fuzzy differential games for nonlinear stochastic systems suboptimal approach a fuzzy differential game theory is proposed to solve the n person or n player nonlinear differential noncooperative game and cooperative game team problems which are not easily tackled by the conventional methods in the paper both noncooperative and cooperative quadratic differential games are considered first the nonlinear stochastic system is approximated by a fuzzy model based on the fuzzy model a fuzzy controller is proposed to deal with the noncooperative differential game in the sense of nash equilibrium strategies or with the cooperative game in the sense of pareto optimal strategies using a suboptimal approach the outcomes of the fuzzy differential games for both the noncooperative and the cooperative cases are parameterized in terms of an eigenvalue problem since the state variables are usually unavailable a suboptimal fuzzy observer is also proposed in this study to estimate the states for these differential game problems finally simulation examples are given to illustrate the design procedures and to indicate the performance of the proposed methods

a deterministic equivalent for the analysis of correlated mimo multiple access channels in this article novel deterministic equivalents for the stieltjes transform and the shannon transform of a class of large dimensional random matrices are provided these results are used to characterize the ergodic rate region of multiple antenna multiple access channels when each point to point propagation channel is modelled according to the kronecker model specifically an approximation of all rates achieved within the ergodic rate region is derived and an approximation of the linear precoders that achieve the boundary of the rate region as well as an iterative water filling algorithm to obtain these precoders are provided an original feature of this work is that the proposed deterministic equivalents are proved valid even for strong correlation patterns at both communication sides the above results are validated by monte carlo simulations

output feedback direct adaptive fuzzy controller based on frequency domain methods this paper describes a design method that guarantees the stability of an adaptive fuzzy control system the system consists of an unstable plant with an irrational transfer function a takagi sugeno fuzzy adaptive controller a nonlinear reference model and an adaptation mechanism the gradient based adaptation mechanism changes the consequents of the controller rules in such a way that the closed loop system behaves like the reference model the proposed design procedure utilizes frequency domain methods in the forms of the nyquist and circle criteria it is assumed that the function of the fuzzy controller is a nonlinearity described by a sector condition this condition means that the controller function lies between two lines passing through the origin in this method the function of the fuzzy controller is verified during online adaptation therefore it stays in the allowed sector this method is illustrated by an example of a control system containing an unstable plant with a transport delay the main contribution of this paper is to use frequency methods combined with adaptive fuzzy control these methods have previously been used for nonadaptive fuzzy control but in this paper they are used for the first time for adaptive fuzzy control

analysis and design of fuzzy control system abstract a continuous time fuzzy control system which is composed of a fuzzy model and a fuzzy controller is proposed under certain conditions the proposed fuzzy control system can be regarded as a fuzzy pid control system the stability analysis of the fuzzy control system is given a sufficient condition to guarantee the stability of the proposed fuzzy control system is proposed in terms of lyapunov s method the results can be applied to the design of a fuzzy pid control system the design procedure can also be applied to the controller design with a non fuzzy model examples are given to illustrate the design of the proposed fuzzy control system

asymptotic capacity and optimal precoding in mimo multi hop relay networks a multihop relaying system is analyzed where data sent by a multi antenna source is relayed by successive multi antenna relays until it reaches a multi antenna destination assuming correlated fading at each hop each relay receives a faded version of the signal from the previous level performs linear precoding and retransmits it to the next level using free probability theory and assuming that the noise power at relays but not at destination is negligible the closed form expression of the asymptotic instantaneous end to end mutual information is derived as the number of antennas at all levels grows large the so obtained deterministic expression is independent from the channel realizations while depending only on channel statistics this expression is also shown to be equal to the asymptotic average end to end mutual information the singular vectors of the optimal precoding matrices maximizing the average mutual information with finite number of antennas at all levels are also obtained it turns out that these vectors are aligned to the eigenvectors of the channel correlation matrices thus they can be determined using only the channel statistics as the structure of the singular vectors of the optimal precoders is independent from the system size it is also optimal in the asymptotic regime

stochastic approximations of perturbed fredholm volterra integro differential equation arising in mathematical neurosciences this paper extends the results of synaptically generated wave propagation through a network of connected excitatory neurons to a continuous model defined by a fredholm volterra integro differential equation fvide which includes memory effects of the past in the propagation stochastic approximation and numerical simulations are discussed

fuzzy learning control for a flexible link robot there are two main drawbacks in fuzzy control 1 the design of fuzzy controllers is usually performed in an ad hoc manner where it is often difficult to choose some of the controller parameters and 2 the fuzzy controller constructed for the nominal plant may later perform inadequately if significant and unpredictable plant parameter variations occur in this paper we illustrate these two problems on a two link flexible robot testbed by 1 developing implementing and evaluating a fuzzy controller for the robotic mechanism and 2 illustrating that payload variations can have negative effects on the performance of a well designed fuzzy control system next we show how to develop and implement a fuzzy model reference learning controller for the flexible robot and illustrate that it can automatically synthesize a rule base for a fuzzy controller that will achieve comparable performance to the case where it was manually constructed and automatically tune the fuzzy controller so that it can adapt to variations in the payload

a self organizing adaptive fuzzy controller abstract there are two main parts in this paper the first part presents a knowledge representation and reasoning scheme called tree searched neural networks tnn the tnn is based on a well known intuitive knowledge representation ikr and can reduce the number of the processing nodes in the neural networks the second part proposes a self organizing adaptive fuzzy controller soafc based on the tnn model it can help acquire control knowledge and thus can reduce the dependence on experts furthermore designers do not need to predefine all membership functions to cover whole input space domain for improving its performance further we design a d controller which is included within the soafc whether the fuzzy controller is incorporated with the d controller or not it is also guaranteed to be globally stable simulation results show that this approach has faster convergence speed results in better transient response and in addition requires less total control energy

