In this paper, a novel neuro-optimal control scheme is proposed for unknown nonaffine nonlinear discretetime systems by using adaptive dynamic programming (ADP) method. A neuro identifier is established by established RNN model, the ADP method is utilized to design the approximate optimal controller. Two neural networks (NNs) are used to implement the iterative algorithm. The convergence of the...

In this paper we present a new affine invariant image transform, based on ridgelets. The proposed transform is directly applicable to segmented image patches. The new method has some similarities with the previously proposed Multiscale Autoconvolution, but it will offer a more general framework and possibilities for variations. The obtained transform coefficients can be used in affine invariant...

Approximate Dynamic Inversion has been established as a method to control minimum-phase, nonaffine-incontrol systems [1]. In this report, we re-state the main results of [1], clarify some minor notational errors, and prove the same results in an expanded form. In the large, the main results of [1] still stand. The development follows [1] closely, and no novelty is claimed herein. The purpose of...

The connection between maximal caps (sometimes called complete caps) and certain binary codes called quasi-perfect codes is described. We provide a geometric approach to the foundational work of Davydov and Tombak who have obtained the exact possible sizes of large maximal caps. A new self-contained proof of the existence and the structure of the largest maximal nonaffine cap in PG(n, 2) is giv...

We investigate experimentally the connection between short time dynamics and long time dynamical heterogeneities within a dense granular media under cyclic shear. We show that dynamical heterogeneities result from a two time scales process. Short time but already collective events consisting in clustered cage jumps concentrate most of the nonaffine displacements. On larger time scales, such clu...

We show that stabilizing tracking proportional-integral (PI) controllers can be constructed for minimum-phase nonaffine-in-control systems. The constructed PI controller is an equivalent realization of an approximate dynamic inversion controller. This equivalence holds only for the time response when applied to the unperturbed system. Even when restricted to unperturbed minimum-phase linear tim...

Linear factor models, where the factors are affine processes, play a key role in Finance, since they allow for quasi-closed form expressions of term structure risks. We introduce class noncausal linear models by considering that reverse time. These especially relevant pricing sequences speculative bubbles. show feature nonaffine dynamics calendar time, while still providing (quasi) closed struc...

Recently introduced constitutive equations for the rheology of dense, disordered materials are investigated in the context of stick-slip experiments in boundary lubrication. The model is based on a generalization of the shear transformation zone (STZ) theory, in which plastic deformation is represented by a population of mesoscopic regions which may undergo nonaffine deformations in response to...

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Spatial normalization is a key process in cross-sectional studies of brain structure and function using MRI, fMRI, PET and other imaging techniques. A wide range of 2D surface and 3D image deformation algorithms have been developed, all of which involve design choices that are subject to debate. Moreover, most have numerical parameters whose value must be specified by the user. This paper propo...