STABILITY OF THE EQUILIBRIUM STATE FOR THE SCALAR CONSERVATION LAW WITH NONLOCAL CHARACTERISTIC VELOCITIES
Keywords:
Abstract
In this paper, we study input-state stability (ISS) of equilibrium for a scalar conservation law with nonlocal velocity and measurement error occurring in a high-volume reproducible system . Using the corresponding Lyapunov function, we derive sufficient and necessary conditions on ISS. We propose a numerical discretization of the scalar conservation law with nonlocal velocity and measurement error. For the proposed numerical approximation, the appropriate discrete Lyapunov function is analyzed to provide the ISS of the discrete equilibrium. For the proposed numerical approximation, the appropriate discrete Lyapunov function is analyzed to provide the ISS of the discrete equilibrium. Finally, we show computational results to confirm the theoretical conclusions.
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References
Armbruster, D.; Degond, P.; Ringhofer, C. A model for the dynamics of large queuing networks and supply chains. SIAM J. Appl.Math. 2006 , 66, 896–920, doi :10.1137 /040604625.
Herty, M.; Klar, A.; Piccoli, B. Existence of solutions for supply chain models based on partial differential equations. SIAM J.
Math. Anal. 2007 , 39, 160–173, doi :10.1137 /060659478.
He, F.; Armbruster, D.; Herty, M.; Dong, M. Feedback control for priority rules in re-entrant semiconductor manufacturing. Appl.Math. Model. 2015 , 39, 4655–4664, doi:10.1016/j.apm.2015.03.061.
D'Apice, C.; Göttlich, S.; Herty, M.; Piccoli, B. Modeling, Simulation, and Optimization of Supply Chains; Society for Industrial and Applied Mathematics (SIAM): Philadelphia, PA, USA, 2010; pp. x+206. A continuous approach, doi:10.1137/1.9780898717600.
Chen, H.; Harrison, JM; Mandelbaum, A.; Van Ackere, A.; Wein, LM Empirical Evaluation of a Queuing Network Model for
Semiconductor Wafer Fabrication. Opera. Res. 1988 , 36, 202–215, doi:10.1287/opre.36.2.202.
Helbing, D. Traffic and related self-driven many-particle systems. Rev. Modern Phys. 2001 , 73, 1067–1141, doi:10.1103/RevModPhys.73.1067.
Coron, JM; Wang, Z. Output Feedback Stabilization for a Scalar Conservation Law with a Nonlocal Velocity. SIAM J. Math. Anal. 2013 , 45, 2646–2665, doi :10.1137 /120902203.
Coron, JM; Kawski, M .; Wang , Z. Analysis of a conservation law modeling a highly re-entrant manufacturing system. Discreet. Contin. Dyn. Syst. Sir. B 2010 , 14, 1337–1359, doi:10.3934/dcdsb.2010.14.1337.
Shang, P.; Wang, Z. Analysis and control of a scalar conservation law modeling a highly re-entrant manufacturing system. J. Differ. Equ. 2011 , 250, 949–982, doi:10.1016/j.jde.2010.09.003.
Chen, W.; Liu, C.; Wang, Z. Global Feedback Stabilization for a Class of Nonlocal Transport Equations: The Continuous and Discrete Case. SIAM J. Control Optim. 2017 , 55, 760–784, doi :10.1137 /15m1048914.
Tanwani, A.; Prieur, C.; Tarbouriech, S. Stabilization of linear hyperbolic systems of balance laws with measurement errors. In Control Subject to Computational and Communication Constraints; Springer: Cham, Switzerland, 2018; Volume 475, pp. 357–374. Lect. Notes Control Inf. Sci.
Dos Santos, V.; Bastin, G.; Coron, JM; d'Andréa Novel, B. Boundary control with integral action for hyperbolic systems of conservation laws: stability and experiments. Automatic. J. IFAC 2008 , 44, 1310–1318, doi:10.1016/j.automatica.2007.09.022.
Bastin, G.; Coron, JM; d'Andréa Novel, B. On Lyapunov stability of linearized Saint-Venant equations for a sloping channel. Netw. Heterog. Media 2009 , 4, 177–187, doi:10.3934/nhm.2009.4.177.
Bastin, G .; Coron, JM Exponential stability of semi-linear one-dimensional balance laws. In Feedback Stabilization of Controlled Dynamical Systems; Springer: Cham, Switzerland, 2017; Volume 473, pp. 265–278. Lect. Notes Control Inf. Sci.
Bastin, G.; Coron, JM Stability and Boundary Stabilization of 1-D Hyperbolic Systems; Springer: Berlin/Heidelberg, Germany, 2016, doi :10.1007 /978-3-319-32062-5.
Coron, JM; d'Andréa Novel, B.; Bastin, G. A strict Lyapunov function for boundary control of hyperbolic systems of conservation laws. IEEE Trans. Automatic. Control 2007 , 52, 2–11, doi:10.1109/TAC.2006.887903.
Diagne, A.; Bastin, G.; Coron, JM Lyapunov exponential stability of 1-D linear hyperbolic systems of balance laws. Auto. J. IFAC 2012 , 48, 109–114, doi:10.1016/j.automatica.2011.09.030.
Gugat, M.; Perrollaz, V.; Rosier, L. Boundary stabilization of quasilinear hyperbolic systems of balance laws: Exponential decay for small source terms. J. Evol. Equ. 2018 , 18, 1471–1500, doi :10.1007 /s00028-018-0449-z.
Cen, LH; Xi, YG Stability of boundary feedback control based on weighted Lyapunov function in networks of open channels. Acta Automat. Sinica 2009 , 35, 97–102. doi:10.3724/SP.J.1004.2009.00097.
Prieur, C.; Mazenc, F. ISS-Lyapunov functions for time-varying hyperbolic systems of balance laws. Math. Control Signal Syst. 2012 , 24, 111–134, doi:10.1007 /s00498-012-0074-2.
