Global Adaptive Stabilization of Neural Mass Models via Constructive Lyapunov Design
الشريط الجانبي للمقالة
محتوى المقالة الرئيسي
الملخص
This paper presents the design, implementation, and simulation of a Lyapunov-based adaptive closed-loop control system for stabilizing nonlinear brain dynamics represented by a Single Neural Mass Model (NMM). The model describes the collective electrical behavior of interconnected neuronal populations and is used to mimic pathological conditions such as epileptic oscillations and Parkinsonian tremor. The proposed controller dynamically estimates and adjusts uncertain parameters in real time using a Lyapunov-guided adaptive law, ensuring stable tracking of a healthy neural rhythm despite parameter drift and external disturbances. The control framework combines Model Reference Adaptive Control (MRAC) with Sliding-Mode robustness, implemented and validated in MATLAB/Simulink with Stateflow for logic-based switching and adaptive rule management. Simulation results across multiple test scenarios demonstrate that the adaptive controller achieves fast convergence, minimal steady-state error, and strong disturbance rejection. Compared to traditional fixed-gain schemes, the proposed design reduces control energy by approximately 45% while maintaining global Lyapunov stability. Overall, this framework provides a mathematically rigorous and biologically interpretable foundation for the next generation of closed-loop neuromodulation systems, offering potential for real-time stabilization of pathological neural activity in disorders such as epilepsy and Parkinson’s disease.
تفاصيل المقالة
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