On the distributivity of implication operators over T and S norms

In this paper, we explore the distributivity of implication operators [especially Residuated (R)- and Strong (S)-implications] over Takagi (T)- and Sugeno (S)-norms. The motivation behind this work is the on going discussion on the law [(p/spl and/q)/spl rarr/r]/spl equiv/[(p/spl rarr/r)/spl or/(q/spl rarr/r)] in fuzzy logic as given in the title of the paper by Trillas and Alsina. The above law is only one of the four basic distributive laws. The general form of the previous distributive law is J(T(p,q),r)/spl equiv/S(J(p,r),J(q,r)). Similarly, the other three basic distributive laws can be generalized to give equations concerning distribution of fuzzy implications J on T- and S- norms. In this paper, we study the validity of these equations under various conditions on the implication operator J. We also propose some sufficiency conditions on a binary operator under which the general distributive equations are reduced to the basic distributive equations and are satisfied. Also in this work, we have solved one of the open problems posed by M. Baczynski (2002).     

Well-behaved Translations between Structural Operational Semantics

We examine two versions of maps between distributive laws as candidates for well-behaved translations between structural operational semantics, and validate that by using simple coalgebraic arguments. We give some concrete examples of well-behaved translations that are maps between distributive laws. The modelling of structural operational semantics uses Turi and Plotkin's categorical models of GSOS. These maps between distributive laws come from the previous work on 2-categories of distributive laws.     

Robust stabilization for uncertain time-delay systems containingsaturating actuators

A class of uncertain time-delay systems containing a saturating actuator is considered. These systems are characterized by delayed state equations (including a saturating actuator) with norm-bounded parameter uncertainty (possibly time varying) in the state and input matrices. The delay is assumed to be constant bounded but unknown. Using a Razumikhin approach for the stability of functional differential equations, upper bounds on the time delay are given such that the considered uncertain system is robustly stabilizable, in the case of constrained input, via memoryless state feedback control laws. These bounds are given in terms of solutions of appropriate finite dimensional Riccati equations     

Über die Distributivgesetze der erweiterten Intervallarithmetik

Further relations between the operations in the extended interval arithmetic are discussed in this paper. In particular, the distributive laws in the extended arithmetic are considered, that is it is shown how to present expressions of the form(A?B) C, (A+B)/C, (A?B)/C etc. in an equivalent form. As a special case the well-known distributive laws for the usual interval operations are obtained.     

Modeling and controlling a robotic convoy using guidance laws strategies.

This paper deals with the problem of modeling and controlling a robotic convoy. Guidance laws techniques are used to provide a mathematical formulation of the problem. The guidance laws used for this purpose are the velocity pursuit, the deviated pursuit, and the proportional navigation. The velocity pursuit equations model the robot's path under various sensors based control laws. A systematic study of the tracking problem based on this technique is undertaken. These guidance laws are applied to derive decentralized control laws for the angular and linear velocities. For the angular velocity, the control law is directly derived from the guidance laws after considering the relative kinematics equations between successive robots. The second control law maintains the distance between successive robots constant by controlling the linear velocity. This control law is derived by considering the kinematics equations between successive robots under the considered guidance law. Properties of the method are discussed and proven. Simulation results confirm the validity of our approach, as well as the validity of the properties of the method. Index Terms-Guidance laws, relative kinematics equations, robotic convoy, tracking.     

输气管线的分布参数数学模型及工程应用

本文研究了用传递函数描述长距离输气管线这种分布参数调节对象的布法.长距离输气 管线输送的是可压缩的天然气,表征其动态特性的偏微分方程组较复杂.本文所用方法是将 其偏微分方程组经拉普拉斯变换,由时域变为频域,直接求解以管线长度为变量的线性变系数 微分方程--贝塞尔方程,从而得到描述这种分布参数调节对象动态特性的传递函数.将此 传递函数经数学处理,得到工程实用的简洁形式,并给出其频率特性曲线和动态响应过程.     

A new generic approach to model reduction for complex physiologically based drug models

This paper explores the identification problem when dealing with physiological models relating to anaesthetic drugs such as fentanyl. The Mapleson model for drug concentration, which will be the focus of this study, is described by algebraic equations, which are derived from the laws of physics and chemistry, and there are some limitations in its system's analysis, i.e. in the study of its relevant dynamics, and its exploitation from a control design viewpoint. Hence, we propose to represent this model via dynamic differential equations with a reduced number of variables using MATLAB–SIMULINK. Using Mapleson's approach for modelling, the input–output data for each organ can be obtained under a particular drug regimen which in turn can be used to obtain a continuous time-transfer function fit for each of these organs.     

