一类具有时变状态约束的非线性系统的渐近跟踪控制

Asymptotic tracking control for a class of nonlinear systems with time-varying state constraints

摘要

为研究一类具有时变状态约束、参数不确定性及外部扰动的非线性系统渐近跟踪控制问题,文章通过状态变换将时变状态约束问题转化为新变量的有界性问题———只要变换后的状态有界,即可确保原系统状态始终处于预设约束范围内。与障碍李雅普诺夫函数(barrier Lyapunov function,BLF)方法相比,该状态变换方法可避免对虚拟误差的可行性检测,拓宽了适用范围,同时构造一种新的指数型Lyapunov函数,只要该函数有界,即可证明误差变量收敛于零,实现系统渐近跟踪,改进现有文献利用传统Lyapunov函数只能实现跟踪误差收敛至零点小邻域的弊端。针对系统存在的参数不确定性与外部扰动,设计调节函数及扰动自适应律,确保系统达到预定控制目标,并通过仿真算例验证所提控制方案的有效性。

Abstract

This study investigates the asymptotic tracking control problem for a class of nonlinear systems with time-varying state constraints, parameter uncertainties and external disturbances. By employing a state transformation, the time-varying state constraint problem is converted into a boundedness problem of transformed variables, such that bounded transformed states guarantee that the original system states remain within the prescribed constraint region. Compared with the barrier Lyapunov function (BLF) approach, the proposed state transformation method eliminates the need for the feasibility verification of virtual errors, thereby broadening its applicability. In addition, a novel exponential Lyapunov function is constructed, through which asymptotic convergence of the tracking error to zero can be guaranteed once the function remains bounded, so as to realize the asymptotic tracking of the system. This improves the drawbacks of using traditional Lyapunov functions in existing literature, which can only achieve tracking error convergence to a small neighborhood around zero. Aiming at parameter uncertainties and external disturbances in the system, a regulating function and adaptive disturbance law are designed to achieve the predetermined control objectives of the system. The effectiveness of the proposed control scheme is verified through simulation examples.

关键词

渐近跟踪 / 状态变换 / 时变状态约束 / Lyapunov函数

Key words

asymptotic tracking / state transformation / time-varying state constraints / Lyapunov function

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基金资助

山东省自然科学基金项目(ZR2023MF055)

山东省自然科学基金项目(ZR2021MF061)

山东省自然科学基金项目(ZR2021MF009)

山东省自然科学基金项目(ZR2020QA036)

山东—以色列科技合作项目(2023KJHZ005)

济南市“新高校20条”引进科技创新团队项目(2021GXRC064)