stability analysis and synthesis of nonlinear time delay systems via linear takagi sugeno fuzzy models abstract this paper concerns with the stability analysis and synthesis of nonlinear retarded systems via linear takagi sugeno ts fuzzy model approach first the ts fuzzy models with time delay are present and the stability conditions are derived using lyapunov razumikhin functional approach then a stabilization approach for nonlinear retarded systems through fuzzy state feedback and fuzzy observer based controller is proposed it shows that the analysis results provide an efficient technique for the design of fuzzy controllers sufficient conditions for the existence of fuzzy state feedback gain and fuzzy observer gain of the time delay systems are derived through the numerical solution of a set of coupled linear matrix inequalities

direct model reference takagi sugeno fuzzy control of siso nonlinear systems this study presents a novel direct model reference fuzzy controller it relaxes the special conditions on the reference model that is required by some of the approaches described in the literature as well as covering a more general class of takagi sugeno t s systems the stability of the proposed method is proved using a proper lyapunov function in addition the effects of modeling errors on the proposed controller are considered and a robust modification algorithm to alleviate this problem is introduced and analyzed the proposed method is then simulated on a flexible joint robot in a feedback linearization form and on chua s chaotic electrical circuit finally it is implemented and tested on a nonlinear dc motor with nonlinear state dependent disturbance

uniqueness for plane crack problems in dipolar gradient elasticity and in couple stress elasticity the present work deals with the uniqueness theorem for plane crack problems in solids characterized by dipolar gradient elasticity the theory of gradient elasticity derives from considerations of microstructure in elastic continua mindlin r d 1964 micro structure in linear elasticity arch ration mech anal 16 51 78 and is appropriate to model materials with periodic structure according to this theory the strain energy density assumes the form of a positive definite function of the strain as in classical elasticity and the second gradient of the displacement additional term specific cases of the general theory employed here are the well known theory of couple stress elasticity and the recently popularized theory of strain gradient elasticity these cases are also treated in the present study we consider an anisotropic material response of the cracked plane body within the linear version of gradient elasticity and conditions of plane strain or anti plane strain it is emphasized that for crack problems in general a uniqueness theorem more extended than the standard kirchhoff theorem is needed because of the singular behavior of the solutions at the crack tips such a theorem will necessarily impose certain restrictions on the behavior of the fields in the vicinity of crack tips in standard elasticity a theorem was indeed established by knowles and pucik knowles j k pucik t a 1973 uniqueness for plane crack problems in linear elastostatics j elast 3 155 160 who showed that the necessary conditions for solution uniqueness are a bounded displacement field and a bounded body force field in our study we show that the additional to the two previous conditions requirement of a bounded displacement gradient field in the vicinity of the crack tips guarantees uniqueness within the general form of the theory of dipolar gradient elasticity in the specific cases of couple stress elasticity and pure strain gradient elasticity the additional requirement is less stringent this only involves a bounded rotation field for the first case and a bounded strain field for the second case

observer based adaptive fuzzy tracking control for a class of uncertain nonlinear mimo systems this paper addresses the adaptive fuzzy tracking control problem for a class of uncertain nonlinear mimo systems with the external disturbances the adaptive fuzzy controllers are designed under the constraint that only system output is available for measurement then it is needed to design a state observer to estimate the unmeasured states in the observer design procedure two prominent advantages are that it does not require the sign of the control gain coefficient to be known and only two parameters need to be adjusted on line for each subsystem by using lyapunov analysis method it is proven that all the signals in the closed loop system are guaranteed to be bounded and the system outputs track the reference signals to a bounded compact set the feasibility of the proposed approach is validated by using two simulation examples

observer based indirect adaptive fuzzy sliding mode control with state variable filters for unknown nonlinear dynamical systems this paper proposes an observer based indirect adaptive fuzzy sliding mode controller with state variable filters for a certain class of unknown nonlinear dynamic systems in which not all the states are available for measurement to design the proposed controller we first construct the fuzzy models to describe the input output behavior of the nonlinear dynamic system then an observer is employed to estimate the tracking error vector based on the observer a fuzzy sliding model controller is developed to achieve the tracking performance then a filtered observation error vector is obtained by passing the observation error vector to a set of state variable filters finally on the basis of the filtered observation error vector the adaptive laws are proposed to adjust the free parameters of the fuzzy models the stability of the overall control system is analyzed based on the lyapunov method simulation results illustrate the design procedures and demonstrate the tracking performance of the proposed controller

two step stability analysis for general polynomial fuzzy model based control systems this paper investigates the stability of a polynomial fuzzy model based pfmb control system formed by a nonlinear plant represented by a polynomial fuzzy model and a polynomial fuzzy controller connected in a closed loop three cases of polynomial fuzzy controllers are proposed for the control process with the consideration of a matched mismatched number of rules and or premise membership functions which demonstrate different levels of controller complexity design flexibility and stability analysis results a general polynomial lyapunov function candidate is proposed to investigate the system stability unlike the published work there is no constraint on the polynomial lyapunov function candidate which is independent of the form of the polynomial fuzzy model thus it can be applied to a wider class of pfmb control systems and potentially produces more relaxed stability analysis results two step stability conditions in terms of sum of squares sos are obtained to numerically find a feasible solution to facilitate the stability analysis and relax the stability analysis result the boundary information of membership functions is taken into account in the stability analysis and incorporated into the sos based stability conditions simulation examples are given to illustrate the effectiveness of the proposed approach

