Control of continuous dynamical systems modeling physiological states

Abstract

• The predictive control to remove periodic orbits and higher order orbits when the dynamic evolves in a continuous time. • The generalization to continuous-time systems of the results obtained on the suppression of periodic dynamics in multidimensional nonlinear discrete-time systems. • The control of some undesirable physiological states in the brain as well as in the heart. • The simulation results are based on the Rossler and the FitzHugh-Nagumo models. The aim of this work is a generalization to continuous dynamical systems of the results obtained for nonlinear discrete dynamical systems, i.e. the suppression of stable periodic dynamics, especially those corresponding to certain undesirable physiological states in the brain as well as in the heart. In most cases, complex pathologies are modeled by nonlinear dynamical systems with chaotic behavior and some pathological states correspond to periodic behaviors. We propose a new strategy using predictive control to suppress periodic and higher-order orbits when the dynamics evolves in continuous time. The feasibility and efficiency of our approach is illustrated using two models, the Rössler and FitzHugh-Nagumo models.