Stability guaranteed backstepping control of nonlinear uncertain systems using time delay estimation and nonlinear damping

Abstract

Time delay estimation (TDE) has been verified as a simple and robust technique for the control of nonlinear uncertain systems. However, the artificial time delay introduced by TDE makes the stability analysis extremely difficult, since the closed-loop dynamics becomes a nonlinear neutral-type time delay system (NTDS) with uncertainties which belongs to a class of most challenging dynamics in the control field.

In order to overcome this barrier regarding stability, we propose a remedy: a nonlinear damping component incorporated with a backstepping design. The time delayed terms introduced by TDE are treated as uncertainties and counteracted by the nonlinear damping. Through a rigorous stability analysis based on a Lyapunov-Krasovskii functional, it is proved that the tracking error of the closed-loop system due to the proposed control is globally uniformly ultimately bounded.

As a result, there are two stability guaranteed controllers proposed in this dissertation. The first controller is proposed for a general class of nonlinear uncertain systems. The effect of the nonlinear damping on the closed-loop dynamics is particularly examined. It is noteworthy that, with a nonlinear damping component (which includes time delayed terms) in the proposed control, the nonlinear NTDS discussed above is theoretically stabilized. The practicability of the proposed control is verified through simulation studies.

The second controller is specifically designed for robot manipulators, which are the major applications of TDE in the literature. This specific design focuses the estimation error, so called TDE error, which inherently exists and critically affects both the closed-loop stability and control performance. The idea is a combination of a nonlinear damping component and a novel fast-convergent error dynamics. The nonlinear damping incorporated with a backstepping design is adopted for counteracting the TDE error and ensuring the closed-loop stability. The fast-converge...