Advances in Control, Communication Networks, and by Eyad H. Abed

By Eyad H. Abed

This unified quantity is a set of invited articles on themes provided on the Symposium on structures, keep watch over, and Networks, held in Berkeley June 5–7, 2005, in honor of Pravin Varaiya on his 65th birthday. Varaiya is an eminent college member of the collage of California at Berkeley, widely recognized for his seminal contributions in parts as varied as stochastic structures, nonlinear and hybrid platforms, dispensed structures, verbal exchange networks, transportation platforms, energy networks, economics, optimization, and platforms education.

The chapters contain fresh effects and surveys via top specialists on subject matters that mirror some of the examine and educating pursuits of Varaiya, including:

* hybrid platforms and purposes

* verbal exchange, instant, and sensor networks

* transportation structures

* stochastic platforms

* structures schooling

Advances on top of things, conversation Networks, and Transportation Systems will function an outstanding source for training and learn engineers, utilized mathematicians, and graduate scholars operating in such components as verbal exchange networks, sensor networks, transportation platforms, regulate idea, 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. sunlight * D. Teneketzis * C.J. Tomlin * J.N. Tsitsiklis * J. Walrand * X. Zhou

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

Example text

5), as well as the available measurements, the realization z = z ∗ (t), t ∈ [t0 , τ ]. 5). The information set W[τ ] is the guaranteed estimate of the realized vector w(τ ). The specification of this set is the subject of the theory of guaranteed (minmax) estimation [16], [5],[18], [19], [3]. However, for the problems of this chapter it is necessary not only to calculate set W[τ ], but to arrange the calculations on-line, following the evolution of W[τ ] in time. Such procedures may be organized through the solution of the following problem of dynamic optimization.

It is also assumed that here the comaximizer α0 ≡ t, which means that α0 (t) has no jump at time τ . The maximizer λ0 (τ ) is assumed continuous and unique, allowing representation dΛ0 (τ )/dτ = λ0 (τ )dα0 (τ ) with Λ(τ ) being a function of bounded variation, of dimension m. The uniqueness of maximizer λ0 (τ ) may be ensured by assuming R(τ ) to be a nondegenerate ellipsoid (such an R is taken in the next section). Here we also used the property that either λ0 (τ )H(τ ) = l0 (τ ), or λ0 (τ ) = 0, (see [23], Section 17).

1) in which there are no disturbances). Assume that x∗ (0) ∈ X0 1 Applications of Polytopic Approximations of Reachable Sets 7 and u∗ (t) ∈ U for all t ≥ 0 such that x∗ (τ ) ∈ X (τ ) (0 ≤ t ≤ τ ). 6) where v + (x∗ , t) is a piecewise continuous function, and μ(t) is a positive-definite, integrable function. 1) at time τ as: τ V + (τ ) = {x|v + (x, τ ) ≤ μ(t)dt + max v + (x(0), 0)}. 7) Next, we review the polytopic overapproximation of reachable sets for linear dynamical systems and derive computational methods for polytopic overapproximate reachable sets for feedback linearizable nonlinear systems, linear dynamic games, and norm-bounded nonlinear systems.

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