Abstract
Deep brain stimulation (DBS) has become an effective therapeutic solution for Parkinson’s disease (PD). Adaptive closed-loop DBS can be used to minimize stimulation-induced side effects by automatically determining the stimulation parameters based on the PD dynamics. In this paper, by modeling the interaction between the neurons in populations of the thalamic, the network-level modulation of thalamic is represented in a standard canonical form as a multi-input multi-output (MIMO) nonlinear first-order system with uncertainty and external disturbances. A class of fast and robust MIMO adaptive fuzzy terminal sliding mode control (AFTSMC) has been presented for control of membrane potential of thalamic neuron populations through continuous adaptive DBS current applied to the thalamus. A fuzzy logic system (FLS) is used to estimate the unknown nonlinear dynamics of the model, and the weights of FLS are adjusted online to guarantee the convergence of FLS parameters to optimal values. The simulation results show that the proposed AFTSMC not only significantly produces lower tracking errors in comparison with the classical adaptive fuzzy sliding mode control (AFSMC), but also makes more robust and reliable outputs. The results suggest that the proposed AFTSMC provides a more robust and smooth control input which is highly desirable for hardware design and implementation.
Highlights
Deep brain stimulation (DBS) has become an effective therapeutic solution for Parkinson’s disease (PD)
Zhu et al proposed a robust control technique based on Sliding mode control (SMC) for control of membrane potential of a thalamic neuron in a thalamocortical computational model of basal ganglia (BG) network consisting of subthalamic nucleus (STN), GPe, internal segment of the globus pallidum (GPi), and TH6
To resolve all the above problems, in this paper, we present a fast adaptive fuzzy terminal sliding mode control (AFTSMC) to control the membrane potential of thalamic neuron populations in a BG–thalamic network model
Summary
To obtain the control input (DBS stimulation) using AFTSMC, the dynamics of thalamic neurons in (1) should be considered in the following canonical form: x(t) = f1(x, t) + F2(x, t) · u(t) + d(t),. If the tracking error of the PD model is considered as ei = xdi − xi , to implement AFTSMC the nonsingular continuous sliding surface is designed as follows:. Remark 3 The terms sig(s)ρ1 and sig(s)ρ2 in control law, and η in the sliding surface are considered as a bridge between classical adaptive fuzzy sliding mode control ( ρ1 → 1, ρ2 → 0, η → 1 ) and AFTSMC (1 < ρ1 < 3, 0 < ρ2 < 1, 1 < η < 2 ) These parameters should be adjusted appropriately to guarantee to reach the sliding manifold in finite time and continuous control input
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
