AI 中文总结
本文针对非线性系统提出渐近行为分配问题，通过引入同步检测信号将其简化为标准镇定问题，以隧道二极管电路和摆的频率匹配为例验证了该框架可避免人为选择特定稳态。
AI 中文摘要
本文针对非线性系统引入渐近行为分配问题。给定一个受控系统和一个具有“开放”输入的参考系统，目标是设计一个调节器，使得对于每个容许输入，闭环系统的渐近输入-输出行为能够复现参考系统的行为。该公式将经典模型匹配、干扰抑制以及主从同步作为特殊情况包含在内，但不假设存在显式的跟踪或调节误差用于反馈。受非线性输出调节的启发，我们讨论了当闭环动力学非自治时，自治系统的稳态概念必须如何调整。在SISO正则形式的设定下，我们通过引入同步检测信号，为行为分配问题的解设计了充分条件，该信号收敛至零等价于成功的行为分配，从而将该问题简化为标准的镇定问题。两个例子，一个具有多个依赖输入平衡点的隧道二极管电路，以及一个摆的频率匹配问题，说明了所提出的框架如何避免人为选择特定的稳态。
英文摘要
This paper introduces the asymptotic behavior assignment problem for nonlinear systems. Given a controlled system and a reference system with an ``open'' input, the goal is to design a regulator such that, for every admissible input, the asymptotic input-output behavior of the closed-loop system reproduces that of the reference. This formulation captures, as special cases, classical model matching, disturbance rejection, and master-slave synchronization, but does not assume that an explicit tracking or regulation error is available for feedback. Motivated by nonlinear output regulation, we discuss how steady-state concepts for autonomous systems must be adapted when the closed-loop dynamics is not autonomous. In a SISO normal-form setting we devise sufficient conditions for the solution of the behavior assignment problem by introducing a synchrony-detection signal whose convergence to zero is equivalent to successful behavior assignment, thereby reducing the problem to a standard stabilization one. Two examples, a tunnel-diode circuit with multiple input-dependent equilibria, and a pendulum frequency-matching problem, illustrate how the proposed framework avoids artificially selecting a specific steady state.
CommentsAccepted for presentation at the 23rd IFAC World Congress 2026
