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2019 | OriginalPaper | Buchkapitel

3. ISS in Spatial L p Norms for Hyperbolic PDEs

verfasst von : Iasson Karafyllis, Miroslav Krstic

Erschienen in: Input-to-State Stability for PDEs

Verlag: Springer International Publishing

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Abstract

The chapter deals with the derivation of ISS estimates expressed in spatial \( L^{p} \) norms for 1-D, first-order, hyperbolic PDEs with a constant transport velocity. Two different methodologies for deriving ISS estimates are provided. The first methodology is the use of ISS-Lyapunov Functionals (ISS-LFs). The second methodology utilizes the transformation to a system of Integral Delay Equations (IDEs). The latter methodology provides ISS estimates expressed only in the sup-norm of the state and the derivation of the ISS estimate is performed by using a Lyapunov-like function (not a functional). Finally, the differences between the two methodologies are explained in detail.

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Vorheriges Kapitel Existence/Uniqueness Results for Hyperbolic PDEs
Nächstes Kapitel Existence/Uniqueness Results for Parabolic PDEs
Literatur
1.
Hale JK, Lunel SMV (1993) Introduction to functional differential equations. Springer, New YorkCrossRef
2.
Karafyllis I, Jiang Z-P (2011) Stability and stabilization of nonlinear systems. Communications and control engineering. Springer, LondonCrossRef
3.
Pepe P (2003) The Liapunov’s second method for continuous time difference equations. Int J Robust Nonlinear Control 13:1389–1405MathSciNetCrossRef
4.
Bastin G, Coron J-M (2016) Stability and boundary stabilization of 1-D hyperbolic systems. Progress in nonlinear differential equations and their applications. Springer, BerlinCrossRef
5.
Karafyllis I, Daoutidis P (2002) Control of hot spots in plug flow reactors. Comput Chem Eng 26:1087–1094CrossRef
6.
Li T-T, Libin W (2009) Global propagation of regular nonlinear hyperbolic waves. Birkhauser, Boston
7.
Perthame B (2007) Transport equations in biology. Birkhäuser Verlag
8.
Krstic M, Smyshlyaev A (2008) Backstepping boundary control for first-order hyperbolic PDEs and application to systems with actuator and sensor delays. Syst Control Lett 57(9):750–758MathSciNetCrossRef
9.
Krstic M (2009) Delay compensation for nonlinear, adaptive, and PDE systems. Birkhäuser, BostonCrossRef
10.
Ha S-Y, Tzavaras A (2003) Lyapunov functionals and L1-stability for discrete velocity boltzmann equations. Commun Math Phys 239:65–92CrossRef
11.
Toth D, Kot M (2006) Limit cycles in a chemostat model for a single species with age structure. Math Biosci 202:194–217MathSciNetCrossRef
12.
Kmit I (2008) Classical solvability of nonlinear initial-boundary problems for first-order hyperbolic systems. Int J Dyn Syst Differ Equ 1(3):191–195MathSciNetMATH
13.
Li TT (2009) Controllability and observability for quasilinear hyperbolic systems, vol 3. Higher Education Press, Beijing
14.
Rauch J, Taylor M (1975) Exponential decay of solutions to hyperbolic equations in bounded domains. Indiana Univ Math J 24
15.
Russell DL (1978) Canonical forms and spectral determination for a class of hyperbolic distributed parameter control systems. J Math Anal Appl 62(1):186–225MathSciNetCrossRef
16.
Xu C-Z, Sallet G (2002) Exponential stability and transfer functions of processes governed by symmetric hyperbolic systems. ESAIM: Control Optim Calculus Var 7:421–442MathSciNetCrossRef
17.
Cooke KL, Krumme DW (1968) Differential-difference equations and nonlinear initial-boundary value problems for linear hyperbolic partial differential equations. J Math Anal Appl 24(2):372–387MathSciNetCrossRef
18.
Karafyllis I, Pepe P, Jiang Z-P (2009) Stability results for systems described by coupled retarded functional differential equations and functional difference equations. Nonlinear Anal Theory Methods Appl 71(7–8):3339–3362MathSciNetCrossRef
