An adaptive dynamic surface control strategy for suppressing pathological oscillations in a neural mass model

Pathological oscillations that have a frequency in the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi>β</mml:mi> </mml:mrow> </mml:math> band are widely recognized to be involved in Parkinson’s disease. Now, we present an adaptive dynamic surface control strategy for suppressing pathological oscillations that exist in the Parkinsonian state. First, the interactions between the subthalamic nucleus and external globus pallidus are fully considered and establish a neural mass model of Parkinson’s disease. Next, by reasonable state transformation, suppressing pathological oscillations can be converted into a tracking control study of a pure-feedback nonlinear system. Moreover, the dynamic surface control technique adopted reduces the dimensionality of the neural network input and effectively eliminates the complexity explosion problem commonly associated with existing methods. By Lyapunov stability analysis, it can be obtained that all the signals of the resulting closed-loop system are bounded, and the tracking error converges to a small neighborhood of zero. Finally, the simulation results demonstrate the effectiveness of the designed control strategy. This work may provide an effective approach to closed-loop deep brain stimulation optimization for the alleviation of the Parkinsonian state.