标题： 具有非渐近保证的解析非线性 dynamical 系统识别 显示英文标题

标题： Identification of Analytic Nonlinear Dynamical Systems with Non-asymptotic Guarantees

摘要： 本文聚焦于一类重要的非线性系统：线性参数化的非线性系统，该类系统在机器人技术和其它机械系统中具有广泛应用。 我们考虑两种系统辨识方法：最小二乘估计（LSE），这是一种点估计方法；以及集员估计（SME），它估计一个包含真实参数的不确定性集合。 我们在独立同分布（i.i.d.）控制输入和具有独立同分布随机扰动的控制策略下，为LSE和SME提供了非渐近收敛率，这两种输入都被视为非主动探索输入。 与文献中基于分段仿射系统的反例相比，在我们的设定中非主动探索的成功依赖于系统动力学的一个关键假设：我们要求系统函数是实解析的。 我们的结果，连同分段仿射反例，揭示了非主动探索在非线性系统辨识中可微性的重要性。 最后，我们在摆锤系统和四旋翼系统的例子上，通过数值比较了我们的理论界与LSE和SME的经验性能。 显示英文摘要

摘要： This paper focuses on the system identification of an important class of nonlinear systems: linearly parameterized nonlinear systems, which enjoys wide applications in robotics and other mechanical systems. We consider two system identification methods: least-squares estimation (LSE), which is a point estimation method; and set-membership estimation (SME), which estimates an uncertainty set that contains the true parameters. We provide non-asymptotic convergence rates for LSE and SME under i.i.d. control inputs and control policies with i.i.d. random perturbations, both of which are considered as non-active-exploration inputs. Compared with the counter-example based on piecewise-affine systems in the literature, the success of non-active exploration in our setting relies on a key assumption on the system dynamics: we require the system functions to be real-analytic. Our results, together with the piecewise-affine counter-example, reveal the importance of differentiability in nonlinear system identification through non-active exploration. Lastly, we numerically compare our theoretical bounds with the empirical performance of LSE and SME on a pendulum example and a quadrotor example.