Integrated damping parameter and control design in structural systems for \bf{\mathcal{H}^2} and {\mathcal{H}^{\infty}} specifications

The paper presents a linear matrix inequality (LMI)-based approach for the simultaneous optimal design of output feedback control gains and damping parameters in structural systems with collocated actuators and sensors. The proposed integrated design is based on simplified $\mathcal{H}^2$ and $\mathcal{H}^{\infty}$ norm upper bound calculations for collocated structural systems. Using these upper bound results, the combined design of the damping parameters of the structural system and the output feedback controller to satisfy closed-loop $\mathcal{H}^2$ or $\mathcal{H}^{\infty}$ performance specifications is formulated as an LMI optimization problem with respect to the unknown damping coefficients and feedback gains. Numerical examples motivated from structural and aerospace engineering applications demonstrate the advantages and computational efficiency of the proposed technique for integrated structural and control design. The effectiveness of the proposed integrated design becomes apparent, especially in very large scale structural systems where the use of classical methods for solving Lyapunov and Riccati equations associated with $\mathcal{H}^2$ and $\mathcal{H}^{\infty}$ designs are time-consuming or intractable.     

Development and Application of Controller for Transition Flight of Tail-Sitter UAV

There is renewed interest in tail-sitter airplanes on account of their vertical takeoff and landing capability as well as their efficient horizontal flight capabilities. The transition from a vertical near-hover mode to a horizontal cruise mode is a critical component of the tail-sitter flight profile. In practice, this transition is often achieved by a stall-and-tumble maneuver, which is somewhat risky and therefore not desirable, so alternative maneuvering strategies along controlled trajectories are sought. Accordingly, this paper presents the synthesis and application of a transition controller to a tail-sitter UAV for the first time. For practical reasons, linear controllers are designed using the PID technique and linked by gain scheduling. The limits of the PID controller are complemented by a so-called $\mathcal{L}_{1}$ adaptive controller that considers the coupling effect, reduces the effort for appropriate gain selection, and improves the tracking performance at different points during operation. Each transition trajectory is controlled by the flight velocity and path angle using dynamic inversion. The transition control law is tested on a tail-sitter UAV, an 18-kg vehicle that has a 2-m wingspan with an aspect ratio of 4.71 and is powered by a 100-cm³ gasoline engine driving an aft-mounted ducted fan. This paper describes not only the synthesis and the onboard implementation of the control law but also the flight testing of the fixed-wing UAV in hover, transition, and cruise modes.     

Efficient controller synthesis for a fragment of \hbox {MTL}_{0, \infty }

In this paper we offer an efficient controller synthesis algorithm for assume-guarantee specifications of the form $\varphi _1 \wedge \varphi _2 \wedge \cdots \wedge \varphi _n \rightarrow \psi _1 \wedge \psi _2 \wedge \cdots \wedge \psi _m$ . Here, $\{\varphi _i,\psi _j\}$ are all safety-MTL $_{0, \infty }$ properties, where the sub-formulas $\{\varphi _i\}$ are supposed to specify assumptions of the environment and the sub-formulas $\{\psi _j\}$ are specifying requirements to be guaranteed by the controller. Our synthesis method exploits the engine of Uppaal-Tiga and the novel translation of safety- and co-safety-MTL $_{0, \infty }$ properties into under-approximating, deterministic timed automata. Our approach avoids determinization of Büchi automata, which is the main obstacle for the practical applicability of controller synthesis for linear-time specifications. The experiments demonstrate that the chosen specification formalism is expressive enough to specify complex behaviors. The proposed approach is sound but not complete. However, it successfully produced solutions for all the experiments. Additionally we compared our tool with Acacia+ and Unbeast, state-of-the-art LTL synthesis tools; and our tool demonstrated better timing results, when we applied both tools to the analogous specifications.     

