Design of variable structure control for fuzzy nonlinear systems

In this paper, the variable structure control problem is presented for Takagi–Sugeno fuzzy systems with uncertainties and external disturbances. The sliding surfaces for the T–S fuzzy system are proposed by using a Lyapunov function and a fuzzy Lyapunov function, respectively. And we design the variable structure controllers such that the global T–S fuzzy system confined on the sliding surfaces is asymptotically stable. Two examples are given to illustrate the effectiveness of our proposed methods.     

Partitioning the parameter domain in a Chebyshev extremal problem

We consider the problem of global extremum of the Stieltjes integral of a given function dependent on parameters, with variable integrating function from the class of distribution functions with two given power moments.Translated from Kibernetika, No. 2, pp. 65–69, March–April, 1990.     

On the Convergence of Empirical Estimates in Problems of Stochastic Programming for Processes with Discrete Time

This paper is devoted to the investigation of a stochastic programming problem with a convex criterion function in the case where the random factor is a stationary ergodic sequence. The problem is approximated by the problem of minimization of an empirical function. It is proved that, under some conditions, the empirical estimate coincides with the solution of the former problem in the case of a great number of observations and that the probability of large deviations of the empirical estimate from the solution of the initial problem decreases exponentially with increasing the number of observations.__________Translated from Kibernetika i Sistemnyi Analiz, No. 1, pp. 175–178, January–February 2005.     

A globally convergent method based on Fischer–Burmeister operators for solving second-order cone constrained variational inequality problems

The Karush–Kuhn–Tucker system of a second-order cone constrained variational inequality problem is transformed into a semismooth system of equations with the help of Fischer–Burmeister operators over second-order cones. The Clarke generalized differential of the semismooth mapping is presented. A modified Newton method with Armijo line search is proved to have global convergence with local superlinear rate of convergence under certain assumptions on the variational inequality problem. An illustrative example is given to show how the globally convergent method works.     

Image Registration Using Wavelet-Based Motion Model

An image registration algorithm is developed to estimate dense motion vectors between two images using the coarse-to-fine wavelet-based motion model. This motion model is described by a linear combination of hierarchical basis functions proposed by Cai and Wang (SIAM Numer. Anal., 33(3):937–970, 1996). The coarser-scale basis function has larger support while the finer-scale basis function has smaller support. With these variable supports in full resolution, the basis functions serve as large-to-small windows so that the global and local information can be incorporated concurrently for image matching, especially for recovering motion vectors containing large displacements. To evaluate the accuracy of the wavelet-based method, two sets of test images were experimented using both the wavelet-based method and a leading pyramid spline-based method by Szeliski et al. (International Journal of Computer Vision, 22(3):199–218, 1996). One set of test images, taken from Barron et al. (International Journal of Computer Vision, 12:43–77, 1994), contains small displacements. The other set exhibits low texture or spatial aliasing after image blurring and contains large displacements. The experimental results showed that our wavelet-based method produced better motion estimates with error distributions having a smaller mean and smaller standard deviation.     

On NURBS algorithms using tangent cones

This paper considers tangent cones for NURBS surfaces. The first part gives new bounds for the tangent field, which extends the results of [Wang, G.-J., Sederberg, T.W., Saito, T., 1997. Partial derivatives of rational Bézier surfaces. Computer Aided Geometric Design 14, 377–381] to NURBS surfaces. In particular, if the weights of the NURBS surface have a tensor product structure, the tangent cones are spanned by the differences of the control points in one direction. The second part revisits uniqueness criteria for intersections between curves and surfaces and non-existence criteria for self-intersections, which are based on tangent cones. Using a unified proof, we reprove known theorems and deduce new criteria, e.g. for the non-existence of self-intersections.     

Stochastic Finite-State Models for Spoken Language Machine Translation

The problem of machine translation can be viewed as consisting of twosubproblems (a) lexical selection and (b) lexical reordering. In thispaper, we propose stochastic finite-state models for these two subproblems. Stochastic finite-state models are efficiently learnablefrom data, effective for decoding and are associated with a calculusfor composing models which allows for tight integration of constraintsfrom various levels of language processing. We present a method forlearning stochastic finite-state models for lexical selection andlexical reordering that are trained automatically from pairs of sourceand target utterances. We use this method to develop models forEnglish–Japanese and English–SPANISH translation and present the performance of these models for translation on speech and text. We also evaluate the efficacy of such a translation model in the context of a call routing task of unconstrained speech utterances.     