robust observer based tracking control of hodgkin huxley neuron systems under environmental disturbances a nervous system consists of a large number of highly interconnected nerve cells nerve cells communicate by generation and transmission of short electrical pulses action potential in addition membrane voltage is the only measurable state in nervous systems a robust observer based model reference tracking control is proposed for hodgkin huxley hh neuron systems to generate a desired reference response in spite of environmental noises uncertain initial values and diffusion currents from other interconnected nerve cells in order to simplify the robust tracking control design of nonlinear stochastic hh neuron systems a fuzzy interpolation method is employed to interpolate several linear stochastic systems to approximate a nonlinear stochastic hh neuron system so that the nonlinear robust tracking control problem can be solved by the linear matrix inequality lmi technique with the help of robust control toolbox in matlab the proposed robust observer based tracking control scheme can provide new methods for desired action potential generation suppression of oscillations and blockage of action potential transmission under environmental noise and diffusion currents these new methods are useful for patients with different neuron system dysfunctions finally three simulation examples of tracking control of nervous systems are given to illustrate the design procedure and confirm the tracking performance of the proposed method

sum rate optimal precoding for multi cell large scale mimo uplink based on statistical csi we investigate the sum rate optimal precoding for the uplink of the multi cell large scale mimo systems specifically we focus on transmitter precoder design based only on the statistical channel state information csi we first consider the partial cooperation system where only the csi is shared among cells and its base station bs decodes its in cell users by treating out cell signals as colored gaussian noise we derive the ergodic sum rate and its deterministic approximation for the regime where both the number of total user antennas and the number of bs antennas are large we obtain the necessary conditions to maximize the deterministic approximation of the sum rate under the transmit power constraint based on which a gradient search algorithm is proposed to find the local optimal precoders furthermore a super cell system is also considered where users from all cells are jointly decoded the deterministic approximation to the sum rate and optimal precoder design for such systems are given numerical experiments show that the proposed precoders achieve significant performance gains over systems with no precoding compared with the existing precoding methods that require perfect csi the proposed precoders achieve similar sum rates and require only the statistical csi

a robust self tuning scheme for pi and pd type fuzzy controllers proposes a simple but robust model independent self tuning scheme for fuzzy logic controllers flcs here the output scaling factor sf is adjusted online by fuzzy rules according to the current trend of the controlled process the rule base for tuning the output sf is defined on error e and change of error spl delta e of the controlled variable using the most natural and unbiased membership functions mfs the proposed self tuning technique is applied to both pi and pd type flcs to conduct simulation analysis for a wide range of different linear and nonlinear second order processes including a marginally stable system where even the well known ziegler nichols tuned conventional pi or pid controllers fail to provide an acceptable performance due to excessively large overshoot performances of the proposed self tuning flcs are compared with those of their corresponding conventional flcs in terms of several performance measures such as peak overshoot settling time rise time integral absolute error and integral of time multiplied absolute error in addition to the responses due to step set point change and load disturbance and in each case the proposed scheme shows a remarkably improved performance over its conventional counterpart

chebyshev neural network based model for solving lane emden type equations the objective of this paper is to solve second order non linear ordinary differential equations of lane emden type using chebyshev neural network chnn model these equations are categorized as singular initial value problems artificial neural network ann model is used here to overcome the difficulty of the singularity a single layer neural network is used and the hidden layer is eliminated by expanding the input pattern by chebyshev polynomials here we have used feed forward neural network model and principle of error back propagation homogeneous and non homogeneous lane emden equations are considered to show effectiveness of chebyshev neural network model

study on stability of fuzzy closed loop control systems abstract the problem of stability of fuzzy closed loop control systems has long been unsolved through analyzing the max min composition operator in fuzzy systems this paper presents a reasonable analytical model of fuzzy closed loop systems and then proposes a method to analyze the stability of control systems by the relational matrix of fuzzy systems an example is given to show the method available

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

ergodic channel capacities for the amplify and forward half duplex cooperative systems in this paper the ergodic channel capacities are established for the amplify and forward af half duplex cooperative systems which consist of a source node a destination and multiple relay nodes the relay nodes assist the transmission from the source node to the destination since the channel matrices for the cooperative systems involve product of gaussian random variables which are no longer gaussian the approach in obtaining the ergodic channel capacity for conventional multiple input multiple output mimo gaussian channels telatar 1999 is not applicable by using a novel approach we have arrived at the following conclusions about the ergodic channel capacities for the af cooperative systems for the single antenna af relay systems in which all nodes are equipped with one antenna the optimal covariance matrix of the input signals to achieve the ergodic channel capacity is diagonal and the diagonal elements are obtained by solving optimization problems of multidimensional integrals these diagonal entries are not all equal even if all the channel gains in the cooperative systems are independent and identically distributed i i d gaussian with unit variance therefore a white input signal for the af cooperative system may not achieve the ergodic channel capacity of the system this is in direct contrast to the case of conventional multiple input single output miso systems having i i d gaussian channel gains of unit variance in which case the ergodic capacity is achieved if the input covariance matrix is a scaled identity matrix for the mimo relay system in which the nodes have multiple antennas the input covariance matrix to achieve the ergodic capacity is block diagonal and each block diagonalizes the autocorrelation of channel matrix from the source to the destination this is different from the case of conventional mimo systems where the input covariance matrix to achieve the ergodic channel capacity diagonalizes the channel autocorrelation matrix of the mimo system tulina lozano and verdu 2006 if the channel gains in conventional mimo systems are correlated gaussian random variables the input covariance matrix is a full matrix not block diagonal and if the channel gains are i i d gaussians the optimal input covariance matrix is a scaled identity the observations obtained in this paper reveal useful insights of how the af cooperative systems ldquomimicrdquo the conventional miso and mimo systems from the ergodic channel capacity perspective

