Motor Parameter-Free Predictive Current Control of Synchronous Motors by Recursive Least-Square Self-Commissioning Model

This article deals with a finite-set model predictive current control in synchronous motor drives. The peculiarity is that it does not require the knowledge of any motor parameter. The inherent advantage of this method is that the control is self-adapting to any synchronous motor, thus easing the matching between motor and inverter coming from different manufacturers. Overcoming the flaws of the existing lookup table based parameter-free techniques, the article elaborates the past current measurements by a recursive least-square algorithm to estimate the future behavior of the current in response to a finite set of voltage vectors. The article goes through the mathematical basis of the algorithm till a complete set of experiments that prove the feasibility and the advantages of the proposed technique

An Effective Model-Free Predictive Current Control for Synchronous Reluctance Motor Drives

The performances of a model predictive control algorithm largely depend on the knowledge of the system model. A model-free predictive control approach skips all the effects of parameters variations or mismatches, as well as of model nonlinearity and uncertainties. A finite-set model-free current predictive control is proposed in this paper. The current variations predictions induced by the eight base inverter voltage vectors are estimated by means of the previous measurements stored into lookup tables. To keep the current variations information up to date, the three current measurements due to the three most recent feeding voltages are combined together to reconstruct all the others. The reconstruction is performed by taking advantage of the relationships between the three different base voltage vectors involved in the process. In particular, 210 possible combinations of three-state voltage vectors can be found, but they can be gathered together in six different groups. A light and computationally fast algorithm for the group identification is proposed in this paper. Finally, the current reconstruction for the prediction of future steps is thoroughly analyzed. A compensation of the motor rotation effect on the input voltages is proposed, too. The control scheme is evaluated by means of both simulation and experimental evidences on two different synchronous reluctance motors

Enumeration of hypermaps and Hirota equations for extended rationally constrained KP

We consider the Hurwitz Dubrovin--Frobenius manifold structure on the space of meromorphic functions on the Riemann sphere with exactly two poles, one simple and one of arbitrary order. We prove that the all genera partition function (also known as the total descendant potential) associated with this Dubrovin--Frobenius manifold is a tau function of a rational reduction of the Kadomtsev--Petviashvili hierarchy. This statement was conjectured by Liu, Zhang, and Zhou. We also provide a partial enumerative meaning for this partition function associating one particular set of times with enumeration of rooted hypermaps.Comment: 39 page

A complete characterization of plateaued Boolean functions in terms of their Cayley graphs

In this paper we find a complete characterization of plateaued Boolean functions in terms of the associated Cayley graphs. Precisely, we show that a Boolean function $f$ is $s$-plateaued (of weight $=2^{(n+s-2)/2}$) if and only if the associated Cayley graph is a complete bipartite graph between the support of $f$ and its complement (hence the graph is strongly regular of parameters $e=0,d=2^{(n+s-2)/2}$). Moreover, a Boolean function $f$ is $s$-plateaued (of weight $\neq 2^{(n+s-2)/2}$) if and only if the associated Cayley graph is strongly $3$-walk-regular (and also strongly $\ell$-walk-regular, for all odd $\ell\geq 3$) with some explicitly given parameters.Comment: 7 pages, 1 figure, Proceedings of Africacrypt 201

Rational reductions of the 2D-Toda hierarchy and mirror symmetry

We introduce and study a two-parameter family of symmetry reductions of the two-dimensional Toda lattice hierarchy, which are characterized by a rational factorization of the Lax operator into a product of an upper diagonal and the inverse of a lower diagonal formal di erence operator. They subsume and generalize several classical 1+1 integrable hierarchies, such as the bigraded Toda hierarchy, the Ablowitz–Ladik hierarchy and E. Frenkel's q-deformed Gelfand–Dickey hierarchy. We establish their characterization in terms of block T oeplitz matrices for the associated factorization problem, and study their Hamiltonian structure. At the dispersionless level, we show how the Takasaki–Takebe classical limit gives rise to a family of non-conformal Frobenius manifolds with flat identity. We use this to generalize the relation of the Ablowitz–Ladik hierarchy to Gromov–Witten theory by proving an analogous mirror theorem for the general rational reduction: in particular, we show that the dual-type Frobenius manifolds we obtain are isomorphic to the equivariant quantum cohomology of a family of toric Calabi–Yau threefolds obtained from minimal resolutions of the local orbifold line

Normal forms of dispersive scalar Poisson brackets with two independent variables

We classify the dispersive Poisson brackets with one dependent variable and two independent variables, with leading order of hydrodynamic type, up to Miura transformations. We show that, in contrast to the case of a single independent variable for which a well-known triviality result exists, the Miura equivalence classes are parametrised by an infinite number of constants, which we call numerical invariants of the brackets. We obtain explicit formulas for the first few numerical invariants

Semiclassical expansions in the Toda hierarchy and the hermitian matrix model

An iterative algorithm for determining a class of solutions of the dispersionful 2-Toda hierarchy characterized by string equations is developed. This class includes the solution which underlies the large N-limit of the Hermitian matrix model in the one-cut case. It is also shown how the double scaling limit can be naturally formulated in this schemeComment: 22 page

The Seventh International Olympiad in Cryptography: problems and solutions

The International Olympiad in Cryptography NSUCRYPTO is the unique Olympiad containing scientific mathematical problems for professionals, school and university students from any country. Its aim is to involve young researchers in solving curious and tough scientific problems of modern cryptography. In 2020, it was held for the seventh time. Prizes and diplomas were awarded to 84 participants in the first round and 49 teams in the second round from 32 countries. In this paper, problems and their solutions of NSUCRYPTO'2020 are presented. We consider problems related to attacks on ciphers and hash functions, protocols, permutations, primality tests, etc. We discuss several open problems on JPEG encoding, Miller -- Rabin primality test, special bases in the vector space, AES-GCM. The problem of a modified Miller -- Rabin primality test was solved during the Olympiad. The problem for finding special bases was partially solved