adaptive fuzzy control for uncertain interconnected time delay systems in this paper the problem of control for a class of uncertain interconnected time delay systems is studied the interconnections of the system possess time varying delay characteristics and the bounds of uncertainties are not precisely known a decentralized adaptive feedback controller is designed which is independent of the delays lyapunov krasovskii approach is employed to show that the corresponding closed loop system is asymptotically stable a simulation example is given to demonstrate the potential of the proposed techniques

finite elements for materials with strain gradient effects a finite element implementation is reported of the fleck hutchinson phenomenological strain gradient theory this theory fits within the toupin mindlin framework and deals with first order strain gradients and the associated work conjugate higher order stresses in conventional displacement based approaches the interpolation of displacement requires c1 continuity in order to ensure convergence of the finite element procedure for higher order theories mixed type finite elements are developed herein for the fleck hutchinson theory these elements use standard c0 continuous shape functions and can achieve the same convergence as c1 elements these c0 elements use displacements and displacement gradients as nodal degrees of freedom kinematic constraints between displacement gradients are enforced via the lagrange multiplier method the elements developed all pass a patch test the resulting finite element scheme is used to solve some representative linear elastic boundary value problems and the comparative accuracy of various types of element is evaluated copyright 1999 john wiley sons ltd

on concentrated surface loads and green s functions in the toupin mindlin theory of strain gradient elasticity the two dimensional green s functions are derived for the half plane in the context of the complete toupin mindlin theory of isotropic strain gradient elasticity two types of green s functions exist for a concentrated force and a concentrated force dipole acting upon the surface of a traction free half plane our purpose is to examine the possible deviations from the predictions of classical theory of elasticity as well as from the simplified strain gradient theory which is frequently utilized in the last decade for the solution of boundary value problems of special importance is the behavior of the new solutions near to the point of application of the loads where pathological singularities and discontinuities exist in the classical solutions the boundary value problems are attacked with the aid of the fourier transform and exact full field solutions are provided our results indicate that in all cases the displacement field is bounded and continuous at the point of application of the concentrated loads the new solutions show therefore a more natural material response for the concentrated force problem both displacements and strains are found to be bounded whereas the strain gradients exhibit a logarithmic singularity thus in marked contrast with the classical elasticity solution a finite strain energy is contained within any finite portion of the body on the other hand in the case of the concentrated dipole force the strains are logarithmically singular and the strain gradients exhibit a cauchy type singularity the nature of the boundary conditions in strain gradient elasticity is highlighted through the solution of the pertinent boundary value problems finally based on our analytical solution the role of edge forces in strain gradient elasticity is elucidated employing simple equilibrium considerations

some exact algorithms for the knapsack sharing problem abstract the knapsack sharing problem ksp is formulated as an extension to the ordinary knapsack problem the ksp is n p hard we present a branch and bound algorithm and a binary search algorithm to solve this problem to optimality these algorithms are implemented and computational experiments are carried out to analyse the behavior of the developed algorithms as a result we find that the binary search algorithm solves ksps with up to 20 000 variables in less than a minute in our computing environment

fuzzy model based control stability robustness and performance issues a nonlinear controller based on a fuzzy model of mimo dynamical systems is described and analyzed the fuzzy model is based on a set of arx models that are combined using a fuzzy inference mechanism the controller is a discrete time nonlinear decoupler which is analyzed both for the adaptive and the fixed parameter cases a detailed stability analysis is carried out and the main result is that the closed loop is globally stable and robust with respect to unstructured uncertainty which may include modeling error and disturbances in addition bounds on the asymptotic and transient performance are given the main assumptions on the system and model are that they must not have strong nonminimum phase effects except time delay and the unstructured uncertainty must not be too large a simulation example illustrates some of the properties of the modeling method and model based control structure

technical note integer allocation problems of min max type with quasiconvex separable functions the paper treats the problem of integer resource allocations using the min max criterion the objective function is assumed to be strictly quasiconvex in the integer sense and separable the optimality conditions are used to obtain a solution algorithm which may be simplified in the case of strict monotonicity

robust design of rule based fuzzy controllers this paper deals with the design of stable and robust rule based fuzzy control systems new expressions to compute indices which provide a measure of the stability and robustness of fuzzy control systems are presented the relation between the modification of the rules and the stability is studied through the so called sensitivity indices the paper presents procedures that make use of these indices to improve the design of fuzzy control systems including the modification of the rules to obtain the global stability of an unstable system with multiple attractors and to improve the dynamic behavior or the robustness of a non linear plant an example with a fuzzy controller for a system with non linear damping and saturation in the actuation is presented to illustrate the design procedure

variable structure adaptive fuzzy control for a class of nonlinear time delay systems abstract in this paper the problem of variable structure adaptive fuzzy control for a class of nonlinear time delay systems is investigated sliding surface dependent of the time delay is constructed based on the lyapunov krasovskii method two adaptive fuzzy logic systems are proposed to approximate two unknown continuous nonlinear functions containing the current state and the delayed state respectively the corresponding reaching law is designed which can drive the state trajectory of the closed system onto the sliding surface within limited time simulation investigation verifies the effect of the main results of the paper