nested design of fuzzy controllers with partial fuzzy rule base abstract in this paper a systematic nested design approach with a partial fuzzy if then rule base is proposed to reduce the complexity of the fuzzy controllers in the design procedure the fuzzy controller is first constructed with a basic fuzzy rule base when the fuzzy rule base is not sufficient to provide the performance that meets the requirement of the fuzzy control system the fuzzy rule base contains some unsatisfactory fuzzy rules and needs to be adjusted after the unsatisfactory fuzzy rules are identified the fuzzy region controlled by each unsatisfactory fuzzy rule is further partitioned into sub regions based on the nested design procedure the partial fuzzy rule base of the fuzzy controller is modified by replacing each unsatisfactory fuzzy rule with new fuzzy rules for the corresponding sub regions each fuzzy region of the input space can be partitioned independently into fuzzy sub regions to avoid generating the redundant rules the parameters in the fuzzy mechanism are tuned by minimizing a cost function simulations are carried out to show the effectiveness of the fuzzy controllers with nested fuzzy if then rules

the linear rational collocation method we introduce the collocation method based on linear rational interpolation for solving general hyperbolic problems prove its stability and its convergence in weighted norms and give numerical examples for its use

h spl infin decentralized fuzzy model reference tracking control design for nonlinear interconnected systems in general due to the interactions among subsystems it is difficult to design an h sub spl infin decentralized controller for nonlinear interconnected systems the model reference tracking control problem of nonlinear interconnected systems is studied via h sub spl infin decentralized fuzzy control method first the nonlinear interconnected system is represented by an equivalent takagi sugeno type fuzzy model a state feedback decentralized fuzzy control scheme is developed to override the external disturbances such that the h spl infin model reference tracking performance is achieved furthermore the stability of the nonlinear interconnected systems is also guaranteed if states are not all available a decentralized fuzzy observer is proposed to estimate the states of each subsystem for decentralized control consequently a fuzzy observer based state feedback decentralized fuzzy controller is proposed to solve the h sub spl infin tracking control design problem for nonlinear interconnected systems the problem of h sub spl infin decentralized fuzzy tracking control design for nonlinear interconnected systems is characterized in terms of solving an eigenvalue problem evp the evp can be solved very efficiently using convex optimization techniques finally simulation examples are given to illustrate the tracking performance of the proposed methods

limited feedback unitary precoding for spatial multiplexing systems multiple input multiple output mimo wireless systems use antenna arrays at both the transmitter and receiver to provide communication links with substantial diversity and capacity spatial multiplexing is a common space time modulation technique for mimo communication systems where independent information streams are sent over different transmit antennas unfortunately spatial multiplexing is sensitive to ill conditioning of the channel matrix precoding can improve the resilience of spatial multiplexing at the expense of full channel knowledge at the transmitter which is often not realistic this correspondence proposes a quantized precoding system where the optimal precoder is chosen from a finite codebook known to both receiver and transmitter the index of the optimal precoder is conveyed from the receiver to the transmitter over a low delay feedback link criteria are presented for selecting the optimal precoding matrix based on the error rate and mutual information for different receiver designs codebook design criteria are proposed for each selection criterion by minimizing a bound on the average distortion assuming a rayleigh fading matrix channel the design criteria are shown to be equivalent to packing subspaces in the grassmann manifold using the projection two norm and fubini study distances simulation results show that the proposed system outperforms antenna subset selection and performs close to optimal unitary precoding with a minimal amount of feedback

an approach to systematic design of the fuzzy control system abstract this paper presents a new design method of fuzzy control system fcs the concept from the sliding mode control is adopted to construct fuzzy control scheme if the original control rules are inappropriate the adaptive mechanism will modify these rules according to the proposed algorithms in particular the structure of sliding surface provides a reasonable estimation to the universes of discourse on which the fuzzy control rules are based finally an inverted pendulum system is used to demonstrate the availability of the proposed approaches

application of fuzzy on line self adaptive controller for a contour tracking robot on unknown contours abstract modelling a contour tracking robot on unknown contours is a relatively difficult task therefore a new compliant motion controller is developed in this study by applying the on line rule adaptive fuzzy control to have a cartesian manipulator perform contour tracking on unknown contours also the contact force is controlled here within a certain constant value and the manipulator is controlled along the tangent direction in which the manipulator is unconstrained experimental results verify the feasibility of our designed control strategy

a hybrid neuro fuzzy pid controller a hybrid neuro fuzzy control strategy and its corresponding rule generating approach is proposed according to this approach the fuzzy control rules can be generated automatically via fuzzy inputs and then the appropriate control action can be deduced efficiently by a simplified fuzzy inference engine by combining the use of an incremental pi algorithm and a positional pd algorithm a pid fuzzy control strategy can be implemented simply from two input variables it results in the number of control rules being significantly reduced without decreasing the control performance the control parameters can be self tuned by introducing a single neuron together with a modified back propagation learning algorithm simulation results show that the proposed fuzzy controller is able to control unknown processes and provide good performance compared to traditional self organising and neural network based fuzzy controllers this method has simpler control algorithms and less computational burden

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

fuzzy sliding mode controller design for uncertain time delayed systems with nonlinear input in this paper the theory of sliding mode control is employed to develop a fuzzy controller for uncertain dynamic time delayed systems with series nonlinearities the control method provides a simple way to achieve asymptotic stability of the uncertain time delayed system other attractive features of the method include a minimal realization of the fuzzy controller in spite of the number of state variables as well as insensitivity to the uncertainties and disturbances in addition the method is capable of handling the chattering problem inherent to the sliding mode control easily and effectively also this fuzzy sliding mode controller can be extended to handle the mimo system simulation results are presented to demonstrate the power of the method

design of self learning fuzzy sliding mode controllers based on genetic algorithms abstract in this paper genetic algorithms were applied to search a sub optimal fuzzy rule base for a fuzzy sliding mode controller two types of fuzzy sliding mode controllers based on genetic algorithms were proposed the fitness functions were defined so that the controllers which can drive and keep the state on the user defined sliding surface would be assigned a higher fitness value the sliding surface plays a very important role in the design of a fuzzy sliding mode controller it can dominate the dynamic behaviors of the control system as well as reduce the size of the fuzzy rule base in conventional fuzzy logic control an increase in either input variables or the associated linguistic labels would lead to the exponential growth of the number of rules the number of parameters or the equivalent length of strings used in the computations of genetic algorithms for a fuzzy logic controller are usually quite extensive as a result the considerable computation load prevents the use of genetic operations in the tuning of membership functions in a fuzzy rule base this paper shows that the number of rules in a fuzzy sliding mode controller is a linear function of the number of input variables the computation load of the inference engine in a fuzzy sliding mode controller is thus smaller than that in a fuzzy logic controller moreover the string length of parameters is shorter in a fuzzy sliding mode controller than in a fuzzy logic controller when the parameters are searched by genetic algorithms the simulation results showed the efficiency of the proposed approach and demonstrated the applicability of the genetic algorithm in the fuzzy sliding mode controller design

