In this paper, we consider in R the Cauchy problem for nonlinear Schrödinger equation with initial data in Sobolev space W s,p for p < 2. It is well known that this problem is ill posed. However, We show that after a linear transformation by the linear semigroup the problem becomes locally well posed in W s,p for 2n n+1 < p < 2 and s > n(1− 1 p ). Moreover, we show that in one space dimension, ...

The transformation of a data set using a second-order polynomial mapping to find statistically independent components is considered (quadratic independent component analysis or ICA). Based on overdetermined linear ICA, an algorithm together with separability conditions are given via linearization reduction. The linearization is achieved using a higher dimensional embedding defined by the linear...

A multivariable nonlinear control strategy which accounts for unmeasured state variables and input constraints is developed for the free-radical polymerization of methyl methacrylate in a continuous stirred tank reactor. Monomer concentration and reactor temperature are controlled using a technique which combines nonlinear input–output decoupling and linear model predictive control. Input const...

We consider the problem of transforming a signal to a representation in which the components are statistically independent. When the signal is generated as a linear transformation of independent Gaussian or non-Gaussian sources, the solution may be computed using a linear transformation (PCA or ICA, respectively). Here, we consider a complementary case, in which the source is non-Gaussian but e...

Classification in kernel machines consists of a nonlinear transformation of input data into a feature space, followed by a separation with a linear hyperplane. This transformation is expressed through a kernel function, which is capable of computing similarities between two data points in an abstract geometric space for which individual point vectors are computationally intractable. In this pap...

Forecasting wind power is an important part of a successful integration of wind power into the power grid. Forecasts with lead times longer than 6 hours are generally made by using statistical methods to postprocess forecasts from numerical weather prediction systems. Two major problems that complicate this approach are the nonlinear relationship between wind speed and power production and the ...

Necessary and sufficient geometric conditions for the equivalence of a nonlinear time– delay system with one output, under bicausal change of coordinates and output transformation, to a linear weakly observable time–delay system up to output injection are given. These conditions are derived through the use of the Extended Lie Bracket operator recently introduced in the literature for dealing wi...

Abstract—This study proposes the transformation of nonlinear Magnetic Levitation System into linear one, via state and feedback transformations using explicit algorithm. This algorithm allows computing explicitly the linearizing state coordinates and feedback for any nonlinear control system, which is feedback linearizable, without solving the Partial Differential Equations. The algorithm is pe...

A new nonrecurrent associative memory model is proposed. This model is composed of a nonlinear transformation in the spectral domain followed by the association. The Moore-Penrose pseudoinverse is employed to obtain the least squares optimal solution. Computer simulations are done to evaluate the performance of the model. The simulations use one-dimensional speech signals and two-dimensional he...