Minimum-energy formation achievement problems for networked multiagent systems are investigated, where information networks with leaderless and leader-follower structures respectively addressed randomly switching. The critical feature of this work is that the energy constraint minimum in sense linear matrix inequality, but limited-budget control guaranteed-cost cannot realize a minimum-energy formation. Firstly, problem converted into an asymptotic stability one via nonsingular...

Let ([0, 1), T) be the dynamical system of continued fractions. {zn}n⩾1 a sequence real numbers in [0, 1] and ψ: ℕ × 1) → ℝ+ positive function. A point x∈[0, is said to ψ-approximable by {zn}n ⩾ 1 if |Tnx − zn| < ψ(n, x) holds for infinitely many n ∈ ℕ. In this paper, Hausdorff dimension set points studied. The dimensions are completely determined when = ψ(n) independent on x ψ ( , ) e f + ⋯ T with continuous For proof these results, relationship between ball cylinders defined partial...

Nous calculons presque sûrement la dimension de Hausdorff l’ensemble recouvrement aléatoire $\limsup_{n\to\infty}(g_{n}+\xi_{n})$ dans le tore $\mathbb{T}^{d}$ $d$, où $g_{n}\subset\mathbb{T}^{d}$ sont des parallélépipèdes, ou plus généralement, images linéaires d’un ensemble d’intérieur non vide et $\xi_{n}\in\mathbb{T}^{d}$ points aléatoires indépendants uniformément distribués. La formule dimension, exprimée en fonction valeurs singulières applications linéaires, est valable à condition...

&lt;p style='text-indent:20px;'&gt;We consider a class of neutral type Clifford-valued cellular neural networks with discrete delays and infinitely distributed delays. Unlike most previous studies on networks, we assume that the self feedback connection weights are Clifford numbers rather than real numbers. In order to study existence &lt;inline-formula&gt;&lt;tex-math id="M1"&gt;\begin{document}$ (\mu, \nu) $\end{document}&lt;/tex-math&gt;&lt;/inline-formula&gt;-pseudo compact almost...

We study the dimensional properties of Moran sets and measures in doubling metric spaces. In particular, we consider local dimensions $L^q$-dimensions. generalize extend several existing results this area.

We propose some new concepts of almost periodic time scales and functions on give basic properties these types scales. also comments a recent paper by Wang Agarwal (2014) concerning scale.

We investigate the Fourier dimension, $\dim_F\mu$, of Mandelbrot multiplicative cascade measures $\mu$ on $d$-dimensional unit cube. show that if is measure generated by a sub-Gaussian random variable then \[\dim_F\mu=\min\{2,\dim_2\mu\}\,,\] where $\dim_2\mu$ correlation dimension and it has an explicit formula. For cascades circle $S\subset\mathbb{R}^2$, we obtain \[\dim_F\mu\ge\frac{\dim_2\mu}{2+\dim_2\mu}\,.\]

We calculate the almost sure dimension for a general class of random affine code tree fractals in $\mathbb{R}^{d}$ . The result is based on probabilistic version Falconer–Sloan condition $C(s)$ introduced Falconer and Sloan [Continuity subadditive pressure self-affine sets. Real Anal. Exchange 34 (2009), 413–427]. verify that, general, systems having small number maps do not satisfy However, there exists natural $n$ such that typical family all iterates up to level satisfies

Quasi-cyclic (QC) Low-density paritycheck (LDPC) codes are constructed from combination of weight-0 (null matrix) and Weight-2 (W2) Circulant matrix (CM), which can be seen as a special case the general type-II QC LDPC codes. The shift is built on basis one integer sequence, called perfect Cyclic difference set (CDS), guarantees girth code at least six. Simulation results show that perform well in comparison with variety other They have excellent error floor decoding convergence characteristics.

We determine the structure of set intermediate $\beta$-shifts finite-type. Specifically, we show that this is dense in parameter space \begin{align*} \Delta \coloneq \{ (\beta , \alpha ) \in \mathbb {R}^{2} \colon \beta (1, 2) \; \text {and} 0 \leq 2 - \}. \end{align*} This generalises classical result Parry from 1960 for greedy $\beta$-shifts.

Aiming at the shortcomings of existing control law based on global information, this article studies coverage problem a given region in plane using team USVs. The goal, which is to cover search domain multiple mobile sensors so that each point surveyed until certain preset level achieved, formulated mathematically precise statement. adaptive presented enables multi-USV navigate complex environment presence unknown obstacles and guarantees fully connected system attains goal. In particular,...

A novel graph-based Estimation of Distribution Algorithm (EDA) named Probabilistic Model Building Genetic Network Programming (PMBGNP) has been proposed. Inspired by classical EDAs, PMBGNP memorizes the current best individuals and uses them to estimate a distribution for generation new population. However, can evolve compact programs representing its solutions as graph structures. Therefore, it solve range problems different from conventional ones in EDA literature, such data mining...

Genetic Network Programming (GNP) is a novel evolutionary algorithm. It has graph-based structures which extended from Algorithm (GA) and (GP). Up to now, GNP been applied many research fields such as data mining elevator control systems. On the other hand, automatic program generation way obtain without explicitly programming it, traditional paradigm in this field. Drawn inspiration of GP, for Automatic Program Generation (GNP-APG) proposed. In paper, GNP-APG Tile-world, famous test bed...

An approach for constructing a class of (3, k)-regular quasi-cyclic low-density parity-check (QC-LDPC) codes is proposed, which based on combinatorial objects termed difference sequences. By an efficient algorithm searching good sequences, in this have girth at least eight. Simulation results show that the slightly outperform counterpart PEG and better performance than corresponding MacKay array codes.

"Food is the most important thing for people", Food intricately linked to both national economy and livelihood of people, serving as a vital material our daily existence. Wheat, standing one three core grain crops, holds paramount importance in safeguarding food security. However, wheat planting process remains constantly exposed diverse array environmental factors, ranging from intensity light fluctuations temperature, soil fertility, fertilizer application methods, water availability....

For symbolic dynamics with some mild conditions, we solve the lowering topological entropy problem for subsystems and determine Hausdorff dimension of level set given complexity, where complexity is represented by orbit closure. These results can be applied to dynamical systems such as $\beta$-transformations, conformal expanding repeller, etc. We also Furstenberg set, which related a on orbits under two multiplicatively independent maps.

Abstract In this article, a novel sensitivity minimization approach is proposed to optimize the performance of proportional‐integral (PI) dynamic average consensus (DAC) algorithms subject measurement noises and model uncertainties. Network complementary functions are defined characterize effects reference signals on tracking error, respectively. Minimization norms network functions, describing how large PI DAC algorithm amplifies noise in worst case, conducted with respect without requiring...