fuzzy smoothing algorithms for variable structure systems a variable structure system vss is a control system implementing different control laws in different regions of the state space divided by a set of boundary manifolds the control input switches from one control law to another when the state crosses the boundary manifolds in general the control input may not be smooth when switching at these boundary manifolds and may excite high frequency dynamics this paper proposes two fuzzy rule based algorithms for smoothing the control input the merits of these fuzzy smoothing control algorithms are illustrated by two examples a semiactive suspension system based on optimal control and a direct drive robot arm under discrete time sliding mode control the controller design for these two examples is a blend of traditional control theoretic approaches and fuzzy rule based approaches

model reference adaptive fuzzy control a linguistic space approach in this paper a model reference adaptive fuzzy controller with the adaptivity achieved by tuning both the scaling factors and the control rules is presented the proposed tuning strategy includes two parts 1 by referring a reference trajectory created in the linguistic space to tune the scaling factors and 2 by applying an auxiliary correction matrix generated by specific tuning rules to compensate the control rules since only the control signal the output error and change in output error of the plant are needed in the construction of the reference trajectory and the tuning rules the tuning strategy has the advantage of real time property simulation results with a damping process and an oscillating process as the controlled plants show the performance and adaptivity of the proposed controller

trajectory planning and tracking of ball and plate system using hierarchical fuzzy control scheme ball and plate system is the extension of traditional ball and beam system in this paper a trajectory planning and tracking problem of ball and plate system is put forward to proof test diverse control schemes firstly we derive the mathematical model of the ball and plate system in detail then a hierarchical fuzzy control scheme is proposed to deal with this problem our scheme is composed of three levels the lowest level is a ts type fuzzy tacking controller the middle level is a fuzzy supervision controller that takes actions in extreme situations and the top level is a fuzzy planning controller that determines the desired trajectory in order to optimize the ball s moving trajectory the genetic algorithm is introduced to adjust the output membership functions of the fuzzy planning controller simulation results have shown that the hierarchical fuzzy control scheme can control the ball from a point to another without hitting the obstacles and in the least time

systematic design of unitary space time constellations we propose a systematic method for creating constellations of unitary space time signals for multiple antenna communication links unitary space time signals which are orthonormal in time across the antennas have been shown to be well tailored to a rayleigh fading channel where neither the transmitter nor the receiver knows the fading coefficients the signals can achieve low probability of error by exploiting multiple antenna diversity because the fading coefficients are not known the criterion for creating and evaluating the constellation is nonstandard and differs markedly from the familiar maximum euclidean distance norm our construction begins with the first signal in the constellation an oblong complex valued matrix whose columns are orthonormal and systematically produces the remaining signals by successively rotating this signal in a high dimensional complex space this construction easily produces large constellations of high dimensional signals we demonstrate its efficacy through examples involving one two and three transmitter antennas

a parameterized fuzzy processor and its applications abstract in this paper a parameterized fuzzy processor pfp is presented based on a designed fuzzy instruction set of the parameterized fuzzy number pfn this pfn is presented by some parameters of the universe of the discourse instead of a series of the membership grades the algorithms of these instructions are based on the parameter operations to implement the fuzzy arithmetics and the fuzzy reasoning methods the instruction set supports the versatility of the fuzzy information e g fuzzy arithmetic operations inference operations fuzzy logic operations data translations and data exchangements based upon these the characteristics of the pfn are discussed and the architecture of the pfp outlined is constructed in this paper and its processing time is saved due to the adaptation of the parameterized fuzzy number pfn to evaluate the performance of pfn instructions and pfp structure two experiments are presented one is the speed performance evaluated for the pfn to compare with the discrete fuzzy number dfn the other is the confirmation of the feasibility and the capability of the instructions which is demonstrated by three examples relateld to human inference intuitive control and decision making

derivation and application of an expert fuzzy optimal control system abstract this paper presents derivation of a fuzzy optimal controller which may be used to develop a knowledge based expert control system for supervising and tuning of conventional feedback control loops a general theory based on the conceptual framework for optimization in a fuzzy environment is presented for the development of linear and nonlinear fuzzy optimal control systems this technique is based on integration of the optimal control theorem and fuzzy variables the resulting expert controller is expressed in the form of linguistic fuzzy rules representing the knowledge base for tuning of the feedback control loops tuning inferences are made from the response of local feedback control loops by applying the compositional rule of inference to the knowledge base

a self tuning fuzzy pi controller abstract a robust self tuning pi type fuzzy logic controller flc is presented depending on the process trend the output scaling factor sf of the controller is modified on line by an updating factor the value of is determined from a rule base defined on error e and change of error e of the controlled variable the proposed self tuning controller is designed using a very simple control rule base and the most natural and unbiased membership functions mfs symmetric triangles with equal base and 50 overlap with neighboring mfs the proposed scheme is tested for a wide variety of processes including a marginally stable system with different values of dead time performance comparison between the conventional pi type and proposed self tuning flcs is made in terms of several performance criteria such as peak overshoot settling time rise time integral absolute error and integral of time multiplied absolute error in addition to the responses due to step input and load disturbance results for various processes show that the proposed flc outperforms its conventional counterpart in each case

fuzzy logic in commercial expert system results and prospects abstract this paper surveys the use of fuzzy methods in commercial applications of the technology of expert systems and in commercial products which aim to support such applications it attempts to evaluate the utility of such an approach to uncertainty management compared to other well known methods of handling uncertainty in expert systems starting from this base it attempts an evaluation of the prospects for fuzzy expert systems in the medium term as a survey it attempts to list applications and commercial products as comprehensively as is practical and includes an extensive bibliography on the topic

