面向具有非对称执行器约束的严格反馈非线性系统的保容许性控制

中文摘要 AI 辅助

本文开发了保容许性控制（Admissibility-Preserving Control, APC），这是一种以实现为中心的安全关键控制框架，适用于受非对称执行器极限、时变输出约束和执行器速率限制的严格反馈系统。APC表示整体控制架构，而保容许性输入实现（Admissibility-Preserving Input Realization, APIR）是其约束实现模块。其中，APIR动态生成物理被控对象输入，同时使规定的非对称执行器集向前不变。与代数限幅和后设计饱和补偿不同，执行器极限直接嵌入具有用户可选正则性和可解释调优参数的连续可微动态实现中。APIR通过将实现的被控对象输入视为附加状态，与递归反步方法集成。所得设计不要求未受控被控对象满足输入到状态稳定性假设，而是递归补偿非线性漂移项，且需满足期望运动、可用控制权限与APIR内部增益之间的显式相容性条件。该框架进一步通过平滑非对称对数障碍坐标及其相关李雅普诺夫函数扩展到时变输出安全跟踪，还通过级联APIR扩展到同时处理执行器幅值和速率约束。严格的李雅普诺夫和不变性分析确立了区域渐近跟踪、相容容许集的向前不变性以及所有闭环信号的有界性。数值研究展示了非对称执行器利用、输出安全保持以及幅值-速率约束的执行。

英文摘要

This paper develops Admissibility-Preserving Control (APC), a realization-centered safety-critical control framework for strict-feedback systems subject to asymmetric actuator limits, time-varying output constraints, and actuator-rate limitations. APC denotes the overall control architecture, whereas an Admissibility-Preserving Input Realization (APIR) denotes its constraint-realization module. Therein, the APIR dynamically generates the physical plant input while rendering its prescribed asymmetric actuator set forward invariant. In contrast to algebraic clipping and post-design saturation compensation, the actuator limits are embedded directly in a continuously differentiable dynamic realization with user-selectable regularity and interpretable tuning parameters. The APIR is integrated with recursive backstepping by treating the realized plant input as an additional state. The resulting design does not require an input-to-state stability assumption on the uncontrolled plant. Instead, the nonlinear drift terms are compensated recursively, subject to an explicit compatibility condition between the desired motion, the available control authority, and the APIR interior gain. The framework is further extended to time-varying output-safe tracking through a smooth asymmetric logarithmic barrier coordinate and its associated Lyapunov function and to simultaneous actuator-magnitude and rate constraints through a cascaded APIR. Rigorous Lyapunov and invariance analyses establish regional asymptotic tracking, forward invariance of the compatible admissible sets, and boundedness of all closed-loop signals. Numerical studies illustrate asymmetric actuator utilization, output-safety preservation, and magnitude-rate constraint enforcement.

发表机构

• Indian Institute of Technology Bombay（印度理工学院孟买分校）
• University of Cincinnati（辛辛那提大学）

机构由 AI 辅助整理，请以论文原文为准。