Open and closed-loop stochastic dynamics of a class of nonlinear chemical processes with multiplicative noise. (June 2018)

• Record Type: Journal Article
• Authors: Baratti, Roberto; Tronci, Stefania; Schaum, Alexander; Alvarez, Jesus
• Is Part Of: Journal of process control. Volume 66(2018)
• Page Start: 108
• Page End: 121
• Publication Date: 2018-06
• Subjects: Stochastic system dynamics -- Multiplicative noise -- Fokker-Planck equation -- Stochastic metastability -- Stabilizing robust control of nonlinear uncertain systems; Process control -- Periodicals; Fabrication -- Contrôle -- Périodiques; Process control; Periodicals; Electronic journals; 660.281
• DOI: 10.1016/j.jprocont.2018.03.004
• Languages: English
• ISSNs: 0959-1524

Abstract

Abstract: The open and closed-loop global state probability density function behavior of a class of single-state nonlinear chemical processes subjected to additive and multiplicative white noises is characterized with analytic formulae through Fokker Planck (FP) theory, in terms of: (i) stationary state probability density function (PDF), (ii) PDF evolution along deterministic, diffusion, and escape time scales, (iii) conditions for PDF metastability along escape time scale, and (iv) dependency of PDF motion on deterministic dynamics. Comparing with noise additivity, multiplicativeness can yield similar or substantially different open-loop PDF evolution behavior. The application of control to an open-loop (possibly fragile and metastable) multimodal PDF yields a closed-loop robust monomodal PDF with mode regulation capability. The developments and findings are illustrated with numerical simulations of FP's PDE equation.