19.
Karafyllis I, Krstic M (2014) On the relation of delay equations to first-order hyperbolic partial differential equations. ESAIM Control Optim Calculus Var 20(3):894–923MathSciNetCrossRef
20.
Karafyllis I, Krstic M (2017) Stability of integral delay equations and stabilization of age-structured models. ESAIM Control Optim Calculus Var 23(4):1667–1714MathSciNetCrossRef
21.
Russell DL (1991) Neutral FDE canonical representations of hyperbolic systems. J Integr Eq Appl 3(1):129–166MathSciNetCrossRef
22.
Anfinsen H, Diagne M, Aamo OM, Krstic M (2016) An adaptive observer design for n + 1 coupled linear hyperbolic PDEs based on swapping. IEEE Trans Autom Control 61:3979–3990MathSciNetCrossRef
23.
Anfinsen H, Diagne M, Aamo OM, Krstic M (2017) Estimation of boundary parameters in general heterodirectional linear hyperbolic systems. Automatica 79:185–197MathSciNetCrossRef
24.
Bernard P, Krstic M (2014) Adaptive output-feedback stabilization of non-local hyperbolic PDEs. Automatica 50:2692–2699MathSciNetCrossRef
25.
Bribiesca-Argomedo F, Krstic M (2015) Backstepping-forwarding control and observation for hyperbolic PDEs With fredholm integrals. IEEE Trans Autom Control 60(8):2145–2160MathSciNetCrossRef
26.
Coron J-M, Vazquez R, Krstic M, Bastin G (2013) Local exponential H2 stabilization of a 2 × 2 quasilinear hyperbolic system using backstepping. SIAM J Control Optim 51(3):2005–2035MathSciNetCrossRef
27.
Coron J-M, Hu L, Olive G (2016) Stabilization and controllability of first-order integro-differential hyperbolic equations. J Funct Anal 271:3554–3587MathSciNetCrossRef
28.
29.
Di Meglio F, Vazquez R, Krstic M (2013) Stabilization of a system of n + 1 coupled first-order hyperbolic linear PDEs with a single boundary input. IEEE Trans Autom Control 58(12):3097–3111MathSciNetCrossRef
30.
Hasan A, Aamo OM, Krstic M (2016) Boundary observer design for hyperbolic PDE-ODE cascade systems. Automatica 68:75–86MathSciNetCrossRef
31.
Hu L, Di Meglio F, Vazquez R, Krstic M (2016) Control of homodirectional and general heterodirectional linear coupled hyperbolic PDEs. IEEE Trans Autom Control 61:3301–3314MathSciNetCrossRef
32.
Krstic M, Smyshlyaev A (2008) Boundary control of PDEs: A course on backstepping designs. In: SIAM
33.
Prieur C, Winkin J, Bastin G (2008) Robust boundary control of systems of conservation laws. Math Control Signals Syst 20(2):173–197MathSciNetCrossRef
34.
Vazquez R, Coron J-M, Krstic M, Bastin G (2012) Collocated output-feedback stabilization of a 2 × 2 quasilinear hyperbolic system using backstepping. In: Proceedings of the 2012 American Control conference, Montreal, Canada, pp 2202–2207
35.
Vazquez R, Krstic M (2014) Marcum Q-functions and explicit kernels for stabilization of 2 × 2 linear hyperbolic systems with constant coefficients. Syst Control Lett 68:33–42MathSciNetCrossRef
36.
Zhang L, Prieur C (2017) Necessary and sufficient conditions on the exponential stability of positive hyperbolic systems. IEEE Trans Autom Control 62(7):3610–3617MathSciNetCrossRef
37.
Prieur C, Mazenc F (2012) ISS-Lyapunov functions for time-varying hyperbolic systems of balance laws. Math Control Signals Syst 24(1):111–134MathSciNetCrossRef
38.
Karafyllis I, Krstic M (2017) Predictor feedback for delay systems: Implementations and approximations. Mathematics, systems & control: foundations & applications. Birkhäuser, BostonCrossRef
39.
Pazy A (1983) Semigroups of linear operators and applications to partial differential equations. Springer, New YorkCrossRef
Metadaten
Titel
ISS in Spatial L p Norms for Hyperbolic PDEs
verfasst von
Iasson Karafyllis
Miroslav Krstic
Copyright-Jahr
2019
Buch
Input-to-State Stability for PDEs

Print ISBN: 978-3-319-91010-9

Electronic ISBN: 978-3-319-91011-6

Copyright-Jahr: 2019

DOI
https://doi.org/10.1007/978-3-319-91011-6_3

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