componentwise decomposition of some lattice valued fuzzy integrals lattice valued fuzzy measures are lattice valued set functions which assign the bottom element of the lattice to the empty set the top element of the lattice to the entire universe and satisfy the property of monotonicity if the lattice is complete then a lattice valued fuzzy integral of sugeno type with similar properties such as the sugeno integral in its original form can be introduced in a natural way the main result of the paper is a componentwise decomposition theorem of an l valued fuzzy integral to its l valued fuzzy integrals components where l is a complete lattice with negation and l a b a email protected l a email protected is organized as a complete lattice too this result is useful to obtain the properties of l valued fuzzy integrals from the properties of l valued fuzzy integrals and to calculate in a simple way the values of some integrals from the values of the components the important case l 0 1 when l becomes the lattice of the intuitionistic fuzzy values is distinctly discussed an idea of application to synthetic evaluation of objects is also suggested

adaptive fuzzy backstepping tracking control for strict feedback systems with input delay this paper investigates the problem of adaptive fuzzy tracking control for nonlinear strict feedback systems with input delay and output constraint input delay is handled based on the information of pade approximation and output constraint problem is solved by barrier lypaunov function some adaptive parameters of the controller need to be updated online through considering the norm of membership function vector instead of all sub vectors a novel adaptive fuzzy tracking control scheme is developed to guarantee all variables of the closed loop systems are semiglobally uniformly ultimately bounded and the tracking error can be adjusted around the origin with a small neighborhood the stability of the closed loop systems is proved and simulation results are given to demonstrate the effectiveness of the proposed control approach

decomposable measures and nonlinear equations abstract using integrals based on decomposable measures with respect to a pseudo addition related to a semiring a b a b a unified method is given for solving some nonlinear differential ordinary and partial difference and optimization equations for that purpose important tools as pseudo superposition principle and pseudolaplace transform are used

contact force distribution optimization and control for quadruped robots using both gradient and adaptive neural networks this paper investigates optimal feet forces distribution and control of quadruped robots under external disturbance forces first we formulate a constrained dynamics of quadruped robots and derive a reduced order dynamical model of motion force consider an external wrench on quadruped robots the distribution of required forces and moments on the supporting legs of a quadruped robot is handled as a tip point force distribution and used to equilibrate the external wrench then a gradient neural network is adopted to deal with the optimized objective function formulated as to minimize this quadratic objective function subjected to linear equality and inequality constraints for the obtained optimized tip point force and the motion of legs we propose the hybrid motion force control based on an adaptive neural network to compensate for the perturbations in the environment and approximate feedforward force and impedance of the leg joints the proposed control can confront the uncertainties including approximation error and external perturbation the verification of the proposed control is conducted using a simulation

adaptive fuzzy reliable control for switched uncertain nonlinear systems based on closed loop reference model abstract this paper investigates an input to state practical stability isps problem for a class of switched strict feedback nonlinear systems with closed loop reference model the considered systems are with unmodeled dynamics dynamic disturbances and actuator failures fuzzy logical systems flss are utilized to approximate the unknown functions different from the open loop model reference adaptive control a feedback gain term is introduced into the reference model to improve the transient performance of the considered systems especially when actuator failures occur and switchings take place by combining the small gain approach and backstepping technique an adaptive fuzzy control method is proposed it is shown that under the developed control scheme the tracking error converges to a small neighborhood of the origin while all the signals of the closed loop system are semi globally uniformly ultimately bounded sguub simulation study is given to illustrate the effectiveness of our results

a limit theorem for triangle functions a wide class of triangle functions that can be interpreted as generalized pseudo convolutions of distribution functions has been considered in order to find out whether a nontrivial limit for the sequence of the pseudo convolutions of distribution functions exists or not some pseudo laplace type transformations have been introduced the main result is illustrated with a family of pseudo convolutions based on a family of schweizer sklar t norms and another example is given with a calculation of the analytical form of the limit function

extension of a class of decomposable measures using fuzzy pseudometrics in this paper we consider a topological approach to extension of t conorm based decomposable measures by introducing a fuzzy pseudometric structure on an algebra of sets we prove that every non strict continuous archimedean t conorm based decomposable measure can be extended from an algebra to the completion of this algebra under the fuzzy pseudometric and then to the sigma algebra generated by this algebra the existence of such an extension follows very simply from the well known caratheodory result however our topological proof offers an intuitive interpretation of the extension of decomposable measures

boundary element approach for dynamic poroelastic problems a boundary element approach for dynamic poroelastic problems in the frequency domain is presented the technique is based on an integral equation formulation in terms of solid displacements and fluid stress the analogy between dynamic poroelasticity and thermoelasticity in the frequency domain is used to obtain the fundamental solution the boundary elements formulation is developed and the numerical aspects related to the integration of the fundamental solution kernels analysed a computer code for two dimensional problems is implemented and validated by solving two basic problems the obtained numerical results are compared with the corresponding exact solutions

