observer based adaptive fuzzy decentralized control for stochastic large scale nonlinear systems with unknown dead zones this paper studies the problem of adaptive fuzzy decentralized output feedback control for a class of uncertain stochastic large scale nonlinear systems the considered systems have unknown nonlinear functions unknown dead zones unmodeled dynamics and unmeasurable state variables therefore fuzzy logic systems are utilized to approximate the unknown nonlinear functions and a fuzzy state observer is established to estimate the unmeasurable states based on the backstepping design and the supply changing function technique a robust adaptive fuzzy decentralized output feedback control approach is developed the proposed control approach can ensure the closed loop system to be input state practically stable isps in probability and accommodate the unmodeled dynamics and unknown dead zones as well the effectiveness of the proposed control approach is illustrated by a simulation example

topological gauge theories and group cohomology we show that three dimensional chern simons gauge theories with a compact gauge groupg not necessarily connected or simply connected can be classified by the integer cohomology grouph4 bg z in a similar way possible wess zumino interactions of such a groupg are classified byh3 g z the relation between three dimensional chern simons gauge theory and two dimensional sigma models involves a certain natural map fromh4 bg z toh3 g z we generalize this correspondence to topological spin theories which are defined on three manifolds with spin structure and are related to what might be calledz2 graded chiral algebras or chiral superalgebras in two dimensions finally we discuss in some detail the formulation of these topological gauge theories for the special case of a finite group establishing links with two dimensional holomorphic orbifold models

remarks on the behavior of the ising chain in the generalized statistics abstract the behavior of the ising chain within tsallis generalization of the boltzmann gibbs statistics is reanalyzed taking into account a recently proposed connection between this theory and a generalized thermodynamics

quantized output feedback control for networked control systems this paper addresses the problem of output feedback control for networked control systems ncss with limited communication capacity firstly we propose a new model to describe the non ideal network conditions and the input output state quantization of the ncss in a unified framework secondly based on our newly proposed model and an improved separation lemma the observer based controller is developed for the asymptotical stabilization of the ncss which are shown in terms of nonlinear matrices inequalities the nonlinear problems can be computed through solving a convex optimization problems and the observed and controller gains could be derived by solving a set of linear matrix inequalities thirdly two simulation examples are given to demonstrate the effectiveness of the proposed method

dynamical aspects of tsallis entropy abstract the description of the temporal evolution of some physical systems is tackled from an information theory view point in which tsallis entropy is extremalized with the constraints posed by the knowledge of the generalized expectation values of a selected set of observables the concomitant tsallis density operator is shown to be a particular solution of von neumann s equation and tsallis entropy is seen to provide one with a constant of the motion the pertinent ideas are illustrated with reference to the larmor precession

adaptive neural control for a class of switched nonlinear systems in this paper adaptive neural control is presented for a class of switched nonlinear systems with switching jumps and uncertainties in both system models and switching signals condition on limiting variation of the lyapunov function is given for input to state asymptotic stability of switched systems with switching jumps the control objective is achieved uniformly with respect to a class of switching signals the coupled difficulties from the discrepancy between control gains and switching jumps are overcome by discontinuous adaptive neural control combined with the classical adaptive control smooth approximations of the discontinuous controls are then presented for a systematic design procedure

generalization of the maier saupe theory of the nematics within tsallis thermostatistics abstract in this study one of the mean field theories in nematics the maier saupe theory mst is generalized within tsallis thermostatistics tt the variation of the order parameter versus temperature has been investigated and compared with experimental data for p azoxyanisole paa so far we believe that this is the first attempt at the application of tt in liquid crystals it is well known that mst fails to explain the experimental data for some of the nematics one of which is paa however generalized mst is able to account for the experimental data for a long range of temperatures also in this study the effect of nonextensivity is shown for various values of the entropic index

adaptive output feedback control for nonlinear time delay systems by fuzzy approximation approach in this paper the problem of adaptive fuzzy tracking control via output feedback for a class of uncertain single input single output siso strict feedback nonlinear systems with unknown time delay functions is investigated dynamic surface control technique is used to avoid the problem of explosion of complexity which is caused by repeated differentiation of certain nonlinear functions in the backstepping design process in addition the fuzzy logic systems are utilized to approximate the unknown and desired control input signals directly instead of the unknown nonlinear functions the designed controller can guarantee all the signals in the closed loop system to be semiglobally uniformly ultimately bounded and the tracking error to converge to a small neighborhood of the origin simulations results are provided to demonstrate the effectiveness of the proposed methods