On (\overline{\in},\overline{\in} \vee \overline{q})-fuzzy ideals of BCI-algebras

The concepts of $(\overline{\in},\overline{\in} \vee \overline{q})$ -fuzzy (p-, q- and a-) ideals of BCI-algebras are introduced and some related properties are investigated. In particular, we describe the relationships among ordinary fuzzy (p-, q- and a-) ideals, (??,?????? q)-fuzzy (p-, q- and a-) ideals and $(\overline{\in},\overline{\in} \vee \overline{q})$ -fuzzy (p-,q- and a-) ideals of BCI-algebras. Moreover, we prove that a fuzzy set??? of a BCI-algebra X is an $(\overline{\in},\overline{\in} \vee \overline{q})$ -fuzzy a-ideal of X if and only if it is both an $(\overline{\in},\overline{\in} \vee \overline{q})$ -fuzzy p-ideal and an $(\overline{\in},\overline{\in} \vee \overline{q})$ -fuzzy q-ideal. Finally, we give some characterizations of three particular cases of BCI-algebras by these generalized fuzzy ideals.     

Arithmetizing Classes Around \textsf{NC} 1 and \textsf{L}

The parallel complexity class $\textsf{NC}$ ¹ has many equivalent models such as polynomial size formulae and bounded width branching programs. Caussinus et al. (J. Comput. Syst. Sci. 57:200–212, 1992) considered arithmetizations of two of these classes, $\textsf{\#NC}$ ¹ and $\textsf{\#BWBP}$ . We further this study to include arithmetization of other classes. In particular, we show that counting paths in branching programs over visibly pushdown automata is in $\textsf{FLogDCFL}$ , while counting proof-trees in logarithmic width formulae has the same power as $\textsf{\#NC}$ ¹. We also consider polynomial-degree restrictions of $\textsf{SC}$ ⁱ , denoted $\textsf{sSC}$ ⁱ , and show that the Boolean class $\textsf{sSC}$ ¹ is sandwiched between $\textsf{NC}$ ¹ and $\textsf{L}$ , whereas $\textsf{sSC}$ ⁰ equals $\textsf{NC}$ ¹. On the other hand, the arithmetic class $\textsf{\#sSC}$ ⁰ contains $\textsf{\#BWBP}$ and is contained in $\textsf{FL}$ , and $\textsf{\#sSC}$ ¹ contains $\textsf{\#NC}$ ¹ and is in $\textsf{SC}$ ². We also investigate some closure properties of the newly defined arithmetic classes.     

Branching Time Logics \mathcal {BTL}^{\mathrm {U,S}}_{\mathrm {N},\mathrm {N}^{-1}}(\mathcal {Z})_{\alpha } with Operations Until and Since Based on Bundles of Integer Numbers, Logical Consecutions, Deciding Algorithms

This paper is intended as an attempt to describe logical consequence in branching time logics. We study temporal branching time logics $\mathcal {BTL}^{\mathrm {U,S}}_{\mathrm {N},\mathrm {N}^{-1}}(\mathcal {Z})_{\alpha }$ which use the standard operations Until and Next and dual operations Since and Previous (LTL, as standard, uses only Until and Next). Temporal logics $\mathcal {BTL}^{\mathrm {U,S}}_{\mathrm {N},\mathrm {N}^{-1}}(\mathcal {Z})_{\alpha }$ are generated by semantics based on Kripke/Hinttikka structures with linear frames of integer numbers $\mathcal {Z}$ with a single node (glued zeros). For $\mathcal {BTL}^{\mathrm {U,S}}_{\mathrm {N},\mathrm {N}^{-1}}(\mathcal {Z})_{\alpha }$ , the permissible branching of the node is limited by α (where 1≤α≤ω). We prove that any logic $\mathcal {BTL}^{\mathrm {U,S}}_{\mathrm {N},\mathrm {N}^{-1}}(\mathcal {Z})_{\alpha }$ is decidable w.r.t. admissible consecutions (inference rules), i.e. we find an algorithm recognizing consecutions admissible in $\mathcal {BTL}^{\mathrm {U,S}}_{\mathrm {N},\mathrm {N}^{-1}}(\mathcal {Z})_{\alpha }$ . As a consequence, it implies that $\mathcal {BTL}^{\mathrm {U,S}}_{\mathrm {N},\mathrm {N}^{-1}}(\mathcal {Z})_{\alpha }$ itself is decidable and solves the satisfiability problem.     

