complementation in spaces of continuous functions on compact lines abstract we characterize order preserving continuous surjections between compact linearly ordered spaces which admit an averaging operator together with estimates of the norm of such an operator this result is used to the study of strengthenings of the separable complementation property in spaces of continuous functions on compact lines these properties include in particular continuous separable complementation property and existence of a projectional skeleton

on stability of fuzzy systems expressed by fuzzy rules with singleton consequents addresses the issue of stability of a fuzzy system described by fuzzy rules with singleton consequents it first presents two canonical forms of a fuzzy system a parametric expression and a state space expression a fuzzy system with singleton consequents is found to be a piecewise polytopic affine system then the paper gives stability theorems for a discrete time system as well as for a continuous time system it also gives a brief survey on the stability issues of fuzzy control systems

adaptive robot under fuzzy control an arc welding industrial robot isotron 251 is treated its adaptation is considered as an attribute of the robot to trace an arbitrary pretaught welding seam by means of a noncontact laser sensor the control strategy is proposed to use a fuzzy model describing uncertainty of working conditions the experience shows how the notion of fuzzy sets powers is used for on line estimation prediction and control of robot motions the control algorithm has been tested by a three level microprocessor controller

tracking control of a manipulator under uncertainty by fuzzy p id controller one of the most important manipulator operations is the control of the manipulator to track a given trajectory most commercial robot systems currently are equipped with conventional pid controllers due to their simplicity in structure and ease of design using pid control however it is di cult to achieve a desired tracking control performance since the dynamic equations of a mechanical manipulator are tightly coupled highly nonlinear and uncertain in order to improve the tracking control performance under uncertainty this paper presents a new hybrid control scheme for the manipulator which consists of a fuzzy logic proportional controller and a conventional integral and derivative controller fuzzy p id in comparison with a conventional pid controller only one additional parameter has to be adjusted to tune the fuzzy p id controller the proposed control scheme has been implemented on a direct drive two link manipulator the outlined experimental results on tracking control under inertial parameters changes demonstrate the eaectiveness and the robustness of the new fuzzy p id controller c 2001 elsevier science b v all rights reserved

hybrid adaptive fuzzy controllers with application to robotic systems this paper presents a hybrid adaptive fuzzy control hafc design methodology where the nonlinear system is controlled by a state feedback controller and an adaptive fuzzy controller in the adaptive fuzzy controller an adaptive law is developed to tune a robust gain of the sliding mode controller smc so as to cope with the uncertainties and model errors the proposed design method is applied to investigate the position and tracking control of a two link robot a comparison between the proportional derivative control smc adaptive control and the proposed hafc for a two link robot is made the simulation results demonstrate that by using the hafc the system performances is improved and the system also exhibits stability and robustness

complete quadratic lyapunov functionals for distributed delay systems this paper is concerned with the stability analysis of distributed delay systems using complete lyapunov functionals numerous articles aim at approximating their parameters thanks to a discretization method or polynomial modeling the interest of such approximations is the design of tractable sufficient stability conditions in the present article we provide an alternative method based on polynomial approximation which takes advantages of the legendre polynomials and their properties the resulting stability conditions are scalable with respect to the maximum degree of the polynomials and are expressed in terms of tractable linear matrix inequalities several examples of delayed systems are tested to show the effectiveness of the method

design of a new fuzzy suction controller using fuzzy modeling for nonlinear boundary layer there are two types of fuzzy modeling 1 imitating an expert experiment or fulfilling an engineering knowledge and 2 modeling a complex or unknown system in this paper based on the first type of fuzzy modeling a new fuzzy suction controller nfsc is proposed using its linguistic rules to design nonlinear boundary layer two kinds of nonlinear boundary layers are discussed the first kind is designed by three rules derived according to a new interpretation of the switching conditions for a suction controller such that the new controller reduces chattering and spends less energy than a suction controller does a design procedure summarizes the nfsc design the second kind of nonlinear boundary layer is the linguistic rules designed to have sliding sectors to control a mobile robot for trajectory tracking the discussion emphasizes the advantage of nonlinear boundary layers compared with traditional suction controllers usually using linear boundary in addition the proposed nfsc provides a flexible way to adjust the controller functions using linguistic rules based on the first type of fuzzy modeling

rich families and projectional skeletons in asplund wcg spaces abstract we show a way of constructing projectional skeletons using the concept of rich families in banach spaces which admit a projectional generator our next result is that a banach space x is asplund and weakly compactly generated if and only if there exists a commutative 1 projectional skeleton q on x such that q is a commutative 1 projectional skeleton on x we consider both real and also complex banach spaces

control of a redundant manipulator using fuzzy rules abstract sophisticated robot tasks require a kinematical redundancy which enables the robot links to avoid obstacles whereas the effector follows a planned path in this connection the solution of the inverse problem i e the determination of the internal joint coordinates from a given position in the operational space e g cartesian coordinates is an essential problem the special relations between external and internal coordinates lead to an introduction of restrictions for the internal joint coordinates depending on appropriate criteria such as distances of the links from the boundaries as well as from external obstacles these criteria lead in a classical way to corrections from which the desired robot motion can be obtained by using the pseudo inverse jacobi matrix a new method of choosing appropriate joint angles using fuzzy logic is presented in this connection distances and corrections are denoted as fuzzy terms in this way various criteria for controlling a redundant arm are formulated linguistically by fuzzy production rules the advantage of the fuzzy method is evident in the presence of multi criteria decisions simulation results demonstrate the practicability of the method

