A class of systems of bilinear integral Volterra equations of the first kind of the second order

A class of bilinear systems of integral Volterra equations of the first kind related to the problem of automatic control of a nonlinear dynamic system (object) with unknown structure and vector input and output is studied. Algorithms for an analytic solution to corresponding bilinear systems and its numerical approximation are developed. A special character of the algorithms is illustrated by model examples.     

Feature detection of triangular meshes based on tensor voting theory

This paper presents n-dimensional feature recognition of triangular meshes that can handle both geometric properties and additional attributes such as color information of a physical object. Our method is based on a tensor voting technique for classifying features and integrates a clustering and region growing methodology for segmenting a mesh into sub-patches. We classify a feature into a corner, a sharp edge and a face. Then, finally we detect features via region merging and cleaning processes. Our feature detection shows good performance with efficiency for various dimensional models.     

On the properties of the identically singular Lagrange problem

We consider the identically singular Lagrange problem of the calculus of variations. It is investigated how the conjugate points and the Jacobi equation index are related to the solvability conditions of the appropriate matrix Riccati equation and the reducibility of the functional to a perfect square. The criterion of the trajectory variation smallness at a small variation of the functional in the neighborhood of the extremal is obtained.     

Control of complex ecological-economic systems

The paper is devoted to developing methods for control of ecological-economic systems consisting of three hierarchically subordinate subjects of control. In describing the dynamics of a system state, equations in partial derivatives that are solved numerically according to a semi-implicit scheme of the finite-difference method are used. To achieve its main goal (maintenance of an ecological subsystem in stable state), the subject of control of the upper level applies different control methods. Methods of hierarchical control (motivation, enforcement, and persuasion) that differ in the direction of action (on the objective function or domain of admissible controls) are proposed; examples of their use are represented and a comparative analysis of the obtained results is made.     

Minimum of power consumption in the problem of oscillation damping

Consideration was given to minimization of the L ¹-norm of control of the linear oscillatory system. For consumption of the energy resources required to damp oscillations, bilateral estimates were obtained.     

Optimization of interval type-2 fuzzy logic controllers for a perturbed autonomous wheeled mobile robot using genetic algorithms

We describe a tracking controller for the dynamic model of a unicycle mobile robot by integrating a kinematic and a torque controller based on type-2 fuzzy logic theory and genetic algorithms. Computer simulations are presented confirming the performance of the tracking controller and its application to different navigation problems.     

Designing of a type-2 fuzzy logic filter for improving edge-preserving restoration of interlaced-to-progressive conversion

This paper focuses on recently advanced fuzzy models and the application of type-2 fuzzy sets in video deinterlacing. The final goal of the proposed deinterlacing algorithm is to exactly determine an unknown pixel value while preserving the edges and details of the image. To begin, we will discuss some artefacts of spatial, temporal, and spatio-temporal domain deinterlacing methods. In order to address the aforementioned issues, we adopted type-2 fuzzy sets concepts to design a weight evaluating approach. In the proposed method, the upper and lower fuzzy membership functions of the type-2 fuzzy logic filters are derived from the type-1 (or primary) fuzzy membership function. The weights from upper and lower membership functions are considered to be multiplied with the candidate deinterlaced pixels. Experimental results proved that the performance of the proposed method was superior, both objectively and subjectively to other different conventional deinterlacing methods. Moreover, the proposed method preserved the smoothness of the original image edges and produced a high-quality progressive image.     

A systematic approach to improve multiple Lyapunov function stability and stabilization conditions for fuzzy systems

This paper presents a systematic approach for decreasing conservativeness in stability analysis and control design for Takagi-Sugeno (TS) systems. This approach is based on the idea of multiple Lyapunov functions together with simple techniques for introducing slack matrices. Unlike some previous approaches based on multiple Lyapunov functions, both the stability and the stabilization conditions are written as linear matrix inequality (LMI) problems. The proposed approach reduces the number of inequalities and guarantees extra degrees of freedom to the LMI problems. Numeric examples illustrate the effectiveness of this method.     

The pseudo-linear semantics of interval-valued fuzzy logics

Triangle algebras are equationally defined structures that are equivalent with certain residuated lattices on a set of intervals, which are called interval-valued residuated lattices (IVRLs). Triangle algebras have been used to construct triangle logic (TL), a formal fuzzy logic that is sound and complete w.r.t. the class of IVRLs.In this paper, we prove that the so-called pseudo-prelinear triangle algebras are subdirect products of pseudo-linear triangle algebras. This can be compared with MTL-algebras (prelinear residuated lattices) being subdirect products of linear residuated lattices.As a consequence, we are able to prove the pseudo-chain completeness of pseudo-linear triangle logic (PTL), an axiomatic extension of TL introduced in this paper. This kind of completeness is the analogue of the chain completeness of monoidal T-norm based logic (MTL).This result also provides a better insight in the structure of triangle algebras; it enables us, amongst others, to prove properties of pseudo-prelinear triangle algebras more easily. It is known that there is a one-to-one correspondence between triangle algebras and couples (L,α), in which L is a residuated lattice and α an element in that residuated lattice. We give a schematic overview of some properties of pseudo-prelinear triangle algebras (and a number of others that can be imposed on a triangle algebra), and the according necessary and sufficient conditions on L and α.     

Hybrid learning for interval type-2 fuzzy logic systems based on orthogonal least-squares and back-propagation methods

This paper presents a novel learning methodology based on a hybrid algorithm for interval type-2 fuzzy logic systems. Since only the back-propagation method has been proposed in the literature for the tuning of both the antecedent and the consequent parameters of type-2 fuzzy logic systems, a hybrid learning algorithm has been developed. The hybrid method uses a recursive orthogonal least-squares method for tuning the consequent parameters and the back-propagation method for tuning the antecedent parameters. Systems were tested for three types of inputs: (a) interval singleton, (b) interval type-1 non-singleton, and (c) interval type-2 non-singleton. Experiments were carried out on the application of hybrid interval type-2 fuzzy logic systems for prediction of the scale breaker entry temperature in a real hot strip mill for three different types of coil. The results proved the feasibility of the systems developed here for scale breaker entry temperature prediction. Comparison with type-1 fuzzy logic systems shows that hybrid learning interval type-2 fuzzy logic systems provide improved performance under the conditions tested.