some basic contact problems in couple stress elasticity indentation tests have long been a standard method for material characterization due to the fact that they provide an easy inexpensive non destructive and objective method of evaluating basic properties from small volumes of materials as the contact scales in such experiments reduce progressively micro to nano scales the internal material lengths become important and their effect upon the macroscopic response cannot be ignored in the present study we derive general solutions for three basic two dimensional 2d plane strain contact problems within the framework of the generalized continuum theory of couple stress elasticity this theory introduces characteristic material lengths in order to describe the pertinent scale effects that emerge from the underlying microstructure and has proved to be very effective for modeling microstructured materials by using this theory we initially study the problem of the indentation of a deformable elastic half plane by a flat punch then by a cylindrical indentor and finally by a shallow wedge indentor our approach is based on singular integral equations which have resulted from a treatment of the mixed boundary value problems via integral transforms and generalized functions the results show significant departure from the predictions of classical elasticity revealing that it is inadequate to analyze indentation problems in microstructured materials employing only classical contact mechanics

a novel robust adaptive fuzzy tracking control for a class of nonlinearmulti input multi output systems robust adaptive fuzzy tracking control of a class of uncertain multi input multi output nonlinear systems with coupled interconnections is considered in this paper takagi sugeno t s fuzzy systems are used to approximate the unknown system functions a novel adaptive control scheme is developed on the basis of the so called dynamic surface control and minimal learning parameters techniques the proposed scheme has following two key features first the number of parameters updated online for each subsystem is reduced to one and both problems of curse of dimension for high dimensional systems and explosion of complexity inherent in the conventional backstepping methods are circumvented second the potential controller singularity problem in some of the existing adaptive control schemes with feedback linearization techniques is overcome it is shown via lyapunov theory that all the signals in the closed loop system are semiglobally uniformly ultimately bounded finally simulation results via two examples are presented to demonstrate the effectiveness and advantages of the proposed scheme

relative degrees and adaptive feedback linearization control of t s fuzzy systems this paper presents a new study on the relative degrees of single input and single output t s fuzzy systems in general noncanonical forms and proposes a feedback linearization based control design method for such systems the study extends the system relative degree concepts commonly used for the control of nonlinear systems to general t s fuzzy systems derives various relative degree conditions for general t s fuzzy systems and establishes the relative degree dependent normal forms a feedback linearization based control design framework is developed for general t s fuzzy systems using its normal form to achieve closed loop stability and asymptotic output tracking under relaxed design conditions a new adaptive feedback linearization based control scheme for t s fuzzy systems in general noncanonical forms with parameter uncertainties is designed and analyzed some extensions of relative degrees and their possible application to robust adaptive control for noncanonical form t s fuzzy systems are also demonstrated an illustrative example is presented with simulation results to demonstrate the control system design procedure and to show the effectiveness of the proposed control scheme

design of a fuzzy controller with fuzzy sliding surface abstract fuzzy logic controllers have succeeded in many control problems that the conventional control theories have difficulties to deal with however the design of the fuzzy logic controllers depends to a large extent on the expert s knowledge or on trial and error moreover due to the linguistic expression of the fuzzy controller it has not been easy to guarantee the stability and robustness of the fuzzy control systems to overcome these drawbacks we propose to design a fuzzy controller with the fuzzy sliding surface the fuzzy rules are defined based on this fuzzy sliding surface and the output of the fuzzy controller is inferred by the proper compositional rule of inference then we show the stability of this fuzzy control system and the boundedness of the tracking error by using the lyapunov theory finally we apply this fuzzy controller to control a nonlinear time varying system and confirm the validity of the controller

adaptive fuzzy control of uncertain stochastic nonlinear systems with unknown dead zone using small gain approach this paper considers the adaptive fuzzy robust control problem for a class of single input and single output siso stochastic nonlinear systems in strict feedback form the systems under study possess unstructured uncertainties unknown dead zone uncertain dynamics and unknown gain functions in the controller design fuzzy logic systems are adopted to approximate the unknown functions and the uncertain nonlinear system is therefore transformed into an uncertain parameterized system with unmodeled dynamics by combining the backstepping technique with the stochastic small gain approach a novel adaptive fuzzy robust control scheme is developed it is shown that the proposed control approach can guarantee that the closed loop system is input state practically stable isps in probability and the output of the system converges to a small neighborhood of the origin by appropriately tuning several design parameters simulation results are provided to illustrate the effectiveness of the proposed control approach

mixed finite element formulations of strain gradient elasticity problems theories on intrinsic or material length scales find applications in the modeling of size dependent phenomena in elasticity length scales enter the constitutive equations through the elastic strain energy function which in this case depends not only on the strain tensor but also on gradients of the rotation and strain tensors in the present paper the strain gradient elasticity theories developed by mindlin and co workers in the 1960s are treated in detail in such theories when the problem is formulated in terms of displacements the governing partial differential equation is of fourth order if traditional finite elements are used for the numerical solution of such problems then c 1 displacement continuity is required an alternative mixed finite element formulation is developed in which both the displacement and the displacement gradients are used as independent unknowns and their relationship is enforced in an integralsense a variational formulation is developed which can be used for both linear and non linear strain gradient elasticity theories the resulting finite elements require only c 0 continuity and are simple to formulate the proposed technique is applied to a number of problems and comparisons with available exact solutions are made 2002 elsevier science b v all rights reserved

variable structure robust control of uncertain time delay systems abstract this paper introduces a variable structure output feedback robust control for uncertain time delay systems new types of switching manifolds with integral terms are implemented to consider larger class of linear systems by overcoming both the observability constraints of the reduced order system and the kimura davison condition two types of control laws are introduced by which an estimate of a region of asymptotic stability to the origin and a region of attraction to the switching manifold are defined