fuzzy system technologies at siemens r d abstract applications of fuzzy logic are usually identified with fuzzy control but besides fuzzy control there are many other fuzzy theories that are used in applications among them fuzzy classification and diagnosis fuzzy control has to do with closed loops but besides the large amount of fuzzy control applications there are many other fuzzy theories being used in applications among them fuzzy classification and diagnosis we consider several recent results in fuzzy control and show their use in applications furthermore we give some examples of applications in fuzzy classification and fuzzy diagnosis

a reinforcement learning adaptive fuzzy controller for robots in this paper a new reinforcement learning scheme is developed for a class of serial link robot arms traditional reinforcement learning is the problem faced by an agent that must learn behavior through trial and error interactions with a dynamic environment in the proposed reinforcement learning scheme an agent is employed to collect signals from a fixed gain controller an adaptive critic element and a fuzzy action generating element the action generating element is a fuzzy approximator with a set of tunable parameters and the performance measurement mechanism sends an error metric to the adaptive critic element for generating and transferring a reinforcement learning signal to the agent moreover a tuning algorithm of the proposed scheme that can guarantee both tracking performance and stability is derived from the lyapunov stability theory therefore a combination of adaptive fuzzy control and reinforcement learning scheme is also concerned with algorithms for eliminating a sequence of decisions from experience simulations of the proposed reinforcement adaptive fuzzy control scheme on the cart pole balancing problem and a two degree of freedom 2dof manipulator scara robot arm verify the effectiveness of our approach

simultaneous projectional skeletons abstract we prove the existence of a simultaneous projectional skeleton for certain subspaces of c k spaces this generalizes a result on simultaneous projectional resolutions of identity proved by m valdivia we collect some consequences of this result in particular we give a new characterization of asplund spaces using the notion of projectional skeleton

fuzzy controller for a sensor guided robot manipulator sensor guided robots require according to nonlinear characteristics of certain interaction processes between robot effector and object appropriate robust control algorithms for the external sensory control loop this paper deals with a fuzzy controller which bases on linguistic production rules following the pattern of the suboptimal control method its structure is available in a large field of applications simulations and real time experiments concerning the contour tracking problem show compared with a conventional pd controller the high tracking quality of the controller

natural examples of valdivia compact spaces abstract we collect examples of valdivia compact spaces their continuous images and associated classes of banach spaces which appear naturally in various branches of mathematics we focus on topological constructions generating valdivia compact spaces linearly ordered compact spaces compact groups l 1 spaces banach lattices and noncommutative l 1 spaces

almost disjoint families of countable sets and separable complementation properties abstract we study the separable complementation property scp and its natural variations in banach spaces of continuous functions over compacta k a induced by almost disjoint families a of countable subsets of uncountable sets for these spaces we prove among other things that c k a has the controlled variant of the separable complementation property if and only if c k a is lindelof in the weak topology if and only if k a is monolithic we give an example of a for which c k a has the scp while k a is not monolithic and an example of a space c k a with controlled and continuous scp which has neither a projectional skeleton nor a projectional resolution of the identity finally we describe the structure of almost disjoint families of cardinality 1 which induce monolithic spaces of the form k a they can be obtained from countably many ladder systems and pairwise disjoint families by applying simple operations

a heuristic self tuning fuzzy controller abstract in this paper a self tuning fuzzy controller based on the tuning of scaling factors is presented the tuning schemes are tuning the scaling factors is individual tuning rules the tuning rules are transformed into numeric tuning tables by applying suitable membership functions so that the adjustings of the scaling factors are merely matrix mappings since the tuning rules are constructed with the control signal and the output error and change in output error of the plant as their antecedent parts the tuning processes have the advantage of real time property simulation results with a perturbed servo and the inverted pendulum system as the controlled plants show the performance and adaptivity of the proposed controller

stabilization of uncertain linear distributed delay systems with dissipativity constraints abstract this paper examines the problem of stabilizing linear distributed delay systems with nonlinear distributed delay kernels and dissipativity constraints specifically the nonlinear distributed kernel includes functions such as polynomials trigonometric and exponential functions by constructing a liapunov krasovskii functional related to the distributed kernels sufficient conditions for the existence of a state feedback controller which stabilizes the uncertain distributed delay systems with dissipativity constraints are given in terms of linear matrix inequalities lmis in contrast to existing methods the proposed scenario is less conservative or requiring less number of decision variables based on the application of a new derived integral inequality finally numerical examples are presented to demonstrate the validity and effectiveness of the proposed methodology

on projective banach lattices of the form c k and fbl e abstract we show that if a banach lattice is projective then every bounded sequence that can be mapped by a homomorphism onto the basis of c 0 must contain an l 1 subsequence as a consequence if banach lattices l p or f b l e are projective then p 1 or e has the schur property respectively on the other hand we show that c k is projective whenever k is an absolute neighbourhood retract answering a question by de pagter and wickstead

