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2018 | OriginalPaper | Chapter

5. Dynamic Routing Problem in Distributed Parameter Setting

Authors : Pushkin Kachroo, Kaan M. A. Özbay

Published in: Feedback Control Theory for Dynamic Traffic Assignment

Publisher: Springer International Publishing

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Abstract

The aim of this chapter is to design control law for the DTR (Dynamic Traffic Routing) problem modeled in the distributed parameter setting. For the control design, the chapter uses the sliding mode control technique for regulating the error. Sliding mode control provides a robust method against bounded uncertainties. The price to pay for that robustness is chattering. The chapter shows methods to deal with chattering reduction in the control implementation. Control design and its software simulation using sliding mode control are presented in this chapter. The chapter also provides a simple study of discretization errors that are obtained in the numerical approximation of the distributed model for software simulation. The chapter shows the development of a simple software simulation code and its simulation to study this problem.

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previous chapter Modeling and Problem Formulation
next chapter Dynamic Routing Problem in Distributed Parameter Setting Using Semigroup Theory
Literature
1.
Vidyasagar M (1992) Nonlinear systems analysis, 2nd edn. Prentice-Hall Inc
2.
Filippov AF (1960) Differential equations with discontinuous right-hand side. Matematicheskii sbornik 93(1):99–128MathSciNetMATH
3.
Filippov AF (1980) Differential equations with second members discontinuous on intersecting surfaces. Differ Equ 415:1292–1299MATH
4.
Paden B, Sastry S (1987) A calculus for computing filippov’s differential inclusion with application to the variable structure control of robot manipulators. IEEE Trans Circuits Syst 34(1):73–82MathSciNetCrossRef
5.
Shevitz D, Paden B (1994) Lyapunov stability theory of nonsmooth systems. IEEE Trans Autom Control 39(9):1910–1914MathSciNetCrossRef
6.
Kachroo P (1999) Existence of solutions to a class of nonlinear convergent chattering-free sliding mode control systems. IEEE Trans Autom Control 44(8):1620–1624MathSciNetCrossRef
7.
Kachroo P, Tomizuka M (1996) Chattering reduction and error convergence in the sliding-mode control of a class of nonlinear systems. IEEE Trans Autom Control 41(7):1063–1068MathSciNetCrossRef
8.
Slotine JJE, Li W (1991) Applied nonlinear control. Prentice-Hall
9.
Slotine J-J, Sastry SS (1983) Tracking control of non-linear systems using sliding surfaces, with application to robot manipulators. Int J Control 38(2):465–492CrossRef
10.
Slotine J-J, Coetsee JA (1986) Adaptive sliding controller synthesis for non-linear systems. Int J Control 43(6):1631–1651CrossRef
11.
Bartolini G, Pydynowski P (1996) An improved, chattering free, VSC scheme for uncertain dynamical systems. IEEE Trans Autom Control 41(8):1220–1226CrossRef
12.
Bartolini G, Ferrara A, Usani E (1998) Chattering avoidance by second-order sliding mode control. IEEE Trans Autom Control 43(2):241–246MathSciNetCrossRef
13.
Bartolini G, Pydynowski P (1993) Asymptotic linearization of uncertain nonlinear systems by means of continuous control. Int J Robust Nonlinear Control 3(2):87–103CrossRef
14.
Kachroo P (1993) Nonlinear control strategies and vehicle traction control. University of California, Berkeley
15.
Kachroo P, Tomizuka M (1995) Sliding mode control with chattering reduction and error convergence for a class of discrete nonlinear systems with application to vehicle control. In: Proceedings of the international mechanical engineering congress and expo, pp 225–233
16.
Francis BA, Wonham WM (1975) The internal model principle for linear multivariable regulators. Appl Math Optim 2(2):170–194MathSciNetCrossRef
17.
Kachroo P, Ozbay K (1997) Sliding mode for user equilibrium dynamic traffic routing control. In: IEEE conference on intelligent transportation system, ITSC’97. IEEE, pp 70–75
18.
Kachroo P, Tomizuka M (1992) Integral action for chattering reduction and error convergence in sliding mode control. In: American control conference. IEEE, pp 867–870
19.
Stewart J (2012) Essential calculus: Early transcendentals. Cengage Learning
20.
Kachroo P, Sastry S (2016a) Travel time dynamics for intelligent transportation systems: theory and applications. IEEE Trans Intell Transp Syst 17(2):385–394CrossRef
21.
Kachroo P, Sastry S (2016b) Traffic assignment using a density-based travel-time function for intelligent transportation systems. IEEE Trans Intell Transp Syst 17(5):1438–1447CrossRef
22.
LeVeque RJ (1990) Numerical methods for conservation laws. Birkhäuser VerlagCrossRef
23.
LeVeque RJ (2002) Finite volume methods for hyperbolic problems, vol 31. Cambridge University Press
24.
Toro EF (2013) Riemann solvers and numerical methods for fluid dynamics: a practical introduction. Springer Science & Business Media
Metadata
Title
Dynamic Routing Problem in Distributed Parameter Setting
Authors
Pushkin Kachroo
Kaan M. A. Özbay
Copyright Year
2018
Book
Feedback Control Theory for Dynamic Traffic Assignment

Print ISBN: 978-3-319-69229-6

Electronic ISBN: 978-3-319-69231-9

Copyright Year: 2018

DOI
https://doi.org/10.1007/978-3-319-69231-9_5