Feedback control for biomechanical systems in the presence of asynchronous sampling based on high-gain observers

In this paper, the problem of designing an asynchronous sampling observer and controller for the biomechanical nonlinear systems is investigated. The central nervous system controls biomechanical limb movements through complex neurophysiological mechanisms. The state sampling input observation obtained by the proprioceptor exhibits asynchronous phenomena when transmitted to the central nervous system. The observation information about parts of the body suffers unmodeled dynamics and nonlinear dynamics in transmissions to the central nervous system. Firstly, unmodeled dynamics are introduced to a class of biomechanical hybrid systems, which can be mitigated by increasing the gain of the observer. The high-gain observer designed can solve the problem of obtaining the state information of various parts of the human body and analyze the stability of the error system. Then, the asynchronous sampling controller is structured to realize the nervous system feedback control based on the high-gain observer. Sufficient conditions for the existence of controllers for observer-based sampled data in discrete time are obtained by using the Lyapunov functions and separation principle. Finally, the effectiveness of the method is illustrated by a numerical example.