Comparison of fuzzy implication operators by means of fuzzy relational products used for intelligent local path-planning of AUVs

This paper describes the best choice to fuzzy implication operator and α-cut that are proper to the heuristic search technique for real-time collision avoidance of autonomous underwater vehicles (AUVs). A fuzzy implication operator is applied to the computation of fuzzy triangle product that constructs a new fuzzy relation between two fuzzy relations. An α-cut transforms a fuzzy relation into a crisp relation which is represented as a matrix. Those are the theoretical basis of heuristic search technique. In this paper, we review briefly our previous work—a heuristic search technique using fuzzy relational products for the collision avoidance system of AUVs, and propose the selection of a fuzzy implication operator and α-cut which are the most suitable for the search technique. In order to verify the optimality and the efficiency of the selected fuzzy implication operator and α-cut, we simulate every case of α-cut for each fuzzy implication operator in view of the cost of path and the number of α -cut generating acceptable path to the goal. This work was supported by the Korea Research Foundation Grant funded by the Korean Government (MOEHRD) (KRF-2007-521-D00433).     

New approaches to robust l2?l∞ and H∞ filtering for uncertain discrete-time systemsfiltering for uncertain discrete-time systems

The problems of robust l ₂−l _∞ and H _∞ filtering for discrete-time systems with parameter uncertainty residing in a polytope are investigated in this paper. The filtering strategies are based on new robust performance criteria derived from a new result of parameter-dependent Lyapunov stability condition, which exhibit less conservativeness than previous results in the quadratic framework. The designed filters guaranteeing a prescribed l ₂−l _∞ or H _∞ noise attenuation level can be obtained from the solution of convex optimization problems, which can be solved via efficient interior point methods. Numerical examples have shown that the filter design procedures proposed in this paper are much less conservative than earlier results.     

Fuzzy <Emphasis Type="Italic">R</Emphasis>-subgroups with thresholds of near-rings and implication operators

Using the belongs to relation (∈) and quasi-coincidence with relation (q) between fuzzy points and fuzzy sets, the concept of (α, β)-fuzzy R-subgroup of a near-ring where α , β are any two of {∈, q, ∈∨q , ∈∧q} with α ≠ ∈∧q is introduced and related properties are investigated. We also introduce the notion of a fuzzy R-subgroup with thresholds which is a generalization of an ordinary fuzzy R-subgroup and an (∈, ∈∨q)-fuzzy R-subgroup. Finally, we give the definition of an implication-based fuzzy R-subgroup.     

Relaxed stability condition and state feedback H ∞ controller design for T-S fuzzy systems

In this paper, a fuzzy Lyapunov approach is presented for stability analysis and state feedback H _∞ controller design for T-S fuzzy systems. A new stability condition is obtained by relaxing the ones derived in previous papers. Then, a set of LMI-based sufficient conditions which can guarantee the existence of state feedback H _∞ controller for T-S fuzzy systems is proposed. In comparison with the existing literature, the proposed approach not only provides more relaxed stability conditions but also ensures better H _∞ performance. The effectiveness of the proposed approach is shown through two numerical examples. Recommended by Editor Young-Hoon Joo. Xiao-Heng Chang received the B.E. and M.S. degrees from Liaoning Technical University, China, in 1998 and 2004, respectively, and the Ph.D. degree from Northeastern University, China, in 2007. He is currently a Lecturer in the School of Information Science and Engineering, Bohai University, China. His research interests include fuzzy control and robust control as well as their applications. Guang-Hong Yang received the B.S. and M.S. degrees in Northeast University of Technology, China, in 1983 and 1986, respectively, and the Ph.D. degree in Control Engineering from Northeastern University, China (formerly, Northeast University of Technology), in 1994. He was a Lecturer/Associate Professor with Northeastern University from 1986 to 1995. He joined the Nanyang Technological University in 1996 as a Postdoctoral Fellow. From 2001 to 2005, he was a Research Scientist/Senior Research Scientist with the National University of Singapore. He is currently a Professor at the College of Information Science and Engineering, Northeastern University. His current research interests include fault-tolerant control, fault detection and isolation, nonfragile control systems design, and robust control. Dr. Yang is an Associate Editor for the International Journal of Control, Automation, and Systems (IJCAS), and an Associate Editor of the Conference Editorial Board of the IEEE Control Systems Society.     

