a new algorithm for testing diagnosability of fuzzy discrete event systems failure diagnosis and detection of fuzzy discrete event systems play a significant role in the study of complex systems in this paper we investigate the diagnosability of fuzzy discrete event systems by proposing a new algorithm based on the concept of undistinguishable strings moreover a necessary and sufficient condition for fuzzy diagnosability is obtained in terms of certain properties of the diagnoser which is constructed with respect to the minimal observable event the computing process to check the diagnosability of fuzzy dess and some examples serving to illuminate the applications are developed and described

coexistence of symmetric periodic points in the standard map the problem of the coexistence of symmetric periodic points of the standard map has been investigated first it is shown that there is another reversibility in addition to the one already known the dominant axis of this reversibility is the remaining coordinate axis using these reversibilities simple recursion formulas that determine the positions of symmetric periodic points have been derived second bifurcation structures of symmetric periodic points from the fixed point at the origin have been investigated it is shown that periodic points bifurcate along both the dominant axes of two reversibilities every time the rotation number of the fixed point passes through a rational number third the problem of the coexistence of symmetric periodic points has been numerically investigated with the aid of the recursion formulas a devil s staircase form of the evolution of the outermost kolmogorov arnold moser kam curve of the fixed point with the change of the perturbation parameter is observed this indicates that bifurcated periodic points do not disappear by inverse bifurcation as long as they are in the invariant region of the fixed point

control of stochastic discrete event systems modeled by probabilistic languages in garg et al 1999 and garg 1992 the formalism of probabilistic languages for modeling the stochastic qualitative behavior of discrete event systems dess was introduced in this paper we study their supervisory control where the control is exercised by dynamically disabling certain controllable events thereby nulling the occurrence probabilities of disabled events and increasing the occurrence probabilities of enabled events proportionately this is a special case of probabilistic supervision introduced in lawford and wonham 1993 the control objective is to design a supervisor such that the controlled system never executes any illegal traces their occurrence probability is zero and legal traces occur with minimum prespecified occurrence probabilities in other words the probabilistic language of the controlled system lies within a prespecified range where the upper bound is a nonprobabilistic language representing a legality constraint we provide a condition for the existence of a supervisor we also present an algorithm to test this existence condition when the probabilistic languages are regular so that they admit probabilistic automata representation with finitely many states next we give a technique to compute a maximally permissive supervisor online

growth and integrability in the dynamics of mappings the growth of some numerical characteristics of the mappings under their iterations in the context of the general problem of integrability is discussed in the general case such characteristics as complexity by arnold or the number of the different images for the multiple valued mappings are growing exponentially it is shown that the integrability is closely related with thepolynomial growth the analogies with quantum integrable systems are discussed

periodic orbits in k symmetric dynamical systems abstract a map l is called k symmetric if itskth iterate lk possesses more symmetry than l for some value of k in k symmetric systems there exists a notion of k symmetric orbits this paper deels with k symmetric periodic orbits we derive a relation between orbits that are k symmetric with respect to reversing k symmetries and symmetric orbits of lk with this relation we set out an efficient method for finding systematically all periodic orbits that are k symmetric with respect to reversing k symmetries this k symmetric fixed set iteration fsi method generalizes a celebrated method due to devogelaere that applies to symmetric periodic orbits in reversible dynamical systems we use the fsi method to study k symmetric periodic orbits of a map of the planer2 possessing a crystallographic reversing k symmetry group the explicit findings illustrate a typically k symmetric phenomenon consisting of a nontrivial relation between the symmetry properties of periodic orbits and their periods

non algebraic integrability of the chew low reversible dynamical system of the cremona type and the relation with the 7th hilbert problem non resonant case abstract a smooth reversible dynamical system srds and a system of nonlinear functional equations defined by a certain rational quadratic cremona mapping and arising from the static model of the dispersion approach in the theory of strong interactions the chew low equations for p wave n scattering are considered this srds is splitted into 1 and 2 dimensional ones an explicit cremona transformation that completely determines the exact solution of the two dimensional system is found this solution depends on an odd function satisfying a nonlinear autonomous 3 point functional equation non algebraic integrability of srds under consideration is proved using the method of poincare normal forms and the siegel theorem on biholomorphic linearization of a mapping at a non resonant fixed point the proof is based on the classical feldman baker theorem on linear forms of logarithms of algebraic numbers which in turn relies upon solving the 7th hilbert problem by a i gel fond and t schneider and new powerful methods of a baker in the theory of transcendental numbers the general theorem following from the feldman baker theorem on applicability of the siegel theorem to the set of the eigenvalues c n of a mapping at a non resonant fixed point which belong to the algebraic number field a is formulated and proved the main results are presented in theorems 1 3 5 7 8 and remarks 3 7