on the equality of integrals considering a finite space x several necessary conditions and one rather general sufficient condition describing when the choquet integral coincides with the pan integral with respect to the standard arithmetic operations are shown these conditions are characterized by using the minimal atoms of monotone measure under the introduced constraints the calculation of these coinciding two integrals is also given

globally stable adaptive system design for minimum phase siso plants with input saturation model reference adaptive control problem for single input single output time invariant continuous time plants with input saturation is considered with main attention focused on global properties a sufficient condition is presented and a new design method of adaptive control systems is proposed if a priori information about the plant is available to choose the reference model and the reference input so that the sufficient condition holds the closed loop adaptive control system designed by the proposed method can have global stability and globally output tracking property it is shown that the sufficient condition becomes necessary in some cases

the range of null additive fuzzy and non fuzzy measures abstract in this paper a wide class of non additive set functions is investigated for finite null additive fuzzy and non fuzzy measures saks decomposition type theorem theorem on darboux property and lyapunov s type theorems are proved

globally stable adaptive backstepping fuzzy control for output feedback systems with unknown high frequency gain sign this paper addresses the problem of globally stable adaptive backstepping output feedback tracking control for a class of nonlinear systems with unknown high frequency gain sign the fuzzy systems are used as feedforward compensators to model some system functions depending on the reference signal thus the global stability of closed loop system can be guaranteed under the assumption that the unknown system functions are bounded by partly known nonlinear functions the other advantage of the proposed control scheme is that the designer can determine the approximation domain a priori via the bound of the reference signal which is very important for the choice of the centers and widths of membership functions moreover the nussbaum type function is employed to deal with the unknown high frequency gain sign two simulation examples are provided to illustrate the feasibility of control scheme presented in this paper

pseudo analysis and its applications in railway routing using as a base the pseudo analysis the problem of railway routing is treated first a deterministic approach is applied on three and four stations these problems are treated also with a stochastic approach when one variable is randomized

adaptive tracking control of uncertain mimo nonlinear systems with input constraints in this paper adaptive tracking control is proposed for a class of uncertain multi input and multi output nonlinear systems with non symmetric input constraints the auxiliary design system is introduced to analyze the effect of input constraints and its states are used to adaptive tracking control design the spectral radius of the control coefficient matrix is used to relax the nonsingular assumption of the control coefficient matrix subsequently the constrained adaptive control is presented where command filters are adopted to implement the emulate of actuator physical constraints on the control law and virtual control laws and avoid the tedious analytic computations of time derivatives of virtual control laws in the backstepping procedure under the proposed control techniques the closed loop semi global uniformly ultimate bounded stability is achieved via lyapunov synthesis finally simulation studies are presented to illustrate the effectiveness of the proposed adaptive tracking control

holder and minkowski type inequalities for pseudo integral abstract there are proven generalizations of the holder s and minkowski s inequalities for the pseudo integral there are considered two cases of the real semiring with pseudo operations one when pseudo operations are defined by monotone and continuous function g the second semiring a b sup where is generated and the third semiring where both pseudo operations are idempotent i e sup and inf

discrete bipolar pseudo integrals abstract in the authors paper strboja et al 2016 42 the notion of the bipolar pseudo integral has been introduced this paper extends investigations related to this new type of bipolar integrals defined with respect to decomposable bi capacities we consider the main properties of the discrete bipolar pseudo integral a characterization theorem for the discrete bipolar pseudo integral is proven monotone convergence theorems and the fatou type lemma for the discrete bipolar pseudo integral are considered in order to illustrate obtained results many interesting examples are provided

robust adaptive control of uncertain nonlinear systems in the presence of input saturation and external disturbance in this technical note we consider adaptive control of single input uncertain nonlinear systems in the presence of input saturation and unknown external disturbance by using backstepping approaches two new robust adaptive control algorithms are developed by introducing a well defined smooth function and using a nussbaum function the nussbaum function is introduced to compensate for the nonlinear term arising from the input saturation unlike some existing control schemes for systems with input saturation the developed controllers do not require assumptions on the uncertain parameters within a known compact set and a priori knowledge on the bound of the external disturbance besides showing global stability transient performance is also established and can be adjusted by tuning certain design parameters

adaptive backstepping fuzzy control for nonlinearly parameterized systems with periodic disturbances a novel function approximator is constructed by combining a fuzzy logic system with a fourier series expansion in order to model unknown periodically disturbed system functions then an adaptive backstepping tracking control scheme is developed where the dynamic surface control approach is used to solve the problem of explosion of complexity in the backstepping design procedure and the time varying parameter dependent integral lyapunov function is used to analyze the stability of the closed loop system the semiglobal uniform ultimate boundedness of all closed loop signals is guaranteed and the tracking error is proved to converge to a small residual set around the origin two simulation examples are provided to illustrate the effectiveness of the control scheme designed in this paper