stability analysis for coupled systems with time delay on networks abstract in this paper the stability problem for some coupled systems with time delay on networks csdns is investigated we provide a systematic method for constructing a global lyapunov functional for csdns by using graph theory the stability uniform stability and global uniform stability of the systems are investigated and by using the lyapunov functional constructed some sufficient conditions of stability are obtained

dynamic output feedback h control synthesis for discrete time t s fuzzy systems via switching fuzzy controllers this paper studies the problem of dynamic output feedback h control of discrete time takagi sugeno t s fuzzy systems via a switched dynamic parallel distributed compensation dpdc scheme the considered switched dpdc control structure is determined based on the values of membership functions some new properties of membership functions are obtained and exploited to derive sufficient conditions for designing switching dpdc controllers that guarantee the stability and h performances of closed loop nonlinear systems the design conditions are given in terms of solvability of a set of linear matrix inequalities lmis it is shown that the new approach provides results at least as good as the corresponding dpdc methods a numerical example is given to illustrate the effectiveness of the proposed approach

adaptive neural tracking control for a class of nonstrict feedback stochastic nonlinear systems with unknown backlash like hysteresis this paper considers the problem of adaptive neural control of stochastic nonlinear systems in nonstrict feedback form with unknown backlash like hysteresis nonlinearities to overcome the design difficulty of nonstrict feedback structure variable separation technique is used to decompose the unknown functions of all state variables into a sum of smooth functions of each error dynamic by combining radial basis function neural networks universal approximation capability with an adaptive backstepping technique an adaptive neural control algorithm is proposed it is shown that the proposed controller guarantees that all the signals in the closed loop system are four moment semiglobally uniformly ultimately bounded and the tracking error eventually converges to a small neighborhood of the origin in the sense of mean quartic value simulation results further show the effectiveness of the presented control scheme

generalization of the single site callen identity within tsallis statistics abstract within the framework of a generalized thermostatistics introduced by tsallis we establish the generalization of the single site callen identity it is used to calculate the critical temperature of the ising ferromagnet within a consistently generalized mean field approximation

on smith s determinant abstract we give a brief review of papers relating to smith s determinant and point out a common structure that can be found in many extensions and analogues of smith s determinant we present the common structure in the language of posets we also make an investigation on a conjecture of beslin and ligh on greatest common divisor gcd matrices in the sense of meet matrices and give characterizations of the posets satisfying the conjecture further we give a counterexample for the conjecture of bourque and ligh that the least common multiple matrix on any gcd closed set is invertible

generalized kolmogorov entropy in the dynamics of multifractal generation abstract we point out that applying a maximization principle on a tsallis like generalized form of the kolmogorov entropy for iterated function systems naturally provides a canonical statistical frame for the description of the multifractal measures generated by such dynamical processes multifractal spectra can then be characterized by usual statistical parameters in particular the temperature we show that in the limit of zero temperature the multifractal measure collapses to a homogeneous distribution over a fractal support for finite temperatures multifractal spectra are studied numerically in an illustrative example

possible generalization of boltzmann gibbs statistics with the use of a quantity normally scaled in multifractals a generalized form is postulated for entropy namelys q k 1 i 1 w p i q q 1 whereq characterizes the generalization andp i are the probabilities associated withw microscopic configurations w the main properties associated with this entropy are established particularly those corresponding to the microcanonical and canonical ensembles the boltzmann gibbs statistics is recovered as theq 1 limit

generalized distribution functions and an alternative approach to generalized planck radiation law abstract in this study recently introduced generalized distribution functions are summarized and by using one of these distribution functions namely generalized planck distribution an alternative approach to the generalized planck law for the blackbody radiation has been tackled the expression obtained is compared with the expression given by c tsallis et al phys rev e 52 1995 1447 and it is found that this approximate scheme provides bounds to the exact result depending on the values of q index

variational method in generalized statistical mechanics concavity properties of a recently generalized not necessarily extensive entropy enable among others the generalization of the bogolyubov inequality hence of the variational method in equilibrium statistical mechanics

specific heat of a free particle in a generalized boltzmann gibbs statistics abstract we discuss some relevant properties within the framework of a recently proposed generalized boltzmann gibbs statistics we then apply this formalism to calculate the thermal dependence of the specific heat associated with a free particle e n an 2 b a 0 in addition to that we calculate the classical limit for a larger family of systems e n an r b a r 0

