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

By Eyad H. Abed

This unified quantity is a suite of invited articles on subject matters awarded on the Symposium on platforms, 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, well known for his seminal contributions in parts as different as stochastic structures, nonlinear and hybrid structures, allotted platforms, communique networks, transportation structures, strength networks, economics, optimization, and structures education.

The chapters comprise fresh effects and surveys by way of best specialists on themes that replicate a number of the examine and educating pursuits of Varaiya, including:

* hybrid platforms and functions

* verbal exchange, instant, and sensor networks

* transportation platforms

* stochastic platforms

* platforms schooling

Advances up to the mark, communique Networks, and Transportation Systems will function a superb source for practising and examine engineers, utilized mathematicians, and graduate scholars operating in such components as conversation networks, sensor networks, transportation structures, keep an eye on 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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Additional resources for Advances in Control, Communication Networks, and Transportation Systems: In Honor of Pravin Varaiya

Example text

In this chapter, we review the method proposed by Varaiya [1] to compute reachable sets for linear time invariant systems. Inspired by Kurzhanski and Varaiya [16, 17, 19, 20] and by the work of Khrustalev [23], we compute approximate reachable sets for feedback linearizable nonlinear systems, linear dynamic games, and norm-bounded nonlinear systems. We present three examples, one of which is a twoaircraft three-dimensional collision avoidance example which we have used in other work [5]. This chapter is organized as follows.

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. Chutinan and Krogh [9, 10] present a method to approximate the flows of autonomous systems with convex polyhedra. An experimental system called d/dt [7, 11, 12] has been developed to approximate reachable sets for linear dynamical systems using griddy orthogonal polyhedra.

33) . Here L(·) ∈ K may be chosen in a compact set K of piecewise - continuous matrix functions, while πu (t) > 0, πz (t) > 0 among continuous positive functions. Let us denote the external ellipsoids as E(w+ (τ ), W+ (τ )|ω(τ )} indicating their dependence on the parametrizing functions ω(τ ) = {L(·), πu (·), πz (·)}, L(·) ∈ K; πu (t) > 0, πz (t) > 0, t ∈ [t0 , τ ]. The next assertion is true (see [14]). Theorem 3. Set W[τ ] may be described either through its support function ρ(l|W[τ ]) = − inf{ρ(l|E(w+ (τ ), W+ (τ )|ω(τ )))|ω(τ )}, or, in set-valued terms, as W[τ ] = ∩{E(w+ (τ ), W+ (τ )|ω(τ )))|ω(τ )}.

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