approximation by pseudo linear operators the approximation operators provided by classical approximation theory use exclusively as underlying algebraic structure the linear structure of the reals also they are all linear operators we address in the present paper the following problems need all the approximation operators be linear is the linear structure the only one which allows us to construct particular approximation operators as an answer to this problem we propose new particular pseudo linear approximation operators which are defined in some ordered semirings we study these approximations from a theoretical point of view and we obtain that these operators have very similar properties to those provided by classical approximation theory in this sense we obtain uniform approximation theorems of weierstrass type and jackson type error estimates in approximation by these operators

a 2 5 d dynamic model for a saturated porous medium part ii boundary element method the 3 d boundary integral equation is derived in terms of the reciprocal work theorem and used along with the 2 5 d green s function developed in part i lu j f jeng d s williams s submitted for publication a 2 5 d dynamic model for a saturated porous medium part i green s function int j solids struct to develop the 2 5 d boundary integral equation for a saturated porous medium the 2 5 d boundary integral equations for the wave scattering problem and the moving load problem are established the cauchy type singularity of the 2 5 d boundary integral equation is eliminated through introduction of an auxiliary problem and the treatment of the weakly singular kernel is also addressed discretisation of the 2 5 d boundary integral equation is achieved using boundary iso parametric elements the discrete wavenumber domain solution is obtained via the 2 5 d boundary element method and the space domain solution is recovered using the inverse fourier transform to validate the new methodology numerical results of this paper are compared with those obtained using an analytical approach also some numerical results and corresponding analysis are presented

decomposable measures and information measures for intuitionistic fuzzy sets the aim of this paper is to construct a decomposable measure on the class of measurable intuitionistic fuzzy sets extending thus the corresponding result for fuzzy sets in a very recent paper the main tool in this construction is a non trivial approximation with restrictions result concerning the intuitionistic fuzzy sets as an application we construct a compositive information measure on the class of intuitionistic fuzzy sets

fuzzy measures and integrals defined on algebras of fuzzy subsets over complete residuated lattices this paper presents basic notions about fuzzy measures over algebras of fuzzy subsets of a fuzzy set it also presents basic ideas on fuzzy integrals defined using these fuzzy measures definitions of new types of fuzzy measures and integrals are motivated by our research on generalized quantifiers several useful properties of fuzzy measures and fuzzy integrals are stated and proved definitions presented in this paper and its results will be employed in subsequent papers on generalized quantifiers defined using this type of fuzzy integral

a note on the idempotent functions with respect to pseudo convolution a general notion of pseudo convolution based on pseudo arithmetical operations is recalled the idempotents with respect to pseudo convolutions are investigated complete characterization of idempotents with respect to pseudo convolutions based on the generalized sugeno integral is given several other cases based on the idempotent pseudo additions are studied

generalization of the jensen inequality for pseudo integral generalizations of the jensen integral inequality for the pseudo integral are proven there are considered two cases of the real semiring with pseudo operations one when pseudo operations are defined by monotone and continuous function g then the pseudo integral reduces on g integral and the second semiring a b max where the pseudo multiplication is generated

extension of a class of decomposable measures via generalized pseudo metrics abstract this study considers the application of generalized pseudo metrics to the extension of decomposable measures we prove that the extension of a non strict archimedean t conorm based decomposable measure can be formulated as the closure of a subset of a certain generalized pseudo metric space we show that the extension via generalized pseudo metrics is equivalent to the completion of t conorm based decomposable measures and the well known caratheodory extension

neural network based near optimal control for a class of discrete time affine nonlinear systems with control constraints in this paper the near optimal control problem for a class of nonlinear discrete time systems with control constraints is solved by iterative adaptive dynamic programming algorithm first a novel nonquadratic performance functional is introduced to overcome the control constraints and then an iterative adaptive dynamic programming algorithm is developed to solve the optimal feedback control problem of the original constrained system with convergence analysis in the present control scheme there are three neural networks used as parametric structures for facilitating the implementation of the iterative algorithm two examples are given to demonstrate the convergence and feasibility of the proposed optimal control scheme

robust stability analysis and fuzzy scheduling control for nonlinear systems subject to actuator saturation takagi sugeno ts fuzzy models can provide an effective representation of complex nonlinear systems in terms of fuzzy sets and fuzzy reasoning applied to a set of linear input output submodels in this paper the ts fuzzy modeling approach is utilized to carry out the stability analysis and control design for nonlinear systems with actuator saturation the ts fuzzy representation of a nonlinear system subject to actuator saturation is presented in our ts fuzzy representation the modeling error is also captured by norm bounded uncertainties a set invariance condition for the system in the ts fuzzy representation is first established based on this set invariance condition the problem of estimating the domain of attraction of a ts fuzzy system under a constant state feedback law is formulated and solved as a linear matrix inequality lmi optimization problem by viewing the state feedback gain as an extra free parameter in the lmi optimization problem we arrive at a method for designing state feedback gain that maximizes the domain of attraction a fuzzy scheduling control design method is also introduced to further enlarge the domain of attraction an inverted pendulum is used to show the effectiveness of the proposed fuzzy controller

