Nonlinear Optimal Control for a Cells Signaling Pathway Model Under Time-Delays

Abstract

A nonlinear optimal control method is proposed for a cells signaling pathway model (JAK-STAT) that exhibits time-delays. The purpose of this model is to demonstrate the cells signaling pathway. Actually the model shows the variation of the concentration of phosphorylated STAT5 kinases, and is driven by the levels of the Erythropoietin at the cells' membrane. By raising the concentration of such kinases, the transcription of the cells' DNA is activated. The dynamic model of the cells signaling pathway is subjected to approximate linearization around a temporary equilibrium which is recomputed at each iteration of the control method. In this linearization procedure, the Jacobian matrices of the state-space model have to be computed. Moroever, an H-infinity (optimal) feedback controller is designed for the linearized equivalent model of the system. Additionally, the controller's feedback gains are computed by repetitively solving an algebraic Riccati equation, at each time-step of the control method. Finally, Lyapunov analysis is used to prove the global stability properties of the control scheme.