a combinatorial problem on trapezoidal words in this paper we investigate some combinatorial properties concerning the family of the so called trapezoidal words trapezoidal words considered in de luca theoret comput sci 218 1999 13 39 are finite words over the two letter alphabet a a b whose subword complexity has the same behaviour as that of finite sturmian words in de luca theoret comput sci 218 1999 13 39 it has been proved that the family of finite sturmian words is properly contained in that one of trapezoidal words we carry on with the studying of the family of trapezoidal words and in particular of its relation with that one of finite sturmian words

on the defect of additivity of fuzzy measures it is well known that fuzzy measures are non additive in this paper we introduce the concept of defect which gives us the degree of non additivity of fuzzy measures for large classes of fuzzy measures this defect is calculated and estimated three kinds of applications are given to the approximative calculation of some fuzzy integrals to the best approximation of a fuzzy measure by classical measures and to the introduction of an invariant at translations distance on the set of fuzzy measures

output feedback control of nonlinear systems using direct adaptive fuzzy neural controller in this paper a direct adaptive fuzzy neural output feedback controller dafoc for a class of uncertain nonlinear systems is developed under the constraint that only the system output is available for measurement an output feedback control law and an update law are derived for on line tuning the weighting factors of the dafoc by using strictly positive real lyapunov theory the stability of the closed loop system compensated by the dafoc can be verified moreover the proposed overall control scheme guarantees that all signals involved are bounded and the output of the closed loop system asymptotically tracks the desired output trajectory to demonstrate the effectiveness of the proposed method simulation results are illustrated in this paper

fuzzy approximate disturbance decoupling of mimo nonlinear systems by backstepping approach the concept of fuzzy approximate disturbance decoupling is introduced for a class of mimo nonlinear systems with unknown nonlinearities based on the backstepping technique a direct adaptive fuzzy almost disturbance decoupling control scheme is proposed the proposed fuzzy controllers guarantee internal uniform ultimate boundedness of the closed loop adaptive systems and render a bounded approximate l 2 gain from the disturbance input to the output the main characteristics of the proposed algorithm is that the adaptive fuzzy controllers have a simple structure and less adaptive parameters than the existing results at last the developed design scheme is applied to control a two continuous stirred tank reactor process the simulation results illustrate the effectiveness of the method proposed in this paper

discrete series characters and two structures let g be a connected semisimple real lie group with compact cartan subgroup harish chandra gave formulas for discrete series characters which are completely explicit except for certain interger constants appearing in the numerators the main result of this paper is a new formula for these constants using two structures the new formula avoids endoscopy and stable discrete series entirely expressing unaveraged discrete series constants directly in terms of unaveraged discrete series constants corresponding to two structures of noncompact type

robust backstepping control of a class of nonlinear systems using fuzzy logic abstract fuzzy logic fl controllers for the robust back stepping control of a class of nonlinear systems in both continuous and discrete time are presented control action is employed to achieve tracking performance for unknown nonlinear system novel parameter tuning algorithms are obtained that are similar to modification in the case of continuous time adaptive control uniform ultimate boundedness of the tracking error and the fuzzy parameter estimates are presented without using the persistency of excitation pe condition initialization of the fuzzy parameters is straightforward simulation results justify the theoretical conclusions

chattering avoidance by second order sliding mode control relying on the possibility of generating a second order sliding motion by using as control the first derivative of the control signal instead of the actual control a new solution to the problem of chattering elimination in variable structure control vsc is presented such a solution inspired by the classical bang bang optimal control strategy is first depicted and expressed in terms of a control algorithm by introducing a suitable auxiliary problem involving a second order uncertain system with unavailable velocity then the applicability of the algorithm is extended via suitable modifications to the case of nonlinear systems with uncertainties of more general types the proposed algorithm does not require the use of observers and differential inequalities and can be applied in practice by exploiting such commercial components as peak detectors or other approximated methods to evaluate the change of the sign of the derivative of the quantity accounting for the distance to the sliding manifold

