Adaptive finite-time prescribed performance control for stochastic nonlinear systems with unknown virtual control coefficients

This paper is devoted to the adaptive finite-time prescribed performance control (FTPPC) for stochastic nonlinear systems with unknown virtual control coefficients (UVCCs), which are functions of system states. To eliminate the condition that the initial value of the performance function (PF) is bigger than the initial tracking error, a novel smooth shifting function, for the first time, is defined and embedded in FTPPC for the tracking error. New control laws are firstly proposed and employed to deal with UVCCs in the controller design, which are different from the Nussbaum gain technology in the existing papers. An adaptive FTPPC strategy is designed so that all of the signals in the closed-loop system are bounded in probability and the tracking error is restrained in a fixed bound after a preset finite time,even that the PF is smaller than the tracking error at the initial time instant.