Related papers: High-order integral-chain differentiator and appli…
Gradient-descent based iterative algorithms pervade a variety of problems in estimation, prediction, learning, control, and optimization. Recently iterative algorithms based on higher-order information have been explored in an attempt to…
We show how to increase the order of one-dimensional discrete gradient numerical integrator without losing its advantages, such as exceptional stability, exact conservation of the energy integral and exact preservation of the trajectories…
This paper presents a high-order differentiator for delayed measurement signal. The proposed differentiator not only can correct the delay in signal, but aslo can estimate the undelayed derivatives. The differentiator consists of two-step…
A nonlinear differentiator being fit for rapid convergence is presented, which is based on singular perturbation technique. The differentiator design can not only sufficiently reduce the chattering phenomenon of derivative estimation by…
In this paper, a high-order nonlinear continuous integral-derivative observer is presented based on finite-time stability and singular perturbation technique. The proposed integral-derivative observer can not only obtain the multiple…
In this paper, we consider the problems of approximating uncertainties and feedback control for a class of nonlinear systems without full-known states, and two approximation methods are proposed: universal approximation using integral-chain…
Linear differential equations are ubiquitous in science and engineering. Quantum computers can simulate quantum systems, which are described by a restricted type of linear differential equations. Here we extend quantum simulation algorithms…
High-order finite-difference methods are commonly used in wave propagators for industrial subsurface imaging algorithms. Computational aspects of the reduced linear elastic vertical transversely isotropic propagator are considered. Thread…
Differentiable simulators promise faster computation time for reinforcement learning by replacing zeroth-order gradient estimates of a stochastic objective with an estimate based on first-order gradients. However, it is yet unclear what…
In policy gradient reinforcement learning, access to a differentiable model enables 1st-order gradient estimation that accelerates learning compared to relying solely on derivative-free 0th-order estimators. However, discontinuous dynamics…
Two-dimensional superintegrable systems with one third order and one lower order integral of motion are reviewed. The fact that Hamiltonian systems with higher order integrals of motion are not the same in classical and quantum mechanics is…
The differentiation of noisy signals using the family of homogeneous differentiators is considered. It includes the high-gain (linear) as well as robust exact (discontinuous) differentiator. To characterize the effect of noise and…
This paper proposes a new algorithm for compensating external disturbances for class of multi-channel linear systems. The solution to this problem is based on the use of the internal model principle and the extended error adaptation…
Specialized function gradient computing hardware could greatly improve the performance of state-of-the-art optimization algorithms, e.g., based on gradient descent or conjugate gradient methods that are at the core of control, machine…
Momentum-based gradients are essential for optimizing advanced machine learning models, as they not only accelerate convergence but also advance optimizers to escape stationary points. While most state-of-the-art momentum techniques utilize…
We consider classical nonlinear oscillators on hexagonal lattices. When the coupling between the elements is repulsive, we observe coexisting states, each one with its own basin of attraction. These states differ by their degree of…
In this paper, describing function method is used to analyze the characteristics and parameters selection of differentiators. Nonlinear differentiator is an effective compensation to linear differentiator, and hybrid differentiator…
Nonlinear contraction theory is a comparatively recent dynamic control system design tool based on an exact differential analysis of convergence, in essence converting a nonlinear stability problem into a linear time-varying stability…
The signal differentiation problem involves the development of algorithms that allow to recover a signal's derivatives from noisy measurements. This paper develops a first-order differentiator with the following combination of properties:…
Improved performance in higher-order spectral density estimation is achieved using a general class of infinite-order kernels. These estimates are asymptotically less biased but with the same order of variance as compared to the classical…