adaptive control of robot manipulator using fuzzy compensator this paper presents two kinds of adaptive control schemes for robot manipulator which has the parametric uncertainties in order to compensate these uncertainties we use the fls fuzzy logic system that has the capability to approximate any nonlinear function over the compact input space in the proposed control schemes we need not derive the linear formulation of robot dynamic equation and tune the parameters we also suggest the robust adaptive control laws in all proposed schemes for decreasing the effect of approximation error to reduce the number of fuzzy rules of the fls we consider the properties of robot dynamics and the decomposition of the uncertainty function the proposed controllers are robust not only to the structured uncertainty such as payload parameter but also to the unstructured one such as friction model and disturbance the validity of the control scheme is shown by computer simulations of a two link planar robot manipulator

robust fuzzy model following control of robot manipulators a robust fuzzy model following control system is proposed for the control of robot manipulators the application field to n link robot manipulators with torque disturbance and measurement noise is addressed the control objective is obtained by tailoring a nominal adaptation process of parameters to implement appropriate function approximation and facilitating a self tuning mechanism on the consequent membership functions to overcome the equivalent uncertainty a novel fuzzy system with self tuning mechanism provides robust property and the rule base in the form of if situation then the control input the proposed multilayer fuzzy logic controller can improve both transient and stability margins without a priori knowledge about the dynamic model or parameters of the robotic system using the lyapunov stability method the uniform ultimate boundedness of tracking error has been proved the performance is demonstrated by simulating the control of a two link robot in various situations

the approximation of piecewise linear membership functions and łukasiewicz operators in this paper we propose an approximation of piecewise linear membership functions with the help of sigmoid functions and certain arithmetic operations the gradient based tuning of piecewise linear membership functions can be achieved with the proposed efficient approximation because it has simple continuous derivatives with this construction we can even approximate the lukasiewicz operator family which plays an important role in fuzzy logic first of all from the theoretical point of view although in practice in optimization and learning it is rarely used because the lack of good analytical properties e g a continuous gradient the proposed approximation enlarges the applicability of fuzzy methods to the operators and membership functions where the differentiability is desirable

flexible stability criteria for a linguistic fuzzy dynamic system abstract this paper considers the stability problems of continuous and discrete type fuzzy control systems respectively on the basis of matrix measures and matrix norms several stability criteria for the systems are proposed some of these criteria are flexible with different chosen parameter p that means the trade off between the conservativeness and the computing convenience of the criteria depends on the chosen value of p totally

generalized jensen inequalities with application to stability analysis of systems with distributed delays over infinite time horizons the jensen inequality has been recognized as a powerful tool to deal with the stability of time delay systems recently a new inequality that encompasses the jensen inequality was proposed for the stability analysis of systems with finite delays in this paper we first present a generalized integral inequality and its double integral extension it is shown how these inequalities can be applied to improve the stability result for linear continuous time systems with gamma distributed delays then for the discrete time counterpart we provide an extended jensen summation inequality with infinite sequences which leads to less conservative stability conditions for linear discrete time systems with poisson distributed delays the improvements obtained by the introduced generalized inequalities are demonstrated through examples

fuzzy adaptive control for a class of nonlinear systems an adaptive tracking control architecture is proposed for a class of continuous time nonlinear dynamic systems for which an explicit linear parameterization of the uncertainty in the dynamic is either unknown or impossible the architecture employs fuzzy systems to approximate nonlinear functions uses fuzzy sliding controller to compensate for the plant uncertainties global asymptotic stability is established in the lyapunov sense with the tracking errors converging to a neighborhood of zero

stability analysis of linear coupled differential difference systems with general distributed delays we present a new approach for the stability analysis of linear coupled differential difference systems with a general distributed delay the distributed delay term in this note can contain any mathbb l 2 function which is approximated via a class of elementary functions including polynomial trigonometric exponential functions etc through the application of a new proposed integral inequality a sufficient condition for the stability of the system is derived in terms of linear matrix inequalities based on the construction of a lyapunov krasovskii functional the methods proposed in this note can handle problems that cannot be dealt using existing approaches two numerical examples are presented to show the effectiveness of our proposed stability condition

reducing the complexity of the sum of squares test for stability of delayed linear systems this technical note considers the problem of reducing the computational complexity associated with the sum of squares approach to stability analysis of time delay systems specifically this technical note considers systems with a large state space but where delays affect only certain parts of the system this yields a coefficient matrix of the delayed state with low rank a common scenario in practice the technical note uses the general framework of coupled differential difference equations with delays in feedback channels this framework includes systems of both the neutral and retarded type the approach is based on recent results which introduced a new lyapunov krasovskii structure which was shown to be necessary and sufficient for stability of this class of systems this technical note shows how exploiting the structure of the new functional can yield dramatic improvements in computational complexity numerical examples are given to illustrate this improvement