on equitable resource allocation problems a lexicographic minimax approach in this expository paper we review a variety of resource allocation problems in which it is desirable to allocate limited resources equitably among competing activities applications for such problems are found in diverse areas including distribution planning production planning and scheduling and emergency services location each activity is associated with a performance function representing for example the weighted shortfall of the selected activity level from a specified target a resource allocation solution is called equitable if no performance function value can be improved without either violating a constraint or degrading an already equal or worse off i e larger performance function value that is associated with a different activity a lexicographic minimax solution determines this equitable solution that is it determines the lexicographically smallest vector whose elements the performance function values are sorted in nonincreasing order the problems reviewed include large scale allocation problems with multiple knapsack resource constraints multiperiod allocation problems for storable resources and problems with substitutable resources the solution of large scale problems necessitates the design of efficient algorithms that take advantage of special mathematical structures indeed efficient algorithms for many models will be described we expect that this paper will help practitioners to formulate and solve diverse resource allocation problems and motivate researchers to explore new models and algorithmic approaches

solving knapsack sharing problems with general tradeoff functions a knapsack sharing problem is a maximin or minimax mathematical programming problem with one or more knapsack constraints an inequality constraint with all non negative coefficients all knapsack sharing algorithms to date have assumed that the objective function is composed of single variable functions called tradeoff functions which are strictly increasing continuous functions this paper develops optimality conditions and algorithms for knapsack sharing problems with any type of continuous tradeoff function including multiple valued and staircase functions which can be increasing decreasing unimodal bimodal or even multi modal to do this optimality conditions are developed for a special type of multiple valued nondecreasing tradeoff function called an ascending function the optimal solution to any knapsack sharing problem can then be found by solving an equivalent problem where all the tradeoff functions have been transformed to ascending functions polynomial algorithms are developed for piecewise linear tradeoff functions with a fixed number of breakpoints the techniques needed to construct efficient algorithms for any type of tradeoff function are discussed

robust adaptive sliding mode control for fuzzy systems with mismatched uncertainties this paper is devoted to design adaptive sliding mode controllers for the takagi sugeno t s fuzzy system with mismatched uncertainties and exogenous disturbances the uncertainties in state matrices are mismatched and norm bounded while the exogenous disturbances are assumed to be bounded with an unknown bound which is estimated by a simple and effective adaptive approach both state and static output feedback sliding mode control problems are considered in terms of linear matrix inequalities lmis both sliding surfaces and sliding mode controllers can be easily obtained via a convex optimization technique finally two simulation examples and a real experiment are utilized to illustrate the applicability and effectiveness of the design procedures proposed in this paper

robust adaptive fuzzy controller for nonlinear system using estimation of bounds for approximation errors this paper describes the design of the robust adaptive fuzzy controller for uncertain single input single output nonlinear dynamical systems with unknown nonlinearities these unknown nonlinearities are approximated by the fuzzy system with a set of fuzzy if then rules whose parameters are adjusted on line according to some adaptive laws for the purpose of controlling the output of the nonlinear system to track a given trajectory the lyapunov synthesis approach is used to develop a state feedback adaptive control algorithm based on the adaptive fuzzy model the key assumption is that the reconstruction errors satisfy certain bounding conditions the control law consists of two terms one is the certainty equivalent control and the other is the bounding control a bounding parameter adaptive law is used to obtain this bounding control the overall control system guarantees that the tracking error converges in the small neighborhood of zero and that all signals involved are uniformly bounded it is also shown that in the special case the tracking error exponentially converges to zero even though the approximation errors exist

adaptive parameter estimator based on t s fuzzy models and its applications to indirect adaptive fuzzy control design in this paper a new on line parameter estimation methodology for the general continuous time takagi sugeno t s fuzzy model whose parameters are poorly known or uncertain is presented an estimator with an appropriate adaptive law for updating the parameters is designed and analyzed based on the lyapunov theory the adaptive law is designed so that the estimation model follows the parameterized plant model by the proposed estimator the parameters of the t s fuzzy model can be estimated by observing the behavior of the system and it can be a basis for indirect adaptive fuzzy control in order to show the applicability of the proposed estimator indirect adaptive fuzzy control design examples with the proposed estimator are presented

three dimensional structured networks for matrix equation solving two three dimensional structured networks are developed for solving linear equations and the lyapunov equation the basic idea of the structured network approaches is to first represent a given equation solving problem by a 3 d structured network so that if the network matches a desired pattern array the weights of the linear neurons give the solution to the problem then train the 3 d structured network to match the desired pattern array using some training algorithms and finally obtain the solution to the specific problem from the converged weights of the network the training algorithms for the two 3 d structured networks are proved to converge exponentially fast to the correct solutions simulations were performed to show the detailed convergence behaviors of the 3 d structured networks

stable adaptive fuzzy control of nonlinear systems a direct adaptive fuzzy controller that does not require an accurate mathematical model of the system under control is capable of incorporating fuzzy if then control rules directly into the controllers and guarantees the global stability of the resulting closed loop system in the sense that all signals involved are uniformly bounded is developed the specific formula for the bounds is provided so that controller designers can determine the bounds based on their requirements the direct adaptive fuzzy controller is used to regulate an unstable system to the origin and to control the duffing chaotic system to track a trajectory the simulation results show that the controller worked without using any fuzzy control rules and that after fuzzy control rules were incorporated the adaptation speed became much faster it is shown explicitly how the supervisory control forces the state to remain within the constraint set and how the adaptive fuzzy controller learns to regain control

