A GENERAL SYSTEM LOGICAL THEORY

The General System Logical Theory (GSLT) is obtained by combining Resconi's logical theory of systems with Jessel's theory of secondary sources. In the present paper we give a first account of GSLT, of its foundation, its main features, and most obvious applications. GSLT is defined by its aims and concretized by a new specific concept, that of an Elementary Logical System (ELS). ELS may be connected with Lie algebras. The systems formerly dealt with by Resconi's and Jessel's separate theories are identified as particular ELS. Subsequently are built up various networks of ELS, leading thus to natural and powerful extensions of the classical feedback theory. Finally GSLT is applied to three very different topics: wave propagations (or any physical nature), Riemann geometries and chemical controls, showing thus its versatility and usefulness.     

Sequential least-squares prediction based on spectral analysis

A spectral representation for time series analysis is formulated on the basis of classical least-squares theory, and is extended for application to the prediction of a random sequence with a sequential updating of model coefficients based on pre-computed eigenvector components and current online data. The solution for updating the time series coefficients is shown to be directly analogous to the form of piecewise solution of the steady-state electrical network problem based on Kron's method of tearing and interconnection. The sensitivity of the spectral prediction algorithm based on the eigenvalue properties of the defining covariance data matrix is also developed.     

On the Minimal Realizations of a Finite Sequence

We develop a theory of minimal realizations of a finite sequence over an integral domain R, from first principles. Our notion of a minimal realization is closely related to that of a linear recurring sequence and of a partial realization (as in Mathematical Systems Theory). From this theory, we derive Algorithm MR. which computes a minimal realization of a sequence of L elements using at most L(5L + 1)/2 R-multiplications. We also characterize all minimal realizations of a given sequence in terms of the computed minimal realization.This algorithm computes the linear complexity of an R sequence, solves non-singular linear systems over R (extending Wiedemann's method), computes the minimal polynomial of an R-matrix, transfer/growth functions and symbolic Padé approximations. There are also a number of applications to Coding Theory.We thus provide a common framework for solving some well-known problems in Systems Theory, Symbolic/Algebraic Computation and Coding Theory.     

System concepts in Kron's polyhedron model and the scattering problem

Kron's polyhedron model based on a sequence of transformations related to the orthogonal electrical network problem was proposed for a wide range of system problems. The scattering formulation for a flow process introduces a similar sequence of ‘ obstacles ’ and can form an analytical basis for many of the concepts discussed by Kron. It can be associated with the system problems incorporating an optimality condition and the updating of a priori information, and can also be identified in the sweep method of solution of the two-point boundary-value problems for optimal control and estimation, which would appear to be related to the concept of wave propagation in Kron's model. The sequential networks in the polyhedron model and the scattering problem thus provide a basic analytical structure which has important applications in general systems theory.     

A Computational Method for Stochastic Optimal Control Problems in Financial Mathematics

Principle of optimality or dynamic programming leads to derivation of a partial differential equation (PDE) for solving optimal control problems, namely the Hamilton‐Jacobi‐Bellman (HJB) equation. In general, this equation cannot be solved analytically; thus many computing strategies have been developed for optimal control problems. Many problems in financial mathematics involve the solution of stochastic optimal control (SOC) problems. In this work, the variational iteration method (VIM) is applied for solving SOC problems. In fact, solutions for the value function and the corresponding optimal strategies are obtained numerically. We solve a stochastic linear regulator problem to investigate the applicability and simplicity of the presented method and prove its convergence. In particular, for Merton's portfolio selection model as a problem of portfolio optimization, the proposed numerical method is applied for the first time and its usefulness is demonstrated. For the nonlinear case, we investigate its convergence using Banach's fixed point theorem. The numerical results confirm the simplicity and efficiency of our method.     

Uniform random generation of expressions respecting algebraic identities

Algorithms for the uniform random generation of a particular class of formal expressions (containing arithmetical expressions, propositional calculus formulas, tree representations, special algebraic expressions and program structures) are described. “Uniform” means that all non-equivalent expressions of the same size are equiprobable, where equivalence is induced by commutative or associative properties of certain symbols (e.g.“a+b”≡“b+a”). In the special case where no commutative symbols occur, it is shown that the problem can be treated by a modification of Hickey's and Cohen's well known generation algorithm for context-free languages. In order to obtain a speed up in the generation time, a new, parallelizable algorithm is developed, which turns out to be applicable also to the general case (occurrence of commutative symbols).     

A Kleene Theorem for Weighted Tree Automata over Distributive Multioperator Monoids

Kleene’s theorem on the equivalence of recognizability and rationality for formal tree series over distributive multioperator monoids is proved. As a consequence of this, Kleene’s theorem for weighted tree automata over arbitrary, i.e., not necessarily commutative, semirings is derived.     

