Designing high performance two-degree of freedom controllers

COMBINED IDENTIFICATION AND CONTROL: ANOTHER WAY

Adaptive Pole Positioning in MIMO Linear Systems by Periodic Multirate-Input Controllers

Nowadays, mathematicians are very interested in discovering new and advanced methods for determining the solution of Diophantine equations. Diophantine equations are those equations that have more unknowns than equations. Diophantine equations appear in astronomy, cryptography, abstract algebra, coordinate geometry and trigonometry. Congruence theory plays an important role in finding the solution of some special type Diophantine equations. The absence of any generalized method, which can handle each Diophantine equation, is challenging for researchers. In the present paper, the authors have discussed the existence of the solution of exponential Diophantine equation (132m) + (6r + 1)n = Z2, where m, n, r, z are whole numbers. Results of the present paper show that the exponential Diophantine equation (132m) + (6r + 1)n = Z2, where m, n, r, z are whole numbers, has no solution in the whole number.

The paper is focused on systems with delay terms at the left (and the right) side of differential equations. Analysis and synthesis of delay systems can be conveniently studied through a special ring of RQ-meromorphic functions. The control methodology is based on a solution of Diophantine equations in this ring. Final controllers result in the Smith predictor like structure. Controller parameters are tuned through a pole-placement problem as a desired multiple root of the characteristic closed loop equation. The methodology is illustrated by a stable second order transfer function with a dead-time term. Then the paper brings an autotuning method as a combination of biased-relay feedback estimation and the proposed algebraic control design. The developed approach is illustrated by examples in the Matlab and Simulink environment.

We show how the solution to certain diophantine equations involving the discriminant of complex quadratic fields leads to the divisibility of the class numbers of the underlying fields. This not only generalizes certain results in the literature such as [2], [4]–[6] but also shows why certain hypotheses made in these results are actually unnecessary since, as our criteria demonstrate, these hypotheses are forced by the solution of the diophantine equations involved. Our methods are based only on the most elementary properties of a principal ideal in a complex quadratic field.

Let $f \in \mathbb{Z}[X,Y,Z]$ be a non-constant, absolutely irreducible, homogeneous polynomial with integer coefficients, such that the projective curve given by $f=0$ has a~function field isomorphic to the rational function field $\mathbb{Q} (T)$. We show that all integral solutions of the Diophantine equation $f=0$ (up to those corresponding to some singular points) can be parametrized by a single triple of integer-valued polynomials. In general, it is not possible to parametrize this set of solutions by a~single triple of polynomials with integer coefficients.

The Undecidability of Exponential Diophantine Equations

In this paper, we are focusing on solving Diophantine equations with geometry. Integers that are solutions of Diophantine equations are represented in space by a lattice. We will use the fact that equations can be interpreted geometrically as curves or surfaces. To determine the properties of the solutions, we will use tangents (of the surface).

Diophantine equation is an important concept while studying number theory. But there is as such no standard method or procedure to find the solution of the Diophantine equation. In this article, the numerical solution of Diophantine equation has been discussed using the concept of Artificial Neural Network (ANN). A four layer ANN architecture has been constructed for solving Diophantine eqution. Detail ANN procedure with few example problems and their network architectures have been addressed. Convergence plots and/or convergence tables for different example problems have also been included to validate the proposed method.

We extend the Kannan contraction principle and obtain a result that holds for both contractive and non-expansive mappings. Such mappings admit multiple fixed-points and the fixed-point sets and domains of these mappings display interesting algebraic, geometric and dynamical features. Since contraction mappings admit only one fixed-point, almost all the existing results on contractive mappings can be generalized in the light of our theorem. As an application of our main theorem, we obtain the integral solutions of a nonlinear Diophantine equation; the solutions are Pythagorean triples, which represent right angled triangles, and each integer of the triple belongs to a Fibonacci type sequence. These results can be generalised to obtain integral solutions of Diophantine equations of the type (n+k)2 – n2 = p2, k > 1, and to check whether the related sequences are Fibonacci sequences.

Methods of the theory of transcendental numbers, Diophantine approximations and solutions of Diophantine equations

Neste trabalho estudamos condições necessárias e suficientes para que uma equação diofantina linear sobre um domínio euclidiano tenha solução. Apresentamos uma série de algoritmos (funções) que podem ser implementados em planilhas eletrônicas (por exemplo LibreOffice Calc, Microsoft Excel, etc.), com o intuito de determinar (caso existam) soluções de equações diofantinas sobre Z[i].

Performance output tracking and disturbance rejection for an Euler–Bernoulli beam equation with unmatched boundary disturbance

Robust model reference adaptive output feedback tracking for uncertain linear systems with actuator fault based on reinforced dead-zone modification

The number of chemical species of modest molecular weight that can be accessed with known synthetic methods is astronomical. An open challenge is to explore this space in a manner that will enable the discovery of molecular species and materials with optimized properties. Recently, an inverse molecular design strategy, the linear combination of atomic potentials (LCAP) approach [J. Am. Chem. Soc. 128, 3228 (2006)] was developed to optimize electronic polarizabilities and first hyperpolarizabilities. Here, using a simple tight-binding (TB) approach, we show that continuous optimization can be carried out on the LCAP surface successfully to explore vast chemical libraries of 10(2) to 10(16) extended aromatic compounds. We show that the TB-LCAP optimization is not only effective in locating globally optimal structures based on their electronic polarizabilities and first hyperpolarizabilities, but also is straightforwardly extended to optimize transition dipole moments and HOMO-LUMO energy gaps. This approach finds optimal structures among 10(4) candidates with about 40 individual molecular property calculations. As such, for structurally similar molecular candidates, the TB-LCAP approach may provide an effective means to identify structures with optimal properties.