dynamic surface control using neural networks for a class of uncertain nonlinear systems with input saturation in this paper a dynamic surface control dsc scheme is proposed for a class of uncertain strict feedback nonlinear systems in the presence of input saturation and unknown external disturbance the radial basis function neural network rbfnn is employed to approximate the unknown system function to efficiently tackle the unknown external disturbance a nonlinear disturbance observer ndo is developed the developed ndo can relax the known boundary requirement of the unknown disturbance and can guarantee the disturbance estimation error converge to a bounded compact set using ndo and rbfnn the dsc scheme is developed for uncertain nonlinear systems based on a backstepping method using a dsc technique the problem of explosion of complexity inherent in the conventional backstepping method is avoided which is specially important for designs using neural network approximations under the proposed dsc scheme the ultimately bounded convergence of all closed loop signals is guaranteed via lyapunov analysis simulation results are given to show the effectiveness of the proposed dsc design using ndo and rbfnn

robust adaptive neural network control for a class of uncertain mimo nonlinear systems with input nonlinearities in this paper robust adaptive neural network nn control is investigated for a general class of uncertain multiple input multiple output mimo nonlinear systems with unknown control coefficient matrices and input nonlinearities for nonsymmetric input nonlinearities of saturation and deadzone variable structure control vsc in combination with backstepping and lyapunov synthesis is proposed for adaptive nn control design with guaranteed stability in the proposed adaptive nn control the usual assumption on nonsingularity of nn approximation for unknown control coefficient matrices and boundary assumption between nn approximation error and control input have been eliminated command filters are presented to implement physical constraints on the virtual control laws then the tedious analytic computations of time derivatives of virtual control laws are canceled it is proved that the proposed robust backstepping control is able to guarantee semiglobal uniform ultimate boundedness of all signals in the closed loop system finally simulation results are presented to illustrate the effectiveness of the proposed adaptive nn control

idempotent integral as limit of g integrals we show that sup and inf decomposable measures can be obtained as limits of families of pseudo additive measures with respect to generated pseudo additions the corresponding integrals with respect to sup or inf decomposable measures can be obtained as limits of families of g integrals

dynamic surface control for a class of nonlinear systems a method is proposed for designing controllers with arbitrarily small tracking error for uncertain mismatched nonlinear systems in the strict feedback form this method is another synthetic input technique similar to backstepping and multiple surface control methods but with an important addition spl tau 1 low pass filters are included in the design where spl tau is the relative degree of the output to be controlled it is shown that these low pass filters allow a design where the model is not differentiated thus ending the complexity arising due to the explosion of terms that has made other methods difficult to implement in practice the backstepping approach while suffering from the problem of explosion of terms guarantees boundedness of tracking errors globally however the proposed approach while being simpler to implement can only guarantee boundedness of tracking error semiglobally when the nonlinearities in the system are non lipschitz

pseudo additive measures and integrals abstract we suggest pseudo additive measures based on a pseudo addition and discuss integrals with respect to pseudo additive measures a pseudo additive measure is a special type of fuzzy measures to define an integral a multiplication corresponding to a pseudo addition is introduced the resulting integral is an extension of the lebesgue integral in this context radon nikodym like theorems are shown

possibility and necessity integrals abstract in this paper we introduce seminormed and semiconormed fuzzy integrals associated with confidence measures these confidence measures have a field of sets as their domain and a complete lattice as their codomain in introducing these integrals the analogy with the classical introduction of lebesgue integrals is explored and exploited it is amongst other things shown that our integrals are the most general integrals that satisfy a number of natural basic properties in this way our dual classes of fuzzy integrals constitute a significant generalization of sugeno s fuzzy integrals a large number of important general properties of these integrals is studied furthermore and most importantly the combination of seminormed fuzzy integrals and possibility measures on the one hand and semiconormed fuzzy integrals and necessity measures on the other hand is extensively studied it is shown that these combinations are very natural and have properties which are analogous to the combination of lebesgue integrals and classical measures using these results the very basis is laid for a unifying measure and integral theoretic account of possibility and necessity theory in very much the same way as the theory of lebesgue integration provides a proper framework for a unifying and formal account of probability theory