mixed feedforward feedback based adaptive fuzzy control for a class of mimo nonlinear systems this paper proposes a mixed feedforward feedback ffb based adaptive fuzzy controller design for a class of multiple input multiple output mimo uncertain nonlinear systems by integrating both feedforward and feedback compensation we introduce the ffb based fuzzy controller composed of a feedforward fuzzy compensator and a robust error feedback compensator to achieve a forward compensation of uncertainties the feedforward fuzzy compensator takes the desired commands as premise variables of fuzzy rules and adaptively adjusts the consequent part from an error measure meanwhile the feedback controller part is constructed based on hinfin control techniques and nonlinear damping design then the attenuation of both disturbances and estimated fuzzy parametric errors is guaranteed from a linear matrix inequality lmi based gain design the main advantages are i a simpler architecture for implementation is provided and ii the typical boundedness of assumption on fuzzy universal approximation errors is not required finally an inverted pendulum system and a two link robot are taken as application examples to show the expected performance

multiobjective output feedback control via lmi optimization this paper presents an overview of a linear matrix inequality lmi approach to the multiobjective synthesis of linear output feedback controllers the design objectives can be a mix of h sub spl infin performance h sub 2 performance passivity asymptotic disturbance rejection time domain constraints and constraints on the closed loop pole location in addition these objectives can be specified on different channels of the closed loop system when all objectives are formulated in terms of a common lyapunov function controller design amounts to solving a system of linear matrix inequalities the validity of this approach is illustrated by a realistic design example

on the number of factors of sturmian words abstract we prove that for m 1 card a m 1 m i 1 m i 1 i where a m is the set of factors of length m of all the sturmian words and is the euler function this result was conjectured by dulucq and gouyou beauchamps 1987 who proved that this result implies that the language m 0 a m c is inherently ambiguous we also give a combinatorial version of the riemann hypothesis

chattering reduction and error convergence in the sliding mode control of a class of nonlinear systems to reduce chattering in sliding mode control a boundary layer around the switching surface is used and a continuous control is applied within the boundary the effects of various control laws within the boundary layer on chattering and error convergence in different systems are studied new functions for chattering reduction and error convergence inside the boundary layer are proposed which are discontinuous in magnitude but not in sign the internal model principle has been used to generalize the design for the class of nonlinear systems being considered

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

robust control with structure perturbations the problem of making a given stabilizing controller robust so that the closed loop system remains stable for prescribed ranges of variations of a set of physical parameters in the plant the problem is treated in the state space and transfer function domains in the state space domain a stability hypersphere is determined in the parameter space using lyapunov theory the radius of this hypersphere is iteratively increased by adjusting the controller parameters until the prescribed perturbation ranges are contained in the stability hypersphere in the transfer function domain a corresponding stability margin is defined and optimized on the basis of the recently introduced concept of the largest stability hypersphere in the space of coefficients of the closed loop characteristic polynomial the design algorithms are illustrated by examples

output feedback model reference sliding mode control of uncertain multivariable systems this note considers the robust output tracking problem using a model reference sliding mode controller for linear multivariable systems of relative degree one it is shown that the closed loop system is globally exponentially stable and the performance is insensitive to bounded input disturbances and parameter uncertainties the strategy is based on output feedback unit vector control to generate sliding mode the only required a priori information about the plant high frequency gain matrix k sub p is the knowledge of a matrix s sub p such that k sub p s sub p is hurwitz which relaxes the positive definiteness requirement usually needed by other methods

fuzzy adaptive output feedback control for mimo nonlinear systems in this paper two observer based adaptive fuzzy output feedback control schemes are presented for a class of uncertain continuous time multi input multi output mimo nonlinear dynamics systems whose states are not available within these schemes fuzzy logic systems are employed to approximate the plant s unknown nonlinear functions and then the state observer is designed for estimating the states of the plant upon which a fuzzy adaptive output feedback controller is firstly investigated in order to overcome the controller singularity problem and relax the requirement of bounding parameter values a second modified fuzzy adaptive output feedback controller is proposed by using a regularized inverse and a robustifying control term all parameter adaptive laws and robustifying control terms are derived based on lyapunov stability analysis so that convergence to zero of tracking errors and boundedness of all signals in the closed loop system can be guaranteed simulations performed on a two link robot manipulator illustrate the approach and exhibit its performance

