| The brain exhibits complex kinetic properties at different temporal and spatial scales that correlate with band-specific neural oscillatory activity,as well as with the functional state of the brain and the pathological state of many brain disorders.Studies have shown that brain functions such as cognition,behavior,and perception originate from collective neural oscillations in the cortical system,that collective nonlinear dynamics are central to cortical neural oscillations,and that abnormal dynamical processes can cause numerous brain diseases.Therefore,the ability to effectively control brain dynamics holds great promise for enhancing human cognitive functions and improving their quality of life.In this paper,we investigate the identification and control of brain dynamics based on the neural mass model,and the main research is as follows:(1)A parameter estimation problem for brain electrical signals that belong to a class of unknown physiological states and may undergo abrupt changes and are influenced by unknown noise is studied.A constrained strong tracking self-adaptive unscented Kalman filter method is proposed,which can accurately estimate the parameters of the simulated signals.It is used for inference and tracking of key physiological variables and to determine the current state of the brain based on these estimates.Compared with the traditional unscented Kalman filter,this method introduces gradient and forgetting factors to enhance the tracking ability of the algorithm.By combining a suboptimal Sage-Husa estimator,it can estimate and correct the measurement noise matrix in real-time.In addition,the sequential updating stage with two observations and constraints is employed to absorb constraints and observations,ensuring that the values of the parameters to be identified remain within a reasonable range that conforms to their physiological meaning.The effectiveness of the constrained strong tracking self-adaptive unscented Kalman filter method in parameter estimation is validated through numerical simulations.(2)The brain dynamical modulation problem for a single neural mass model representing the abnormal brain rhythm in pathological states is investigated.A state feedback control scheme based on constrained strong tracking self-adaptive unscented Kalman filter,local linearization,and traditional optimal controller design is designed to modulate the brain dynamical model simulated by the neural mass model,in order to suppress the generation of abnormal brain rhythms and make the model output closely track the desired output.The selection of the optimal controller aims to balance control energy and control error to make the modulation scheme more suitable for specific requirements.The effectiveness of the designed control scheme is verified through numerical simulations.(3)A problem in which the traditional optimal controller requires local linearization of the model and involves a large number of matrix computations is addressed.A bacteria foraging optimization algorithm-based optimal controller is proposed,which can obtain numerical solutions without the need for linearization processing.The effectiveness of the bacteria foraging optimization algorithm in obtaining optimal control inputs is validated through numerical simulations.Furthermore,a comparison with the traditional optimal controller is conducted,highlighting the advantages and disadvantages of the two types of optimal controllers.This study belongs to the field of computational neuroscience.Although the methods used to solve the problem are relatively traditional,their application in addressing critical issues in cutting-edge interdisciplinary fields such as computational neuroscience is novel. |
