Related papers: Integral Equations & Model Reduction For Fast Comp…
In recent years, a new method for experimental nonlinear modal analysis has been developed, which is based on the extended periodic motion concept. The method is well suited to experimentally obtain amplitude-dependent modal properties…
We describe a method to model nonlinear dynamical systems using periodic solutions of delay-differential equations. We show that any finite-time trajectory of a nonlinear dynamical system can be loaded approximately into the initial…
Hybrid dynamical systems characterized by discrete switching of smooth dynamics have been used to model various rhythmic phenomena. However, the phase reduction theory, a fundamental framework for analyzing the synchronization of…
This paper introduces new techniques for using convex optimization to fit input-output data to a class of stable nonlinear dynamical models. We present an algorithm that guarantees consistent estimates of models in this class when a small…
A high-frequency recovered fully discrete low-regularity integrator is constructed to approximate rough and possibly discontinuous solutions of the semilinear wave equation. The proposed method, with high-frequency recovery techniques, can…
We show that, even for extremely stiff systems, explicit integration may compete in both accuracy and speed with implicit methods if algebraic methods are used to stabilize the numerical integration. The required stabilizing algebra depends…
A dynamic backstepping method is proposed to design controllers for nonlinear systems in the pure-feedback form, for which the traditional backstepping method suffers from solving the implicit nonlinear algebraic equation. The idea of this…
We present a fast method for nonlinear data-driven model reduction of dynamical systems onto their slowest nonresonant spectral submanifolds (SSMs). We use observed data to locate a low-dimensional, attracting slow SSM and compute a…
We present a modification to the Berger and Oliger adaptive mesh refinement algorithm designed to solve systems of coupled, non-linear, hyperbolic and elliptic partial differential equations. Such systems typically arise during constrained…
Reset controllers have demonstrated their effectiveness in enhancing performance in precision motion systems. To further exploiting the potential of reset controllers, this study introduces a parallel-partial reset control structure.…
In this contribution we develop an efficient reduced order model for solving parametrized linear-quadratic optimal control problems with linear time-varying state system. The fully reduced model combines reduced basis approximations of the…
The utilization of renewable energy technologies, particularly hydrogen, has seen a boom in interest and has spread throughout the world. Ethanol steam reformation is one of the primary methods capable of producing hydrogen efficiently and…
In the design of engineered components, rigorous vibration testing is essential for performance validation and identification of resonant frequencies and amplitudes encountered during operation. Performing this evaluation numerically via…
Many real-world systems are governed by the time-dependent, nonlinear differential equations. Dynamics of an electrical system are also best described using the very equations. Being one of the preferred machines when using advanced control…
Engineered systems naturally experience large disturbances that can disrupt desired operation because the system may fail to recover to a stable equilibrium point. It is valuable to determine the mechanism of instability when the system is…
This paper presents a robust fixed lag smoother for a class of nonlinear uncertain systems. A unified scheme, which combines a nonlinear robust estimator with a stable fixed lag smoother, is presented to improve the error covariance of the…
A general method for accelerating fixed point schemes for problems related to partial differential equations is presented in this article. The speedup is obtained by training a reduced-order model on-the-fly, removing the need to do an…
The paper deals with the problem of output regulation of nonlinear systems by presenting a learning-based adaptive internal model-based design strategy. We borrow from the adaptive internal model design technique recently proposed in [1]…
This paper considers the regularization continuation method and the trust-region updating strategy for the nonlinearly equality-constrained optimization problem. Namely, it uses the inverse of the regularization quasi-Newton matrix as the…
From weather to neural networks, modeling is not only useful for understanding various phenomena, but also has a wide range of potential applications. Although nonlinear differential equations are extremely useful tools in modeling, their…