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

pid type fuzzy controller and parameters adaptive method abstract the authors of this paper try to analyze the dynamic behavior of the product sum crisp type fuzzy controller revealing that this type of fuzzy controller behaves approximately like a pd controller that may yield steady state error for the control system by relating to the conventional pid control theory we propose a new fuzzy controller structure namely pid type fuzzy controller which retains the characteristics similar to the conventional pid controller in order to improve further the performance of the fuzzy controller we work out a method to tune the parameters of the pid type fuzzy controller on line producing a parameter adaptive fuzzy controller simulation experiments are made to demonstrate the fine performance of these novel fuzzy controller structures

fuzzy self organizing controller and its application for dynamic processes abstract this paper deals with a self organizing controller used in real time and its application for dynamic processes the control policy of the controller is able to develop and improve automatically a new self organizing control algorithm which modifies the fuzzy control decision table is presented in this paper the control algorithm needs much less computation time and memory of the computer this paper provides two examples of the fuzzy self organizing control a set of experiment results is described it shows that the controller can be applied to some processes such as processes with time lag and non linearity or one whose parameter or running conditions are varied which were usually not controlled very well with a conventional controller

fuzzy adaptive approach to fuzzy controllers with spacial model in this paper a fuzzy adaptive approach to fuzzy controllers designed with the spacial model is proposed the complexity which is defined as the size of the fuzzy rule base of the fuzzy controller is significantly reduced based on the proposed approach in order to reduce the number of fuzzy if then rules the multidimensional space of input variables instead of the individual input variable of fuzzy controllers is partitioned into fuzzy sets however this space partition method may degrade the performances of fuzzy controllers since the degree of freedom is decreased to avoid the drawback of the fixed space partitioned fuzzy controllers a flexible spacial model design with fuzzy adaptive approach is introduced moreover the fuzzy adaptive mechanism is designed to accelerate the convergence to the desired system output the cascade decomposition of the fuzzy controllers designed with the flexible spacial model approach is presented to make these fuzzy controllers easy to implement and the discussions on more general types of the membership functions for the flexible spacial fuzzy model and the stability of the system with the proposed fuzzy controller are provided the simulation results are also included to show the effectiveness of the fuzzy controller by the flexible spacial model design approach we will show that the complexity reduced fuzzy controller with flexible spacial model and original fuzzy controller have similar performances and perform better than the fuzzy controller with simple fixed spacial fuzzy partition

fuzzy hierarchical swing up and sliding position controller for the inverted pendulum cart system in this paper a fuzzy hierarchical swing up and sliding position controller is proposed for the swing up and position controls of an inverted pendulum cart system the proposed fuzzy hierarchical swing up and sliding position controller includes a fuzzy switching controller a fuzzy swing up controller and a twin fuzzy sliding position controller the fuzzy switching controller is designed to smoothly switch between the swing up and position controls with the inverted pendulum cart system decomposed into a pendulum subsystem and a cart subsystem fuzzy sliding position controllers are presented to robustly balance the pendulum and cart at the desired positions the sliding mode and stability of the fuzzy sliding position control systems are guaranteed moreover an adaptive mechanism is provided to on line adjust the parameters in the fuzzy sliding position controllers simulation results are included to illustrate the effectiveness of the proposed fuzzy hierarchical swing up and sliding position controller

a delay reaction diffusion model of the spread of bacteriophage infection this paper is a continuation of recent attempts to understand via mathematical modeling the dynamics of marine bacteriophage infections previous authors have proposed systems of ordinary differential delay equations with delay dependent coefficients in this paper we continue these studies in two respects first we show that the dynamics is sensitive to the phage mortality function and in particular to the parameter we use to measure the density dependent phage mortality rate second we incorporate spatial effects by deriving in one spatial dimension a delay reaction diffusion model in which the delay term is rigorously derived by solving a von foerster equation using this model we formally compute the speed at which the viral infection spreads through the domain and investigate how this speed depends on the system parameters numerical simulations suggest that the minimum speed according to linear theory is the asymptotic speed of propagation ks t p t di dt ii t ks t p t e it ks t t p t t dp dt pp t ks t p t be it ks t t p t t

a novel adaptive fuzzy variable structure control for a class of nonlinear uncertain systems via backstepping abstract this paper presents a new design of adaptive fuzzy variable structure control to solve the traditional problem of model reference adaptive control mrac for a class of single input single output minimum phase uncertain nonlinear systems via backstepping instead of taking the tedious coordinate transformation and yielding a hard high gain controller we introduce smooth b spline type membership functions into the controller so as to compensate for the uncertainties much softer i e in a much smoother and locally weighted manner to be rigorous it is shown that the stability of the closed loop system can be assured and the tracking error can globally approach to an arbitrary preset dead zone range in order to demonstrate the effectiveness of the developed novel controller an example is extensively simulated to provide quite satisfactory performance

sufficient conditions on general fuzzy systems as function approximators abstract in a constructive way we have found sufficient conditions under which general fuzzy systems can uniformly approximate any real continuous function on a compact domain to any degree of accuracy more importantly we have revealed the underlying mechanism of such function approximation the fuzzy systems can uniformly approximate any polynomials which according to the weierstrass approximation theorem can uniformly approximate any continuous function on a compact domain these findings lead to the following practical results 1 explicit fuzzy rules of fuzzy systems can now be easily obtained according to functions to be approximated and 2 formulas are derived which can calculate the number of input fuzzy sets output fuzzy sets and fuzzy rules needed in order to satisfy any given approximation accuracy the number increases as required approximation error decreases and as approximation error approaches zero the number approaches these formulas also reveal that the number is minimal when the maximum number of intersection between adjacent input fuzzy sets is one practical implications of these results will be discussed especially in the context of fuzzy control and fuzzy modeling two examples are provided to demonstrate how to design fuzzy systems to approximate given functions with required approximation accuracy