基于改进蝙蝠算法和三次样条插值的机器人路径规划

为更好地解决移动机器人路径规划问题,改进蝙蝠算法的寻优性能,拓展其应用领域,提出了一种具有反向学习和正切随机探索机制的蝙蝠算法.在全局搜索阶段的位置更新中引入动态扰动系数,提高算法全局搜索能力;在局部搜索阶段,融入正切随机探索机制,增强算法局部寻优的策略性,避免算法陷入局部极值.同时,加入反向学习选择策略,进一步平衡蝙...     

Optimal control of stochastic dynamic systems with past history and poison switchings

An optimal control problem for systems of stochastic differential-functional linear equations with past history and Poisson switchings is formulated. The Bellman equation is solved for this problem.Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 112–118, November–December 2004.This revised version was published online in April 2005 with a corrected cover date.     

On global stabilization of Burgers’ equation by boundary control

Although often referred to as a one-dimensional “cartoon” of Navier–Stokes equation because it does not exhibit turbulence, the Burgers equation is a natural first step towards developing methods for control of flows. Recent references include Burns and Kang [Nonlinear Dynamics 2 (1991) 235–262], Choi et al. [J. Fluid Mech. 253 (1993) 509–543], Ito and Kang [SIAM J. Control Optim. 32 (1994) 831–854], Ito and Yan [J. Math. Anal. Appl. 227 (1998) 271–299], Byrnes et al. [J. Dynam. Control Systems 4 (1998) 457–519] and Van Ly et al. [Numer. Funct. Anal. Optim. 18 (1997) 143–188]. While these papers have achieved tremendous progress in local stabilization and global analysis of attractors, the problem of global asymptotic stabilization has remained open. This problem is non-trivial because for large initial conditions the quadratic (convective) term – which is negligible in a linear/local analysis – dominates the dynamics. We derive nonlinear boundary control laws that achieve global asymptotic stability. We consider both the viscous and the inviscid Burgers’ equation, using both Neumann and Dirichlet boundary control. We also study the case where the viscosity parameter is uncertain, as well as the case of stochastic Burgers’ equation. For some of the control laws that would require the measurement in the interior of the domain, we develop the observer-based versions.     

A note on continuous-time ELS

The parameter estimation of continuous-time finite-dimensional linear stochastic systems is a problem of long-standing interest. The method usually used is the extended least-squares (ELS) algorithm described by a nonlinear stochastic differential equation (SLD), with the existence of the global strong solution assumed. This paper shows that the ELS estimate does exist in [0, ∞), and at the same time presents a number of convergence results paralleling those for the discrete-time case.     

Asymptotic characterizations of input–output-to-state stability for discrete-time systems

We establish the equivalence between global detectability and output-to-state stability for difference inclusions with outputs, and we present equivalent asymptotic characterizations of input–output-to-state stability for discrete-time nonlinear systems. These new stability characterizations for discrete-time systems parallel what have been developed for continuous-time systems in Angeli et al. [Uniform global asymptotic stability of differential inclusions, J. Dynamical Control Systems 10 (2004) 391–412] and Angeli et al. [Seperation principles for input–output and integral-input-to-state stability, SIAM J. Control Optim. 43 (2004) 256–276].     

A constrained, globalized, and bounded Nelder–Mead method for engineering optimization

One of the fundamental difficulties in engineering design is the multiplicity of local solutions. This has triggered much effort in the development of global search algorithms. Globality, however, often has a prohibitively high numerical cost for real problems. A fixed cost local search, which sequentially becomes global, is developed in this work. Globalization is achieved by probabilistic restarts. A spacial probability of starting a local search is built based on past searches. An improved Nelder–Mead algorithm is the local optimizer. It accounts for variable bounds and nonlinear inequality constraints. It is additionally made more robust by reinitializing degenerated simplexes. The resulting method, called the Globalized Bounded Nelder–Mead (GBNM) algorithm, is particularly adapted to tackling multimodal, discontinuous, constrained optimization problems, for which it is uncertain that a global optimization can be afforded. Numerical experiments are given on two analytical test functions and two composite laminate design problems. The GBNM method compares favorably with an evolutionary algorithm, both in terms of numerical cost and accuracy.     