asplund spaces characterized by rich families and separable reduction of frechet subdifferentiability abstract asplund property of a banach space x is characterized by the existence of a rich family in the product x x consisting of some carefully chosen separable subspaces this structural result is then used to add a lot of precision and simplicity to the known separable reductions of frechet subdifferentials

state observer based adaptive fuzzy output feedback control for a class of uncertain nonlinear systems this paper aims to develop state observer based adaptive fuzzy control techniques for controlling a class of uncertain nonlinear systems with bounded external disturbances an adaptive fuzzy observer is proposed to estimate the system state variables it is shown that the observation errors obtained from the observer are uniformly ultimately bounded applying the estimated system state for design of an output feedback controller the uniformly ultimate boundedness of the tracking errors for the resulting closed loop system can be guaranteed a typical robot arm system is employed in our simulation studies and the results demonstrate the usefulness and effectiveness of the proposed techniques for controlling nonlinear systems with bounded external disturbances

stability issues on takagi sugeno fuzzy model parametric approach the main objective of this research is to provide a systematic stability analysis technique for fuzzy systems using well established results from robust stability of a family of polynomials the model based takagi sugeno 1985 fuzzy control system is considered and shown to have a dependent coefficient structure involving firing strengths two kharitonov regions via overbounding are established to facilitate the extreme results for stability test in the space of polynomials as well as the complex plane the criterion obtained is a sufficient condition for a fuzzy logic controller three nonlinear examples are demonstrated to show that the systematic approach proposed here can be used to solve fuzzy stability problems fuzzy users concerned over stability issues may find these analytic tools useful

robust fuzzy logic control of mechanical systems an approach for the design of fuzzy control laws for tracking control of a large class of mechanical systems is proposed the approach employs the framework of lyapunov s stability theory to formulate a class of control laws that guarantee convergence of the tracking errors to within specification limits in presence of bounded parameter uncertainties and input disturbances the proposed control laws possess a large number of parameters and functional relationships to be chosen by the designer according to a methodology developed in the paper the large number of design degrees of freedom makes the approach suitable for fuzzy logic implementation a number of fuzzy implementations of the proposed control methodology are provided all implementations guarantee tracking error convergence to within prespecified performance limits an extensive simulation study using a model of a two degree of freedom robot manipulator was conducted fuzzy and non fuzzy implementations of the proposed methodology were compared to control laws designed using other design methods simulation study results indicate a superiority of the proposed control methodology compared to other approaches the study also demonstrates better performance of the fuzzy control implementation compared to its non fuzzy counterpart

the unconditional basic sequence problem we construct a banach space that does not contain any infinite un conditional basic sequence and investigate further properties of this space for example it has no subspace that can be written as a topological direct sum of two infinite dimensional spaces this property implies that every operator on the space is a strictly singular perturbation of a multiple of the identity in par ticular it is either strictly singular or fredholm with index zero this implies that the space is not isomorphic to any proper subspace trinity college cambridge cb2 1tq england current address department of mathematics university college london gower street lon don wc1e 6bt england e mail address wtg l o phx cam ac uk universit paris vii u f r de mathtmatiques 2 place jussieu 75251 paris cedex 05 france current address equipe d analyse et mathematiques appliquees universite de mamne la vallee 93160 noisy le grand france e mail address maurey logiquejussieu fr this content downloaded from 157 55 39 105 on fri 07 oct 2016 04 30 48 utc all use subject to http about jstor org terms

robot control via robust estimated state feedback the problem of controlling a robot manipulator without needing the precise knowledge of the robot model physical parameters and by using only angular position feedback is considered sliding observers are used to estimate the link velocities this observer and a nonlinear control law are modified according to the leitmann procedure in order to face uncertainties on the robot model parameters and to yield locally exponentially closed loop systems the use of discontinuous functions seems to be necessary to reach exponential stability for this particular problem formulation the same type of results would be difficult if not impossible to obtain using only nonlinear smooth functions because the switching terms generate a special kind of dynamics into the sliding patch which is created only by the sign functions

fuzzy direct adaptive control for a class of nonlinear systems a direct adaptive tracking control architecture is proposed for a class of continuous time nonlinear dynamic systems for which an explicit linear parameterization of the uncertainty in the dynamics is either unknown or impossible the architecture employs fuzzy systems to approximate the optimal controller which is designed on the assumption that all the dynamics in the system are known develops fuzzy sliding controller to compensate for the plant uncertainties smooth the control signals and increase robustness global asymptotic stability is established in the lyapunov sense with the tracking errors converging to a neighborhood of zero the simulation results verify the effectiveness of the proposed control algorithm

decompositions of preduals of jbw and jbw algebras abstract we prove that the predual of any jbw algebra is a complex 1 plichko space and the predual of any jbw algebra is a real 1 plichko space i e any such space has a countably 1 norming markushevich basis or equivalently a commutative 1 projectional skeleton this extends recent results of the authors who proved the same for preduals of von neumann algebras and their self adjoint parts however the more general setting of jordan algebras turned to be much more complicated we use in the proof a set theoretical method of elementary submodels as a byproduct we obtain a result on amalgamation of projectional skeletons