observer based adaptive neural network control for nonlinear stochastic systems with time delay this paper considers the problem of observer based adaptive neural network nn control for a class of single input single output strict feedback nonlinear stochastic systems with unknown time delays dynamic surface control is used to avoid the so called explosion of complexity in the backstepping design process radial basis function nns are directly utilized to approximate the unknown and desired control input signals instead of the unknown nonlinear functions the proposed adaptive nn output feedback controller can guarantee all the signals in the closed loop system to be mean square semi globally uniformly ultimately bounded simulation results are provided to demonstrate the effectiveness of the proposed methods

aggregation functions construction methods conjunctive disjunctive and mixed classes in this second part of our state of the art overview on aggregation theory based again on our recent monograph on aggregation functions we focus on several construction methods for aggregation functions and on special classes of aggregation functions covering the well known conjunctive disjunctive and mixed aggregation functions some fields of applications are included

pseudo optimal measures based on a pseudo addition on 0 pseudo optimal measures related to non negative set functions vanishing at the empty set non negative games are introduced for a fixed pseudo addition an equivalence on non negative set functions is studied a special stress is given to pure pseudo optimal measures admitting no other equivalent set function

transformation theorems of abstract integrals on fuzzy sets abstract the concept of abstract integrals on fuzzy sets is introduced and some elementary properties for such type of integrals are given this paper also proves some transformation theorems for abstract integrals on fuzzy sets and presents some convergence theorems of a sequence of abstract integrals

a unified approach to define fuzzy integrals recently the two most general and well known fuzzy integrals sugeno s integral and choquet s integral were characterized it was also shown how both integrals fitted the same formal model and they only differed in the operators used in this paper we try to analyze whether it is possible to improve those characterization theorems and we also study the possibility of defining other fuzzy integrals following the same model but using other operators in a recent paper campos and bolafios 6 characterized two general and well known fuzzy integrals sugeno s integral 11 and choquet s integral 7 the last one also called monotone expectation 2 4 5 6 the two characterization theorems are based on the same formal model of four properties which only differ in the operators used sum and product for choquet s integral maximum and minimum for sugeno s integral two important questions remained open one involved the characterization theorems of these integrals in an attempt to further refine them the second question was to investigate the possibility of defining other fuzzy integrals using different operators but following the same model in this paper we give answers to those problems section 2 is devoted to describing fuzzy integrals defined on sugeno s fuzzy measures particularly sugeno s and choquet s integrals and their characterizations in section 3 we show how the characterization of choquet s integral can be refined whereas the same cannot be made for sugeno s integral finally other fuzzy integrals fitting our formal model are obtained in section 4

on nonlinear functional spaces based on triangular conorms abstract in this paper we discuss the nonlinear functional spaces based on triangular conorms particularly we discuss the properties of the upper closures of the regular subspaces of the nonlinear functional space based on a continuous triangular conorm furthermore we prove that with respect to a strict triangular conorm a subset of the nonlinear functional space is an upper complete normal subspace if and only if the family of all sets whose characteristic functionals are contained in the given subset of the nonlinear functional space is a sigma algebra

convergence in measure theorems of nonlinear integrals of functions integrable to the pth power abstract one can find a subadditive measure and a sequence f n n n of nonnegative measurable functions converging in measure to such a function f with the property that for any p 1 f n p no longer converges in measure to f p therefore in nonadditive measure theory an additional and intrinsic discussion is needed to prove integral convergence theorems for functions integrable to the pth power the purpose of the paper is to propose a method for automatically deriving pth power versions of convergence in measure theorems of nonlinear integrals from already established ones the proposed method is based on the robustness of some properties of integral functional under the operation f f p raising a nonnegative function f to the pth power

simultaneous quadratic stabilization for a class of non linear systems with input saturation using dynamic surface control in this paper a new method to estimate the initial condition set which guarantees the quadratic stability for a class of non linear systems via dynamic surface control dsc in the presence of input saturation has been proposed the estimated set is enlarged to allow some degree of input saturation while achieving the simultaneous quadratic stability of the system in the domain a convex optimization problem to obtain ellipsoidal initial condition sets via a linear matrix inequality lmi approach as well as an illustrative example will be presented

integrals based on monotone set functions an overview of various integrals is given which can be defined on arbitrary monotone set functions vanishing in the empty set called here monotone measures our survey includes not only the choquet integral 1954 10 the shilkret integral 1971 66 and the sugeno integral 1974 71 and some of their properties but also some more general and more recent concepts as universal integrals klement et al 2010 27 and decomposition integrals even 2014 13 together with some of their properties such as integral inequalities and convergence theorems