continuous state feedback guaranteeing uniform ultimate boundedness for uncertain dynamic systems we consider a dynamic system containing uncertain elements only the set of possible values of these uncertainties is known based on this information a class of state feedback controls is proposed in order to guarantee uniform ultimate boundedness of every system response within an arbitrarily small neighborhood of the zero state these feedback controls are continuous functions of the state

on multi input chattering free second order sliding mode control a solution to the problem of eliminating the chattering effect which is always associated with practical implementations of variable structure control is presented with reference to a class of uncertain multi input nonlinear systems the solution procedure relies on the application of an original control approach capable of enforcing a second order sliding mode i e a sliding regime on a surface s x t 0 in the system state space with s spl dot x t identically equal to zero a regime enforced by a control signal depending on s x t but directly acting only on s spl uml x t such an approach in its original formulation only applies to single input nonlinear systems with particular types of uncertainties in the present paper its validity is extended to multi input nonlinear systems characterized by uncertainties of more general nature covering a wide class of real processes

static output feedback controller design for fuzzy systems an ilmi approach this paper examines the problem of static output feedback control of a takagi sugeno ts fuzzy system the existence of a static output feedback control law is given in terms of the solvability of bilinear matrix inequalities an iterative algorithm based on the linear matrix inequality is proposed to compute the static output feedback gain to reduce the conservatism of the design the structural information of the membership function of the fuzzy rules is incorporated numerical examples are used to illustrate the validity of the methods

robust h control analysis and synthesis for takagi sugeno general uncertain fuzzy systems abstract in this paper robust h control for takagi sugeno general uncertain fuzzy systems where uncertainties come into all the system matrices is considered the main result is to establish equivalent relationships between quadratic stability and quadratic stability with h disturbance attenuation of general uncertain fuzzy systems and h control for fuzzy systems without uncertainty these relationships imply that quadratically stabilizing controllers and quadratically stabilizing controllers with h disturbance attenuation for general uncertain fuzzy systems can be obtained by designing h controllers for fuzzy systems without uncertainties we first give sufficient conditions for the h norm being less than a given number we then consider a general h problem with output feedback controllers and give a design method of h controllers and sufficient conditions which guarantee the required h performance of the closed loop system this design method can be applied to quadratic stabilizing controllers and quadratic stabilizing controllers with h disturbance attenuation for general uncertain fuzzy systems next we analyze quadratic stability and quadratic stability with h disturbance attenuation of general uncertain fuzzy systems and establish equivalent relationships to h control of fuzzy systems without uncertainties based on these relationships we design robust controllers for uncertain fuzzy systems finally examples are given to illustrate the theory

sturmian words structure combinatorics and their arithmetics abstract we prove some new results concerning the structure the combinatorics and the arithmetics of the set per of all the words w having two periods p and q p q which are coprimes and such that w p q 2 a basic theorem relating per with the set of finite standard sturmian words was proved in de luca and mignosi 1994 the main result of this paper is the following simple inductive definition of per the empty word belongs to per if w is an already constructed word of per then also aw and bw belong to per where denotes the operator of palindrome left closure i e it associates to each word u the smallest palindrome word u having u as a suffix we show that by this result one can construct in a simple way all finite and infinite standard sturmian words we prove also that up to the automorphism which interchanges the letter a with the letter b any element of per can be codified by the irreducible fraction p q this allows us to construct for any n 0 a natural bijection that we call farey correspondence of the set of the farey series of order n 1 and the set of special elements of length n of the set st of all finite sturmian words finally we introduce the concepts of farey tree and farey monoid this latter is obtained by defining a suitable product operation on the developments in continued fractions of the set of all irreducible fractions p q