a new adaptive law for robust adaptation without persistent excitation a new adaptive law motivated by the work of loannou and kokotovic 1983 is proposed for the robust adaptive control of plants with unknown parameters in this adaptive law the output error plays a dual role in the adjustment of the control parameter vector the advantages of using the adaptive law over others proposed in the literature are discussed in the ideal case the adaptive system has bounded solutions in addition the origin of the error equations is exponentially stable when the reference input is persistently exciting and has a sufficiently large amplitude the adaptive system is also shown to be robust under bounded external disturbances finally it is shown that by suitably modifying the adaptive law the overall system can be made robust in the presence of a class of unmodeled dynamics of the plant simulation results are presented throughout the paper to complement the theoretical developments

design of a multi layer fuzzy logic controller for multi input multi output systems abstract in this paper we propose a multi layer fuzzy logic controller mlflc for multi input multi output mimo systems for the convenience of analysis the structure of the multi layer fuzzy logic controller is divided into multi input single output miso controllers each multi input single output controller consists of many fuzzy logic controllers flc in the fuzzy logic controller the linguistic rules are designed as a suction controller a theorem shows that such fuzzy logic controller has a switching line the results of analysis show that the multi layer fuzzy logic controller has a switching manifold and its parameters are the scaling factors which normalize the input variables moreover a theorem which shows the stability of the proposed multi layer fuzzy logic controller can easily be formulated by properly selecting the denormalizing scaling factors a cart pole system with two links is used as an illustrated example for demonstration the demonstrations also include the links controlled to track a set of desired trajectories simulation results show that the fuzzy control system is asymptotically stable and the desired trajectories can be followed very closely

banach spaces of continuous functions with few operators we present two constructions of infinite separable compact hausdorff spaces k for which the banach space c k of all continuous real valued functions with the supremum norm has remarkable properties in the first construction k is zero dimensional and c k is non isomorphic to any of its proper subspaces nor any of its proper quotients in particular it is an example of a c k space where the hyperplanes one co dimensional subspaces of c k are not isomorphic to c k in the second construction k is connected and c k is indecomposable which implies that it is not isomorphic to any c k for k zero dimensional all these properties follow from the fact that there are few operators on our c k s if we assume the continuum hypothesis the spaces have few operators in the sense that every linear bounded operator t c k c k is of the form gi s where g c k and s is weakly compact or equivalently in c k spaces strictly singular

multiple integral inequalities and stability analysis of time delay systems abstract this paper is devoted to stability analysis of continuous time delay systems based on a set of lyapunov krasovskii functionals new multiple integral inequalities are derived that involve the famous jensen s and wirtinger s inequalities as well as the recently presented bessel legendre inequalities of seuret and gouaisbaut 2015 and the wirtinger based multiple integral inequalities of park et al 2015 and lee et al 2015 the present paper aims at showing that the proposed set of sufficient stability conditions can be arranged into a bidirectional hierarchy of lmis establishing a rigorous theoretical basis for comparison of conservatism of the investigated methods numerical examples illustrate the efficiency of the method

monotone retractability and retractional skeletons abstract we prove that a countably compact space is monotonically retractable if and only if it has a full retractional skeleton in particular a compact space is monotonically retractable if and only if it is corson this gives an answer to a question of r rojas hernandez and v v tkachuk further we apply this result to characterize retractional skeleton using a topology on the space of continuous functions answering thus a question of the first author and a related question of w kubi

decoupled fuzzy sliding mode control a decoupled fuzzy sliding mode controller design is proposed the decoupled method provides a simple way to achieve asymptotic stability for a class of fourth order nonlinear systems with only five fuzzy control rules the ideas behind the controller are as follows first decouple the whole system into two second order systems such that each subsystem has a separate control target expressed in terms of a sliding surface then information from the secondary target conditions the main target which in turn generates a control action to make both subsystems move toward their sliding surface respectively a closely related fuzzy controller to the sliding mode controller is also presented to show the theoretical aspect of the fuzzy approach in which the characteristics of fuzzy sets are determined analytically to ensure the stability and robustness of the fuzzy controller finally the decoupled sliding mode control smc is used to control three highly nonlinear systems and confirms the validity of the proposed approach

a monotone version of the sokolov property and monotone retractability in function spaces abstract we introduce the monotone sokolov property and show that it is dual to monotone retractability in the sense that x is monotonically retractable if and only if c p x is monotonically sokolov besides a space x is monotonically sokolov if and only if c p x is monotonically retractable monotone retractability and monotone sokolov property are shown to be preserved by r quotient images and f subspaces furthermore every monotonically retractable space is sokolov so it is collectionwise normal and has countable extent we also establish that if x and c p x are lindelof spaces then they are both monotonically retractable and have the monotone sokolov property an example is given of a space x such that c p x has the lindelof property but neither x nor c p x is monotonically retractable we also establish that every lindelof space with a unique non isolated point is monotonically retractable on the other hand each lindelof space with a unique non isolated point is monotonically sokolov