LQ终端控制器设计的生成函数方法及其应用

利用哈密顿系统生成函数的性质求解LQ终端控制问题,并给出了相应的数值方法.针对现有文献中此类问题的最优控制律在终端时刻存在无穷大增益的情况,利用第二类生成函数的性质求解哈密顿系统两端边值问题并构造了无终端奇异性的时变最优控制律.然后根据哈密顿系统状态的正则变换性质导出了求解生成函数系数矩阵微分方程和计算时变控制律的矩阵递推格式.最后用所提出的方法研究了以能量均衡消耗为约束条件的卫星编队重构问题,设计了符合要求的闭环控制系统并给出了数值仿真结果.     

A Local Graph-rewriting System for Deciding Equality in Sum-product Theories

In this paper we give a graph-based decision procedure for a calculus with sum and product types. Although our motivation comes from the Bird-Meertens approach to reasoning algebraically about functional programs, the language used here can be seen as the internal language of a category with binary products and coproducts. As such, the decision procedure presented has independent interest.A standard approach based on term rewriting would work modulo a set of equations; the present work proposes a simpler approach, based on graph-rewriting. We show in turn how the system covers reflection equational laws, fusion laws, and cancellation laws.     

Coalgebraic semantics for timed processes

We give a coalgebraic formulation of timed processes and their operational semantics. We model time by a monoid called a “time domain”, and we model processes by “timed transition systems”, which amount to partial monoid actions of the time domain or, equivalently, coalgebras for an “evolution comonad” generated by the time domain. All our examples of time domains satisfy a partial closure property, yielding a distributive law of a monad for total monoid actions over the evolution comonad, and hence a distributive law of the evolution comonad over a dual comonad for total monoid actions. We show that the induced coalgebras are exactly timed transition systems with delay operators. We then integrate our coalgebraic formulation of time qua timed transition systems into Turi and Plotkin’s formulation of structural operational semantics in terms of distributive laws. We combine timing with action via the more general study of the combination of two arbitrary sorts of behaviour whose operational semantics may interact. We give a modular account of the operational semantics for a combination induced by that of each of its components. Our study necessitates the investigation of products of comonads. In particular, we characterise when a monad lifts to the category of coalgebras for a product comonad, providing constructions with which one can readily calculate.     

Sequential circle criterion approach for robustly stabilizing individual generators with SVC

Absolute stability with the spatially defined linear time‐invariant (LTI) state‐space modelings is scrutinized by means of what we call the sequential Lyapunov approach, which possesses independent significance in stabilization when gain‐scheduling control laws are adopted. Then, this theoretical result is exploiting for stabilization of individual generators via SVC actions. More precisely, by remodeling the perturbed swing equations of synchronous generators in multimachine networks through spatially defined LTI state‐space expressions subjected to uncertainties and power disturbance, which are viewed as sector nonlinearities, we introduce frequency responses for coping with nonlinear power swing dynamics of individual generators. By sequentially relating the frequency responses to the circle criterion (substantially, the KYP theorem or the positive real lemma) claimed for LTI systems subject to sector disturbances, output feedback control laws for static VAR compensators are worked out to stabilize individual generators. The frequency‐domain approach is also useful in steady‐state specification besides stabilization in individual generators. Examples show efficacy of the suggested stabilization and steady‐state specification technique. Copyright © 2014 John Wiley & Sons, Ltd.     

Boundary stabilisation to non-stationary solutions for deterministic and stochastic parabolic-type equations

In this work, we design explicit, finite-dimensional boundary feedback laws for stabilisation to trajectories for parabolic-type equations. The simple form of the feedback allows to write the solution of the corresponding closed-loop equation in a mild formulation via a kernel; then, taking advantage of this, the stability is shown. As an application, null stabilisation for stochastic parabolic-type equations is deduced as well. As far as we know, the present work is the first result on boundary feedback stabilisation to trajectories and for stochastic parabolic-type equations, with stability guaranteed independent of how large the level of the noise is.     

Bialgebras for structural operational semantics: An introduction

Bialgebras and distributive laws are an abstract, categorical framework to study various flavors of structural operational semantics. This paper aims to introduce the reader to the basics of bialgebras for operational semantics, and to sketch the state of the art in this research area.     

Remarks on minimal solutions of a system of fuzzy relation equations over complete infinitely distributive lattices

In Section 3.6 of Fuzzy relation equations and their applications to knowledge engineering. Kluwer Academic Publishers, Boston (1989), Di Nola et al. presented a procedure to find a minimal solution from a fixed solution of a system of fuzzy relation equations over complete infinitely distributive lattices, and put the question: is the minimal solution found by the procedure unique or not? In this paper, we give a negative answer to the question and make some further remarks. We not only give a necessary and sufficient condition for the uniqueness of such minimal solutions, but also characterize the existence of the least solution and a unique solution of a system of fuzzy relation equations over complete infinitely distributive lattices.     