some combinatorial properties of sturmian words abstract in this paper we give a characterization of finite sturmian words by palindrome words which generalizes a property of the fibonacci words we prove that the set st of finite sturmian words coincides with the set of the factors of all the words w such that w ab cxy with a b c palindromes x y a b and x y moreover using this result we prove that st is equal to the set of the factors of all words w having two periods p and q which are coprimes and such that w p q 2 several other combinatorial properties concerning special and bispecial elements of st are shown as a consequence we give a new and purely combinatorial proof of the enumeration formula of st

stable indirect fuzzy adaptive control this paper investigates new fuzzy model based observer adaptive control for multi input multi output continuous time nonlinear systems the proposed adaptive scheme uses takagi seguno ts fuzzy models to estimate the plant states and dynamics using stability arguments it is shown that the proposed scheme is globally asymptotically stable the observation and tracking errors are shown to converge asymptotically to zero despite the presence of external disturbances and approximation errors the performance of the developed approach is illustrated by simulation on two link robot model

output feedback control of uncertain nonlinear systems using a self structuring adaptive fuzzy observer this paper describes the design of an output feedback controller based on an adaptive fuzzy observer for uncertain single input single output nonlinear dynamical systems we have focused on the realization of a minimal dynamic order for the adaptive fuzzy observer for this purpose we adopt an adaptive fuzzy observer in which no strictly positive real spr condition is needed and we combine a self structuring scheme with an on line estimation of fuzzy parameters by using this proposed scheme we can reduce the dynamic order of the adaptive output feedback fuzzy control system the lyapunov synthesis approach is used to guarantee a global uniform ultimate boundedness property of the state estimation error and tracking error as well as all other signals in the closed loop system no a priori knowledge of an upper limits on the uncertainties including optimal parameters and modeling errors is required the theoretical results are illustrated through simulation examples

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

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

brief variable structure output feedback control design for a class of uncertain dynamic systems in this paper we consider the problem of designing a variable structure output feedback control vsofc law for a class of uncertain systems with mismatched uncertainty in the state matrix we derive existence conditions of linear sliding surfaces in terms of constrained linear matrix inequalities lmis and we give vsofc strategies we also give a simple design procedure and parameterizations of the linear switching surfaces together with solvability conditions for the given constrained lmis finally we give a design example in order to show the effectiveness of our method

robust h fuzzy static output feedback control of t s fuzzy systems with parametric uncertainties this paper addresses robust h fuzzy static output feedback control problem for t s fuzzy systems with time varying norm bounded uncertainties sufficient conditions for synthesis of a fuzzy static output feedback controller for t s fuzzy systems are derived in terms of a set of linear matrix inequalities lmis in comparison with the existing literatures the proposed approach not only simplifies the design procedure but also achieves a better h performance three drawbacks existing in the previous papers such as coordinate transformation same output matrices and bmi problem have been eliminated the effectiveness of the proposed design method is demonstrated by an example for the control of a truck trailer system

some characterizations of finite sturmian words in this paper we give some new characterizations of words which are finite factors of sturmian words an enumeration formula for primitive finite sturmian words is given moreover we provide two linear time algorithms to recognize whether a finite word is sturmian

output feedback stabilization of uncertain fuzzy systems using variable structure system approach based on the variable structure system theory an output feedback fuzzy control design method is developed for a class of uncertain nonlinear systems that can be represented by a t s takagi sugeno fuzzy model the uncertain fuzzy systems under consideration may have mismatched uncertainties in the state matrix as the local controller a compensator based sliding mode output feedback controller with a nonlinear discontinuous term is used in terms of linear matrix inequalities lmis a sufficient condition is derived for the existence of the fuzzy controller guaranteeing a stable sliding motion it is shown that the compensator gain and the switching surface parameter matrix can be characterized in terms of the solution of the lmi existence condition finally an lmi based design algorithm and numerical design examples are given