adaptive indirect fuzzy sliding mode controller for networked control systems subject to time varying network induced time delay two major challenges in networked control systems are the time varying networked induced delays and the packet losses to alleviate these problems this study presents a novel fuzzy sliding mode controller where a fuzzy system is used to estimate the nonlinear dynamical system online and the networked induced delay is handled by pade approximation the problem of packet losses is handled by viewing them as large time varying delays in the system the sliding mode based design procedure used ensures the stability and the robustness of the proposed controller in the presence of disturbances and time varying networked induced time delays using an appropriate lyapunov function it is proved that the tracking error converges to the neighborhood of zero asymptotically furthermore since the adaptation laws of the parameters are derived by using of the lyapunov function these laws are also found to be stable simulation results show that the proposed fuzzy sliding mode controller is capable of controlling nonlinear dynamical systems over a network which is subject to bounded external disturbances time varying network induced delays and packet losses with adequate performance

decentralized adaptive fuzzy control for large scale nonlinear systems abstract a decentralized adaptive fuzzy control scheme for a class of large scale nonlinear systems is proposed in this paper the design is based on the principle of sliding mode control and the approximation capability of fuzzy systems the control architecture employs decentralized fuzzy systems to adaptively compensate for plant uncertainties by using the lyapunov function method the control algorithm is proved to be globally stable with tracking errors converging to a neighborhood of zero

technical note on min max integer allocation problems this note treats a bottleneck integer allocation problem the results obtained supercede those in this journal due to zeitlin zeitlin z 1981 integer allocation problems of min max type with quasiconvex separable functions opns res 29 207 211 who has considered a similar allocation problem with a strictly quasiconvex objective function

memoryless state feedback controller design for time delay systems with matched uncertain nonlinearities the robust control problem for a class of uncertain time delay systems is investigated the systems include multiple time delays and uncertain nonlinear functions to our best knowledge no controller design method for the systems is reported in the literature except for sliding mode control smc however the sliding mode controller must use the delayed state of the system so that the precise time delays have to be known and also a large memory is needed for controller implementation to overcome the shortcomings we employ the backstepping method to design a memoryless state feedback controller by constructing a novel lyapunov krasovskii functional we show that the resulting closed loop system is asymptotically stable simulations are done to verify the effectiveness of the proposed method

adaptive fuzzy sliding mode control of nonlinear system in this paper the fuzzy approximator and sliding mode control smc scheme are considered we propose two methods of adaptive smc schemes that the fuzzy logic systems approximators are used to approximate the unknown system functions in designing the smc of nonlinear system in the first method a fuzzy logic system is utilized to approximate the unknown function f of the nonlinear system x sup n f x t b x t u and the robust adaptive law is proposed to reduce the approximation errors between the true nonlinear functions and fuzzy approximators in the second method two fuzzy logic systems are utilized to approximate the f and b respectively and the control law which is robust to approximation error is also designed the stabilities of proposed control schemes are proved and these schemes are applied to an inverted pendulum system the comparisons between the proposed control schemes are shown in simulations

bending and stability analysis of gradient elastic beams abstract the problems of bending and stability of bernoulli euler beams are solved analytically on the basis of a simple linear theory of gradient elasticity with surface energy the governing equations of equilibrium are obtained by both a combination of the basic equations and a variational statement the additional boundary conditions are obtained by both variational and weighted residual approaches two boundary value problems one for bending and one for stability are solved and the gradient elasticity effect on the beam bending response and its critical buckling load is assessed for both cases it is found that beam deflections decrease and buckling load increases for increasing values of the gradient coefficient while the surface energy effect is small and insignificant for bending and buckling respectively

second order sliding fuzzy interval type 2 control for an uncertain system with real application a new second order sliding mode type 2 fuzzy controller for nonlinear uncertain perturbed systems is developed in this paper to overcome the constraint on the knowledge of the system model we have used local models that are related to some operating points to synthesize a type 2 nominal fuzzy global model the control is based on the super twisting algorithm which is among second order sliding mode controls smcs moreover two adaptive fuzzy type 2 systems have been introduced to generate the two super twisting signals to avoid both the chattering and the constraint on the knowledge of disturbances and uncertainties upper bounds these adaptive fuzzy type 2 systems are adjusted online by two adaptation laws that are deduced from the stability analysis in the lyapunov sense it has only one input i e the sliding surface and one output i e the optimal values of the gains control which are hard to compute with the original algorithm many results of the one link manipulator are obtained first by the simulation in order to compare the performances of the proposed method with that given by levant and then in a real time application in order to confirm the efficiency of the proposed approach the experimentation and simulation are done for the tracking control problem

observer based adaptive fuzzy control for siso nonlinear systems abstract the observer based indirect and direct adaptive fuzzy controllers are developed for a class of siso uncertain nonlinear systems the proposed approaches do not need the availability of the state variables by designing the state observer the adaptive fuzzy systems which are used to model the unknown functions can be constructed using the state estimations thus a new hybrid adaptive fuzzy control method is proposed by combining the above adaptive fuzzy system with the h control technique based on lyapunov stability theorem the proposed adaptive fuzzy control system can guarantee the stability of the whole closed loop systems and obtain good tracking performance as well the proposed methods are applied to an inverted pendulum system and a chaotic system and achieve satisfactory simulation results

universal fuzzy controllers for a class of nonlinear systems in this paper we address the issues of universal fuzzy controllers we first present a universal function approximation theorem based on a fuzzy dynamic model then we show the results of universal fuzzy controllers for a large class of nonlinear systems