Delay-dependent robust H ∞ control for uncertain fuzzy Markovian jump systems

This paper is concerned with the problem of delay-dependent robust H _∞ control for uncertain fuzzy Markovian jump systems with time delays. The purpose is to design a mode-dependent state-feedback fuzzy controller such that the closed-loop system is robustly stochastically stable and satisfies an H _∞ performance level. By introducing slack matrix variables, a delay-dependent sufficient condition for the solvability of the problem is proposed in terms of linear matrix inequalities. An illustrative example is finally given to show the applicability and effectiveness of the proposed method. Recommended by Editorial Board member Young Soo Suh under the direction of Editor Jae Weon Choi. This work is supported by the National Science Foundation for Distinguished Young Scholars of P. R. China under Grant 60625303, the Specialized Research Fund for the Doctoral Program of Higher Education under Grant 20060288021, and the Natural Science Foundation of Jiangsu Province under Grant BK2008047. Yashun Zhang received the B.S. and M.S. degrees in Control Science and Control Engineering from Hefei University of Science and Technology in 2003 and 2006. He is currently a Ph.D. student in Control Science and Control Engineering, Nanjing University of Science and Technology. His research interests include fuzzy control, sliding mode control and nonlinear control. Shengyuan Xu received the Ph.D. degree in Control Science and Control Engineering from Nanjing University of Science and Technology in 1999. His research interests include robust filtering and control, singular systems, time-delay systems and nonlinear systems. Jihui Zhang is a Professor in the School of Automation Engineering of Qingdao University, China. His main areas of interest are discrete event dynamic systems, production planning and control, and operations research.     

An Optimal Algorithm for the Minimum Disc Cover Problem

The minimum disc cover can be used to construct a dominating set on the fly for energy-efficient communications in mobile ad hoc networks, but the approach used to compute the minimum disc cover proposed in previous studies is computationally relatively expensive. In this paper, we show that the disc cover problem is in fact a special case of the general α-hull problem. In spite of being a special case, the disc cover problem is not easier than the general α-hull problem. In addition to applying the existing α-hull algorithm to solve the disc cover problem, we present a simple, yet optimal divide-and-conquer algorithm that constructs the minimum disc cover for arbitrary cases, including those degenerate cases where the α-hull approach would fail.     

Mixed <Emphasis Type="Italic">H</Emphasis><Subscript>2</Subscript>/<Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> filtering for a class of high-speed sampling uncertain systems

The problem of mixed H2/H∞ filtering for polytopic Delta operator systems is investigated. The aim is to design a linear asymptotically stable filter which guarantees that the filtering error system has different performances in different filtering channels. Based on a parameter-dependent Lyapunov function, a new mixed H2/H∞ performance criterion is presented. Upon this performance criterion, a sufficient condition for the full-order mixed H2/H∞ filter is derived in terms of linear matrix inequalities. The filter can be obtained from the solution of a convex optimization problem. The proposed filter design procedure is less conservative than the strategy based on the quadratic stability notion. A numerical example is given to illustrate the feasibility of the proposed approach.     

Robust fuzzy stabilization of dithered chaotic systems using island-based random optimization algorithm

Applying dither to highly nonlinear systems may suppress chaotic phenomena, but dynamic performance, such as convergence rate and disturbance attenuation, is usually not guaranteed. This paper presents a dithered H_∞ robust fuzzy control scheme to stabilize chaotic systems that ensures disturbance attenuation bounds. In the proposed scheme, Takagi-Sugeno (T-S) fuzzy linear models are used to describe the relaxed models of the dithered chaotic system, and fuzzy controllers are designed based on an extension to the concept of parallel distributed compensation (PDC). Sufficient condition for the existence of the H_∞ robust fuzzy controllers is presented in terms of a novel linear matrix inequalities (LMI) form which takes full consideration of modeling error and disturbances, but cannot be solved by the standard procedures. In order to solve the LMI problem and to identify the chaotic systems as T-S fuzzy modes, we propose a compound optimization strategy called the island-based random-walk algorithm (IRA). The algorithm is composed of a set of communicating random-walk optimization procedures concatenated with the down-hill simplex method. The design procedure and validity of the proposed scheme is demonstrated via numerical simulation of the dithered fuzzy control of a chaotic system.     