disturbance observer based adaptive fuzzy control for nonlinear state constrained systems with input saturation and input delay abstract in this paper the problem of disturbance observer based adaptive fuzzy control is studied for nonlinear systems with full state constraints input constraints and unknown external disturbance compared with existing results the unknown compound disturbance is estimated by nonlinear disturbance observer ndo and the input delay is effectively processed by pade approximation different from the mean value theorem and nussbaum function method an auxiliary variable is introduced to obtain the actual control input which reduces the conservativeness of controller design in order to solve the difficulties caused by input saturation and state constraints the auxiliary design functions and barrier lyapunov functions blfs are employed respectively by utilizing adaptive backstepping technique and lyapunov stability theorem a ndo based novel controller is developed it is proved that all the signals of the closed loop systems are semi globally uniformly ultimately bounded sguub the disturbance estimation errors and the tracking errors converge on a small neighborhood of the origin and the full state constraints are not violated simulation results are provided to demonstrate the effectiveness of the proposed method

brief paper adaptive dynamic surface control for linear multivariable systems in this paper an output feedback adaptive control is presented for linear time invariant multivariable plants by using the dynamic surface control technique it is shown that the explosion of complexity problem in multivariable backstepping design can be eliminated the proposed scheme has the following features 1 the l performance of the system s tracking error can be guaranteed 2 it has least number of updated parameters in comparison with other multivariable adaptive schemes and 3 the adaptive law is necessary only at the first design step which significantly reduces the design procedure simulation results are presented to demonstrate the effectiveness of the proposed scheme

pseudo lp space and convergence in the framework of the pseudo analysis the classical l p space is generalized and there are proved important properties of introduced space three types of convergence of sequences of measurable functions are considered in this space the inequalities for integrals based on pseudo integral have been recently proposed as the holder minkowski and markov inequalities which are applied in observing relationship among introduced convergences

adaptive finite time coordinated consensus for high order multi agent systems finite time consensus for multi agent systems mas with high order nonlinear uncertain dynamics under directed communication topology is still an open problem due to the involvement of high order nonlinear uncertain dynamics one way directed communication constraints and unknown time varying control effectiveness gain in this paper based upon the locally defined consensus error and fractionally composed virtual error a number of useful intermediate results are derived with which a finite time consensus solution is established for networked mas with high order uncertain dynamics under single way directed communication topology by including fraction power integration as part of the lyapunov function candidate and by using inductive analysis it is shown that the proposed distributed solution is able to achieve consensus in finite time with sufficient accuracy the benefits and effectiveness of the developed algorithm are also confirmed by numerical simulations

distributivity and conditional distributivity of a uninorm and a continuous t conorm the open problem recalled by klement in the linz2000 closing session related to distributivity and conditional distributivity of a uninorm and a continuous t conorm is solved for the most usual known classes of uninorms from the obtained results it is deduced that distributivity and conditional distributivity are equivalent for these cases it is remarkable that solutions appear involving not only strict t conorms but also ordinal sums of the maximum with a strict t conorm conversely the distributivity of a t conorm over a uninorm is also studied leading only to already known solutions moreover the dual case of distributivity and conditional distributivity involving uninorms and continuous t norms is also solved proving again the equivalence of both kinds of distributivities

fuzzy integrals based on pseudo additions and multiplications on definit un semi groupe ou un groupe qui est isomorphe au semi groupe ou du groupe ou la mesure de lebesque est definie on definit une integrale par pseudo addition et pseudo multiplication qui sont des operations de semi anneaux distributives et associatives

on pseudo metric spaces induced by σ decomposable measures in this paper we study the relationship between the pseudo metric and decomposable measures with respect to a triangular conorm decomposable measures for short we first construct a pseudo metric on the measurable sets of a given decomposable measure and then discuss several properties such as completeness and continuity of the constructed pseudo metric space finally we show that the separability and nonatom of the decomposable measure can be characterized in the constructed pseudo metric space our results suggest that the standard approach for obtaining a metric from a given probability measure can be generalized to the setting of decomposable measure

chebyshev type inequalities for pseudo integrals abstract chebyshev type inequalities for two classes of pseudo integrals are shown one of them concerning the pseudo integrals based on a function reduces on the g integral where pseudo operations are defined by a monotone and continuous function g another one concerns the pseudo integrals based on a semiring a b max where is generated moreover a strengthened version of chebyshev s inequality for pseudo integrals is proved

aggregating membership values by a choquet fuzzy integral based operator a new type of aggregator the choquet fuzzy integral based operator is introduced and applied in aggregation of membership values in this paper we generalized the definition of the fuzzy integral as a tool for membership aggregation the generalization involves replacing the max or min operator in information integration with a choquet fuzzy integral based aggregator resulting in increased flexibility the characteristics of the choquet fuzzy integral are studied and a two phase aggregating process is proposed also we demonstrate a good classification result using the proposed aggregator to integrate the memberships of several clusters in a complex unconstrained handwritten digit recognition domain