a systematic study of fuzzy pid controllers function based evaluation approach a function based evaluation approach is proposed for a systematic study of fuzzy proportional integral derivative pid like controllers this approach is applied for deriving process independent design guidelines from addressing two issues simplicity and nonlinearity to examine the simplicity of fuzzy pid controllers we conclude that direct action controllers exhibit simpler design properties than gain scheduling controllers then we evaluate the inference structures of direct action controllers in five criteria control action composition input coupling gain dependency gain role change and rule parameter growth three types of fuzzy pid controllers using one two and three input inference structures are analyzed the results according to the criteria demonstrate some shortcomings in mamdani s two input controllers for keeping the simplicity feature like a linear pid controller a one input fuzzy pid controller with one to three mapping inference engine is recommended we discuss three evaluation approaches in a nonlinear approximation study function estimation based generalization capability based and nonlinearity variation based approximations the study focuses on the last approach a nonlinearity evaluation is then performed for several one input fuzzy pid controllers based on two measures nonlinearity variation index and linearity approximation index using these quantitative indices one can make a reasonable selection of fuzzy reasoning mechanisms and membership functions without requiring any process information from the study we observed that the zadeh mamdani s max min gravity scheme produces the highest score in terms of nonlinearity variations which is superior to other schemes such as mizumoto s product sum gravity and takagi sugeno kang schemes

fuzzy basis functions universal approximation and orthogonal least squares learning fuzzy systems are represented as series expansions of fuzzy basis functions which are algebraic superpositions of fuzzy membership functions using the stone weierstrass theorem it is proved that linear combinations of the fuzzy basis functions are capable of uniformly approximating any real continuous function on a compact set to arbitrary accuracy based on the fuzzy basis function representations an orthogonal least squares ols learning algorithm is developed for designing fuzzy systems based on given input output pairs then the ols algorithm is used to select significant fuzzy basis functions which are used to construct the final fuzzy system the fuzzy basis function expansion is used to approximate a controller for the nonlinear ball and beam system and the simulation results show that the control performance is improved by incorporating some common sense fuzzy control rules

fuzzy adaptive control of multivariable nonlinear systems abstract the robust fuzzy adaptive control scheme is developed for a class of unknown nonlinear mimo systems two types of uncertainties are considered i e the matched uncertainty and the unmatched uncertainties in the control procedure fuzzy logic systems are implemented to estimate the unknown functions and robust compensators are designed in h sense for attenuating the unmatched uncertainties it is shown that the proposed control is continuous guarantees global stability and the h performance index extensive simulations on the tracking control of a two link rigid robotics manipulator verify the effectiveness of the proposed algorithms

families of continuous retractions and function spaces in this paper we mainly study certain families of continuous retractions r skeletons having some rich properties it is shown that if the space x has a full r skeleton then its alexandroff duplicate also has a full r skeleton in a very similar way it is proved that the alexandroff duplicate of a monotonically retractable space is monotonically retractable by using monotonically retractable spaces we solve a question posed by r z buzyakova in 7 concerning the alexandroff duplicate of a space the notion of q skeleton is introduced and it is shown that every compact subspace of cp x is corson when x has a full q skeleton the notion of strong r skeleton is also introduced to answer a question suggested by f casarrubias segura and the second author in 8 certainly it is established that a space x is monotonically sokolov if and only if it is monotonically monolithic and has a strong r skeleton the techniques used here allow us to give a topological proof of a result of i bandlow 5 who used elementary submodels and uniform spaces

how to design a fuzzy adaptive controller based on observers for uncertain affine nonlinear systems this paper focuses on the construction of a fuzzy adaptive output feedback control based on any observer high gain hg observer sliding mode like observer etc for a class of single input single output siso uncertain or ill defined affine nonlinear systems indeed the corrective term of the proposed observer involves a well defined design function which is shown to be satisfied by the commonly used hg based observers namely for the usual hg observers and the sliding mode observers together with their implementable versions the design of the underlying update law as well as the robust control term is based on an appropriate filtering of the output tracking error this particularly allows to overcome the output observation error filtering or the necessity of the famous strictly positive real spr condition

genetic algorithm for the design of a class of fuzzy controllers an alternative approach a simple easy to implement alternative method for designing fuzzy logic controllers flcs with symmetrically distributed fuzzy sets in a universe of discourse is introduced the design parameters include the parameters of the membership functions of the inputs and outputs and the rule base the method is based on a network implementation of the flc with real and binary weights with constraints due to the presence of the binary weights the backpropagation technique cannot be used the learning problem is cast as a mixed integer constrained dynamic optimization problem and solved using the genetic algorithm ga the crossover and mutation are slightly disrupted in order to cope with the constraints on the binary weights training of the controller is carried out in a closed loop simulation with the controller in the loop

extracting long basic sequences from systems of dispersed vectors abstract we study banach spaces satisfying some geometric or structural properties involving tightness of transfinite sequences of nested linear subspaces these properties are much weaker than wcg and closely related to corson s property c given a transfinite sequence of normalized vectors which is dispersed or null in some sense we extract a subsequence which is a biorthogonal sequence or even a weakly null monotone basic sequence depending on the setting the separable complementation property is established for spaces with an m basis under rather weak geometric properties we also consider an analogy of the baire category theorem for the lattice of closed linear subspaces

