Algorithms based on Mercer kernels construct their solutions in terms of expansions in a high-dimensional feature space F. Previous work has shown that all algorithms which can be formulated in terms of dot products in F can be performed using a kernel without explicitly working in F. The list of such algorithms includes support vector machines and nonlinear kernel principal component extractio...

An analytical solution to the nonlinear model predictive control (NMPC) optimization problem is derived for single–input single–output (SISO) systems modeled by second–order Volterra–Laguerre models. All input moves except the current move (m > 1 in the NMPC framework) are approximated by solving an unconstrained linear MPC problem which utilizes a locally accurate linear model of the process. ...

Keywords: Discrete Homological nontrivial critical point Morse theory Local linking a b s t r a c t In this paper, the existence and multiplicity results of solutions are obtained for the discrete nonlinear two point boundary value problem (BVP) ÀD 2 uðk À 1Þ ¼ kf ðk; uðkÞÞ k 2 þ is a parameter. By using the critical point theory and Morse theory, we obtain that the above (BVP) has solutions fo...

In this paper an H∞ controller is designed for a hydraulically actuated active suspension system of a half-modeled vehicle in a cascade feedback structure. Using the proposed structure the nonlinear behavior of actuator is reduced significantly. In the controller synthesis, a proportional controller is used in the inner loop, and a robust H∞ controller forms the outer loop. Two H∞ controllers a...

In this article, we present an inverse problem for the nonlinear 1-d Kuramoto-Sivashinsky (K-S) equation. More precisely, we study the nonlinear inverse problem of retrieving the anti-diffusion coefficient from the measurements of the solution on a part of the boundary and also at some positive time in the whole space domain. The Lipschitz stability for this inverse problem is our main result a...

For a < 0 one obtains solitary patterns having cusps or infinite slopes [2]. They discovered solitary waves, called compactons, with a compact support characterized by the absence of infinite wings or the absence of infinite tails. If a = 1, then (1) has a focusing (+) branch that exhibits compacton solutions. If a = −1, then (1) has a defocusing (−) branch that exhibits solitary pattern soluti...

We propose a numerical method for finding solitary wave solutions of generalized Korteweg-de Vries equations by solving the nonlinear eigenvalue problem on an unbounded domain. The artificial boundary conditions are obtained to make the domain finite. We specially discuss the soliton solutions of the K(m, n) equation and KdV-K(m, n) equation. Furthermore for the mixed models of linear and nonli...

Synopsis Parallel imaging relies on fully-sampled calibration data to estimate k-space kernels or sensitivities used to reconstruct subsampled acquisitions. Emerging techniques use low-rank modeling, or joint estimation of sensitivities and image content via nonlinear optimization, to reduce the dependency on calibration data. In a typical study, images at multiple echoes/contrasts are acquired...

This paper discusses the existence and decay of solutions u(t) of the variational inequality of parabolic type: >_ 0 for v e LP([O,=);V (p>2) with v(t) e K a.e. in [0,=), where K is a closed convex set of a separable uniformly convex Banach space V, A is a nonlinear monotone operator from V to V* and B is a nonlinear operator from Banach space W to W*. V ...

We prove a number of homeomorphism results for nonlinear Fredholm maps of index zero and their perturbations. Moreover, we show that k-ball and k-set perturbations of these homeomorphisms are again homeomorphisms or that the corresponding equations are finitely solvable. Various generalized first Fredholm theorems are given and finite solvability of general ( odd ) Fredholm maps is also studied...