Previous |  Up |  Next

Article

Keywords:
stabilization; stochastic sensitivity; flow reactor; incomplete information
Summary:
Complex dynamic regimes connected with the noise-induced mixed-mode oscillations in the thermochemical model of flow reactor are studied. It is revealed that the underlying reason of such excitability is in the high stochastic sensitivity of the equilibrium. The problem of stabilization of the excitable equilibrium regimes is investigated. We develop the control approach using feedback regulators which reduce the stochastic sensitivity and keep the randomly forced system near the stable equilibrium. We consider also a case when the information about system state is incomplete. Our new mathematical technique is applied to the stabilization of operating modes in the flow chemical reactors forced by random disturbances.
References:
[1] Albert, A.: Regression and the Moore-Penrose Pseudoinverse. Academic Press, New York 1972. DOI 10.1016/s0076-5392(08)x6167-3
[2] Anishchenko, V. S., Astakhov, V. V., Neiman, A. B., Vadivasova, T. E., Schimansky-Geier, L.: Nonlinear Dynamics of Chaotic and Stochastic Systems. Tutorial and Modern Development. Springer-Verlag, Berlin/Heidelberg 2007. MR 2298691
[3] Astrom, K. J.: Introduction to the Stochastic Control Theory. Academic Press, New York 1970. MR 0270799
[4] Bashkirtseva, I., Ryashko, L.: On control of stochastic sensitivity. Automat. Rem. Contr. 69 (2008), 1171-1180. DOI 10.1134/s0005117908070084 | MR 2442517
[5] Bashkirtseva, I., Chen, G., Ryashko, L.: Analysis of stochastic cycles in the Chen system. Int. J. Bifurcat. Chaos 20 (2010), 1439-1450. DOI 10.1142/s0218127410026587
[6] Bashkirtseva, I., Chen, G., Ryashko, L.: Stochastic equilibria control and chaos suppression for 3D systems via stochastic sensitivity synthesis. Commun. Nonlinear Sci. Numer. Simul. 17 (2012), 3381-3389. DOI 10.1016/j.cnsns.2011.12.004 | MR 2904229
[7] Bashkirtseva, I., Chen, G., Ryashko, L.: Controlling the equilibria of nonlinear stochastic systems based on noisy data. J. Franklin Inst. 354 (2017), 1658-1672. DOI 10.1016/j.jfranklin.2016.11.011 | MR 3596653
[8] Gammaitoni, L., Hanggi, P., Jung, P., Marchesoni, F.: Stochastic resonance. Rev. Mod. Phys. 70 (1998), 223-287. DOI 10.1103/revmodphys.70.223
[9] Gonzalez-Hernandez, J., Lopez-Martinez, R. R., Minjarez-Sosa, J. A.: Approximation, estimation and control of stochastic systems under a randomized discounted cost criterion. Kybernetika 45 (2009), 737-754.
[10] Guo, L., Wang, H.: Stochastic Distribution Control System Design: a Convex Optimization Approach. Springer-Verlag, New York 2010. DOI 10.1007/978-1-84996-030-4
[11] Horsthemke, W., Lefever, R.: Noise-Induced Transitions. Theory and Applications in Physics, Chemistry, and Biology. Springer, Berlin 1984.
[12] Jakobsen, H. A.: Chemical Reactor Modeling: Multiphase Reactive Flows. Springer, Berlin 2014. DOI 10.1007/978-3-319-05092-8
[13] Kawczyński, A. L., Nowakowski, B.: Stochastic transitions through unstable limit cycles in a model of bistable thermochemical system. Phys. Chem. Chem. Phys. 10 (2008), 289-296. DOI 10.1039/b709867g
[14] Kushner, H. J.: Stochastic Stability and Control. Academic Press, New York 1967. MR 0216894
[15] Lindner, B., Garcia-Ojalvo, J., Neiman, A., Schimansky-Geier, L.: Effects of noise in excitable systems. Phys. Rep. 392 (2004), 321-424. DOI 10.1016/j.physrep.2003.10.015
[16] Ryashko, L., Bashkirtseva, I.: Analysis of excitability for the FitzHugh-Nagumo model via a stochastic sensitivity function technique. Phys. Rev. E 83 (2011), 061109. DOI 10.1103/physreve.83.061109
[17] Shen, B., Wang, Z., Shu, H.: Nonlinear Stochastic Systems with Incomplete Information, Filtering and Control. Springer, Berlin 2013. DOI 10.1007/978-1-4471-4914-9 | MR 3014902
[18] Sun, J.-Q.: Stochastic Dynamics and Control. Elsevier, Amsterdam 2006. DOI 10.1016/s1574-6917(06)04001-3 | MR 2404208
[19] Volter, B. V., Salnikov, I. Y.: Modeling and Optimization of Catalytic Processes (in Russian). Nauka, Moscow 1996.
[20] Wonham, W.: On the separation theorem of stochastic control. SIAM J. Control 6 (1968), 312-326. DOI 10.1137/0306023
[21] Zaks, M. A., Sailer, X., Schimansky-Geier, L.: Noise induced complexity: From subthreshold oscillations to spiking in coupled excitable systems. Chaos 15 (2005), 026117. DOI 10.1063/1.1886386 | MR 2150239
[22] Zhang, J., Liu, Y., Mu, X.: Further results on global adaptive stabilisation for a class of uncertain stochastic nonlinear systems. DOI 10.1080/00207179.2014.956339
[23] Zheng, Y., Wang, Q., Danca, M.-F.: Noise-induced complexity: patterns and collective phenomena in a small-world neuronal network. Cogn. Neurodyn. 8 (2014), 143-149. DOI 10.1007/s11571-013-9257-x
Partner of
EuDML logo