无需自适应调节,实现高阶非线性系统输出反馈控制
Nonadaptive Learning in Robust Nonlinear Output Regulation

- 用输入驱动滤波器+通用内模+递归反步法设计控制律
- 在标准假设下实现全局渐近调节,可验证增益选择条件
- 适合动态复杂或部分未知的系统,不依赖李雅普诺夫函数构造
本文研究具有任意高相对阶的广义非线性系统在输出反馈设置下的鲁棒非自适应调节问题。提出一种结合输入驱动滤波器与通用内模的非自适应设计,并采用递归反步法,将调节问题转化为增广误差系统的鲁棒输入-状态稳定化问题。与自适应方法不同,该方法不依赖线性参数化回归器,也不要求构造仅具非正导数的李雅普诺夫函数。在标准外系统假设(包括纯虚且单重特征值)及内部动力学满足最小相位输入-状态稳定性条件下,建立了全局渐近调节性,并给出了可显式验证的设计增益选择不等式。所提非自适应框架即使在被控系统动态复杂或仅部分已知时,也能保证估计误差和跟踪误差收敛。理论结果通过基准的Duffing系统控制案例得到验证。
原文摘要 · Abstract (English)
This paper considers robust nonadaptive regulation for general nonlinear systems in an output-feedback setting with arbitrarily high relative degree. We develop a nonadaptive design that combines an input-driven filter and a generic internal model with a recursive backstepping law, thereby recasting the regulation problem as the robust input-to-state stabilization of an augmented error system. Unlike adaptive schemes, the proposed method does not rely on linearly parameterized regressors and does not require the construction of Lyapunov functions having merely nonpositive derivatives. Under standard assumptions on the exosystem, including purely imaginary and simple eigenvalues, together with a minimum-phase input-to-state stability condition on the internal dynamics, we establish global asymptotic regulation and derive explicit, verifiable inequalities for selecting the design gains. The resulting nonadaptive framework guarantees convergence of the estimation and tracking errors even when the controlled-system dynamics are complex or only partially known. The effectiveness of the theoretical results is demonstrated using a benchmark controlled Duffing system.
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