Research map / Probabilistic and scientific modeling / Dynamical systems
Identification of Analytic Nonlinear Dynamical Systems with Non-asymptotic Guarantees
Read the paperCheck your idea against 108,967 papers
AI-extracted summary. Written by AI from the paper's full text. Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.
Shows that least-squares and set-membership estimation with i.i.d. random (non-active) inputs and disturbances provably identify linearly parameterized nonlinear systems whose features are real-analytic, giving non-asymptotic rates of 1/sqrt(T) (LSE) and 1/T (SME diameter).
Problem
Non-active exploration (i.i.d. inputs and noise) is known to fail for linearly parameterized nonlinear systems with piecewise-affine features; it is unclear when i.i.d. random inputs suffice for identification of such systems with non-asymptotic guarantees.
Approach
Real-analytic feature functions cannot vanish on positive-measure sets, so combined with semi-continuous bounded noise, any direction of the feature vector has non-vanishing probability of being large; this establishes a block-martingale small-ball (BMSB) condition that gives LSE and SME convergence rates under i.i.d. inputs.
Key results
- Empirical LSE error decays as O(1/sqrt(T)) on pendulum and quadrotor with uniform and truncated-Gaussian noise, consistent with the theoretical rate.
- Empirical SME diameter decays as O(1/T) on pendulum and quadrotor, consistent with the corollary.
- Theory shows non-active i.i.d. exploration suffices for real-analytic linearly parameterized systems, contrasting with the piecewise-affine counter-example.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use non-active i.i.d. inputs and disturbances with real-analytic feature functions | LSE for linearly parameterized nonlinear systems · Pendulum and quadrotor | LSE estimation error rate: O(1/√T) | Helped |
| Use non-active i.i.d. inputs and disturbances with real-analytic feature functions | SME for linearly parameterized nonlinear systems · Pendulum and quadrotor | SME uncertainty-set diameter rate: O(1/T) | Helped |
| Use real-analytic feature functions rather than general non-smooth feature functions | Non-active exploration for nonlinear system identification · Linearly parameterized nonlinear systems | identification under non-active exploration | Helped |
Limitations
- Assumes bounded, semi-continuous noise and inputs, which excludes discrete distributions.
- Constants s_phi and p_phi are shown to exist but not given explicit formulas; they are estimated numerically.
- Imperfect (noisy) state observations are not considered.
Experimental setup
Datasets: simulated pendulum trajectories simulated quadrotor trajectories
Benchmarks: pendulum simulation quadrotor simulation
Metrics: parameter estimation error (normalized l2) SME uncertainty set diameter
Baselines: piecewise-affine counter-example
Builds on: block-martingale small-ball condition (Simchowitz et al.) Paley-Zygmund inequality least-squares estimation meta-theorem for linear systems set-membership estimation for linear regression
Closest papers by meaning
- Learning the Uncertainty Sets of Linear Control Systems via Set Membership: A Non-asymptotic Analysis (ICML 2024 · similarity 0.88)
- Robust System Identification: Finite-sample Guarantees and Connection to Regularization (ICLR 2025 · similarity 0.88)
- Finite Sample Analyses for Continuous-time Linear Systems: System Identification and Online Control (NeurIPS 2025 · similarity 0.85)
- Analytical Lyapunov Function Discovery: An RL-based Generative Approach (ICML 2025 · similarity 0.82)
- ASID: Active Exploration for System Identification in Robotic Manipulation (ICLR 2024 · similarity 0.82)
- Stability Analysis of Switched Linear Systems with Neural Lyapunov Functions (AAAI 2024 · similarity 0.81)
Writing a paper in this area? scime draft is a free LaTeX editor with AI included, real-time co-authors and a check of your references and venue rules before you submit. It also imports OpenAI Prism projects.