stable adaptive control using fuzzy systems and neural networks stable direct and indirect adaptive controllers are presented which use takagi sugeno fuzzy systems conventional fuzzy systems or a class of neural networks to provide asymptotic tracking of a reference signal for a class of continuous time nonlinear plants with poorly understood dynamics the indirect adaptive scheme allows for the inclusion of a priori knowledge about the plant dynamics in terms of exact mathematical equations or linguistics while the direct adaptive scheme allows for the incorporation of such a priori knowledge in specifying the controller we prove that with or without such knowledge both adaptive schemes can learn how to control the plant provide for bounded internal signals and achieve asymptotically stable tracking of a reference input in addition for the direct adaptive scheme a technique is presented in which linguistic knowledge of the inverse dynamics of the plant may be used to accelerate adaptation the performance of the indirect and direct adaptive schemes is demonstrated through the longitudinal control of an automobile within an automated lane

further remarks on additional dynamics in various model transformations of linear delay systems this paper focuses on the analysis of conservatism introduced due to some model transformations used in the control literature this work is an extension of a previous paper by the authors 1999 on additional dynamics the additional dynamics of the second order and parametrized model transformations are examined the neutral model transformation introduces additional constraints for stability which can be analyzed in a very similar manner to additional dynamics

couple stress based strain gradient theory for elasticity the deformation behavior of materials in the micron scale has been experimentally shown to be size dependent in the absence of stretch and dilatation gradients the size dependence can be explained using classical couple stress theory in which the full curvature tensor is used as deformation measures in addition to the conventional strain measures in the couple stress theory formulation only conventional equilibrium relations of forces and moments of forces are used the couple s association with position is arbitrary in this paper an additional equilibrium relation is developed to govern the behavior of the couples the relation constrained the couple stress tensor to be symmetric and the symmetric curvature tensor became the only properly conjugated high order strain measures in the theory to have a real contribution to the total strain energy of the system on the basis of this modification a linear elastic model for isotropic materials is developed the torsion of a cylindrical bar and the pure bending of a flat plate of infinite width are analyzed to illustrate the effect of the modification

indirect adaptive fuzzy sliding mode control part i fuzzy switching in this paper by using the concept of sliding mode control design and lyapunov synthesis approach we propose an indirect adaptive fuzzy sliding mode control iafsmc scheme for a class of nonlinear systems in contrast to the existing sliding mode fuzzy control system designs where the sliding mode control law is directly substituted by a fuzzy controller in our approach both the equivalent control term and switching type control term in the sliding mode control law are approximated by fuzzy systems respectively an on line adaptive tuning algorithm for the consequent parameters in the fuzzy rules is also designed the sliding mode based design procedure ensures the stability and robustness of the proposed iafsmc we prove that the proposed adaptive scheme can achieve asymptotically stable tracking of a reference input with a guarantee of the bounded system signals the chattering phenomena in the sliding mode control is attenuated and the steady error is also alleviated simulation studies have shown that the presented adaptive design of fuzzy sliding mode controller performs very well in the presence of an unknown disturbance

adaptive fuzzy controller application to the control of the temperature of a dynamic room in real time this paper presents a direct adaptive fuzzy controller for unknown monotonic nonlinear systems thus not requiring the system model but only a little information about it the plant monotonicity and its delay without any off line pre training the algorithm achieves very high control performance through a three stage algorithm 1 output scale factor 2 adaptation of the fuzzy rule consequents and 3 optimization of the position of the membership functions the design is simple in the sense that both the membership functions and the rule base can be initialized from arbitrary values it can be applied to a large class of monotonic dynamic or static plants due the fact that the system is able to modify its behaviour in real time i e during the control process

nonlinear control via approximate input output linearization the ball and beam example approximate input output linearization of nonlinear systems which fail to have a well defined relative degree is studied for such systems a method for constructing approximate systems that are input output linearizable is provided the analysis presented is motivated through its application to a common undergraduate control laboratory experiment the ball and beam where it is shown to be more effective for trajectory tracking than the standard jacobian linearization

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

adaptive control of a class of nonlinear pure feedback systems using fuzzy backstepping approach a controller is proposed for the robust backstepping control of a class of nonlinear pure feedback systems using fuzzy logic the proposed control scheme utilizes fuzzy logic systems to learn the behavior of the unknown plant dynamics filtered signals are employed to circumvent algebraic loop problems encountered in the implementation of the usual controllers and the approximation errors can be efficiently counteracted by employing smooth robust compensators most importantly the uniform ultimate boundedness of all signals in the closed loop system can be guaranteed and a priori knowledge of the plant dynamics is no longer required furthermore the proposed method can be used for adaptive control of a large class of single input single output nonlinear systems in both strict feedback and pure feedback forms and has great potential in many diverse applications the performance of the proposed approach is demonstrated through three simulation examples including one nonlinear pure feedback and two nonlinear strict feedback systems

balance laws and energy release rates for cracks in dipolar gradient elasticity abstract it is the purpose of this work to derive the balance laws in the gunther knowles sternberg sense pertaining to dipolar gradient elasticity the theory of dipolar gradient or grade 2 elasticity derives from considerations of microstructure in elastic continua mindlin r d 1964 microstructure in linear elasticity arch rational mech anal 16 51 78 and is appropriate to model materials with periodic structure according to this theory the strain energy density assumes the form of a positive definite function of the strain as in classical elasticity and the gradient of both strain and rotation additional terms the balance laws are derived here through a more straightforward procedure than the one usually employed in classical elasticity i e noether s theorem indeed the pertinent balance laws are obtained through the action of the standard operators of vector calculus grad curl and div on appropriate forms of the hamiltonian of the system under consideration these laws are directly related to the energy release rates in the processes of crack translation rotation and self similar expansion under certain conditions they are identified with conservation laws and path independent integrals are obtained