Editorial

This special issue is to honor professor Tzyh-Jong Tarn for his 80 birthday. Prof. Tarn is a world outstanding expert in Systems and Control Theory, Robotics and Quantum Control, etc. He received the D.Sc. degree in control system engineering from Washington University at St. Louis, Missouri, U.S.A. He is at present a Professor in the Department of Electrical Engineering and the Director of the Center for Robotics and Automation at Washington University. Dr. Tarn served as the President of the IEEE Robotics and Automation Society, the Director of IEEE Division X (Systems and Control), and a member of the IEEE Board of Directors. The Japan Foundation for the Promotion of Advanced Automation Technology presented him with the Best Research Article Award in March 1994. He also is a recipient of the Best Paper Award at the 1995 IEEE/RSJ International Conference on Intelligent Robots and Systems. Prof. Tarn has also made significant contribution to enhance the academic exchange between Chinese scholars and world systems science and automation society. This special issues contains 10 papers covering 1) Robot Control; 2) Quantum Control; 3) System Identification; 4) Advanced linear/Nonlinear Control Technique; and 5) Multi-agent Systems. These fields are closely related to Prof. Tarn''s research interests. The papers are arranged according to their categories....     

Land cover discrimination potential of radar multitemporal series and optical multispectral images in a Mediterranean cultural landscape

The aim of the present study is (1) to evaluate the performances of two series of European Remote Sensing (ERS) Synthetic Aperture Radar (SAR) images for land cover classification of a Mediterranean landscape (Minorca, Spain), compared with multispectral information from Système Pour l'Observation de la Terre (SPOT) and Landsat Thematic Mapper (TM) sensors, and (2) to test the synergy of SAR and optical data with a fusion method based on the Demspter–Shafer evidence theory, which is designed to deal with imprecise information. We have evaluated as a first step the contribution of multitemporal ERS data and contextual methods of classification, with and without filtering, for the discrimination of vegetation types. The present study shows the importance of time series of the ERS sensor and of the vectorial MMSE (minimum mean square error) filter based on segmentation for land cover classification. Fifteen land cover classes were discriminated (eight concerning different vegetation types) with a mean producer's accuracy of 0.81 for a five-date time series within 1998, and of 0.71 for another four-date time series for 1994/1995. These results are comparable to those from SPOT XS images: 0.69 for July, 0.67 for October (0.85 for July plus October), and also from TM data (0.81). These results are corroborated by the kappa coefficient of agreement. The fusion between the 1994 series of ERS and XS (July), based on a derived method of the Dempster–Shafer evidence theory, shows a slight improvement on overall accuracies: +0.06 of mean producer's accuracy and +0.04 of kappa coefficient.     

Computing Green's function of the initial-boundary value problem for the wave equation in a layered cylinder

A new analytical method for the approximate computation of the time-dependent Green's function for the initial-boundary value problem of the three-dimensional wave equation on multi-layered bounded cylinder is suggested in this paper. The method is based on the derivation of eigenvalues and eigenfunctions for an ordinary differential equation with piecewise constant coefficients, and an approximate computation of Green's function in the form of the Fourier series with a finite number of terms relative to the orthogonal set of the derived eigenfunctions. The computational experiment confirms the robustness of the method.     

A detailed study of the Wolf's algorithm

The objective of this paper is the analytical presentation of the Alan Wolf's Algorithm with the derivation of the equations needed to implement BASGEN and fixed evolution time algorithms, used for the numerical calculation of the largest positive Lyapunov exponent of an unknown time series. An improvement of the above algorithm is proposed by introducing a new stability criterion to make the algorithm more robust and improve its reliability.     

Additive Number Theory via Automata Theory

Theory of Computing Systems - We show how some problems in additive number theory can be attacked in a novel way, using techniques from the theory of finite automata. We start by recalling the...     

关于大系统理论的几个问题

本文讨论关于大系统理论的几个问题,即:什么是大系统?大系统理论与控制理论的关系;大系统理论与系统工程的关系;大系统理论与控制论的关系;大系统理论的特殊问题. 作者认为,大系统理论是第三代控制理论的重要内容,是综合自动化的理论基础.另一方面,大系统理论也是系统工程发展的新阶段--动态系统工程.也可以说,大系统理论是控制论的新分支--大系统控制论.大系统理论不是关于系统大小的分类学,而是大规模复杂控制与信息系统分析和综合的方法学,是研究大系统的系统科学.     