simple lie algebras of small characteristic ii exceptional roots abstract letlbe a finite dimensional simple lie algebra of absolute toral rank 2 over an algebraically closed field of characteristicp 3 andta 2 dimensional torus in the semisimplep envelope ofl suppose thatlis not isomorphic to a melikian algebra it is proved in this paper that for every root l t the subalgebrak generated by i f pki whereki x li x l i 0 acts triangulably onl in particular this implies that in the terminology of r e block and r l wilson 1988 j algebra114 115 259 all roots of l t are nonexceptional

supervisory control of a class of discrete event processes this paper studies the control of a class of discrete event processes i e processes that are discrete asynchronous and possibly nondeter ministic the controlled process is described as the generator of a formal language while the controller or supervisor is constructed from the grammar of a specified target language that incorporates the desired closed loop system behavior the existence problem for a supervisor is reduced to finding the largest controllable language contained in a given legal language two examples are provided

simple lie algebras of small characteristic iv solvable and classical roots abstract let l be a finite dimensional simple lie algebra over an algebraically closed field f of characteristic p 3 and t a torus of maximal dimension in the p envelope of l in der l in this paper we describe the t semisimple quotients of the 2 sections of l relative to t and prove that if all 1 sections of l relative to t are compositionally classical or solvable then l is either classical or a block algebra or a filtered lie algebra of type s

reversing symmetry group of and matrices with connections to cat maps and trace maps dynamical systems can have both symmetries and time reversing symmetries together these two types of symmetries form a group called the reversing symmetry group with the symmetries forming a normal subgroup of we give a complete characterization of and hence in the dynamical systems associated with the groups of integral matrices and to do this we use well known methods of number theory such as dirichlet s unit theorem for quadratic fields and gaus results on the equivalence of integer quadratic forms and employ the algebraic structure of the modular group as a free product we show how some recently discussed generalizations of the reversing symmetry group are also nicely illustrated when we consider affine extensions of these matrix groups our results are applicable to hyperbolic toral automorphisms anosov or cat maps pseudo anosov maps and the group of three dimensional 3d trace maps that preserve the fricke vogt invariant

a belief evolution based approach for online control of fuzzy discrete event systems under partial observation in this paper we investigate the partially observed supervisor synthesis problem in the framework of fuzzy discrete event systems dess the goal is to synthesize a fuzzy supervisor such that the behavior of the closed loop system is within a given fuzzy language a new approach for solving this problem is proposed based on the idea of belief evolution specifically we propose an algorithm that can be implemented in an online manner we show that the proposed algorithm is both sound and complete i e it effectively solves the supervisor synthesis problem to the best of our knowledge this is the first algorithm with such a property for fuzzy dess as previous works on this topic mostly focus on the supervisor existence condition rather than the supervisor synthesis problem

tupling in three dimensional reversible mappings feigenbaum s parameter scaling exponents s are calculated for l 3m l 5m l 7m l 9m sequences of periodic orbits in a class of three dimensional non measure preserving reversible mappings some preliminary results on orbit scaling exponents for l 3m sequences are also included scaling exponents found so far are the same as those found for two dimensional reversible mappings

an iterated implicit complex map abstract iterated complex maps defined by a root of a biquadratic equation g z z 0 are studied numerical studies suggest conjugacy functions with differentiable natural boundaries and maps having island chains occupying much of the riemann sphere an analogy with hamiltonian systems is discussed

exact results for an approximate renormalisation scheme and some predictions for the breakup of invariant ori abstract an approximate renormalisation scheme is derived for the breakup of invariant tori of arbitrary winding ratio in hamiltonian systems of one and a half degrees of freedom similar to that of escande and doveil it is a free semi group with two generators this scheme is solved exactly for its orbits stable manifolds unstable manifolds and critical set various results are found including a cantor set of universal fractal diagrams the robustness of noble tori and a scaling law for areas near critical circles

simple lie algebras of small characteristic iii the toral rank 2 case abstract it is proved that every finite dimensional simple lie algebra of absolute toral rank 2 over an algebraically closed field of characteristic p 3 is of classical or cartan type or a melikian algebra

