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This paper introduces a novel optimization-based approach for parametric nonlinear system identification. Building upon the prediction error method framework, traditionally used for linear system identification, we extend its capabilities…
Neural networks have demonstrated remarkable success in modeling nonlinear dynamical systems. However, identifying these systems from closed-loop experimental data remains a challenge due to the correlations induced by the feedback loop.…
Learning from examples is one of the key problems in science and engineering. It deals with function reconstruction from a finite set of direct and noisy samples. Regularization in reproducing kernel Hilbert spaces (RKHSs) is widely used to…
In this paper, we study the stabilization problem for the Ito systems with both multiplicative noise and multiple delays which exist widely in applications such as networked control systems. Sufficient and necessary conditions are obtained…
We prove that the ordinary least-squares (OLS) estimator attains nearly minimax optimal performance for the identification of linear dynamical systems from a single observed trajectory. Our upper bound relies on a generalization of…
The demand for faster protection algorithms is growing due to the increasingly faster dynamics in the system. The majority of existing algorithms require empirically selected set-points, which may reduce sensitivity to internal faults and…
Production cost minimization (PCM) simulation is commonly employed for assessing the operational efficiency, economic viability, and reliability, providing valuable insights for power system planning and operations. However, solving a PCM…
Accurate modeling of nonlinear systems is essential for reliable control, yet conventional identification methods often struggle to capture latent dynamics while maintaining stability. We propose a \textit{stable-by-design LPV neural…
In this paper, the reinforcement learning (RL)-based optimal control problem is studied for multiplicative-noise systems, where input delay is involved and partial system dynamics is unknown. To solve a variant of Riccati-ZXL equations,…
Learning stable dynamical systems from data is crucial for safe and reliable robot motion planning and control. However, extending stability guarantees to trajectories defined on Riemannian manifolds poses significant challenges due to the…
We propose a stochastic variance-reduced cubic regularized Newton algorithm to optimize the finite-sum problem over a Riemannian submanifold of the Euclidean space. The proposed algorithm requires a full gradient and Hessian update at the…
Riemannian optimization has drawn a lot of attention due to its wide applications in practice. Riemannian stochastic first-order algorithms have been studied in the literature to solve large-scale machine learning problems over Riemannian…
Linearized numerical stability bounds for solving the nonlinear time-dependent Schr\"odinger equation (NLSE) using explicit finite-differencing are shown. The bounds are computed for the fourth-order Runge-Kutta scheme in time and both…
We provide the first known algorithm that provably achieves $\varepsilon$-optimality within $\widetilde{\mathcal{O}}(1/\varepsilon)$ function evaluations for the discounted discrete-time LQR problem with unknown parameters, without relying…
This work addresses the problem of risk-sensitive control for nonlinear systems with imperfect state observations, extending results for the linear case. In particular, we derive an algorithm that can compute local solutions with…
A linear-quadratic (LQ, for short) optimal control problem is considered for mean-field stochastic differential equations with constant coefficients in an infinite horizon. The stabilizability of the control system is studied followed by…
Self-sustained oscillations are ubiquitous in nature and engineering. In this paper, we propose a novel output-only system-identification framework for identifying the system parameters of a self-sustained oscillator affected by Gaussian…
Linear Quadratic Regulator (LQR) is often combined with feedback linearization (FBL) for nonlinear systems that have the nonlinearity additive to the input. Conventional approaches estimate and cancel the nonlinearity based on the first…
This paper investigates the adaptive identification and prediction problems for stochastic dynamical systems with saturated observations, which arise from various fields in engineering and social systems, but up to now still lack…
We study the fundamental problem of learning a marginally stable unknown nonlinear dynamical system. We describe an algorithm for this problem, based on the technique of spectral filtering, which learns a mapping from past observations to…