Adaptive tracking control of high-order nonlinear systems under asymmetric output constraint

Abstract

This paper addresses the tracking control problem of a class of high-order uncertain nonlinear systems under time-varying asymmetric output constraints. Most relevant results in the literature have two main restrictions: R1) some constraints need to be imposed on powers and growth conditions have to be established for the nonlinear functions of the system; R2) nonlinear bounding functions must be derived based on repeated derivations of virtual control variables during the design process. By integrating an improved technique of adding a power integrator with a dynamic surface control (DSC) method, we develop a systematic tracking control scheme that eliminates both of the above restrictions. Moreover, with an improved time-varying nonlinear transformed function introduced for high-order systems, the proposed scheme can be regarded as a unified tool in the sense that it works no matter whether the constraint is symmetric, asymmetric, or even without a constraint. The above results are also extended to systems with uncertain gain functions, and the proposed scheme estimates only one adaptive parameter. The simulation results of two deterministic practical applications show that the proposed control scheme is effective not only for high-order systems, but also for high-order-free systems.