on set valued fuzzy measures so far there have been many discussions on sugeno s fuzzy measures and fuzzy integrals but most of them are concentrated on single valued functions motivated by aumann s set valued integral j math anal appl 12 1965 1 we have introduced the fuzzy integral of set valued functions fuzzy sets syst 56 1993 237 fuzzy sets syst 76 1995 365 fuzzy sets syst 78 1996 341 ph d dissertation harbin institute of technology 1998 it is a well behaved extension of fuzzy integrals of single valued functions it is well known that arstein s set valued measure trans am math soc 165 1972 103 is an important branch in set valued analysis set valued analysis birkhauser berlin 1990 or theory of correspondences theory of correspondences wiley new york 1984 compared to it the present paper will try to establish the basic idea of set valued fuzzy measures which are monotone set valued set functions it is also a natural generalization of single valued fuzzy measures as well as an extension of set valued measures in the case of one dimension these works include the concept of set valued fuzzy measures set valued fuzzy measures defined by set valued fuzzy integrals and set valued pseudo additive measures it can be viewed as a continuation of previous work fuzzy sets syst 56 1993 237 fuzzy sets syst 76 1995 365 fuzzy sets syst 78 1996 341

different interpretations of triangular norms and related operations triangular norms and triangular conorms and uni norms can be treated as semigroup two place function also as commutative semiring multiplications it can also be derived from the difference operation in a difference poset we discuss here these different interpretations and their consequences

generalized transformed t conorm integral and multifold integral fuzzy integrals are commonly used as aggregation operators in this paper we present new composite models based on fuzzy integrals with several t conorms these models permit to further increase the computational power of the previous models basic properties of new composite models are studied in particular it is shown that for composite models the only meaningful case is when not all the t conorms are the same

on the generated hsb type equation and plsp abstract the aim of this paper is to study sustainability of the pseudo linear superposition principle that is of the nonlinear superposition principle nlsp observed in the pseudo analysis framework the focus of this paper is on the so called generated partial differential equation that is for the purpose of this study based on the stochastic burger s equation

weak convergence of nonadditive measures based on nonlinear integral functionals abstract in this paper we formulate a general portmanteau theorem for a perturbative nonlinear integral functional and discuss the uniformity of weak convergence of nonadditive measures based on such a functional as their direct consequences it turns out that levy convergence of nonadditive measures coincides with every one of three types of weak convergence that is weak choquet weak sugeno and weak shilkret convergence and they are uniform on every bounded subset of lipschitz functions those results are applied when discussing the metrizability of the levy topology on the space of nonadditive measures and defining the fortet mourier type metrics on a uniformly equi autocontinuous set of nonadditive measures

choquet like integrals abstract integrals based on a pseudo addition and a pseudo multiplication with properties similar to those of the choquet and the sugeno integral respectively are introduced the structure of convenient pseudo arithmetical operations leading to a choquet like integral is studied

jensen type inequality for the bipolar pseudo integrals abstract the main purpose of this paper is to establish conditions under which the jensen type inequality for the discrete bipolar pseudo integral is valid besides we extend investigations of the properties of the bipolar pseudo integral the observations concern the discrete bipolar pseudo integrals based on the following three canonical cases of two binary symmetric operations in the first case they are generated by an odd strictly increasing and continuous function in the remaining two cases a symmetric addition is the symmetric maximum while in the second case the corresponding pseudo multiplication is a non idempotent operation and in the third case it is the symmetric minimum

a 2 5d boundary element formulation for modeling damped waves in arbitrary cross section waveguides and cavities a regularized 2 5d boundary element method bem is proposed to predict the dispersion properties of damped stress guided waves in waveguides and cavities of arbitrary cross section the wave attenuation induced by material damping is introduced using linear viscoelastic constitutive relations and described in a spatial manner by the imaginary component of the axial wavenumber the discretized dispersive wave equation results in a nonlinear eigenvalue problem which is solved obtaining complex axial wavenumbers for a fixed frequency using a contour integral algorithm due to the singular characteristics and the multivalued feature of the wave equation the requirement of holomorphicity inside the contour region over the complex wavenumber plane is fulfilled by the introduction of the sommerfeld branch cuts and by the choice of the permissible riemann sheets a post processing analysis is developed for the extraction of the energy velocity of propagative guided waves the reliability of the method is demonstrated by comparing the results obtained for a rail and a bar with square cross section with those obtained from a 2 5d finite element formulation also known in literature as semi analytical finite element safe method next to show the potential of the proposed numerical framework dispersion properties are predicted for surface waves propagating along cylindrical cavities of arbitrary cross section it is demonstrated that the attenuation of surface waves approaches asymptotically the attenuation of rayleigh waves

pan operations structure abstract the structure of pan addition and pan multiplication of a commutative isotonic semiring r is analyzed we show that if v supremum then r is a g semiring i e a b g 1 g a g b and d a b g 1 g a g b conclusions for pan integrals with respect to a measure are shown

