This paper focuses on developing a data-driven trajectory tracking control approach for autonomous underwater vehicles (AUV) under uncertain external disturbance and time-delay. A novel model-free adaptive predictive (MFAPC) based fuzzy state observer (FSO) was designed to achieve high precision. Concretely, the mathematical model of AUV motion analyzed, simplified via decoupling, thus providin...

Estimating the Jacobian matrix of a nonlinear dynamical system through observed time-series data is one of the important steps in predicting future states of the time series. The Jacobian matrix is estimated using local information about divergences of nearby trajectories. Although the basic algorithm for estimating the Jacobian matrix generally works well, it often fails for short or noisy dat...

­z ­t 5 J(z, c), (2) The integral constraints on quadratic quantities of physical importance, such as conservation of mean kinetic energy and mean square vorticity, will not be maintained in finite difference analogues of or the equation of motion for two-dimensional incompressible flow, unless the finite difference Jacobian expression for the advection term is restricted to a form which proper...

In hyperelliptic curve cryptography, finding a suitable hyperelliptic curve is an important fundamental problem. One of necessary conditions is that the order of its Jacobian is a product of a large prime number and a small number. In the paper, we give a probabilistic polynomial time algorithm to test whether the Jacobian of the given hyperelliptic curve of the form Y 2 = X+uX+vX satisfies the...

From a small number of calls to a given “blackbox" on random input perturbations, we show how to efficiently recover its unknown Jacobian, or estimate the left action of its Jacobian on a given vector. Our methods are based on a novel combination of compressed sensing and graph coloring techniques, and provably exploit structural prior knowledge about the Jacobian such as sparsity and symmetry ...

The Jacobian Conjecture is established : If f1, · · · , fn be elements in a polynomial ring k[X1, · · · , Xn] over a field k of characteristic zero such that det(∂fi/∂Xj) is a nonzero constant, then k[f1, · · · , fn] = k[X1, · · · , Xn]. Let k be an algebraically closed field, let k be an affine space of dimension n over k and let f : k −→ k be a morphism of algebraic varieties. Then f is given...

Among offshore hydrocarbon exploration technologies, the controlled source electromagnetic (CSEM) method have gained a lot of interest in both academia and industry because of its ability to detect hydrocarbon reservoirs [1]. In order to maximally extract information from the data, a full nonlinear inversion approach is employed [2]. In such an approach, the investigation domain is subdivided i...

We study the implications of the index theorem and chiral Jacobian in lattice gauge theory , which have been formulated by Hasenfratz, Laliena and Niedermayer and by Lüscher, on the continuum formulation of the chiral Jacobian and anomaly. We take a continuum limit of the lattice Jacobian factor without referring to perturbative expansion and recover the result of continuum theory by using only...

We study the implications of the index theorem and chiral Jacobian in lattice gauge theory , which have been formulated by Hasenfratz, Laliena and Niedermayer and by Lüscher, on the continuum formulation of the chiral Jacobian and anomaly. We take a continuum limit of the lattice Jacobian factor without referring to perturbative expansion and recover the result of continuum theory by using only...

The use of elliptic and hyperelliptic curves in cryptography relies on the ability to compute the Jacobian order of a given curve. Recently, Satoh proposed a probabilistic polynomial time algorithm to test whether the Jacobian – over a finite field Fq – of a hyperelliptic curve of the form Y 2 = X + aX + bX (with a, b ∈ Fq) has a large prime factor. His approach is to obtain candidates for the ...