Nonlinear Control of Synaptic Plasticity Model for Constraining Bursting Activity in Epileptic Seizures

In this paper, we address the problem of controlling the synaptic plasticity to constraint bursting activity in epileptic seizures by a direct drug injection. With a good understanding of dynamical changes in seizures onset and the mechanisms that cause these changes, we design a control based on a model of interaction between synaptic strength and the intracellular calcium concentration [Ca²⁺]_i. By exploring the dynamic properties of the system, the original system is first regrouped into two subsystems, the first one is a self-stable system; and the second one is a second order system in strict feedback form. Then, nonlinear control for the second subsystem is presented through backstepping design. The closed-loop system is shown to be globally stable. Simulation studies are conducted to show the effectiveness of the control for stopping the bursting activity in brain with epilepsy.