Chain conditions on \textit{BL}-algebras

The aim of this paper is to solve the open problem appeared in Motamed and Moghaderi (Soft Comput 2012), about the relation between Noetherian (Artinian) $\textit{BL}$ -algebras in short exact sequences. Also, a better theorem to improve its results is suggested. The relation between Noetherian and Artinian $\textit{BL}$ -algebras is found, the concept of length for a filter in $\textit{BL}$ -algebras is introduced and properties of finite length $\textit{BL}$ -algebras are developed. Finally, it is proved that any $\textit{BL}$ -algebra has finite length if and only if be Noetherian and Artinian.     

A sparse {\varvec{L}}_{2}-regularized support vector machines for efficient natural language learning

Linear kernel support vector machines (SVMs) using either $L_{1}$ -norm or $L_{2}$ -norm have emerged as an important and wildly used classification algorithm for many applications such as text chunking, part-of-speech tagging, information retrieval, and dependency parsing. $L_{2}$ -norm SVMs usually provide slightly better accuracy than $L_{1}$ -SVMs in most tasks. However, $L_{2}$ -norm SVMs produce too many near-but-nonzero feature weights that are highly time-consuming when computing nonsignificant weights. In this paper, we present a cutting-weight algorithm to guide the optimization process of the $L_{2}$ -SVMs toward a sparse solution. Before checking the optimality, our method automatically discards a set of near-but-nonzero feature weight. The final objects can then be achieved when the objective function is met by the remaining features and hypothesis. One characteristic of our cutting-weight algorithm is that it requires no changes in the original learning objects. To verify this concept, we conduct the experiments using three well-known benchmarks, i.e., CoNLL-2000 text chunking, SIGHAN-3 Chinese word segmentation, and Chinese word dependency parsing. Our method achieves 1–10 times feature parameter reduction rates in comparison with the original $L_{2}$ -SVMs, slightly better accuracy with a lower training time cost. In terms of run-time efficiency, our method is reasonably faster than the original $L_{2}$ -regularized SVMs. For example, our sparse $L_{2}$ -SVMs is 2.55 times faster than the original $L_{2}$ -SVMs with the same accuracy.     

The categories L-\mathbf{Top}_{0} and L-\mathbf{Sob} as epireflective hulls

We show that the category \(L\) - \(\mathbf{Top}_{0}\) of \(T_{0}\) - \(L\) -topological spaces is the epireflective hull of Sierpinski \(L\) -topological space in the category \(L\) - \(\mathbf{Top}\) of \(L\) -topological spaces and the category \(L\) - \(\mathbf{Sob}\) of sober \(L\) -topological spaces is the epireflective hull of Sierpinski \(L\) -topological space in the category \(L\) - \(\mathbf{Top}_{0}\) .     

Yang-Baxter {\breve R} matrix, entanglement and Yangian

We present a method to construct ??X?? form unitary Yang-Baxter ${\breve R}$ matrices, which act on the tensor product space ${V_{i}^{j_{1}}\otimes V_{i+1}^{j_{2}}}$ . We can obtain a set of entangled states for (2j ₁?+?1)?× (2j ₂?+?1)-dimensional system with these Yang-Baxter ${\breve R}$ matrices. By means of Yang-Baxter approach, a 8?× 8 Yang-Baxter Hamiltonian is constructed. Yangian symmetry and Yangian generators as shift operators for this Yang-Baxter system are investigated in detail.     

\lambda -Statistical convergence of fuzzy numbers and fuzzy functions of order \theta

In this paper, we introduce the concept of $\lambda $ -statistical convergence of order $\theta $ and strong $\lambda $ -summability of order $\theta $ for the sequence of fuzzy numbers. Further the same concept is extended to the sequence of fuzzy functions and introduce the spaces like $S_\lambda ^\theta (\hat{f})$ and $\omega _{\lambda p} ^\theta (\hat{f})$ . Some inclusion relations in those spaces and also the underlying relation between these two spaces are also obtained.     