trace maps as 3d reversible dynamical systems with an invariant one link between the theory of quasicrystals and the theory of nonlinear dynamics is provided by the study of so called trace maps a subclass of them are mappings on a one parameter family of 2d surfaces that foliate 3 and also 3 they are derived from transfer matrix approaches to properties of 1d quasicrystals in this article we consider various dynamical properties of trace maps we first discuss the fibonacci trace map and give new results concerning boundedness of orbits on certain subfamilies of its invariant 2d surfaces we highlight a particular surface where the motion is integrable and semiconjugate to an anosov system i e the mapping acts as a pseudo anosov map we identify properties of symmetry and reversibility time reversal symmetry in the fibonacci trace map dynamics and discuss the consequences for the structure of periodic orbits we show that a conservative period boubling sequence can be identified when moving through the one parameter family of 2d surfaces by using generator trace maps in terms of which all trace maps obtained from invertible two letter substitution rules can be expressed we show that many features of the fibonacci trace map hold in general the role of the fricke character hat i x y z x 2 y 2 z 2 2xyz 1 its symmetry group and reversibility for the nielsen trace maps are described algebraically finally we outline possible higher dimensional generalizations

reversible systems with first integrals abstract a reversible system of ordinary differential equations ode possessing some first integrals is considered a simple description of the first integral space is given it is shown that under the auxiliary assumption that the integrals are symmetric i e they do not change sign under the action of the reversing involution the presence of the integrals allows one to bring the problem of dynamical stability for a symmetric equilibrium to the similar problem but for the reduced system the reduced system is merely the restriction of the initial system to the intersection of the surfaces of level of the integrals passing through the equilibrium

the finite dimensional reversible kam theory abstract the main results of the theory of quasi periodic motions in finite dimensional reversible dynamical systems are surveyed lower dimensional invariant tori and excitation of elliptic normal modes are discussed in detail the case where the reversing involution is perturbed is considered several fundamental differences between the reversible and hamiltonian theories are listed

invariant circles for the piecewise linear standard map we investigate invariant circles for a one parameter family of piecewise linear twist homeomorphisms of the annulus we show that invariant circles of all types and rotation numbers occur and we classify them into families we compute parameter ranges in which there are no invariant circles

reliable decentralized supervisory control of fuzzy discrete event systems decentralized supervisory control has been introduced to deal with a class of fuzzy discrete event systems des in which state transitions are uncertain in this paper we develop the work on fuzzy des to consider the reliable decentralized supervisor problem with possible failures of some local supervisors by presenting a new definition of co observable language the reliable decentralized supervisory control problem is solved since the co observable languages are not closed under union a new normal language that is co observable is defined to solve the synthesis problem finally a numerical example is given

reversing symmetries in dynamical systems dynamical systems may possess in addition to symmetries that leave the equations of motion invariant reversing symmetries that invert the equations of motion such dynamical systems are called weakly reversible some consequences of the existence of reversing symmetries for dynamical systems with discrete time mappings are discussed a reversing symmetry group is introduced and it is shown that every weakly reversible mapping l can be decomposed into two mappings k0 and k1 of the same order 2l limit l to infinity included such that k02 k12 i some applications are discussed briefly

time reversibility and particle sedimentation this paper studies an ordinary differential equation ode model called the stokeslet model and describes sedimentation of small clusters of particles in a highly viscous fluid this model has a trivial solution in which the n particles arrange themselves at the vertices of a regular n sided polygon when n 3 hocking j fluid mech 20 1964 pp 129 139 and caflisch et al phys fluids 31 1988 pp 3175 3179 prove the existence of periodic motion in the frame moving with the center of gravity in the cluster in which the particles form an isosceles triangle the study of periodic and quasiperiodic solutions of the stokeslet model is continued with emphasis on the spatial and time reversal symmetry of the model time reversibility is due to infinite viscosity and spatial dihedral symmetry is due to the assumption of identical particles and the symmetry of the trivial solution for three particles the existence of a second family of periodic solutions and a family of quasiperiodic solu

classification of the restricted simple lie algebras soit l une algebre de lie simple restreinte de dimension finie sur un corps algebriquement clos f de caracteristique p 7 alors l est de type classique ou de cartan

mating quadratic maps with the modular group in 1994 s bullett and c penrose introduced the one complex parameter family of 2 2 holomorphic correspondences mathcal f a begin aligned left frac aw 1 w 1 right 2 left frac aw 1 w 1 right left frac az 1 z 1 right left frac az 1 z 1 right 2 3 end aligned and proved that for every value of a in 4 7 subset mathbb r the correspondence mathcal f a is a mating between a quadratic polynomial q c z z 2 c c in mathbb r and the modular group vargamma psl 2 mathbb z they conjectured that this is the case for every member of the family mathcal f a which has a in the connectedness locus we show here that matings between the modular group and rational maps in the parabolic quadratic family per 1 1 provide a better model we prove that every member of the family mathcal f a which has a in the connectedness locus is such a mating

