Universal adaptive control strategies for stochastic nonlinear time-delay systems with odd rational powers

Abstract

This paper studies the universal adaptive control for a class of stochastic nonlinear time-delay systems, which involve odd rational powers, multiple time-varying delays and parameter uncertainties. Since many new obstacles that have not been encountered should be carefully dealt with, the adaptive control problem remains challenging. A universal controller which employs the dynamic gain and the adaptive control strategy is firstly constructed to ensure that all signals of the closed-loop systems are bounded almost surely and the states of the considered systems converge to the origin almost surely. By proposing an extended method, another universal adaptive controller which removes the dynamic gain and reduces the order of the controller is also designed. A single-link robot system is considered to verify the effectiveness of the developed theory.