Parallel black box \mathcal {H}-LU preconditioning for elliptic boundary value problems

Hierarchical ( $\mathcal {H}$ -) matrices provide a data-sparse way to approximate fully populated matrices. The two basic steps in the construction of an $\mathcal {H}$ -matrix are (a) the hierarchical construction of a matrix block partition, and (b) the blockwise approximation of matrix data by low rank matrices. In the context of finite element discretisations of elliptic boundary value problems, $\mathcal {H}$ -matrices can be used for the construction of preconditioners such as approximate $\mathcal {H}$ -LU factors. In this paper, we develop a new black box approach to construct the necessary partition. This new approach is based on the matrix graph of the sparse stiffness matrix and no longer requires geometric data associated with the indices like the standard clustering algorithms. The black box clustering and a subsequent $\mathcal {H}$ -LU factorisation have been implemented in parallel, and we provide numerical results in which the resulting black box $\mathcal {H}$ -LU factorisation is used as a preconditioner in the iterative solution of the discrete (three-dimensional) convection-diffusion equation.     

Local Discontinuous Galerkin Methods for One-Dimensional Second Order Fully Nonlinear Elliptic and Parabolic Equations

This paper is concerned with developing accurate and efficient nonstandard discontinuous Galerkin methods for fully nonlinear second order elliptic and parabolic partial differential equations (PDEs) in the case of one spatial dimension. The primary goal of the paper to develop a general framework for constructing high order local discontinuous Galerkin (LDG) methods for approximating viscosity solutions of these fully nonlinear PDEs which are merely continuous functions by definition. In order to capture discontinuities of the first order derivative $u_x$ of the solution $u$ , two independent functions $q^-$ and $q^+$ are introduced to approximate one-sided derivatives of $u$ . Similarly, to capture the discontinuities of the second order derivative $u_{xx}$ , four independent functions $p^{- -}, p^{- +}, p^{+ -}$ , and $p^{+ +}$ are used to approximate one-sided derivatives of $q^-$ and $q^+$ . The proposed LDG framework, which is based on a nonstandard mixed formulation of the underlying PDE, embeds a given fully nonlinear problem into a mostly linear system of equations where the given nonlinear differential operator must be replaced by a numerical operator which allows multiple value inputs of the first and second order derivatives $u_x$ and $u_{xx}$ . An easy to verify set of criteria for constructing “good” numerical operators is also proposed. It consists of consistency and generalized monotonicity. To ensure such a generalized monotonicity property, the crux of the construction is to introduce the numerical moment in the numerical operator, which plays a critical role in the proposed LDG framework. The generalized monotonicity gives the LDG methods the ability to select the viscosity solution among all possible solutions. The proposed framework extends a companion finite difference framework developed by Feng and Lewis (J Comp Appl Math 254:81–98, 2013) and allows for the approximation of fully nonlinear PDEs using high order polynomials and non-uniform meshes. Numerical experiments are also presented to demonstrate the accuracy, efficiency and utility of the proposed LDG methods.     

Design and implementation of LQG\LTR controller for a magnetic telemanipulation system-performance evaluation and energy saving

This paper deals with designing a telemanipulation system (TMS) for microrobotics applications. The TMS uses magnetic levitation technology for the three-dimensional (3-D) manipulation of a microrobot. The TMS is made up of two separate components: a magnetic drive unit and a microrobot. The magnetic drive unit is developed to generate the magnetic field for propelling the microrobot in an enclosed environment. The drive unit consists of electromagnets, a disc pole-piece for connecting the magnetic poles, and a yoke. To handle the 3-D high precision motion control of the microrobot, experimental magnetic field measurements coupled with numerical analysis were done to identify the dynamic model of levitation. This approach leads to the design of a linear quadratic gaussian (LQG) control system, based on the derived state-space model. Based on the PID controller performance, the LQG controller provides considerable improvement in transient response and cross coupling errors. The 3-D motion control capability of the LQG control method is verified experimentally, and it is demonstrated that the microrobot can be operated in the TMS workspace, vertical range of 30?mm and the horizontal range of $32\times 32\,{\text{mm}}^2$ , with RMS error on the order of $10\,\upmu {\text{m}}$ in the vertical and $2.2\,\upmu {\text{m}}$ in the horizontal direction. In the vertical motion, the cross coupling error of the LQG controller is nine times smaller than that of the PID controller. A pre-magnetized pole-piece is proposed to compensate for gravity effect and reduces the system??s energy consumption. This pole-piece provides 66% energy saving for the system??s workspace operations.     