think globally act locally decentralized supervisory control decentralized supervisory control is investigated by considering problem formulations that model systems whose specifications are given as global constraints but whose solution is described by local controllers a necessary and sufficient condition is given for the existence of a solution to the problem of finding decentralized supervisors that ensure that the behavior of the closed loop system lies in a given range where the range of behavior can be described by regular languages it can be effectively tested whether the decentralized control problem is solvable in this case a procedure is given to compute the associated supervisors

simple lie algebras of small characteristic i sandwich elements abstract let l be a finite dimensional simple lie algebra over an algebraically closed field of characteristic p 3 of absolute toral rank 2 and t a 2 dimensional torus in the semisimple p envelope of l it is proved that l is either classical or a block algebra or contains sandwich elements which are homogeneous with respect to t or a conjugate to t in addition several dimension estimates are given

a probabilistic language formalism for stochastic discrete event systems the formalism of probabilistic languages has been introduced for modeling the qualitative behavior of stochastic discrete event systems a probabilistic language is a unit interval valued map over the set of traces of the system satisfying certain consistency constraints regular language operators such as choice concatenation and kleene closure have been defined in the setting of probabilistic languages to allow modeling of complex systems in terms of simpler ones the set of probabilistic languages is closed under such operators thus forming an algebra it also is a complete partial order under a natural ordering in which the operators are continuous hence recursive equations can be solved in this algebra this is alternatively derived by using the contraction mapping theorem on the set of probabilistic languages which is shown to be a complete metric space the notion of regularity i e finiteness of automata representation of probabilistic languages has been defined and it is shown that regularity is preserved under choice concatenation and kleene closure we show that this formalism is also useful in describing system performance measures such as completion time reliability etc and present properties to aide their computation

toral rank one lie algebras let l be a finite dimensional lie algebra over an algebraically closed field f of characteristic p 0 assume that h is a cartan subalgebra of l we say that l has toral rank m relative to h if dim pa m where a is the set of roots with respect to h p is the prime field and pa is the p vector space spanned by a in this work we study lie algebras of toral rank one the motivation to investigate this class of algebras comes from the problem of classifying simple lie algebras if a is a finite dimensional simple lie algebra with cartan subalgebra h and if ci is a root of h then the subalgebra a ciep a has toral rank one relative to h in 12 133 wilson has shown that if a simple algebra a has characteristic p 7 then the restricted closure w of h in der a has the form r t z where i is the nil radical of b and t is the maximal torus which is central in j it follows that ad r on each root space a can be simultaneously upper triangularized indeed i is a lie algebra of nilpotent transformations on a and thus by 8 theorem 3 31 it annihilates a nonzero vector the space of such vectors is t invariant and so t i has a common eigenvector u on a one can proceed inductively on ajfu to argue that each root space a has a basis relative to which ad r is upper triangular with that in mind we say in what follows that a cartan subalgebra his triangularizable if there is a basis for each root space relative to which ad h is upper triangular we show in section 1 that if l is a lie algebra having a toral rank one cartan subalgebra h and if h is triangularizable then l modulo its maximal solvable ideal either is 0 or consists of a simple toral rank one lie algebra s together with derivations of s in h in the first case we say that the core of l is 0 and in the second case that the core of l is s wilson 141 has classified the simple toral rank one lie algebras using

euler poisson equations and existence of quasi periodic motions of heavy tops abstract we study the existence of quasi periodic motions of an asymmetric heavy top by using two different approaches the standard moser weinstein theorem and an extended liapounov center theorem we take advantage of the multiple reversibility of the euler poisson equations and are able to show that the extended liapounov center theorem yields more normal modes than does the moser weinstein theorem

h tracking adaptive fuzzy integral sliding mode control for parallel manipulators abstract highly nonlinear coupling phenomenon is an inherently inevitable in parallel manipulators in which limbs links undergo rotating and sliding with without fixed base in this paper an h tracking adaptive fuzzy integral sliding mode control scheme is proposed for controlling parallel manipulators with nonlinear unmodeled dynamics external disturbances and limb to limb couples in which each coupled uncertainty is assumed to be bounded by an unknown gain the dynamics of the parallel manipulator is formulated as an error dynamics according to a specified reference model then a fuzzy model is used to approximate the uncertainties two on line estimation schemes are developed to overcome the uncertainties and identify the gains of the unknown coupled uncertainty bounds from limb to limb couples simultaneously the advantage of employing an adaptive fuzzy system is the use of linear analytical results instead of estimating nonlinear uncertain functions with an on line update law by the concept of parallel distributed compensation pdc the adaptive fuzzy scheme uses an integral sliding mode control scheme to resolve the system uncertainties unknown limb to limb coupled uncertainties and the external disturbances such that h tracking performance is achieved the control laws are derived based on a lyapunov criterion and the riccati inequality such that all states of the system are uniformly ultimately bounded uub and the effect on the tracking error can be attenuated to any prescribed level to achieve h tracking performance finally a numerical example of a planar 2 dof parallel robot system is given to verify the effectiveness of the proposed control scheme

