This work presents a control strategy using a network with radial basis function (RBF network) with adaptation in dual mode. The objective of the strategy is to use the approximate capacity of the RBF network to control nonlinear systems with unknown parameters or with uncertainties. The proposed control uses the structure of Model Reference Adaptive Control (MRAC) and a RBF network whose param...

In this paper, the hyperbolic tangent function method is applied for constructing exact solutions space-time conformal fractional Burgers’ equation. Furthermore, equation tested Painlevé property, and consequently, new numerous are generated via Bäcklund transform.

We consider the notion of shift tangent vector introduced in [6] for real valued BV functions and introduced in [8] for vector valued BV functions. Using a simple decomposition of u ∈ BV in terms of its derivative, we extend the results of [8] to more general shift tangent vectors. This extension allows us to study the shift differentiability of the flow generated by a hyperbolic system of cons...

A theorem of Bôcher and Grace states that the critical points of a cubic polynomial are the foci of an ellipse tangent to the sides of the triangle joining the zeros. A more general result of Siebert and others states that the critical points of a polynomial of degree N are the algebraic foci of a curve of class N − 1 which is tangent to the lines joining pairs of zeroes. We prove the analogous...

In the Compressed Sensing (CS) framework, underdetermined system of linear equation (USLE) can have infinitely many possible solutions. However, we intend to find sparsest solution, which is l0-norm minimization. finding an l0 norm solution out solutions NP-hard problem that becomes non-convex optimization problem. It has been a practically proven fact penalty be adequately estimated by l1 norm...

We perform a numerical study of the breakdown of hyperbolicity of quasi-periodic attractors in the dissipative standard map. In this study, we compute the quasi-periodic attractors together with their stable and tangent bundles. We observe that the loss of normal hyperbolicity comes from the collision of the stable and tangent bundles of the quasi-periodic attractor. We provide numerical eviden...