By Eyad H. Abed

ISBN-10: 0817643850

ISBN-13: 9780817643850

ISBN-10: 0817644091

ISBN-13: 9780817644093

This unified quantity is a suite of invited articles on themes awarded on the Symposium on structures, keep an eye on, and Networks, held in Berkeley June 5–7, 2005, in honor of Pravin Varaiya on his 65th birthday. Varaiya is an eminent school member of the college of California at Berkeley, widely recognized for his seminal contributions in components as diversified as stochastic structures, nonlinear and hybrid structures, dispensed platforms, conversation networks, transportation structures, strength networks, economics, optimization, and structures education.

The chapters comprise contemporary effects and surveys by way of top specialists on issues that mirror a few of the examine and educating pursuits of Varaiya, including:

* hybrid structures and functions

* communique, instant, and sensor networks

* transportation platforms

* stochastic structures

* platforms schooling

Advances up to speed, communique Networks, and Transportation Systems will function a good source for working towards and study engineers, utilized mathematicians, and graduate scholars operating in such components as verbal exchange networks, sensor networks, transportation platforms, regulate conception, hybrid structures, and purposes.

Contributors: J.S. Baras * V.S. Borkar * M.H.A. Davis * A.R. Deshpande * D. Garg * M. Gastpar * A.J. Goldsmith * R. Gupta * R. Horowitz * I. Hwang * T. Jiang * R. Johari * A. Kotsialos * A.B. Kurzhanski * E.A. Lee * X. Liu * H.S. Mahmassani * D. Manjunath * B. Mishra * L. Muñoz * M. Papageorgiou * C. Piazza * S.E. Shladover * D.M. Stipanovic * T.M. Stoenescu * X. solar * D. Teneketzis * C.J. Tomlin * J.N. Tsitsiklis * J. Walrand * X. Zhou

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Extra info for Advances in Control, Communication Networks, and Transportation Systems: In Honor of Pravin Varaiya

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In order to achieve a guaranteed estimate VE (τ, x∗ , W) of V(τ, x∗ , W), we shall substitute an internal ellipsoid E(wc , W+ (τ )|ω(τ )) for X ∗ [τ ] and an external ellipsoid X− (τ )|χ− (τ )) for W[τ ]. Then we will have 2 On the Problem of Measurement Feedback Control 33 VE (τ, x∗ , W) ≤ max{(l, x∗ ) + ρ(l|E(wc , W+ (τ )|ω(τ )) l − ρ(l|E(xc (τ ), X− (τ )|χ− (τ ))|(l, l) ≤ 1} = VE (τ, x∗ , W). 40) We shall now calculate the total derivative dVE (τ, x∗ , W)/dτ . 36), we shall use the specific parametrizing functions πf , πz , γf and matrices S1 that ensure the respective ellipsoids E(wc , W+ ), E(xc , X− ) to be tight.

19) Problem CS-V: Find the value function V(ϑ, τ, x∗ , W), according to the formula V(ϑ, τ, x∗ , W) = max min d(x∗ (ϑ), W (ϑ, z(·); τ, W)), ζ u with fixed {x∗ (τ ) = x∗ , W(τ ) = W}. Here the minimum is to be taken over all functions u(s) ∈ P(s), s ∈ [τ, ϑ], and the maximum over all triplets ζ = {w, f (·), ξ(·)}, where ζ ∈ Zτ (W) and 2 On the Problem of Measurement Feedback Control 27 Zτ (W ) = {w, f (·), ξ(·)} : w ∈ W, f (t) ∈ Q(t), ξ(t) ∈ R(t), t ∈ [τ, ϑ] . Remark 2. In the monograph [5] it is demonstrated that the maximum over triplets Zτ (W ) in Problem V-1 is equivalent to the maximum over all pairs {w, z(·)}, where w ∈ W and z(t) ∈ Z(τ, W) = {H(t)w(t) + ξ(t)|ζ ∈ Z(τ, W), , t ∈ [τ, ϑ]}, due to equality t w(t) = w + C(s)f (s)ds.

4 I. M. J. Tomlin models from complex, infinite state models, which are used to find approximate reachable sets of the original systems. In [8], Hwang et al. have used an augmented form of predicate abstraction to compute reachable sets for a simple biological cell network. However, since the accuracy of reachability analysis using predicate abstraction greatly depends on the choice of polynomials for abstraction, it is important to have information about a given system a priori (from analysis and simulations) to get good results in the reachability analysis.

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Advances in Control, Communication Networks, and Transportation Systems: In Honor of Pravin Varaiya by Eyad H. Abed


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