(∈, ∈ ∨ q)-fuzzy subnear-rings and ideals

Our aim in this paper is to introduce and study the new sort of fuzzy subnear-ring (ideal and prime ideal) of a near-ring called (∈, ∈ ∨q)-fuzzy subnear-ring (ideal and prime ideal). These fuzzy subnear-rings (ideals) are characterized by their level ideals. Finally, we give a generalization of (∈, ∈ ∨q)-fuzzy subnear-rings (ideals).     

New approaches to H∞ controller designs based on fuzzy observers for T-S fuzzy systems via LMI

The problems of relaxed quadratic stability conditions, fuzzy observer designs and H_∞ controller designs for T-S fuzzy systems have been studied. First new stability conditions are obtained by relaxing the stability conditions derived in previous papers. Secondly, new fuzzy observers based on the relaxed stability conditions for the T-S fuzzy systems have been proposed. Thirdly two sufficient LMI conditions, which guarantee the existence of the H_∞ controllers based on fuzzy observers for the T-S fuzzy systems have been proposed. The conditions are not only simple, but also consider the interactions among the fuzzy subsystems. Finally by some examples, using the LMI technique, we show that the regulators, the fuzzy observers and the H_∞ controller designs based on new observers for the T-S fuzzy systems are very practical and efficient.     

Improved Parameter-dependent H∞ Filtering for Polytopic Delta Operator Systems

The problem of H∞ filtering for polytopic Delta operator linear systems is investigated. An improved H∞ performance criterion is presented based on the bounded real lemma. Upon the improved performance criterion, a sufficient condition for the existence of parameter-dependent H∞ filtering is derived in terms of linear matrix inequalities. The designed filter can be obtained from the solution of a convex optimization problem. The filter design makes full use of the parameter-dependent approach, which leads to a less conservative result than conventional design methods. A numerical example is given to illustrate the effectiveness of the proposed approach.     

Fuzzy linear regression model based on fuzzy scalar product

The new concept and method of imposing imprecise (fuzzy) input and output data upon the conventional linear regression model is proposed in this paper. We introduce the fuzzy scalar (inner) product to formulate the fuzzy linear regression model. In order to invoke the conventional approach of linear regression analysis for real-valued data, we transact the α-level linear regression models of the fuzzy linear regression model. We construct the membership functions of fuzzy least squares estimators via the form of “Resolution Identity” which is a well-known formula in fuzzy sets theory. In order to obtain the membership value of any given least squares estimate taken from the fuzzy least squares estimator, we transform the original problem into the optimization problems. We also provide two computational procedures to solve the optimization problems.     

The singular zero-sum differential game with stability usingH ∞ control theory

In this paper we consider the zero-sum, infinite-horizon, linear quadratic differential game. We derive sufficient conditions for the existence of (almost) equilibria as well as necessary conditions. Contrary to all classical references we allow for singular weighting on the minimizing player in the cost criterion. It turns out that this problem has a strong relation with the singularH _∞ problem with state feedback, i.e., theH _∞ problem where the direct feedthrough matrix from control input to output is not necessarily injective.     

Worst-case design in the time domain: The maximum principle and the standardH ∞ problem

This paper presents a time-domain, optimal-control approach to worst-case design, an alternative to frequency-domainH _∞ techniques. The generic linear-quadratic set-up of the “standardH _∞ problem” is discussed. The resultsinclude a characterization of suboptimal values, as well as a parametrization of all suboptimal compensators, interms of two coupled indefinite Riccati equations. Both the usual infinite-horizon, time-invariant case and the finite-horizon, time-varying case, are treated. The latter is beyond the scope of frequency-domain analysis. An earlier version of this work was prepared at the Center for Control Sciences, Brown University, and was supported in part by the Air Force Office of Scientific Research under Contract F49620-86-C-011.     

