Stabilization of bilateral teleoperators with asymmetric stochastic delay

摘要

In this paper we consider the problem of position tracking and error boundedness for a master-slave teleoperation system when the communication channel is characterized by a time-varying stochastic delay. In particular, we assume the delay to be a time-varying Markov regime switching process. Our solution is based on a suitable proportional-derivative (PD) like controller. Exploiting a Lyapunov- Krasovskii functional approach, we are able to show that the velocity and position errors remain bounded, provided specific inequality is satisfied. Moreover, zero steady-state position error is achieved when the human operator and the environment do not interact with the system. In order to be able to exploit Lyapunov-Krasovskii approach we need to lift the underlying process to an infinite-dimensional process taking values in a suitable Banach space so that, in the new space, the process is a Markov process. Our conditions for guaranteeing boundedness and the zero steady-state position tracking error are the natural generalization of the deterministic counterparts available in the literature, i.e. when considering the trivial case of a single-state Markov process previous results are recovered. Simulation results show the effectiveness of the proposed approach. (C) 2020 Elsevier B.V. All rights reserved.