observer based fuzzy adaptive control for strict feedback nonlinear systems in this paper a new fuzzy adaptive control approach is developed for a class of siso strict feedback nonlinear systems with unmeasured states using fuzzy logic systems to approximate the unknown nonlinear functions a fuzzy adaptive observer is introduced for state estimation as well as system identification under the framework of the backstepping design fuzzy adaptive output feedback control is constructed recursively it is proven that the proposed fuzzy adaptive control approach guarantees the semi global boundedness property for all the signals and the tracking error to a small neighborhood of the origin simulation studies are included to illustrate the effectiveness of the proposed approach

adaptive fuzzy tracking control of nonlinear mimo systems with time varying delays this paper focuses on the problem of adaptive fuzzy tracking control for a class of nonlinear multi input and multi output mimo time delay systems in strict feedback form the time delays in the systems may be time varying based on razumikhin functional method the state feedback adaptive fuzzy tracking controllers are constructed via backstepping technique the proposed adaptive fuzzy controllers guarantee that all the signals in the closed loop system are bounded and the system s outputs converge to a small neighborhood of the reference signals three examples are used to illustrate the effectiveness of the proposed approach

ising chain in the generalized boltzmann gibbs statistics abstract the partition function and specific heat of the ising chain are evaluated in a generalization of the boltzmann gibbs statistics the extensivity and the influence of the ground state energy in the thermodynamical properties are discussed

adaptive fuzzy decentralized output feedback control for nonlinear large scale systems with unknown dead zone inputs in this paper the problem of adaptive fuzzy decentralized backstepping control is considered for a class of nonlinear large scale strict feedback systems with unknown dead zones and immeasurable states fuzzy logic systems are used to approximate the unknown nonlinear functions and a state filter is designed to estimate the immeasurable states applying an adaptive backstepping design technique and combining it with the dead zone inverse method an adaptive fuzzy decentralized output feedback backstepping control is developed it is proved that all the signals of the resulting closed loop adaptive control system are semiglobally uniformly ultimately bounded and tracking errors converge to a small neighborhood of the origin by appropriate choice of design parameters simulation results are given to demonstrate that the proposed adaptive decentralized control approach has a satisfactory control performance

quasi quantum groups knots three manifolds and topological field theory we show how to construct starting from a quasi hopf algebra or quasiquantum group invariants of knots and links in some cases these invariants give rise to invariants of the three manifolds obtained by surgery along these links this happens for a finite dimensional quasi quantum group whose definition involves a finite groupg and a 3 cocycle which was first studied by dijkgraaf pasquier and roche we treat this example in more detail and argue that in this case the invariants agree with the partition function of the topological field theory of dijkgraaf and witten depending on the same datag

brief paper backstepping design for global stabilization of switched nonlinear systems in lower triangular form under arbitrary switchings this paper is concerned with the global stabilization problem for switched nonlinear systems in lower triangular form under arbitrary switchings two classes of state feedback controllers and a common lyapunov function clf are simultaneously constructed by backstepping the first class uses the common state feedback controller which is independent of switching signals the other class utilizes individual state feedback controllers for the subsystems as an extension of the designed method the global stabilization problem under arbitrary switchings for switched nonlinear systems in nested lower triangular form is also studied an example is given to show the effectiveness of the proposed method

observer based fuzzy adaptive control for multi input multi output nonlinear systems with a nonsymmetric control gain matrix and unknown control direction in this study we present an observer based fuzzy adaptive control scheme for a class of uncertain multi input multi output nonlinear systems with a nonsymmetric control gain matrix unknown control direction and unmeasured states in this scheme fuzzy systems are used to approximate the unknown nonlinear functions and an adaptive fuzzy state observer is designed to estimate the unmeasured states the parameter adaptive laws are designed by fuzzy basis functions rather than by its filtering and a robust control term is used to compensate for the lumped errors the proposed method solves the problem of the nonsymmetric control gain matrix and it requires no a priori knowledge of the control direction for the states that are unmeasured we prove that all of the signals in the resulting closed loop systems are bounded and that the tracking errors converge asymptotically to zero two simulation examples are used to demonstrate the effectiveness of the proposed scheme

on the extended kolmogorov nagumo information entropy theory the q 1 q duality and its possible implications for a non extensive two dimensional ising model abstract the aim of this paper is to investigate the q 1 q duality in an information entropy theory of all q generalized entropy functionals tsallis renyi and sharma mittal measures in the light of a representation based on generalized exponential and logarithm functions subjected to kolmogorov s and nagumo s averaging we show that it is precisely in this representation that the form invariance of all entropy functionals is maintained under the action of this duality the generalized partition function also results to be a scalar invariant under the q 1 q transformation which can be interpreted as a non extensive two dimensional ising model duality between systems governed by two different power law long range interactions and temperatures this does not hold only for tsallis statistics but is a characteristic feature of all stationary distributions described by q exponential boltzmann factors