multivariable adaptive backstepping control a norm estimation approach in this note a novel output feedback adaptive backstepping control is proposed for linear time invariant multivariable plants under a mild assumption that the hurwitz condition for high frequency gain matrix is satisfied by estimating the norm of those unknown parameter matrices instead of their elements it is shown that only one parameter needs to be updated online and therefore the computational burden can be greatly reduced compared with any current multivariable adaptive control scheme

adaptive neural output feedback tracking control for a class of uncertain discrete time nonlinear systems this brief studies an adaptive neural output feedback tracking control of uncertain nonlinear multi input multi output mimo systems in the discrete time form the considered mimo systems are composed of n subsystems with the couplings of inputs and states among subsystems in order to solve the noncausal problem and decouple the couplings it needs to transform the systems into a predictor form the higher order neural networks are utilized to approximate the desired controllers by using lyapunov analysis it is proven that all the signals in the closed loop system is the semi globally uniformly ultimately bounded and the output errors converge to a compact set in contrast to the existing results the advantage of the scheme is that the number of the adjustable parameters is highly reduced the effectiveness of the scheme is verified by a simulation example

on the probabilistic hausdorff distance and a class of probabilistic decomposable measures in this paper some useful properties associated with the probabilistic hausdorff distance are further derived especially we provide a direct proof for an existing important result afterwards the t norm based probabilistic decomposable measure is presented in which the value of measure is characterized by a probability distribution function meantime several examples are constructed to illustrate different notions and then further properties are examined moreover for a given menger pm space a probabilistic decomposable measure can be induced by means of the resulting probabilistic hausdorff distance we prove that this type of measure is s email protected probabilistic subdecomposable measure for the strongest t norm furthermore we also prove that the class of all measurable sets forms an algebra finally an outer probabilistic measure is induced by a class of probabilistic decomposable measures and the t norm based on this kind of measure a menger probabilistic pseudometric space can be obtained for a non strict continuous archimedean t norm

observer based adaptive nn control for a class of uncertain nonlinear systems with nonsymmetric input saturation this paper is concerned with the problem of adaptive tracking control for a class of uncertain nonlinear systems with nonsymmetric input saturation and immeasurable states the radial basis function of neural network nn is employed to approximate unknown functions and an nn state observer is designed to estimate the immeasurable states to analyze the effect of input saturation an auxiliary system is employed by the aid of adaptive backstepping technique an adaptive tracking control approach is developed under the proposed adaptive tracking controller the boundedness of all the signals in the closed loop system is achieved moreover distinct from most of the existing references the tracking error can be bounded by an explicit function of design parameters and saturation input error finally an example is given to show the effectiveness of the proposed method

generalized pseudo convolution in the theory of probabilistic metric spaces information fuzzy numbers optimization system theory a notion of the generalized pseudo convolution of functions based on pseudo operations is introduced it is proved that such general pseudo convolution is commutative associative operation that in some cases has a unit element we present that the generalized pseudo convolution occurs as a basic notion in many different theories as probabilistic metric spaces information theory fuzzy numbers optimization system theory

fuzzy t conorm integral with respect to fuzzy measures generalization of sugeno integral and choquet integral abstract this article discusses integrals with respect to sugeno s fuzzy measures sugeno integrals and choquet integrals with respect to general fuzzy measures are generalized in the setting of a t conorm algebraic system first t conorm integrals with respect to decomposable measures based on t conorm algebraic system are defined they are a modification of the weber integral secondly they are extended to fuzzy t conorm integrals with respect to general fuzzy measures the extension is made in the same way as the extension of the lebesgue integral to the choquet integral the class of fuzzy t conorm integrals includes choquet integrals and sugeno integrals properties of the integrals especially their representation are discussed

dynamic programming with ordered structures theory examples and applications the paper presents a dynamic discrete optimization model with returns in ordered structures it generalizes multiobjective methods used in vector optimization in two ways from real vector spaces to ordered structures and from the static model to the dynamic model the proposed methods are based on isotone homomorphisms these methods can be applied in dynamic programming with returns in ordered structures the provided numerical example shows an application of fuzzy numbers and random variables with stochastic dominance in dynamic programming the paper also proposes applications in the following problems a problem of allocations in the market model a location problem a railway routing problem and a single machine scheduling problem

adaptive dynamic surface control a simplified algorithm for adaptive backstepping control of nonlinear systems in this paper we propose a new algorithm for adaptive backstepping control of non linear uncertain systems current backstepping algorithms require repeated differentiations of the modelled non linearities the addition of n first order low pass filters allows the algorithms to be implemented without differentiating any model non linearities the uncertainties are assumed to be linear in the unknown constant parameters the combined adaptive backstepping first order filter system is proven to be semi globally stable for sufficiently fast filters by a singular perturbation approach