带有定量超调约束的吸引预设性能控制方法

Catch prescribed performance control method with quantitative overshoot constraint

摘要:

为完善非线性系统预设性能跟踪控制过程中约束冲突问题的处理机制,并对系统施加更精细的约束,本文提出了一种基于新型可变障碍函数的性能约束控制方法。首先,对非线性系统约束控制中因初始状态不确定和期望轨迹突变导致的约束冲突问题进行分析,提出了一种新的非对称可变障碍函数构型。该构型为系统引入了吸引函数,能够统一处理约束冲突过程中的约束解除和约束恢复两个阶段,并能够丰富预设性能边界的设置形式,使得约束控制策略更加简单和完善。其次,基于设计的新型非对称可变障碍函数构型,设计一组新型L型预设性能边界函数。该组性能边界函数本身具有约束力,能够对系统输出的超调量施加定量约束,从而更精细地约束系统的行为。最后,对系统误差的有界性和前向不变性进行了证明,并基于Lyapunov函数稳定性理论证明所有闭环信号的一致最终有界性。选取四旋翼无人机系统进行数值仿真和实验对比,数值仿真和实验结果验证了所提方案的有效性和优越性。本文设计的吸引预设性能方法,能够在给系统施加定量超调约束的同时,解决约束过程中产生的约束冲突问题。

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.