a self organizing fuzzy logic controller for dynamic systems using a fuzzy auto regressive moving average farma model the paper proposes a complete design method for an online self organizing fuzzy logic controller without using any plant model by mimicking the human learning process the control algorithm finds control rules of a system for which little knowledge has been known in a conventional fuzzy logic control knowledge on the system supplied by an expert is required in developing control rules however the proposed new fuzzy logic controller needs no expert in making control rules instead rules are generated using the history of input output pairs and new inference and defuzzification methods are developed the generated rules are stored in the fuzzy rule space and updated online by a self organizing procedure the validity of the proposed fuzzy logic control method has been demonstrated numerically in controlling an inverted pendulum

a rule self regulating fuzzy controller abstract the most effective way to improve the performance of a fuzzy controller may be to optimize the fuzzy control rules usually fuzzy control rules are generated by 1 translating the operators experience into fuzzy linguistic form directly 2 monitoring and summarizing the control behaviour of the operators 3 modelling the process to be controlled using fuzzy set theory 4 self organizing in running of the control systems different from the above means the authors in 10 have proposed a method to regulate fuzzy control rules where the control rules are represented by an analytic expression with a regulating factor the authors in this paper employ such a method and use a simplified fuzzy control algorithm which allows fuzzy control rules to be regulated on line thus constructing a rule self regulating fuzzy controller rsfc simulation results demonstrate that the performance of rsfc is better than that of a non rule regulating fuzzy controller

a fine tuning method for fuzzy logic rule bases abstract the problem of fine tuning the rule base of a fuzzy system is addressed in this paper a method is proposed that treats the rule base of the fuzzy system as a multivariate function and performs parameter optimization to approach the desired rule base output with the given set of rules the method is explained in detail and an application of it on two different rule bases is presented this work is part of a research effort in robotic precision assembly using fuzzy logic

application of limit fuzzy controllers to stability analysis abstract we propose a method to examine the stability of fuzzy control systems it is based on the limit law of fuzzy controllers constructed from regular fuzzy rules the main idea is to use lyapunov functions for the system with limit laws to examine the stability of the system with fuzzy controllers this method is particularly useful when the system and the limit law are both linear it is applied to an inverted pendulum system two cases with and without friction are considered simulation results and the analysis confirm certain experimental and theoretical results already reported

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

stablization of an inverted pendulum by a high speed fuzzy logic controller hardware system abstract a high speed fuzzy controller hardware system employing min max operations is presented it has fifteen control rule boards and one defuzzifier grades of membership are represented with 0 v 5 v corresponding to 0 0 1 0 this fuzzy controller facilitates approximate reasoning at 1 000 000 fips fuzzy inferences per second and is able to be used for various purposes by programming on each control rule board it handles fuzzy linguistic information of the form nl negative large nm negative medium ns negative small zr approximately zero ps positive small pm positive medium pl positive large and ng negation this fuzzy controller hardware system makes an inverted pendulum stand on a vehicle by using seven control rules two pendulums 5 mm diameter 15 cm length 3 5 g weight respectively 10 mm 50 cm and 50 g can be stabilized by the same rule set it is much easier to produce control rules than to solve the nonlinear differential equations representing the dynamics of an inverted pendulum this fuzzy controller hardware system can be applied to attitude control of a space booster rocket and satellite an automatic aircraft landing system pattern recognition stabilization of nuclear fuel rods in a reactor an intelligent sensor and many other applications which need swift approximate reasoning

asymptotic and non asymptotic analysis of uplink sum rate for relay assisted mimo cellular systems we consider uplink relay assisted mimo cellular systems with multiple relays deployed in each cell that perform the amplify and forward operations we are interested in obtaining deterministic expressions for the ergodic sum rate of such systems we first consider the large mimo dimension scenario and obtain two asymptotic sum rate expressions corresponding to the cases of fixed number of users and large number of users respectively we then consider the case of arbitrary mimo dimension and large number of users and obtain an upper and lower bound that the sum rate lies in between with high probability the bounds are tight when the number of users is large both single cell and multi cell systems are considered where the latter assumes full base station cooperation numerical experiments show that these deterministic sum rate expressions match well with the monte carlo simulation results therefore they can be useful tools for the design and analysis of relay assisted mimo cellular systems

fuzzy controllers synthesis and equivalences it has been proved that fuzzy controllers are capable of approximating any real continuous control function on a compact set to arbitrary accuracy in particular any given linear control can be achieved with a fuzzy controller for a given accuracy the aim of this paper is to show how to automatically build this fuzzy controller the proposed design methodology is detailed for the synthesis of a sugeno or mamdani type fuzzy controller precisely equivalent to a given pi controller the main idea is to equate the output of the fuzzy controller with the output of the pi controller at some particular input values called modal values the rule base and the distribution of the membership functions can thus be deduced the analytic expression of the output of the generated fuzzy controller is then established for sugeno type fuzzy controllers precise equivalence is directly obtained for mamdani type fuzzy controllers the defuzzification strategy and the inference operators have to be correctly chosen to provide linear interpolation between modal values the usual inference operators satisfying the linearity requirement when using the center of gravity defuzzification method are proposed

stability analysis and design of fuzzy control systems abstract the stability analysis and the design technique of fuzzy control systems using fuzzy block diagrams are discussed first we show the concept of fuzzy blocks and consider the connection problems of fuzzy blocks diagrams we derive some theorems and corollaries with respect to two basic types of connections of fuzzy blocks in order to preserve some properties in a connection of fuzzy blocks continuous piecewise polynomial membership functions are defined secondly a sufficient condition which guarantees the stability of fuzzy systems is obtained in terms of lyapunov s direct method we give an important fact based on this condition thirdly we propose a new design technique of a fuzzy controller the fuzzy block diagrams and the stability analysis are applied to the design problems of a model based fuzzy controller

limit cycle prediction of a fuzzy control system based on describing function method a limit cycle is the phenomenon that can be observed in systems composed of nonlinear elements the phenomenon is of fundamental importance in nonlinear systems and as far as the design of a nonlinear system is concerned it should be considered along with the stability analysis in the paper the limit cycle of a system controlled by a fuzzy logic controller flc is addressed via some of the classical control techniques used to analyze nonlinear systems in the frequency domain first reasonable assumptions are made on the structure of the flc by using fuzzy basis functions fbfs and the describing function of the flc is derived to analyze and predict the existence of the limit cycle of the closed loop system including the flc finally computer simulation is performed to show how the analysis given in the paper is used to predict the existence of the limit cycle of the fuzzy control system

