Zhang-Gradient Controllers for Tracking Control of Multiple-Integrator Systems

Abstract

In this paper, the tracking-control problem of multiple-integrator (MI) systems is considered and investigated by combining Zhang dynamics (ZD) and gradient dynamics (GD). Several novel types of Zhang-gradient (ZG) controllers are proposed for the tracking control of MI systems (e.g., triple-integrator (TI) systems). As an example, the design processes of ZG controllers for TI systems with a linear output function (LOF) and/or a nonlinear output function (NOF) are presented. Besides, the corresponding theoretical analyses are elaborately given to guarantee the convergence performance of both z3g0 controllers (ZG controllers obtained by utilizing the ZD method thrice) and z3g1 controllers (ZG controllers obtained by utilizing the ZD method thrice and the GD method once) for TI systems. Numerical simulations concerning the tracking control of MI systems with different types of output functions are further performed to substantiate the feasibility and effectiveness of ZG controllers for tracking-control problems solving. Besides, comparative simulation results of the tracking control for MI systems with NOFs (e.g., y=cos(x1), y=x12+x22) substantiate that controllers of zmg1 type can resolve the singularity problem effectively with m being the times of using the ZD method.