design of a fuzzy logic controller as a suction controller abstract a fuzzy logic controller flc designed as a suction controller is proposed firstly we prove that there exists a switching line in the flc and the slope of the switching line is determined by scaling factors secondly a lyapunov function is selected and sufficient conditions for the fuzzy control system fcs to be globally asymptotically stable is determined based on the sufficient conditions a design procedure is suggested to guarantee that the fcs is globally asymptotically stable both a nonlinear oscillator and a cart pole system are simulated to demonstrate the proposed flc we show that not only is the flc similar to sliding mode control smc but also a realizable method for a suction controller is described in addition a lemma is introduced to interpret that the rise time of the fcs can be adjusted by the scaling factors

fuzzy model reference adaptive control this paper investigates a fuzzy model reference adaptive controller fmrac for continuous time multiple input multiple output mimo nonlinear systems the proposed adaptive scheme uses a takagi seguno ts fuzzy adaptive system which allows for the inclusion of a priori information in terms of qualitative knowledge about the plant operating points or analytical regulators e g state feedback for those operating points a proportional integral update law is used to obtain a fast parameters adaptation stability and robustness of this adaptive scheme are established using lyapunov stability tools the simulation results for a two link robot confirm the performance of the proposed approach

new methodology for analytical and optimal design of fuzzy pid controllers describes a methodology for the systematic design of fuzzy pid controllers based on theoretical fuzzy analysis and genetic based optimization an important feature of the proposed controller is its simple structure it uses a one input fuzzy inference with three rules and at most six tuning parameters a closed form solution for the control action is defined in terms of the nonlinear tuning parameters the nonlinear proportional gain is explicitly derived in the error domain a conservative design strategy is proposed for realizing a guaranteed pid performance gpp fuzzy controller this strategy suggests that a fuzzy pid controller should be able to produce a linear function from its nonlinearity tuning of the system the proposed pid system is able to produce a close approximation of a linear function for approximating the gpp system this gpp system incorporated with a genetic solver for the optimization will provide the performance no worse than the corresponding linear controller with respect to the specific performance criteria two indexes linearity approximation index lai and nonlinearity variation index nvi are suggested for evaluating the nonlinear design of fuzzy controllers the proposed control system has been applied to several first order second order and fifth order processes simulation results show that the proposed fuzzy pid controller produces superior control performance to the conventional pid controllers particularly in handling nonlinearities due to time delay and saturation

characterizing corson and valdivia compact spaces abstract we give a new characterization of valdivia compact spaces a compact space is valdivia if and only if it has a dense commutatively monotonically retractable subspace this result solves problem 5 12 from 6 besides we introduce the notion of full c skeleton and prove that a compact space is corson if and only if it has a full c skeleton

robust control by fuzzy sliding mode abstract most fuzzy controllers fcs for nonlinear second order systems are designed with a two dimensional phase plane in mind we show that the performance and the robustness of this kind of fc stems from their property of driving the system into the sliding mode sm in which the controlled system is invariant to parameter fluctuations and disturbances additionally the continuous distribution of the control values in the phase plane causes a behavior similar to that of a sliding mode controller smc with a boundary layer bl near the switching line this gives assured tracking quality even in the presence of high model uncertainties tracing the fc back to the principle of an smc one obtains evidence about the stability of the closed loop system the choice of the scaling factors for the crisp inputs and outputs can be guided by the comparison of the fc with the smc and with the modified smc respectively at the end of the paper an fc for a higher order system is proposed simulation results show the practicability of the method

a note on monolithic scattered compacta abstract for a banach space e it is well known that a necessary condition for e to have the controlled separable complementation property cscp for short is that the dual unit ball b e be monolithic in the weak star topology we prove here that when x is a scattered first countable locally compact space then monolithicity of x turns out to be sufficient for c 0 x to enjoy the cscp

a computed torque controller for uncertain robotic manipulator systems fuzzy approach computed torque control ctc is an effective motion control strategy for robotic manipulator systems which can ensure globally asymptotic stability however ctc scheme requires precise dynamical models of robotic manipulators to handle this impossibility in this paper a new approach combing ctc and fuzzy control fc is developed for trajectory tracking problems of robotic manipulators with structured uncertainty and or unstructured uncertainty fuzzy part with a set of tunable parameters is employed to approximate lumped uncertainty due to parameters variations unmodeled dynamics and so on in robotic manipulators based on lyapunov stability theorem it is shown that the proposed controller can guarantee stability of closed loop systems and satisfactory tracking performances the proposed approach indicates that ctc method is also valid for controlling uncertain robotic manipulators as long as compensative controller is appropriately designed finally computer simulation results on a two link elbow planar robotic manipulator are presented to show tracking capability and effectiveness of the proposed scheme

