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Differential Flatness Theory and Flatness-Based Control

2015
The chapter analyzes the concept of differential flatness theory-based control, both for lumped dynamical systems (that is for systems which are described by ordinary differential equations) and for distributed parameter systems (that is for systems which are described by partial differential equations).
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Congenital flat vascular anomalies: differential diagnosis.

European Journal of Pediatric Dermatology, 2020
This is a retrospective study of 81 cases of congenital flat vascular anomalies of the skin – salmon patch, port-wine stain, minimal growth hemangioma, capillary malformation / arteriovenous malformation syndrome and cutis marmorata telangiectatica congenita – consecutively examined from January, 1 to December, 31 2019. Clinical and dermoscopic data of
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Adjustable weak measurement differential microscopy via flat differentiator

Applied Physics Letters
Feature extraction and phase retrieval, as critical technical nodes in imaging technologies, play a pivotal role in label-free biological imaging and target recognition. Optical differential imaging is pivotal for extracting phase information in label-free biological imaging and feature extraction, yet existing techniques often suffer from complexity ...
Yurong Liu   +6 more
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Flat optics for optical image differentiation

Metamaterials, Metadevices, and Metasystems 2020, 2020
The differentiator consists of carefully designed 2D photonic crystal (PhC) slab that can transform an image into its second-order derivative. Based on interference between the direct transmission and low quality factor quasi-guided modes, the PhC slab exhibits angular-dependent transmission for P polarization but remains reflective for S polarization,
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Differentially Flat Design of Bipeds Ensuring Limit Cycles

IEEE/ASME Transactions on Mechatronics, 2007
For bipedal walking, a set of joint trajectories is acceptable as long as it satisfies certain overall motion requirements, such as: 1) it is repetitive (limit cycles); 2) it allows the foot to clear ground; and 3) it allows the biped to move forward.
Vivek Sangwan, Sunil K. Agrawal
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Maximally flat low-pass digital differentiator

IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, 2002
This paper describes the design of type III and type IV linear-phase finite-impulse response (FIR) low-pass digital differentiators according to the maximally flat criterion. We introduce a two-term recursive formula that enables the simple stable computation of the impulse response coefficients.
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Differentially flat nonlinear control systems

1997
Differentially flat systems are underdetermined systems of (nonlinear) ordinary differential equations (ODEs) whose solution curves are in smooth one-one correspondence with arbitrary curves in a space whose dimension equals the number of equations by which the system is underdetermined. For control systems this is the same as the number of inputs. The
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Maximally flat differentiators through WLS Taylor decomposition

Digital Signal Processing, 2011
Instantaneous derivative estimates of a signal are obtained using the wighted least square (WLS) approximation of a Taylor (WLST) signal model, using classical windows as weighting factors. The WLST approximation in time corresponds to a Taylor approximation at the origin of the windowed signal spectrum.
José Antonio de la O Serna   +1 more
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Differential Flatness Theory in Power Electronics

2015
The chapter analyzes methods of nonlinear filtering and control which are based on differential flatness theory and examines their use in power electronics, aiming at connecting various types of power generation units to the grid (e.g., converters and inverters).
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ETA INVARIANTS, DIFFERENTIAL CHARACTERS AND FLAT VECTOR BUNDLES

Chinese Annals of Mathematics, 2005
The paper addresses the heat equation method for obtaining the explicit representation of the Chern character of the index bundle of a family of Dirac operators as a differential form on the base space. In order to formulate a result of the paper let us consider the following situation. Let \(\pi: M\to B\) be a smooth bundle over a closed manifold \(B\)
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