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

robustness design of nonlinear dynamic systems via fuzzy linear control this study introduces a fuzzy linear control design method for nonlinear systems with optimal h sup spl infin robustness performance first the takagi and sugeno fuzzy linear model 1985 is employed to approximate a nonlinear system next based on the fuzzy linear model a fuzzy controller is developed to stabilize the nonlinear system and at the same time the effect of external disturbance on control performance is attenuated to a minimum level thus based on the fuzzy linear model h sup spl infin performance design can be achieved in nonlinear control systems in the proposed fuzzy linear control method the fuzzy linear model provides rough control to approximate the nonlinear control system while the h sup spl infin scheme provides precise control to achieve the optimal robustness performance linear matrix inequality lmi techniques are employed to solve this robust fuzzy control problem in the case that state variables are unavailable a fuzzy observer based h sup spl infin control is also proposed to achieve a robust optimization design for nonlinear systems a simulation example is given to illustrate the performance of the proposed design method

fuzzy systems and controllers lyapunov tools for a regionwise approach this paper reviews a class of tools which can help to check the stability of fuzzy linguistic controllers which is a difficult task due to their regionwise structure the application of conventional methods when considering a fuzzy controller as a global nonlinear controller often leads to conservative stability results the use of appropriate continuous or piecewise continuous lyapunov functions allows to address the stability of nonlinear systems under fuzzy control while taking into account the local structure of the fuzzy controllers some methods are presented which enforce the global lyapunov function to decrease when leaving one subspace for another closer to the equilibrium using concentric domains and providing less conservative conditions

brief paper adaptive controller design for uncertain fuzzy systems using variable structure control approach based on the variable structure control vsc theory we develop an adaptive fuzzy control system design method for uncertain takagi sugeno fuzzy models with norm bounded uncertainties we relax the restrictive assumptions that each nominal local system model shares the same input channel and the norm bound of the uncertainty is known which are usually invoked in the traditional vsc based fuzzy control design methods as the local controller we use a vsc law with a switching feedback control term and an adaptation law to account for the norm bounded uncertainties in terms of lmis we derive a sufficient condition for the existence of linear sliding surfaces guaranteeing the asymptotic stability we present an lmi characterization of such sliding surfaces we also give an lmi based design algorithm together with a numerical design example

function approximation with decomposed fuzzy systems if the number of input signals increases a fuzzy system gets increasingly intractable for two reasons on the one hand the knowledge acquisition suffers increasingly from the knowledge engineering bottleneck on the other hand computational and memory demands of fuzzy systems increase strongly thus suffering from the curse of dimensionality the first problem is classically addressed by learning techniques the second by decomposing the fuzzy system the netfan approach network of fuzzy adaptive nodes combines decomposition with learning in order to apply fuzzy techniques to more complex applications different ways to decompose a fuzzy system are discussed in this paper for the favorite decomposition principle it is shown to be an universal function approximator despite decomposition the real world example of controlling a pneumatic positioning system finally demonstrates the applicability and benefits of this type of hierarchical decomposition namely a significantly reduced number of rules

automatic spectral collocation for integral integro differential and integrally reformulated differential equations automatic chebyshev spectral collocation methods for fredholm and volterra integral and integro differential equations have been implemented as part of the chebfun software system this system enables a symbolic syntax to be applied to numerical objects in order to pose and solve problems without explicit references to discretization the same objects can be used in matrix free iterative methods in linear algebra in order to avoid very large dense matrices or allow application to problems with nonsmooth coefficients as a further application of the ability to implement operator equations a method of greengard 1 for the recasting of differential equations as integral equations is generalized to mth order boundary value and generalized eigenvalue problems in the integral form large condition numbers associated with differentiation matrices in high order problems are avoided the ability to implement the recasting process generally follows from implementation of the operator expressions in chebfun the integral method also can be extended to first order systems although chebfun syntax does not currently allow easy implementation in this case

numerical solution of a fredholm integro differential equation modelling θ neural networks we propose several approaches to the numerical solution of a new fredholm integro differential equations modelling neural networks a solution strategy based on expansions onto standard cardinal basis functions and collocation is presented comparative numerical experiments illustrate specific advantages and drawbacks of the different approaches and are used to motivate alternate strategies

amplify and forward in wireless relay networks rate diversity and network size a wireless network with fading and a single source destination pair is considered the information reaches the destination via multiple hops through a sequence of layers of single antenna relays at high signal to noise ratio snr the simple amplify and forward strategy is shown to be optimal in terms of degrees of freedom because it achieves the degrees of freedom equal to a point to point multiple input multiple output mimo system hence the lack of coordination in relay nodes does not reduce the achievable degrees of freedom the performance of this amplify and forward strategy degrades with increasing network size this phenomenon is analyzed by finding the tradeoffs between network size rate and diversity a lower bound on the diversity multiplexing tradeoff for concatenation of multiple random gaussian matrices is obtained also it is shown that achievable network size in the outage formulation short codes is a lot smaller than the ergodic formulation long codes

