Pathological basal ganglia oscillations with time delays: a memoryless feedback control strategy

Pathological basal ganglia oscillations are associated with the hypokinetic motor symptoms of Parkinson’s disease. In this paper, a memoryless feedback control strategy is proposed to suppress pathological oscillations in the basal ganglia. In the most of closed-loop control strategies, the excitatory subthalamic nucleus populations are both monitored and stimulated targets, neglecting the important contribution of the external globus pallidus populations in suppressing pathological oscillations. To this end, we transform the original model into a time-delay system with a lower-triangular structure, and construct a memoryless state feedback controller utilizing the gain scaling method. It is proved by the Lyapunov–Krasovskii functional method that all the signals of the resulting closed-loop system are bounded, and the system states converge to an adjustable region of the origin. In addition, the input delay in stimulating the target is considered and a corresponding controller is designed to achieve convergence of the states in the resulting closed-loop system with both state delays and input delay. Moreover, simulation tests are conducted to explore the performance of the control strategy. This paper further explores the intrinsic dynamics in the neural system, and provides an effective strategy for closed-loop deep brain stimulation control.