a modified fuzzy pi controller for a flexible joint robot arm with uncertainties abstract fuzzy control strategy offers an alternative approach for many conventional control systems which has certain advantages over the other techniques for example the improved pi fuzzy controller we designed in this paper which is based on an existing fuzzy pi controller can control an uncertain flexible joint robot arm to produce satisfactory tracking results the improved fuzzy pi controller not only can control stable and unstable conventional linear systems performing as well as the conventional pi controller but also is capable of controlling many nonlinear systems such as the flexible joint robot arm under investigation which contains uncertainties within 10 tolerance of all nominal system parameter values in this improved fuzzy pi controller we used only three simple membership functions plus six simple fuzzy logic control rules in this paper we describe the design principle of this controller and demonstrate its tracking performance in handling nonlinearity flexibility and uncertainty within the flexible joint robot arm system

brief intelligent optimal control of robotic manipulators using neural networks the paper is concerned with the application of quadratic optimization for motion control to feedback control of robotic systems using neural networks explicit solutions to the hamilton jacobi bellman h j b equation for optimal control of robotic systems are found by solving an algebraic riccati equation it is shown how neural networks can cope with nonlinearities through optimization with no preliminary off line learning phase required the adaptive learning algorithm is derived from lyapunov stability analysis so that both system tracking stability and error convergence can be guaranteed in the closed loop system the filtered tracking error or critic gain and the lyapunov function for the nonlinear analysis are derived from the user input in terms of a specified quadratic performance index simulation results on a two link robot manipulator show the satisfactory performance of the proposed control schemes even in the presence of large modeling uncertainties and external disturbances

banach spaces with projectional skeletons a projectional skeleton in a banach space is a directed family of projections onto separable subspaces covering the entire space the class of banach spaces with projectional skeletons is strictly larger than the class of plichko spaces i e banach spaces with a countably norming markushevich basis we show that every space with a projectional skeleton has a projectional resolution of the identity and has a norming space with similar properties to spaces we characterize the existence of a projectional skeleton in terms of elementary substructures providing simple proofs of known results concerning weakly compactly generated spaces and plichko spaces we prove a preservation result for plichko banach spaces involving transfinite sequences of projections as a corollary we show that a banach space is plichko if and only if it has a commutative projectional skeleton

a fuzzy variable structure approach to feedback regulation of uncertain dynamical systems with application to robotics this paper develops a fuzzy logic based control design methodology for a large class of nonlinear uncertain dynamical systems the proposed control design approach combines the powerful tools of fuzzy logic and approximate reasoning with the advanced mathematical synthesis techniques used in variable structure control systems theory the rationale for the proposed control design approach is motivated by the results of a recent study that has rigorously established some connections between fuzzy logic and variable structure control systems the results of this paper represent a step in the right direction for systematic design of a less expert dependent fuzzy logic control to illustrate the merits of the new control approach the latter is applied to a 2 degree of freedom robot manipulator preliminary simulation results suggest that the proposed control design deals effectively with the chattering problem encountered when the classical variable structure control is used alone

a stability approach to fuzzy control design for nonlinear systems abstract by the application of fuzzy set theory a method for feedback control of nonlinear systems based on the principle of sliding mode control is developed called fuzzy sliding mode control the control method provides a simple way to achieve asymptotic stability of the systems other attractive features of the method include a minimal realization of the fuzzy controller and robustness against model uncertainties and external disturbances in addition the method is capable of handling the chattering problem inherent to sliding mode control simply and effectively a simulation study of an inverted pendulum system is presented to demonstrate these features of the method also it is indicated that the method is easy to use for practicing control engineers

adaptive control of robot manipulators using fuzzy logic systems under actuator constraints in this paper a stable fuzzy adaptive controller for trajectory tracking is developed for robot manipulators without velocity measurements taking into account the actuator constraints the controller is based on structural knowledge of the dynamics of the robot and measurements of link positions only the gravity torque including system uncertainty like payload variation etc is estimated by a fuzzy logic system fls the adaptive controller represents an amalgamation of a filtering technique to eliminate velocity measurements and the theory of function approximation using fls to estimate the gravity torque the proposed controller ensures the local asymptotic stability and the convergence of the position error to zero the proposed controller is robust not only to structured uncertainty such as payload parameter variation but also to unstructured one such as disturbances the validity of the control scheme is shown by simulations on a two link robot manipulator

neuro fuzzy adaptive control based on dynamic inversion for robotic manipulators this paper presents a stable neuro fuzzy nf adaptive control approach for the trajectory tracking of the robotic manipulator with poorly known dynamics firstly the fuzzy dynamic model of the manipulator is established using the takagi sugeno t s fuzzy framework with both structure and parameters identified through input output data from the robot control process secondly based on the derived fuzzy dynamics of the robotic manipulator the dynamic nf adaptive controller is developed to improve the system performance by adaptively modifying the fuzzy model parameters on line the dynamic nf system aims to approximate the whole robot dynamics rather than its nonlinear components as is done by static neural networks the dynamic inversion introduced for the controller design is constructed by the dynamic nf system and will help the nf controller design because it does not require the assumption that the robot states should be within a compact set it is generally known that the compact set cannot be specified before the control loop is closed thirdly the system stability and the convergence of tracking errors are guaranteed by lyapunov stability theory and the learning algorithm for the dynamic nf system is obtained thereby finally simulation studies are carried out to show the viability and effectiveness of the proposed control approach