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By Eyad H. Abed

This unified quantity is a suite of invited articles on subject matters offered on the Symposium on platforms, regulate, 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 collage of California at Berkeley, widely recognized for his seminal contributions in parts as assorted as stochastic structures, nonlinear and hybrid structures, disbursed structures, verbal exchange networks, transportation platforms, energy networks, economics, optimization, and platforms education.

The chapters contain contemporary effects and surveys through top specialists on subject matters that mirror some of the study and instructing pursuits of Varaiya, including:

* hybrid platforms and purposes

* verbal exchange, instant, and sensor networks

* transportation platforms

* stochastic structures

* structures schooling

Advances up to speed, communique Networks, and Transportation Systems will function a great source for working towards and study engineers, utilized mathematicians, and graduate scholars operating in such parts as communique networks, sensor networks, transportation platforms, keep watch over conception, hybrid platforms, 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 (Systems & Control: Foundations & Applications)

Example text

3 Conflict resolution between two aircraft Last, we consider the two aircraft collision avoidance problem, as an example of feedback linearizable nonlinear systems and linear dynamic games. 2. Fig. 3 shows the relative configuration between two aircraft showing the protected zone. Aircraft 1 tries to avoid a conflict with aircraft 2 within the limits of its capability. Thus, we want to compute a backward reachable set (unsafe set) from the target set (protected zone). The target set represents the states from which the two aircraft would eventually have a conflict no matter how aircraft 1 tries to avoid it [5].

Varaiya, Reach set computation using optimal control, In Proceedings of the KIT Workshop on Verification of Hybrid Systems, 377–383, Grenoble, France, 1998. [2] J. J. Tomlin, and S. Sastry, Controllers for reachability specifications for hybrid systems, Automatica, 35 (3):349–370, 1999. J. Tomlin, J. Lygeros, and S. Sastry, A game theoretic approach to controller design for hybrid systems, Proceedings of the IEEE, 88 (7):949–970, July 2000. [4] I. Mitchell, A. J. D. DiBenedetto and A. , Hybrid Systems: Computation and Control, LNCS 2034:418–431, Springer-Verlag, 2001.

We assume f to be Lipschitz. The spaces of admissible control input trajectories and disturbance input trajectories are denoted as the spaces of piecewise continuous functions U = {u(·) ∈ P C 0 |u(t) ∈ U, 0 ≤ t ≤ tf } and D = {d(·) ∈ P C 0 |d(t) ∈ D, 0 ≤ t ≤ tf } respectively. 1) are defined as follows. Definition 1. 1). Definition 2. 1). It has been shown that a forward reachable set computation can be formulated as a dynamic optimization problem [17, 23]. 3) with v(x, 0) = l(x), < p, q >= pT q the inner product in Rn , and where D() represents the partial derivative with respect to the subscripted variable.

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