all controllers for the general h control problem lmi existence conditions and state space formulas this paper presents all controllers for the general h control problem with no assumptions on the plant matrices necessary and sufficient conditions for the existence of an h controller of any order are given in terms of three linear matrix inequalities lmis our existence conditions are equivalent to scherer s results but with a more elementary derivation furthermore we provide the set of all h controllers explicitly parametrized in the state space using the positive definite solutions to the lmis even under standard assumptions full rank etc our controller parametrization has an advantage over the q parametrization the freedom q a real rational stable transfer matrix with the h norm bounded above by a specified number is replaced by a constant matrix l of fixed dimension with a norm bound and the solutions x y to the lmis the inequality formulation converts the existence conditions to a convex feasibility problem and also the free matrix l and the pair x y define a finite dimensional design space as opposed to the infinite dimensional space associated with the q parametrization

adaptive control of a class of nonlinear systems with fuzzy logic an adaptive tracking control architecture is proposed for a class of continuous time nonlinear dynamic systems for which an explicit linear parameterization of the uncertainty in the dynamics is either unknown or impossible the architecture employs fuzzy systems which are expressed as a series expansion of basis functions to adaptively compensate for the plant nonlinearities global asymptotic stability of the algorithm is established in the lyapunov sense with tracking errors converging to a neighborhood of zero simulation results for an unstable nonlinear plant are included to demonstrate that incorporating the linguistic fuzzy information from human experts results in superior tracking performance

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

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

state observation of nonlinear uncertain dynamical systems this note proposes new types of observers for nonlinear dynamical systems subjected to bounded nonlinearities or uncertainties the design of these observers utilizes techniques related to variable structure systems theory a measure for the rate at which the estimates converge to the actual states is derived

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

stable multi input multi output adaptive fuzzy neural control in this letter stable direct and indirect adaptive controllers are presented that use takagi sugeno t s fuzzy systems 1985 conventional fuzzy systems or a class of neural networks to provide asymptotic tracking of a reference signal vector for a class of continuous time multi input multi output mimo square nonlinear plants with poorly understood dynamics the direct adaptive scheme allows for the inclusion of a priori knowledge about the control input in terms of exact mathematical equations or linguistics while the indirect adaptive controller permits the explicit use of equations to represent portions of the plant dynamics we prove that with or without such knowledge the adaptive schemes can learn how to control the plant provide for bounded internal signals and achieve asymptotically stable tracking of the reference inputs we do not impose any initialization conditions on the controllers and guarantee convergence of the tracking error to zero

fuzzy observer based fuzzy control design for nonlinear systems with persistent bounded disturbances to date nonlinear l gain control problems have not been solved by the conventional control methods for the nonlinear dynamic systems with persistent bounded disturbances this study introduces a fuzzy control design to deal with the nonlinear l gain output feedback control problem first the takagi and sugeno t s fuzzy model is employed to approximate the nonlinear dynamic system next based on the fuzzy model a fuzzy observer based fuzzy controller is developed to minimize the upper bound of l gain of the closed loop system under some linear matrix inequality lmi constraints therefore the nonlinear l gain control problem is transformed into a suboptimal control problem i e to minimize the upper bound of the l gain of the closed loop system subject to some lmi constraints in this situation the nonlinear l gain output feedback control problem can be easily solved by a lmi based optimization method the proposed methods which efficiently attenuate the peak of perturbation due to persistent bounded disturbances extend the l gain control problems from linear dynamic systems to nonlinear dynamic systems

stabilization of uncertain fuzzy time delay systems via variable structure control approach in view of a recent new application of variable structure control vsc to the stabilization problem for takagi sugeno t s fuzzy models this paper aims to study the stabilization of uncertain fuzzy time delay systems in t s fuzzy model via vsc approach there are mainly two features in this paper one lies in the incorporation of time delays both smooth and nonsmooth delays in which case lyapunov functionals and razumikhin theorem are required to solve the stabilization problem the other feature is that not only matched uncertainties but also mismatched uncertainties in the state variables are considered as a sequence the contribution of this paper consists of various control schemes proposed for the vsc design and the present results are in terms of linear matrix inequalities lmis an illustrative example is given to show the effectiveness of our various results