output controllability and optimal output control of state dependent switched boolean control networks in the present paper we investigate the output controllability and optimal output control problems of a state dependent switched boolean control network by using the semi tensor product the algebraic form of the system is obtained then output controllability problems of the system are discussed and some necessary and sufficient conditions are given next the mayer type optimal output control issue is considered and an algorithm is provided to find out the control sequence at last an example is given to show the effectiveness of the main results

fuzzy adaptive quantized output feedback tracking control for switched nonlinear systems with input quantization in this paper the problem of adaptive fuzzy quantized output feedback control is investigated for a class of uncertain switched nonlinear systems in strict feedback form the considered switched systems contain unknown nonlinearities hysteretic quantized input and without requiring the system states being available for measurement fuzzy logic systems are utilized to approximate the unknown nonlinear functions and a switched fuzzy state observer is designed to estimate the unmeasured states the hysteretic quantized input is implemented to avoid the oscillation caused by logarithmic quantizer and decomposed into two bounded nonlinear functions based on the estimated states and using the backstepping design principle an adaptive fuzzy quantized output feedback control scheme is developed it is proved that whole adaptive fuzzy quantized control scheme can guarantee that all the variables in the closed loop system are bounded under a class of switching signals with average dwell time and also that the system output can track a given reference signal as closely as possible the simulation results are given to check the effectiveness of the proposed approach

semisimple hopf algebras via geometric invariant theory abstract we study hopf algebras via tools from geometric invariant theory we show that all the invariants we get can be constructed using the integrals of the hopf algebra and its dual together with the multiplication and the comultiplication and that these invariants determine the isomorphism class of the hopf algebra we then define certain canonical subspaces i n v i j of tensor powers of h and h and use the invariant theory to prove that these subspaces satisfy a certain non degeneracy condition using this non degeneracy condition together with results on symmetric monoidal categories we prove that the spaces i n v i j can also be described as h i h j a where a is the group of hopf automorphisms of h as a result we prove that the number of possible hopf orders of any semisimple hopf algebra over a given number ring is finite we give some examples of these invariants arising from the theory of frobenius schur indicators and from reshetikhin turaev invariants of three manifolds we give a complete description of the invariants for a group algebra proving that they all encode the number of homomorphisms from some finitely presented group to the group we also show that if all the invariants are algebraic integers then the hopf algebra satisfies kaplansky s sixth conjecture the dimensions of the irreducible representations of h divide the dimension of h

fuzzy adaptive controller for mimo nonlinear systems with known and unknown control direction this paper investigates fuzzy adaptive control schemes for a class of multi input multi output mimo unknown nonlinear systems with known and unknown sign of the control gain matrix three fuzzy adaptive control schemes are developed in the design of the second and third controller we will exploit a decomposition of the control gain matrix into a symmetric positive definite matrix a diagonal matrix with diagonal entries 1 or 1 and a unity upper triangular matrix the nussbaum type function is used to deal with the unknown control direction i e the unknown sign of the control gain matrix for updating the parameters of the fuzzy system an adaptation proportional integral pi law is proposed theoretical results are illustrated through two simulation examples

monoidal morita invariants for finite group algebras abstract two hopf algebras are called monoidally morita equivalent if module categories over them are equivalent as linear monoidal categories we introduce monoidal morita invariants for finite dimensional hopf algebras based on certain braid group representations arising from the drinfeld double construction as an application we show for any integer n the number of elements of order n is a monoidal morita invariant for finite group algebras we also describe relations between our construction and invariants of closed 3 manifolds due to reshetikhin and turaev

central invariants and higher indicators for semisimple quasi hopf algebras in this paper we define the higher frobenius schur fs indicators for finite dimensional modules of a semisimple quasi hopf algebra h via the categorical counterpart developed in a 2005 preprint when h is an ordinary hopf algebra we show that our definition coincides with that introduced by kashina sommerhauser and zhu we find a sequence of gauge invariant central elements of h such that the higher fs indicators of a module v are obtained by applying its character to these elements as an application we show that fs indicators are sufficient to distinguish the four gauge equivalence classes of semisimple quasi hopf algebras of dimension eight corresponding to the four fusion categories with certain fusion rules classified by tambara and yamagami three of these categories correspond to well known hopf algebras and we explicitly construct a quasi hopf algebra corresponding to the fourth one using the kac algebra we also derive explicit formulae for fs indicators for some quasi hopf algebras associated to group cocycles