Ergodic Theorem for Stabilization of a Hyperbolic PDE Inspired by Age-Structured Chemostat
作者： Iasson Karafyllis , Michael Malisoff , Miroslav Krstic
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摘要: We study a feedback stabilization problem for rst-order hyperbolic partial dierential equation. The is inspired by the of equilibrium age proles an age-structured chemostat, using dilution rate as control. Two distinguishing features are that (a) PDE has multiplicative (instead additive) input and (b) state fed back to inlet boundary. provide sampled-data ensures under arbitrarily sparse sampling satises constraints. Our chemostat does not require measurement prole, nor it exact knowledge model.
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arxiv.org参考文章(18)
Brian Charlesworth, Evolution in age-structured populations ,(1980)
Damon Toth, Mark Kot, Limit cycles in a chemostat model for a single species with age structure. Bellman Prize in Mathematical Biosciences. ,vol. 202, pp. 194- 217 ,(2006) , 10.1016/J.MBS.2006.03.008
A. Rapaport, J. Harmand, F. Mazenc, Coexistence in the design of a series of two chemostats Nonlinear Analysis: Real World Applications. ,vol. 9, pp. 1052- 1067 ,(2008) , 10.1016/J.NONRWA.2007.02.003
Jean-Michel Coron, Rafael Vazquez, Miroslav Krstic, Georges Bastin, Local exponential H2 stabilization of 2x2 quasilinear hyperbolic systems using backstepping Siam Journal on Control and Optimization. ,vol. 51, pp. 2005- 2035 ,(2013) , 10.1137/120875739
Hisashi Inaba, None, Asymptotic properties of the inhomogeneous Lotka-Von Foerster system. Mathematical Population Studies. ,vol. 1, pp. 247- 264 ,(1988) , 10.1080/08898488809525277
Fred Brauer, Carlos Castillo-Chavez, Carlos Castillo-Chavez, Mathematical Models in Population Biology and Epidemiology ,(2001)
Gonzalo Robledo, Frédéric Grognard, Jean-Luc Gouzé, Global stability for a model of competition in the chemostat with microbial inputs Nonlinear Analysis-real World Applications. ,vol. 13, pp. 582- 598 ,(2012) , 10.1016/J.NONRWA.2011.07.049
Florent Di Meglio, Rafael Vazquez, Miroslav Krstic, Stabilization of a System of $n+1$ Coupled First-Order Hyperbolic Linear PDEs With a Single Boundary Input IEEE Transactions on Automatic Control. ,vol. 58, pp. 3097- 3111 ,(2013) , 10.1109/TAC.2013.2274723
Jean-Luc Gouze, Gonzalo Robledo, Robust control for an uncertain chemostat model International Journal of Robust and Nonlinear Control. ,vol. 16, pp. 133- 155 ,(2006) , 10.1002/RNC.1047