[신간의 별자리x] 우리/미술, 그리고 ‘슬픔의 박물관’

Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.

Convergence of Probability Measures

The author's preface gives an outline: "This book is about weakconvergence methods in metric spaces, with applications sufficient to show their power and utility. The Introduction motivates the definitions and indicates how the theory will yield solutions to problems arising outside it. Chapter 1 sets out the basic general theorems, which are then specialized in Chapter 2 to the space C[0, l ] of continuous functions on the unit interval and in Chapter 3 to the space D [0, 1 ] of functions with discontinuities of the first kind. The results of the first three chapters are used in Chapter 4 to derive a variety of limit theorems for dependent sequences of random variables. " The book develops and expands on Donsker's 1951 and 1952 papers on the invariance principle and empirical distributions. The basic random variables remain real-valued although, of course, measures on C[0, l ] and D[0, l ] are vitally used. Within this framework, there are various possibilities for a different and apparently better treatment of the material. More of the general theory of weak convergence of probabilities on separable metric spaces would be useful. Metrizability of the convergence is not brought up until late in the Appendix. The close relation of the Prokhorov metric and a metric for convergence in probability is (hence) not mentioned (see V. Strassen, Ann. Math. Statist. 36 (1965), 423-439; the reviewer, ibid. 39 (1968), 1563-1572). This relation would illuminate and organize such results as Theorems 4.1, 4.2 and 4.4 which give isolated, ad hoc connections between weak convergence of measures and nearness in probability. In the middle of p. 16, it should be noted that C*(S) consists of signed measures which need only be finitely additive if 5 is not compact. On p. 239, where the author twice speaks of separable subsets having nonmeasurable cardinal, he means "discrete" rather than "separable." Theorem 1.4 is Ulam's theorem that a Borel probability on a complete separable metric space is tight. Theorem 1 of Appendix 3 weakens completeness to topological completeness. After mentioning that probabilities on the rationals are tight, the author says it is an

Convergence of probability measures

Information Theory and Reliable Communication

This paper reviews some main results and progress in distributed multi-agent coordination, focusing on papers published in major control systems and robotics journals since 2006. Distributed coordination of multiple vehicles, including unmanned aerial vehicles, unmanned ground vehicles, and unmanned underwater vehicles, has been a very active research subject studied extensively by the systems and control community. The recent results in this area are categorized into several directions, such as consensus, formation control, optimization, and estimation. After the review, a short discussion section is included to summarize the existing research and to propose several promising research directions along with some open problems that are deemed important for further investigations.

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An Overview of Recent Progress in the Study of Distributed Multi-Agent Coordination

System identification is investigated for plants that are equipped with only binary-valued sensors. Optimal identification errors, time complexity, optimal input design, and impact of disturbances and unmodeled dynamics on identification accuracy and complexity are examined in both stochastic and deterministic information frameworks. It is revealed that binary sensors impose fundamental limitations on identification accuracy and time complexity, and carry distinct features beyond identification with regular sensors. Comparisons between the stochastic and deterministic frameworks indicate a complementary nature in their utility in binary-sensor identification.

/pdf/system-identification-using-binary-sensors-2j525e0l5y.pdf

System identification using binary sensors

This chapter aims at bridging the gap between chemistry scientists and electrical engineers on electric vehicle (EV) batteries. The power and energy of electric propulsion are first reviewed in Sect. 2.2. Commonly used terms to describe battery performance and characterization are then introduced in Sect. 2.3, followed by the review of various battery charging methods and EV charging schemes in Sect. 2.4. The fundamentals of EV battery technologies are addressed in Sect. 2.5. Two currently most common EV battery technologies, namely, nickel metal hydride (NiMH) and lithium-ion (Li-ion), are covered. It is targeted for giving power engineers a basic understanding of battery chemistry. The EV battery modeling is introduced in Sect. 2.6. It is important for power engineers to appreciate the fundamentals of battery chemistry and battery modeling and use it for power electronic interfacing converter design, battery management, and system level studies. Section 2.7 covers the topic on battery characterization including battery model parameter estimation, state of charge (SOC), and state of health (SOH) estimation. The battery aggregation for power grid applications is discussed in Sect. 2.8. The concept of virtual power plant (VPP) for battery aggregation is introduced to support EV’s participation in power markets.

Electric Vehicle Battery Technologies

A novel method to obtain the open circuit voltage for the state of charge of lithium ion batteries in electric vehicles by using H infinity filter

One of the fundamental and challenging issues in microgrids is to guarantee fairness of load sharing while realizing voltage regulation of distributed generations. In order to address this issue, a new multiobjective optimization problem with tunable weighting coefficients is first formulated for dc microgrids. Second, a new distributed control scheme, which only requires local communications among neighbors, is proposed to solve the optimization problem. It is theoretically proved that the distributed control scheme can exponentially achieve the global optimal outputs of voltages and currents at distributed generations. Compared with a centralized control scheme, the proposed distributed control scheme provides remarkable advantages in improving reliability and scalability of microgrids. Third, the distributed control scheme is extended to accommodate a constant communication delay. The effects of the communication delay on the stability of microgrids are explicitly characterized. Finally, the performance of the proposed control schemes is evaluated by a modified six-bus microgrid with dc-powered trolleybus systems in terms of their convergence, robustness to load variations, plug-and-play functionality, tradeoff ability, and effects of communication delays.

Distributed Cooperative Optimal Control of DC Microgrids With Communication Delays

The platooning of autonomous vehicles has the potential to significantly improve traffic capacity, enhance highway safety, and reduce fuel consumption. This paper studies the scalability limitations of large-scale vehicular platoons moving in rigid formation, and proposes two basic ways to improve stability margins, i.e., enlarging information topology and employing asymmetric control. A vehicular platoon is considered as a combination of four components: 1) node dynamics; 2) decentralized controller; 3) information flow topology; and 4) formation geometry. Tools, such as the algebraic graph theory and matrix factorization technique, are employed to model and analyze scalability limitations. The major findings include: 1) under linear identical decentralized controllers, the stability thresholds of control gains are explicitly established for platoons under undirected topologies. It is proved that the stability margins decay to zero as the platoon size increases unless there is a large number of following vehicles pinned to the leader and 2) the stability margins of vehicular platoons under bidirectional topologies using asymmetric controllers are always bounded away from zero and independent of the platoon size. Simulations with a platoon of passenger cars are used to demonstrate the findings.

Le Yi Wang

Papers

System identification using binary sensors

Electric Vehicle Battery Technologies

A novel method to obtain the open circuit voltage for the state of charge of lithium ion batteries in electric vehicles by using H infinity filter

Distributed Cooperative Optimal Control of DC Microgrids With Communication Delays

Stability Margin Improvement of Vehicular Platoon Considering Undirected Topology and Asymmetric Control