论文标题
遗憾的是自适应非线性控制
Regret Bounds for Adaptive Nonlinear Control
论文作者
论文摘要
我们研究了受未经模型障碍的自适应控制已知离散时间非线性系统的问题。我们证明了自适应非线性控制的第一个有限时间的遗憾界限与随机环境中的不确定性相匹配，这表明，与对未建模的障碍的完美了解相比，由于确定性对等适应性控制遭受的遗憾是由$ \ widetilde {o}（O}（O}（\ sqrt {\ sqrt {t}））$。此外，我们表明，当输入受到$ k $ timeStep延迟的约束时，遗憾的降低到$ \ widetilde {o}（k \ sqrt {t}）$。我们的分析在非线性控制理论（Lyapunov稳定性和收缩理论）中的经典稳定性概念与在线凸优化的现代遗憾分析之间建立了联系。稳定理论的使用使我们能够分析具有挑战性的无限马单轨迹设置。
We study the problem of adaptively controlling a known discrete-time nonlinear system subject to unmodeled disturbances. We prove the first finite-time regret bounds for adaptive nonlinear control with matched uncertainty in the stochastic setting, showing that the regret suffered by certainty equivalence adaptive control, compared to an oracle controller with perfect knowledge of the unmodeled disturbances, is upper bounded by $\widetilde{O}(\sqrt{T})$ in expectation. Furthermore, we show that when the input is subject to a $k$ timestep delay, the regret degrades to $\widetilde{O}(k \sqrt{T})$. Our analysis draws connections between classical stability notions in nonlinear control theory (Lyapunov stability and contraction theory) and modern regret analysis from online convex optimization. The use of stability theory allows us to analyze the challenging infinite-horizon single trajectory setting.