analysis and synthesis of nonlinear time delay systems via fuzzy control approach takagi sugeno ts fuzzy models 1985 1992 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 i o submodels in this paper the ts fuzzy model approach is extended to the stability analysis and control design for both continuous and discrete time nonlinear systems with time delay the ts fuzzy models with time delay are presented and the stability conditions are derived using lyapunov krasovskii approach we also present a stabilization approach for nonlinear time delay systems through fuzzy state feedback and fuzzy observer based controller sufficient conditions for the existence of fuzzy state feedback gain and fuzzy observer gain are derived through the numerical solution of a set of coupled linear matrix inequalities an illustrative example based on the cstr model is given to design a fuzzy controller

energy theorems and the j integral in dipolar gradient elasticity within the framework of mindlins dipolar gradient elasticity general energy theorems are proved in this work these are the theorem of minimum potential energy the theorem of minimum complementary potential energy a variational principle analogous to that of the hellinger reissner principle in classical theory two theorems analogous to those of castigliano and engesser in classical theory a uniqueness theorem of the kirchhoff neumann type and a reciprocal theorem these results can be of importance to computational methods for analyzing practical problems in addition the j integral of fracture mechanics is derived within the same framework the new form of the j integral is identified with the energy release rate at the tip of a growing crack and its path independence is proved the theory of dipolar gradient elasticity derives from considerations of microstructure in elastic continua mindlin r d 1964 microstructure in linear elasticity arch rational mech anal 16 51 78 and is appropriate to model materials with periodic structure according to this theory the strain energy density assumes the form of a positive definite function of the strain as in classical elasticity and the second gradient of the displacement additional term specific cases of the general theory considered here are the well known theory of couple stress elasticity and the recently popularized theory of strain gradient elasticity the latter case is also treated in the present study 2005 elsevier ltd all rights reserved

design of interval type 2 fuzzy sliding mode controller in this paper an interval type 2 fuzzy sliding mode controller it2fsmc is proposed for linear and nonlinear systems the proposed it2fsmc is a combination of the interval type 2 fuzzy logic control it2flc and the sliding mode control smc which inherits the benefits of these two methods the objective of the controller is to allow the system to move to the sliding surface and remain in on it so as to ensure the asymptotic stability of the closed loop system the lyapunov stability method is adopted to verify the stability of the interval type 2 fuzzy sliding mode controller system the design procedure of the it2fsmc is explored in detail a typical second order linear interval system with 50 parameter variations an inverted pendulum with variation of pole characteristics and a duffing forced oscillation with uncertainty and disturbance are adopted to illustrate the validity of the proposed method the simulation results show that the it2fsmc achieves the best tracking performance in comparison with the type 1 fuzzy logic controller t1flc the it2flc and the type 1 fuzzy sliding mode controller t1fsmc

a novel takagi sugeno based robust adaptive fuzzy sliding mode controller in this paper a nonlinear dynamic system is first approximated by n fuzzy based linear state space subsystems to track a trajectory dominant by a specific frequency the reference models with desired amplitude and phase features are established by the same fuzzy sets of the system rule similarly the same fuzzy sets of the system rule are employed to design robust fuzzy sliding mode control rfsmc and adaptive fuzzy sliding mode control afsmc the difference between rfsmc and afsmc is that afsmc contains an updating law to learn system uncertainties and then an extra compensation is designed it is different from the most previous papers to learn the whole nonlinear functions as the norm of the sliding surface is inside of a defined set the updating law starts simultaneously as it is outside of the other set the updating law stops for the purpose of smoothing the possibility of discontinuous control input a transition between rfsmc and afsmc is also assigned under the circumstances the proposed control robust adaptive fuzzy sliding mode control rafsmc can automatically tune as a rfsmc or an afsmc then the advantages coming from the rfsmc and afsmc are obtained finally the stabilities of the overall system of rfsmc afsmc and rafsmc are verified by lyapunov stability theory the compared simulations among rfsmc afsmc and rafsmc are also carried out to confirm the usefulness of the proposed control scheme

gaussian networks for direct adaptive control a direct adaptive tracking control architecture is proposed and evaluated 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 uses a network of gaussian radial basis functions to adaptively compensate for the plant nonlinearities under mild assumptions about the degree of smoothness exhibit by the nonlinear functions the algorithm is proven to be globally stable with tracking errors converging to a neighborhood of zero a constructive procedure is detailed which directly translates the assumed smoothness properties of the nonlinearities involved into a specification of the network required to represent the plant to a chosen degree of accuracy a stable weight adjustment mechanism is determined using lyapunov theory the network construction and performance of the resulting controller are illustrated through simulations with example systems