Semi-explicit Solution and Fast Minimization Scheme for an Energy with <Emphasis Type="Italic">ℓ</Emphasis><Subscript>1</Subscript>-Fitting and Tikhonov-Like Regularization

Regularized energies with ℓ ₁-fitting have attracted a considerable interest in the recent years and numerous aspects of the problem have been studied, mainly to solve various problems arising in image processing. In this paper we focus on a rather simple form where the regularization term is a quadratic functional applied on the first-order differences between neighboring pixels. We derive a semi-explicit expression for the minimizers of this energy which shows that the solution is an affine function in the neighborhood of each data set. We then describe the volumes of data for which the same system of affine equations leads to the minimum of the relevant energy. Our analysis involves an intermediate result on random matrices constructed from truncated neighborhood sets. We also put in evidence some drawbacks due to the ℓ ₁-fitting. A fast, simple and exact optimization method is proposed. By way of application, we separate impulse noise from Gaussian noise in a degraded image.

The improved QV signature scheme based on conic curves over ℤ<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>

The classical RSA is vulnerable to low private exponent attacks (LPEA) and has homomorphism. KMOV based on elliptic curve E _n (a,b) over ℤ _n can resist LPEA but still has homomorphism. QV over E _n (a,b) not only can resist LPEA but also has no homomorphism. However, QV over E _n (a,b) requires the existence of points whose order is M _n = lcm{♯E _p (a,b), ♯E _q (a,b)}. This requirement is impractical for all general elliptic curves. Besides, the computation over En(a,b) is quite complicated. In this paper, we further study conic curve C _n (a,b) over ℤ _n and its corresponding properties, and advance several key theorems and corollaries for designing digital signature schemes, and point out that C _n (a,b) always has some points whose order is M _n = lcm{♯E _p (a,b), ♯E _q (a,b)}. Thereby we present an improved QV signature over C _n (a,b), which inherits the property of non-homomorphism and can resist the Wiener attack. Furthermore, under the same security requirements, the improved QV scheme is easier than that over E _n (a,b), with respect plaintext embedding, inverse elements computation, points computation and points’ order calculation. Especially, it is applicable to general conic curves, which is of great significance to the application of QV schemes. Supported by the National Natural Science Foundation of China (Grant No. 10128103)     

Convergence of the generalized-α scheme for constrained mechanical systems

A variant of the generalized-α scheme is proposed for constrained mechanical systems represented by index-3 DAEs. Based on the analogy with linear multistep methods, an elegant convergence analysis is developed for this algorithm. Second-order convergence is demonstrated both for the generalized coordinates and the Lagrange multipliers, and those theoretical results are illustrated by numerical tests.     

<Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> Control Design Using Dynamic Neural Networks

In this paper, a new approach is investigated for adaptive dynamic neural network-based H _∞ control, which is designed for a class of non-linear systems with unknown uncertainties. Currently, non-linear systems with unknown uncertainties are commonly used to efficiently and accurately express the real practical control process. Therefore, it is of critical importance but a great challenge and still at its early age to design a stable and robust controller for such a process. In the proposed research, dynamic neural networks were constructed to precisely approximate the non-linear system with unknown uncertainties first, a non-linear state feedback H _∞ control law was designed next, then an adaptive weighting adjustment mechanism for dynamic neural networks was developed to achieve H _∞ regulation performance, and last a recurrent neural network was employed as a neuro-solver to efficiently and numerically solve the standard LMI problem so as to obtain the appropriate control gains. Finally, case studies further verify the feasibility and efficiency of the proposed research.     

Robust H ∞ networked control for discrete-time fuzzy systems with state quantisation

The problem of robust H _∞ control for uncertain discrete-time Takagi and Sugeno (T-S) fuzzy networked control systems (NCSs) with state quantisation is investigated. A new model of network-based control with simultaneous consideration of network-induced delays and packet dropouts is proposed. By using a fuzzy Lyapunov–Krasovskii functional (LKF), we derive a less conservative delay-dependent stability condition for the closed-loop NCSs. Robust H _∞ fuzzy controller is developed for the asymptotical stabilisation of the NCSs. Since it is not expressed as strict LMI conditions, the cone complementary linearisation procedure is exploited to solve the nonconvex feasibility problem. A numerical example shows the feasibility applications of the proposed technique.