Online Learning for Nonlinear Dynamical Systems without the I.I.D. Condition
This paper investigates online identification and prediction for nonlinear stochastic dynamical systems. In contrast to offline learning methods, we develop online algorithms that learn unknown parameters from a single trajectory. A key challenge in this setting is handling the non-independent data generated by the closed-loop system. Existing theoretical guarantees for such systems are mostly restricted to the assumption that inputs are independently and identically distributed (i.i.d.), or that the closed-loop data satisfy a persistent excitation (PE) condition. However, these assumptions are often violated in applications such as adaptive feedback control. In this paper, we propose an online projected Newton-type algorithm for parameter estimation in nonlinear stochastic dynamical systems, and develop an online predictor for system outputs based on online parameter estimates. By using both the stochastic Lyapunov function and martingale estimation methods, we demonstrate that the average regret converges to zero without requiring traditional persistent excitation (PE) conditions. Furthermore, we establish a novel excitation condition that ensures global convergence of the online parameter estimates. The proposed excitation condition is applicable to a broader class of system trajectories, including those violating the PE condition.
Code (0)
등록된 구현이 없습니다.
Tasks
parameter estimationSimilar Papers 제목 키워드 기반
Observability of Nonlinear Dynamical Systems over Finite Fields
This paper discusses the observability of nonlinear Dynamical Systems over Finite Fields (DSFF) through the Koopman operator framework. In this work, given a nonlinear DSFF, we construct a linear system of the smallest d…
Denoising Diffusion-Based Control of Nonlinear Systems
We propose a novel approach based on Denoising Diffusion Probabilistic Models (DDPMs) to control nonlinear dynamical systems. DDPMs are the state-of-art of generative models that have achieved success in a wide variety o…
DenoisingA Sampling Theorem for Exact Identification of Continuous-time Nonlinear Dynamical Systems
Low sampling frequency challenges the exact identification of the continuous-time (CT) dynamical system from sampled data, even when its model is identifiable. The necessary and sufficient condition is proposed -- which …
LeARN: Learnable and Adaptive Representations for Nonlinear Dynamics in System Identification
System identification, the process of deriving mathematical models of dynamical systems from observed input-output data, has undergone a paradigm shift with the advent of learning-based methods. Addressing the intricate …
Meta-LearningLearning interpretable continuous-time models of latent stochastic dynamical systems
We develop an approach to learn an interpretable semi-parametric model of a latent continuous-time stochastic dynamical system, assuming noisy high-dimensional outputs sampled at uneven times. The dynamics are described …