continuous discontinuous finite element approximations of fourth order elliptic problems in structural and continuum mechanics with applications to thin beams and plates and strain gradient elasticity abstract a new finite element method for fourth order elliptic partial differential equations is presented and applied to thin bending theory problems in structural mechanics and to a strain gradient theory problem the method combines concepts from the continuous galerkin cg method the discontinuous galerkin dg method and stabilization techniques a brief review of the cg method the dg method and stabilization techniques highlights the advantages and disadvantages of these methods and suggests a new approach for the solution of fourth order elliptic problems a continuous discontinuous galerkin c dg method is proposed which uses c 0 continuous interpolation functions and is formulated in the primary variable only the advantage of this formulation over a more traditional mixed approach is that the introduction of additional unknowns and related difficulties can be avoided in the context of thin bending theory the c dg method leads to a formulation where displacements are the only degrees of freedom and no rotational degrees of freedom need to be considered the main feature of the c dg method is the weak enforcement of continuity of first and higher order derivatives through stabilizing terms on interior boundaries consistency stability and convergence of the method are shown analytically numerical experiments verify the theoretical results and applications are presented for bernoulli euler beam bending poisson kirchhoff plate bending and a shear layer problem using toupin mindlin strain gradient theory

robust adaptive fuzzy control in the presence of external disturbance and approximation error robust direct and indirect adaptive fuzzy controllers are proposed for tracking control of a class of nonlinear siso systems the behavior of the adaptive law is investigated in the error state space when the perturbations are introduced in the adaptive fuzzy control system a new adaptation scheme that can eliminate the effect of perturbations on the parameter adaptation is proposed it is proved that all the signals in the closed loop system are bounded in the presence of external disturbances and approximation error of the fuzzy logic system the concept of persistent excitation is utilized to guarantee the convergence and the boundedness of adaptation parameters it has also been observed that the convergence of parameters and tracking error could be smoother and faster with the proposed methods compared with the conventional adaptive fuzzy controllers two simulations have been conducted to demonstrate the effectiveness of the proposed controllers

observer based fuzzy control design with adaptation to delay parameter for time delay systems this paper is concerned with the problem of observer based fuzzy stabilization for time delay systems the time delay under consideration is assumed to be a constant time delay but not known exactly a new design method is proposed for an observer based fuzzy controller with adaptation to the time delay the designed controller simultaneously contains both the current and past state information of the systems and can be derived by solving a set of linear matrix inequalities lmis the existence of the controller is equivalent to that of a controller for time delay systems where the constant time delay is known exactly a numerical example is given to illustrate the effectiveness of the design method

the problem of sharp notch in couple stress elasticity abstract the problem of sharp notch in couple stress elasticity is considered in this paper the problem involves a sharp notch in a body of infinite extent the body has microstructural properties which are assumed to be characterized by couple stress effects both symmetric and anti symmetric loadings at remote regions are considered under plane strain conditions the faces of the notch are considered traction free to determine the field around the tip of the notch a boundary layer approach is followed by considering an expansion of the displacements in a form of separated variables in a polar coordinate system our analysis is in the spirit of the knein williams and karp karal asymptotic techniques but it is much more involved than its corresponding analysis of standard elasticity due to the complicated boundary value problem higher order system of governing pdes and additional boundary conditions as compared to the standard theory eventually an eigenvalue problem is formulated and this along with the restriction of a bounded potential energy provides the asymptotic fields the cases of a crack and a half space are analyzed as limit cases of the general notch problem certain deviations from the standard classical elasticity results are noted

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

indirect adaptive fuzzy sliding mode control part ii parameter projection and supervisory control the objective of this paper is to show that the error dynamics of the lyapunov synthesis is similar to the sliding surface of sliding mode control smc we compare and evaluate the role and performance of sliding surface boundary layer and lyapunov synthesis finally the indirect adaptive fuzzy sliding mode control iafsmc is equipped with state boundedness supervisory controller and parameter projection simulation studies illustrate the application of the proposed method

fuzzy on line identification of siso nonlinear systems abstract a new fuzzy on line identification algorithm for a single input single output continuous time nonlinear dynamic system is presented this method combines the conventional on line identification with fuzzy logic system the nonlinear system is approximated by a set of fuzzy rules that describe the local linear dynamic in each subspace formed by fuzzifying the input and output space the continuous time fuzzy input output model is identified on line by using the input and output measurements a fuzzy identification algorithm has been developed and a convergence analysis is carried out simulation studies have demonstrated that this fuzzy on line identifier can match the time varying nonlinear system within 5 accuracy

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

designing fuzzy controllers from a variable structures standpoint a procedure is presented for designing fuzzy controllers based upon variable structures techniques three such controllers are presented the fuzzy equivalents of sliding mode controllers saturating controllers and tanh controllers by using an approach based upon variables structures vss techniques the stability of each of these controllers is assured by using a sliding surface the order of the rule base is reduced to size r spl times m where r is the number of inputs and m is the number of fuzzification levels this combination makes the proposed design procedure able to generate simple controllers with guaranteed stability properties to illustrate the proposed design procedure fuzzy controllers are designed for a ball and beam system it is demonstrated that in spite of this system being a fourth order unstable system the proposed design procedure results in simple stable fuzzy controllers

decomposition property of fuzzy systems and its applications this paper presents the decomposition property of fuzzy systems using a simple constructive decomposition procedure that is by properly dividing the input space into sub input spaces a general fuzzy system is decomposed into several sub fuzzy systems which are the simplest fuzzy systems in the sub input spaces based on the decomposition property of fuzzy systems the analysis of fuzzy systems can be divided into two steps first analyze the properties of the simplest fuzzy systems and then use the decomposition property to extend the results to general fuzzy systems using this idea two applications of the decomposition property are given the first is the application to the representation capability analysis of fuzzy systems the second is the application to the analysis of a class of nonlinear control systems then based on the piecewise affine fuzzy system model the existence condition and the design of a stable control for a class of single input single output siso nonlinear systems are presented