Constructive description of the effective domain of a dual function

We propose a constructive method of describing the effective domain of a dual function of general form.Translated from Kibernetika, No. 1, pp. 50–54, January–February, 1989.     

Solutions of the Cahn–Hilliard equation

In this paper, we found some exact solutions of the Cahn–Hilliard equation and the system of the equations by considering a modified extended tanh function method. A numerical solution to a Cahn–Hilliard equation is obtained using a homotopy perturbation method (HPM) combined with the Adomian decomposition method (ADM). The comparisons are given in the tables.     

Empirical Investigation of the Convergence Speed of Inclusion Functions in a Global Optimization Context

This paper deals with the empirical convergence speed of inclusion functions applied in interval methods for global optimization. According to our experience the natural interval extension of a given function can be as good as a usual quadratically convergent inclusion function, and although centered forms are in general only of second-order, they can perform as one of larger convergence order. These facts indicate that the theoretical convergence order should not be the only indicator of the quality of an inclusion function, it would be better to know which inclusion function can be used most efficiently in concrete instances. For this reason we have investigated the empirical convergence speed of the usual inclusion functions on some test functions.This work has been supported by the Grants OTKA T 034350 and T 032118, OMFB D–30/2000, and OMFB E–24/2001.The authors are grateful for the anonymous referees for their suggestions.     

Color Characterization and Balancing by a Nonlinear Line Attractor Network for Image Enhancement

A novel method to map high dynamic range scenes to low dynamic range images utilizing the concept of color characterization, enhancement, and balancing is described in this letter. Each pixel of the image is first characterized by extracting the relationship of the red, green, and blue components along with its corresponding neighbors using a nonlinear line attractor network to form an associative memory. Then, the illumination enhancement process is performed using a hyperbolic tangent function to provide dynamic range compression to each pixel in the image. The slope of the hyperbolic tangent function is controlled using a parameter that is determined by the local and global statistics of the image to facilitate the change of the intensity level. A color balancing process restores the original color characteristics of the image based on learned associative memory matrices which eliminate image distortion due to improper recombination of red, green and blue components after enhancement. Experiments conducted on images captured at extremely uneven lighting environments show that the proposed method outperforms other image enhancement algorithms.     

Suboptimal mean controllers for bounded and dynamic stochastic distributions

Based on the recently developed algorithms for the modelling and control of bounded dynamic stochastic systems (H. Wang, J. Zhang, Bounded stochastic distributions control for pseudo ARMAX stochastic systems, IEEE Transactions on Automatic control, 486–490), this paper presents the design of a subotpimal nonlinear mean controller for bounded dynamic stochastic systems with guaranteed stability. The B-spline functional expansion based square root model is used to represent the output probability density function of the system. This is then followed by the design of a mean controller of the output distribution of the system using nonlinear output tracking concept. A nonlinear quadratic optimization is performed using the well known Hamilton–Jacobi–Bellman equation. This leads to a controller which consists of a static unit, a state feedback part and an equivalent output feedback loop. In order to achieve high precision for the output tracking, the output feedback gain is determined by a learning process, where the Lyapunov stability analysis is performed to show the asymptotic stability of the closed loop system under some conditions. A simulation example is included to demonstrate the use of the algorithm and encouraging results have been obtained.     

Queuing Systems with Cyclic Control Processes

An analysis of queuing systems with control processes more general than cyclic ones is proposed. Conditions ensuring stochastic boundedness of cyclic systems and existence of their steady state are analyzed.__________Translated from Kibernetika i Sistemnyi Analiz, No. 1, pp. 54–69, January–February 2005.     

A semi-direct approach to structure from motion

The problem of structure from motion is often decomposed into two steps: feature correspondence and three-dimensional reconstruction. This separation often causes gross errors when establishing correspondence fails. Therefore, we advocate the necessity to integrate visual information not only in time (i.e. across different views), but also in space, by matching regions – rather than points – using explicit photometric deformation models. We present an algorithm that integrates image-feature tracking and three-dimensional motion estimation into a closed loop, while detecting and rejecting outlier regions that do not fit the model. Due to occlusions and the causal nature of our algorithm, a drift in the estimates accumulates over time. We describe a method to perform global registration of local estimates of motion and structure by matching the appearance of feature regions stored over long time periods. We use image intensities to construct a score function that takes into account changes in brightness and contrast. Our algorithm is recursive and suitable for real-time implementation.