Restricted feedback control in discrete-time dynamical systems with memory.
When an equilibrium state of a physical or biological system suffers a loss of stability (e.g., via a bifurcation), it may be both possible and desirable to stabilize the equilibrium via closed-loop feedback control. Significant effort has been devoted towards using such control to prevent oscillatory or chaotic behavior in dynamical systems, both continuous-time and discrete-time. Regarding control in discrete-time systems, most prior attempts to stabilize unstable equilibria require that the system be perturbed once during each time step. However, there are examples of systems for which this is neither feasible nor possible. In this paper, we analyze a restricted feedback control method for discrete-time systems (restricted in the sense that the controller's perturbations may be applied only in every other time step). We apply our theoretical analysis to a specific example from cardiac electrophysiology in which this sort of restricted feedback control is especially relevant. The example is a useful test case for the theory, and one for which an experimental setup is rather straightforward.
Department of Mathematics and Computer Science, University of Richmond, 28 Westhampton Way, Richmond, Virginia 23173, USA.
Kathryn G
KG
Workman
Department of Mathematics and Computer Science, University of Richmond, 28 Westhampton Way, Richmond, Virginia 23173, USA.
Shuang
S
Zhao
Department of Mathematics and Computer Science, University of Richmond, 28 Westhampton Way, Richmond, Virginia 23173, USA and Department of Mathematics, Harvard University, One Oxford Street, Cambridge, Massachusetts 02138, USA.
John W
JW
Cain
D000200:Action Potentials / Q000502:physiology*; D000818:Animals; D003198:Computer Simulation; D025461:Feedback, Physiological / Q000502:physiology*; D006329:Heart Conduction System / Q000502:physiology*; D006339:Heart Rate / Q000502:physiology*; D006801:Humans; D008955:Models, Cardiovascular