鲁棒非线性输出调节中的非自适应学习
Nonadaptive Learning in Robust Nonlinear Output Regulation
- Lingnan University（岭南大学）
- Massachusetts Institute of Technology（麻省理工学院）
- Queen’s University（女王大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
针对相对阶任意高的输出反馈非线性系统，提出结合输入驱动滤波器、通用内模与递归反步律的非自适应调节方法，通过杜芬系统验证其可实现全局渐近调节及误差收敛。
AI中文摘要：
本文考虑在相对阶任意高的输出反馈设置下，一般非线性系统的鲁棒非自适应调节问题。我们开发了一种非自适应设计，将输入驱动滤波器、通用内模与递归反步律相结合，从而将调节问题重构为增广误差系统的鲁棒输入-状态稳定问题。与自适应方案不同，该方法不依赖线性参数化回归量，也不需要构造仅具有非正导数的李雅普诺夫函数。在对外系统的标准假设（包括纯虚单特征值）以及内动力学的最小相位输入-状态稳定条件下，我们建立了全局渐近调节，并推导了用于选择设计增益的显式可验证不等式。即使受控系统动力学复杂或仅部分已知，所得非自适应框架也能保证估计误差和跟踪误差收敛。通过基准受控杜芬（Duffing）系统验证了理论结果的有效性。
英文摘要：
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.