An adaptive economic simulation model

The use of Genetic Algorithms (GA's) in Economic Simulation Models has been introduced by Holland (Holland, 1988) and justified by pointing out the similarities between Economics, Game Theory, Control Theory and Evolutionary Genetics ^{1 1} “It is traditional in economics to carry out this characterization by attaching a utility to the various states of the environment. The role of utility in economics is quite similar to the role of payoffin game theory, the error function in control theory, fitness in evolutionary genetics, and so on.” (Holland, 1988, p. 120). Unfortunately, such a justification is not sufficient in the long run, as similarities between different terms do not necessarily justify the transformation of methods and mechanisms from one domain to the other. The justification problem might be regarded as aggravated by the fact that some researchers - among others (Paul, 1993); (Boehme, 1993) - have been using Genetic Algorithms in a straightforward manner within Economic Simulations whereas Holland's original use of GA's is restricted to rule-generation within Classifier Systems. What therefore is required is the introduction of a justification based on economic theory as a base for such simulations.     

Towards geometric control of max-plus linear systems with applications to queueing networks

The max-plus linear systems have been studied for almost three decades, however, a well-established system theory on such specific systems is still an on-going research. The geometric control theory in particular was proposed as the future direction for max-plus linear systems by Cohen et al. [Cohen, G., Gaubert, S. and Quadrat, J.P. (1999), ‘Max-plus Algebra and System Theory: Where we are and Where to Go Now’, Annual Reviews in Control, 23, 207--219]. This article generalises R.E. Kalman's abstract realisation theory for traditional linear systems over fields to max-plus linear systems. The new generalised version of Kalman's abstract realisation theory not only provides a more concrete state space representation other than just a ‘set-theoretic’ representation for the canonical realisation of a transfer function, but also leads to the computational methods for the controlled invariant semimodules in the kernel and the equivalence kernel of the output map. These controlled invariant semimodules play key roles in the standard geometric control problems, such as disturbance decoupling problem and block decoupling problem. A queueing network is used to illustrate the main results in this article.     

ARMA-models and their equivalences

The classical theory of ‘strict system equivalence’ of Rosenbrock and Fuhrmann is presented in a very general setting, namely, in the setting of ARMA-models defined over an arbitrary commutative ring.     

Exponentially fitted variants of Newton's method with quadratic and cubic convergence

In this paper, we present some new families of Newton-type iterative methods, in which f′(x)=0 is permitted at some points. The presented approach of deriving these iterative methods is different. They have well-known geometric interpretation and admit their geometric derivation from an exponential fitted osculating parabola. Cubically convergent methods require the use of the first and second derivatives of the function as Euler's, Halley's, Chebyshev's and other classical methods do. Furthermore, new classes of third-order multipoint iterative methods free from second derivative are derived by semi-discrete modifications of cubically convergent iterative methods. Further, the approach has been extended to solve a system of non-linear equations.     

A correspondence between type checking via reduction and type checking via evaluation

We describe a derivational approach to proving the equivalence of different representations of a type system. Different ways of representing type assignments are convenient for particular applications such as reasoning or implementation, but some kind of correspondence between them should be proven. In this paper we address two such semantics for type checking: one, due to Kuan et al., in the form of a term rewriting system and the other in the form of a traditional set of derivation rules. By employing a set of techniques investigated by Danvy et al., we mechanically derive the correspondence between a reduction-based semantics for type checking and a traditional one in the form of derivation rules, implemented as a recursive descent. The correspondence is established through a series of semantics-preserving functional program transformations.     

A formal model for knowledge-based systems verification

A logico-algebraic model for verification of Knowledge Based Systems, based on Abraham Robinson's meta-algebra, is presented in this article. the set of rules of Knowledge Based System is considered to be the set of axioms of a theory “T”. the model consists of: (i) the collection “P” of all well formed formulas of the language of T, (ii) a subset P₀ of P that has as its elements the axioms of a given logic (bivalued, intuitionistic, or other), plus all the theorems that can be deduced from this logic inside the language of T, (iii) some distinguished subsets of P, to be called m-ideals and m-filters, that depend on T and P₀. Important concepts that are involved in the verification of Knowledge Based Systems are considered, such as forward and backward reasoning consistencies. Appropriate characterizations are obtained by using properties of m-ideals and m-filters. © 1994 John Wiley & Sons, Inc.     

On proof- and model-based techniques for reasoning with uncertainty

In this article we compare two well-known techniques for reasoning with uncertainty—namely, Incidence Calculus and Fagin-Halpern's version of the Theory of Evidence—from a viewpoint not so frequently explored for such techniques. We argue that, despite the equivalence relations that these techniques have been proved to hold, they have intrinsically different rǒles as representations of uncertainty for automated reasoning, in the sense that the former represents approximations to uncertainty values due to impossibility to achieve exact results by proof-theoretic means, and the latter represents model-theoretic limits of definability of uncertainty values. © 1995 John Wiley & Sons, Inc.