Design and Validation of an ${\mathcal{L}}_{1}$ Adaptive Controller for Mini-UAV Autopilot

The dynamics of Unmanned Aerial Vehicles (UAVs) is nonlinear and subject to external disturbances. The scope of this paper is the test of an \({\mathcal{L}_1}\) adaptive controller as autopilot inner loop controller candidate. The selected controller is based on piecewise constant adaptive laws and is applied to a mini-UAV. Navigation outer loop parameters are regulated via PID control. The main contribution of this paper is to demonstrate that the proposed control design can stabilize the nonlinear system, even if the controller parameters are selected starting from a decoupled linear model. The main advantages of this technique are: (1) the controller can be implemented for both linear and nonlinear systems without parameter adjustment or tuning procedure, (2) the controller is robust to unmodeled dynamics and parametric model uncertainties. The design scheme of a customized autopilot is illustrated and different configurations (in terms of mass, inertia and airspeed variations) are analyzed to validate the presented approach.     

Self-orthogonal codes with dual distance three and quantum codes with distance three over \mathbb F _5

Self-orthogonal codes with dual distance three and quantum codes with distance three constructed from self-orthogonal codes over $\mathbb F _5$ are discussed in this paper. Firstly, for given code length $n\ge 5$ , a $[n,k]_{5}$ self-orthogonal code with minimal dimension $k$ and dual distance three is constructed. Secondly, for each $n\ge 5$ , two nested self-orthogonal codes with dual distance two and three are constructed, and consequently quantum code of length $n$ and distance three is constructed via Steane construction. All of these quantum codes constructed via Steane construction are optimal or near optimal according to the quantum Hamming bound.     

A Terrain Referenced UAV Localization Algorithm Using Binary Search Method

This study focuses on localization of Unmanned Aerial Vehicles (UAV) since permanent navigation has vital significance to support position information and to avoid getting lost. Actually, there exist effective aeronautical navigation systems in use. Inertial Navigation System (INS) and Global Positioning System (GPS) are two representatives of the most common systems utilized in traditional aerial vehicles. However, an alternative supporter system for UAVs should be mentioned since INS and GPS have serious deficiencies for UAVs such as accumulated errors and satellite signal loss, respectively. Such handicaps are coped with integrating these systems or exploiting other localization systems. Terrain Referenced Navigation (TRN) could be a good alternative as a supporter mechanism for these main systems. This study aims to localize a UAV accurately by using only the elevation data of the territory in order to simulate a TRN system. Application of the methodology on a real UAV is also considered for the future. Thus assumptions and limitations are designed regarding the constraints of real systems. In order to represent terrain data, Digital Elevation Model (DEM) with original 30 meter-resolution (Eroglu and Yilmaz 2013) and also synthetically generated 10 meter-resolution maps are utilized. The proposed method is based on searching the measured elevation values of the flight within the DEM and makes use of simulation techniques to test the accuracy and the performance. The whole system uses sequences of elevation values with a predefined length (i.e. profile). Mainly, all possible profiles are generated and stored before the flight. We identify, classify and sort profiles to perform search operations in a small subset of the terrain. During the flight, a measured flight profile is searched by the Binary search method (Eroglu 2013) within a small neighborhood of corresponding profile set.     

Reconfigurable natural interaction in smart environments: approach and prototype implementation

The vision of sensor-driven applications that adapt to the environment hold great promise, but it is difficult to turn these applications into reality because device and space heterogeneity is an obstacle to interoperability and mutual understanding of the smart devices and spaces involved. Smart Spaces provide shared knowledge about physical domains and they inherently enable cooperative and adaptable applications by keeping track of the semantic relations between objects in the environment. In this paper, the interplay between sensor-driven objects and Smart Spaces is investigated and a device with a tangible interface demonstrates the potential of the ${\sl smart{\text -}space{\text -}based}$ and ${\sl sensor{\text -}driven}$ computing paradigm. The proposed device is named REGALS (Reconfigurable Gesture based Actuator and Low Range Smartifier). We show how, starting from an interaction model proposed by Niezen, REGALS can reconfigure itself to support different functions like Smart Space creation (also called ${\sl environment\,smartification}$ ), interaction with heterogeneous devices and handling of semantic connections between gestures, actions, devices, and objects. This reconfiguration ability is based on the context received from the Smart Space. The paper also shows how tagged objects and natural gestures are recognized to improve the user experience reporting a use case and the performance evaluation of REGALS’ gesture classifier.