# Identification of Analytic Nonlinear Dynamical Systems with Non-asymptotic Guarantees

arXiv: https://arxiv.org/abs/2411.00656 · HTML: https://mlsanity.com/paper/2411.00656/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Nov 2024.

## Built on by (most cited first, 7 of 7)

- [Finite Sample Identification of Partially Observed Bilinear Dynamical Systems](https://mlsanity.com/paper/2501.07652/) (2025)
- [Federated Nonlinear System Identification](https://mlsanity.com/paper/2508.15025/) (2025)
- [Non-Asymptotic Bounds for Closed-Loop Identification of Sub-Exponentially Growing Nonlinear Stochastic Systems](https://mlsanity.com/paper/2412.04157/) (2024)
- [Logarithmic Regret for Nonlinear Control](https://mlsanity.com/paper/2501.10261/) (2025)
- [Achieving widetildeO(1/ε) Sample Complexity for Bilinear Systems Identification under Bounded Noises](https://mlsanity.com/paper/2603.20819/) (2026)
- [On Uniform Error Bounds for Kernel Regression under Non-Gaussian Noise](https://mlsanity.com/paper/2605.09757/) (2026)
- [Set Membership Estimation for Stochastic Linear Contextual Bandits](https://mlsanity.com/paper/2606.20022/) (2026)

## Abstract (arXiv)

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.