An Efficient Multigrid Solver based on Distributive Smoothing for Poroelasticity Equations

In this paper, we present a robust distributive smoother in a multigrid method for the system of poroelasticity equations. Within the distributive framework, we deal with a decoupled system, that can be smoothed with basic iterative methods like an equation-wise red-black Jacobi point relaxation. The properties of the distributive relaxation are optimized with the help of Fourier smoothing analysis. A highly efficient multigrid method results, as is confirmed by Fourier two-grid analysis and numerical experiments.AMS Subject Classifications: 65N55, 74F10, 74S10, 65M12.This revised version was published online in December 2004. In the previous version the name of the first author was wrong.     

Galerkin approximationwith Legendre polynomials for a continuous-time nonlinear optimal control problem

We investigate the use of an approximation method for obtaining near-optimal solutions to a kind of nonlinear continuous-time (CT) system. The approach derived from the Galerkin approximation is used to solve the generalized Hamilton-Jacobi-Bellman (GHJB) equations. The Galerkin approximation with Legendre polynomials (GALP) for GHJB equations has not been applied to nonlinear CT systems. The proposed GALP method solves the GHJB equations in CT systems on some well-defined region of attraction. The integrals that need to be computed are much fewer due to the orthogonal properties of Legendre polynomials, which is a significant advantage of this approach. The stabilization and convergence properties with regard to the iterative variable have been proved. Numerical examples show that the update control laws converge to the optimal control for nonlinear CT systems.     

Distributed dynamic programming for discrete-time stochastic control, and idempotent algorithms

Idempotent methods have been found to be extremely fast for the solution of dynamic programming equations associated with deterministic control problems. The original methods exploited the idempotent (e.g., max-plus) linearity of the associated semigroup operator. It is now known that curse-of-dimensionality-free idempotent methods do not require this linearity. Instead, it is sufficient that certain solution forms are retained through application of the associated semigroup operator. Here, we see that idempotent methods may be used to solve some classes of stochastic control problems. The key is the use of the idempotent distributive property. We demonstrate this approach for a class of nonlinear, discrete-time stochastic control problems.     

Coordinated control method of space-tethered robot system for tracking optimal trajectory

Space-tethered robot system is a new kind of space robot, which consists of a robot platform, space tether, and operation robot. This paper presents the coordinated control method in order to save thruster fuel of operation robot in the process of tracking the optimal approach trajectory. First, the optimal approach trajectory of an operation robot is designed using the Gauss pseudospectral method, which resulted in continuous optimal control force using the Lagrange interpolation scheme. The optimal control force is optimized and distributed to space tether and thrusters through simulated annealing algorithm in discrete points, which minimized fuel consumption of thrusters. The distributive continuous force is obtained via cubic polynomial fitting of optimal distributive force in 0.1s discrete time point. To tracking the optimal trajectory, Fuzzy Proportional-Derivative controller is designed with the help of optimal distribution force which come from optimization model. Simultaneously, the relative attitude of the operation robot is stabilized using attitude time-delay algorithm through the reaction wheels. Numerical results are presented, demonstrating the validity of saving thruster fuel and well performance in tracking the optimal trajectory.

     

Transfer matrix approach to the triangular block decoupling problem

The triangular block decoupling problem for linear multivariable systems is studied via the transfer matrix approach. This approach clearly separates the problem of admissible control laws from the one of desired decoupled system specifications. Necessary and sufficient triangular decoupling conditions are given for various control laws. These conditions are expressed in a very simple way in terms of linear dependance among the transfer matrix rows. It turns out that when the problem is solvable, this can be done by static state feedback on a minimal realization of the system. Furthermore it is shown that whenever triangular block decoupling is possible, it is also attainable with stability.     

Consensus of linear multi-agent systems subject to actuator saturation

This paper is aimed at studying the consensus of linear multi-agent systems subject to actuator saturation. In order to solve the consensus problem, a new family of scheduled low-and-high-gain decentralized control laws are designed, provided that the dynamics of each agent is asymptotically null controllable with bounded controls, and such control laws rely on the asymptotic property of a class of parametric algebraic Ricatti equations. It is shown that the consensus of the systems with connected and fixed topology can be achieved semi-globally asymptotically via the local error low-and-high-gain feedback. An illustrative example with simulations shows that our method as well as control protocols is effective for the consensus of the linear multi-agent systems subject to actuator saturation.