropriately chosen chaotic map models capture a range of realistic source characteristics, but by coupling these to network state equations, one can study the effects of network dynamics on the observed scaling behavior. We consider several aspects of TCP feedback, and illustrate by examples that while TCP-type feedback can modify the self-similar scaling behavior of network traffic, it neither generates it nor eliminates it.Ashok Erramilli, Matthew Roughan, Darryl Veitch and Walter Willinge

    What's next? : operational support for business process execution

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    In the last decade flexibility has become an increasingly important in the area of business process management. Information systems that support the execution of the process are required to work in a dynamic environment that imposes changing demands on the execution of the process. In academia and industry a variety of paradigms and implementations has been developed to support flexibility. While on the one hand these approaches address the industry demands in flexibility, on the other hand, they result in confronting the user with many choices between different alternatives. As a consequence, methods to support users in selecting the best alternative during execution have become essential. In this thesis we introduce a formal framework for providing support to users based on historical evidence available in the execution log of the process. This thesis focuses on support by means of (1) recommendations that provide the user an ordered list of execution alternatives based on estimated utilities and (2) predictions that provide the user general statistics for each execution alternative. Typically, estimations are not an average over all observations, but they are based on observations for "similar" situations. The main question is what similarity means in the context of business process execution. We introduce abstractions on execution traces to capture similarity between execution traces in the log. A trace abstraction considers some trace characteristics rather than the exact trace. Traces that have identical abstraction values are said to be similar. The challenge is to determine those abstractions (characteristics) that are good predictors for the parameter to be estimated in the recommendation or prediction. We analyse the dependency between values of an abstraction and the mean of the parameter to be estimated by means of regression analysis. With regression we obtain a set of abstractions that explain the parameter to be estimated. Dependencies do not only play a role in providing predictions and recommendations to instances at run-time, but they are also essential for simulating the effect of changes in the environment on the processes, both locally and globally. We use stochastic simulation models to simulate the effect of changes in the environment, in particular changed probability distribution caused by recommendations. The novelty of these models is that they include dependencies between abstraction values and simulation parameters, which are estimated from log data. We demonstrate that these models give better approximations of reality than traditional models. A framework for offering operational support has been implemented in the context of the process mining framework ProM
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