In this chapter we extend the application of robust controllers for the synchronization of three benchmark models of biochemical oscillators: (i) Goodwin model of genetic oscillations (Goodwin, 1965), (ii) FitzHugh-Nagumo model of neurons (FitzHugh, 1961); and (iii) a model of circadian rhythms in Drosphila (Goldbeter, 1996). We introduce three robust control approaches for the synchronization of biochemical oscillators: (i) A modeling error compensation approach (Alvarez-Ramirez, 1999), (ii) integral sliding mode control (Levant, 2001), and (iii) geometric linearizing control (Alvarez-Ramirez, 1999; Hangos et al., 2004). The proposed controllers have two nice features for biological applications: (i) robustness against model uncertainties, and (ii) simplicity in the resulting controller.We show how a certain class of cellular processes can be dynamically synchronized by appropriate input signals.
- biochemical oscillations,
- robust control
Available at: http://works.bepress.com/hector_puebla/23/