rule regulation of fuzzy sliding mode controller design direct adaptive approach on the basis of sliding mode control smc a fuzzy sliding mode controller fsmc synthesized through rule adaptation is proposed in this paper there are two sets of control rule bases the first set is utilized to approach the equivalent control of smc according to the adaptive scheme another set is used to attenuate the hitting control of smc in the sense of heuristic in particular instead of several tuning parameters needed in conventional fuzzy adaptive approaches only one tuning factor is characterized to adapt the control rules the results show that the rule adaptive fsmc system is stable in the sense of lyapunov under giving a common lyapunov function this direct rule adaptive fsmc is synthesized through the following stages first the control rules are constructed according to the concepts of smc and the fuzzy sets whose membership functions are symmetrically covered in the state space are defined then the derived adaptive law is applied to adjust the given parameter for changing the control rules to meet system dynamic this fsmc is employed to approximate the equivalent control of smc under the situations of the mathematical model of controlled system is unknown third the hitting control which guarantees the stability of control system is developed finally the hitting control signal is smoothed via the constructed heuristic control rules we apply this fsmc to control a nonlinear inverted pendulum system for demonstrating the availability of the proposed approach

decoupled fuzzy controller design with single input fuzzy logic a decoupled fuzzy controller design with single input fuzzy logic is proposed we will utilize the approach of the single input fuzzy logic to explore the fourth order nonlinear systems in addition five fuzzy rules are given to control a class of fourth order nonlinear systems using this approach the system can achieve asymptotic stability and the response of system will converge faster than that of previous reports two simulation studies of a cart pole system and a ball beam system are presented to demonstrate the effectiveness of the method

direct robust adaptive fuzzy control drafc for uncertain nonlinear systems using small gain theorem abstract a novel direct robust adaptive fuzzy control drafc is proposed for a class of nonlinear systems with uncertain system and gain functions which both are unstructured or non repeatable state dependent unknown nonlinear functions takagi sugeno type fuzzy logic systems are used to approximate the uncertain system function and the drafc algorithm is designed by use of input to state stability iss approach and small gain theorem the resulting closed loop system is proven to be semi globally uniformly ultimately bounded in addition the possible controller singularity problem in some of the existing adaptive control schemes met with feedback linearization techniques can be removed and the adaptive mechanism with only one learning parameterization can be achieved the control performance of the closed loop system is guaranteed by appropriately choosing the design parameters an example illustrating the proposed method is included for a ship autopilot system to maintain the ship on a pre determined heading simulation results show the effectiveness of the control scheme

on line off line optimization of complex processes using a linguistic self organized optimizing control scheme abstract chemical processes usually have a complicated structure and are subjected to unknown long term and short term disturbances many process optimization schemes were developed under the assumption of the existence of a model that can predict the process steady state and or dynamics however such a model may not be precise nor even exist a rule based methodology without the need of such a model is hence developed in this work the optimizing control scheme developed here is actually a combination of a modified version of the linguistic control scheme developed by procyk and mamdani and the concept of reduced gradient optimization it is assumed that the objective function and constraints of the optimization problem are functions of manipulated variables and measurements only the optimizing control algorithm is also formulated into a look up table the rule based optimizing control scheme possesses three important properties adapting learning and decision making some numerical examples of multivariable nature and constrained situations are solved by this approach and compared with well known approaches it is shown that the method is superior to the previous methods a process system consisting of a series of cstr has been simulated as an illustrative example the simulation results show that the optimizing control scheme is promising and should be of interest to process industry

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

on the dissipativity of nonlinear systems fuzzy control approach a controller with large dissipativity is designed and implemented the stability margin is increased in order to tolerate the uncertainties and the disturbance in the nonlinear system in this study the dissipativity of a nonlinear system is facilitated via fuzzy control method first the nonlinear system is represented by an takagi and sugeno fuzzy model if the state variables of the nonlinear system are available then a state feedback fuzzy control is developed to guarantee that the nonlinear control system is dissipative this design problem becomes a linear matrix inequality lmi problem the maximum dissipativity design is obtained by solving an eigenvalue problem evp if the state variables are not available a fuzzy observer based state feedback controller will be used to solve the dissipative problem of the nonlinear system simulation examples are given to illustrate the design procedures and performances of the proposed method

neuro fuzzy systems for function approximation abstract we present a neuro fuzzy architecture for function approximation based on supervised learning the learning algorithm is able to determine the structure and the parameters of a fuzzy system the approach is an extension to our already published nefcon and nefclass models which are used for control or classification purposes the proposed extended model which we call nefprox is more general and can be used for any application based on function approximation

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

sliding mode control for singularly perturbed systems this paper addresses the design of sliding mode controllers for singularly perturbed systems the full order system is separated into slow and fast subsystems and a sliding mode controller is designed for each subsystem a composite of these controls is then implemented on the full order system it is shown that if specific reaching conditions are satisfied for the reduced order models and an additional condition is met then the reaching conditions are also satisfied for the full order model furthermore sufficient conditions are derived which guarantee that the approximation error between the controlled reduced order response and the controlled full order model response is small a numerical example is given which successfully demonstrates the techniques developed in this paper

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

fuzzy controllers as gain scheduling approximators abstract nonlinear systems can be linearized according to lyapunov s linearization method and then approximated by takagi sugeno ts fuzzy models the paper shows that the corresponding control strategy with ts controllers is closely related to traditional gain scheduling generally speaking gain scheduling deals with the connection of different linear controllers acting as a global nonlinear control law ts control defines a linear controller for each linearized region as well as smooth control transitions between those regions in this connection slowly varying operating conditions are assumed for the design of the linear controllers the lqr design method has been used which guarantees optimal control of a linearized system with respect to an integral criterion however since ts control is an approximation method solutions are bound to be suboptimal and stability is hence a concern the method is compared with a continuous change of control parameters based on the continuous on line lqr design for each point in state space additional control rule weights have been introduced to promote optimization the above method is illustrated by a simple one link manipulator arm

simplex type fuzzy sliding mode control this paper presents the design of simplex type fuzzy sliding mode control sfsmc for a linear multivariable system two fuzzy controllers are proposed one is the fuzzy singleton vector control and the other one is the fuzzy term set vector control the control rules of these two sfsmcs are derived from the simplex sliding mode control scheme and the fuzzy decision logic a helicopter control system is used to illustrate the effectiveness of the proposed controllers