AI 中文总结
该研究针对设计满足性能规范且有输入约束的反馈控制器的难题，提出基于优化框架，利用状态轨迹数据联合学习性能漏斗及反馈控制器，不依赖控制输入数据，开发非凸合成程序并建立互补保证。
AI 中文摘要
设计满足预定义性能规范同时强制严格输入约束的反馈控制器是一项具有挑战性的任务。我们的工作基于这样的想法，即状态轨迹数据（例如从专家控制器获得）通常隐式编码可行的性能属性和输入限制。我们提出了一个基于优化的框架，利用状态轨迹数据联合学习：（i）一个模仿观察到的轨迹中编码的瞬态和稳态行为的性能漏斗，以及（ii）一个在严格输入约束下执行所学性能规范的反馈控制器。与模仿学习方法不同，该方法不依赖控制输入数据且不重建专家策略。相反，它通过将标称模型补偿与学习到的状态依赖反馈增益相结合来合成规定性能控制器。由此产生的合成问题是非凸的，我们为此开发了一种可行性驱动的活动集合成程序。最后，我们建立了两个互补的保证：一个基于半全局保守执行器权限的规定性能和输入满足证书，以及一个局部数据驱动证书，确保在足够密集的演示轨迹附近具有这些属性。
英文摘要
Designing feedback controllers that satisfy predefined performance specifications while enforcing hard input constraints is a challenging task. Our work is motivated by the idea that state trajectory data, e.g., obtained from an expert controller, often implicitly encode feasible performance attributes and input limitations. We propose an optimization-based framework that uses state trajectory data to jointly learn: (i) a performance funnel that mimics the transient and steady-state behavior encoded within the observed trajectories, and (ii) a feedback controller that enforces the learned performance specifications under hard input constraints. Unlike imitation learning methods, the proposed approach does not rely on control input data and does not reconstruct an expert policy. Instead, it synthesizes a prescribed performance controller by combining nominal model compensation with a learned state-dependent feedback gain. The resulting synthesis problem is nonconvex, for which we develop a feasibility-driven active-set synthesis procedure. Finally, we establish two complementary guarantees: a semi-global conservative actuator-authority-based certificate for prescribed performance and input satisfaction, and a local data-driven certificate ensuring these properties near sufficiently dense demonstrated trajectories.
