Catch prescribed performance control method with quantitative overshoot constraint

Abstract:

To address the constraint conflict issues in the prescribed performance tracking control of nonlinear systems and simultaneously impose more refined constraints on the system, this paper proposes a constrainted performance control method based on a novel variable barrier function. Firstly, the problem of constraint conflicts caused by uncertain initial states and sudden changes in the expected trajectory in the constraint control of nonlinear systems is analyzed, and a new asymmetric variable barrier function configuration is proposed. This configuration introduces an attraction function to the system, which can uniformly handle the two stages of constraint release and constraint recovery during the constraint conflict process, and enrich the setting form of the preset performance boundary, making the constraint control strategy simpler and more complete. Secondly, based on the designed novel asymmetric variable barrier function configuration, a set of new L-shaped preset performance boundary functions is designed. These performance boundary functions are inherently constraining, capable of imposing quantitative constraints on the overshoot of the system output, thereby more precisely confining the system behavior. Finally, the boundedness of the system error and the forward invariance are proved, and the uniform ultimate boundedness of all closed-loop signals is proved based on the Lyapunov stability theory. A quadrotor unmanned aerial vehicle system is selected for numerical simulation and experimental comparison. The final numerical simulation and experimental results verify the effectiveness and superiority of the proposed scheme. The designed attraction-preserving performance method in this paper can not only impose quantitative overshoot constraints on the system, but also solve the constraint conflict problems arising during the constraint process.