on the supermal controllable sublanguage of a given language the concept of controllable language has been shown to play a basic role in the existence theory of supervisory controls for discrete event processes in this paper the supremal controllable sublanguage s of a given language l is characterized as the largest fixpoint of a monotone operator omega in the case where the languages involved are regular it is shown that the fixpoint s can be computed as the limit of the finite sequence k j given by k j 1 omega k j k 0 l an effective computational algorithm is developed and three examples are provided for illustration

symmetries and reversing symmetries of area preserving polynomial mappings in generalised standard form abstract we determine the symmetries and reversing symmetries within g the group of real planar polynomial automorphisms of area preserving nonlinear polynomial maps l in generalised standard form l x x p 1 y y y p 2 x where p 1 and p 2 are polynomials we do this by using the amalgamated free product structure of g our results lead to normal forms for polynomial maps in generalised standard form and to a classification of the group structures of the reversing symmetry groups for such maps

time reversal symmetry in dynamical systems a survey abstract in this paper we survey the topic of time reversal symmetry in dynamical systems we begin with a brief discussion of the position of time reversal symmetry in physics after defining time reversal symmetry as it applies to dynamical systems we then introduce a major theme of our survey namely the relation of time reversible dynamical sytems to equivariant and hamiltonian dynamical systems we follow with a survey of the state of the art on the theory of reversible dynamical systems including results on symmetric periodic orbits local bifurcation theory homoclinic orbits and renormalization and scaling some areas of physics and mathematics in which reversible dynamical systems arise are discussed in an appendix we provide an extensive bibliography on the topic of time reversal symmetry in dynamical systems

observability and decentralized control of fuzzy discrete event systems fuzzy discrete event systems as a generalization of crisp discrete event systems have been introduced in order that it is possible to effectively represent uncertainty imprecision and vagueness arising from the dynamic of systems a fuzzy discrete event system has been modeled by a fuzzy automaton its behavior is described in terms of the fuzzy language generated by the automaton in this paper we are concerned with the supervisory control problem for fuzzy discrete event systems with partial observation observability normality and co observability of crisp languages are extended to fuzzy languages it is shown that the observability together with controllability of the desired fuzzy language is a necessary and sufficient condition for the existence of a partially observable fuzzy supervisor when a decentralized solution is desired it is proved that there exist local fuzzy supervisors if and only if the fuzzy language to be synthesized is controllable and co observable moreover the infimal controllable and observable fuzzy superlanguage and the supremal controllable and normal fuzzy sublanguage are also discussed simple examples are provided to illustrate the theoretical development

supervisory control of fuzzy discrete event systems for simulation equivalence the supervisory control theory of fuzzy discrete event systems fdess for fuzzy language equivalence has been developed however in a way language equivalence has limited expressiveness therefore if the given specification can not be expressed by language equivalence then the control for language equivalence does not work in this paper we further establish the supervisory control theory of fdess for fuzzy simulation equivalence whose expressiveness is stronger than that of fuzzy language equivalence first we formalize the notions of fuzzy simulation and fuzzy simulation equivalence between two fdess then we present a method for deciding whether there is a fuzzy simulation or not in addition we also show several basic properties of fuzzy simulation relations afterward we put forward the notion of fuzzy simulation based controllability and in particular show that it serves as a necessary and sufficient condition for the existence of the fuzzy supervisors of fdess moreover we study the range control problem of fdess some examples are given to illustrate the main results obtained

generalized henon maps the cubic diffeomorphisms of the plane abstract in general a polynomial diffeomorphism of the plane can be transformed into a composition of generalized henon maps these maps exhibit some of the familiar properties of the quadratic henon map including a bounded set of bounded orbits and an anti integrable limit we investigate in particular the cubic area preserving case which reduces to two two parameter families of maps the bifurcations of low period orbits of these maps are discussed in detail

generating functions for dynamical systems with symmetries integrals and differential invariants abstract we give a survey and some new examples of generating functions for systems with symplectic structure systems with a first integral systems that preserve volume and systems with symmetries and or time reversing symmetries both odes and maps are treated and we discuss how generating functions may be used in the structure preserving numerical integration of odes with the above properties