on variable structure output feedback controllers for uncertain dynamic systems a class of variable structure output feedback controllers for uncertain dynamic systems with bounded uncertainties is proposed no statistical information about the uncertain elements is assumed a variable structure systems approach and a geometric approach to the analysis and synthesis of system zeros are employed in the synthesis of the proposed controllers

a generalized harish chandra method of descent for reductive lie algebras abstract let g be a connected real reductive group and m a connected reductive subgroup of g with lie algebras g and m respectively we assume that g and m have the same rank we define a map from the space of orbital integrals of m into the space of orbital integrals of g which we call a transfer we then consider the transpose of the transfer this can be viewed as a map from the space of g invariant distributions of g to the space of m invariant distributions of m and can be considered as a restriction map from g to m we prove that this map extends harish chandra method of descent and we obtain a generalization of the radial component theorem we give an application

rich sturmian and trapezoidal words in this paper we explore various interconnections between rich words sturmian words and trapezoidal words rich words first introduced by the second and third authors together with j justin and s widmer constitute a new class of finite and infinite words characterized by having the maximal number of palindromic factors every finite sturmian word is rich but not conversely trapezoidal words were first introduced by the first author in studying the behavior of the subword complexity of finite sturmian words unfortunately this property does not characterize finite sturmian words in this note we show that the only trapezoidal palindromes are sturmian more generally we show that sturmian palindromes can be characterized either in terms of their subword complexity the trapezoidal property or in terms of their palindromic complexity we also obtain a similar characterization of rich palindromes in terms of a relation between palindromic complexity and subword complexity

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

direct adaptive fuzzy tracking control for a class of perturbed strict feedback nonlinear systems in this paper a novel direct adaptive fuzzy tracking control scheme is presented for a class of perturbed strict feedback nonlinear systems with unknown virtual control coefficients based on the mamdani type fuzzy logic system online approximation capability a direct adaptive fuzzy tracking controller is developed by using the backstepping approach the proposed design scheme guarantees that all the signals in the resulting closed loop system are uniform ultimate bounded and the tracking error converges to an arbitrarily small neighborhood of the origin in addition the number of the online adaptive parameters is not more than the order of the considered system and the possible controller singularity problem is removed by introducing the modified integral lyapunov functions finally two simulation examples are used to demonstrate the effectiveness of the proposed control scheme

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

fuzzy approximate disturbance decoupling of mimo nonlinear systems by backstepping and application to chemical processes fuzzy approximate disturbance decoupling concept is introduced for a class of multiple input multiple output mimo nonlinear systems with completely unknown nonlinearities based on backstepping technique a fuzzy almost disturbance decoupling control scheme is proposed the fuzzy controllers guarantee internal uniform ultimate boundedness of the closed loop adaptive systems and render a bounded approximate l sub 2 gain from the disturbance input to the output the developed design scheme is applied to control a two continuous stirred tank reactor process the simulation results illustrate the effectiveness of the method proposed in this paper

output feedback lmi tracking control conditions with h criterion for uncertain and disturbed t s models this work concerns the tracking problem of uncertain takagi sugeno t s continuous fuzzy model with external disturbances the objective is to get a model reference based output feedback tracking control law the control scheme is based on a pdc structure a fuzzy observer and a h performance to attenuate the external disturbances the stability of the whole closed loop model is investigated using the well known quadratic lyapunov function the key point of the proposed approaches is to achieve conditions under a lmi linear matrix inequalities formulation in the case of an uncertain and disturbed t s fuzzy model this formulation facilitates obtaining solutions through interior point optimization methods for some nonlinear output tracking control problems finally a simulation is provided on the well known inverted pendulum testbed to show the efficiency of the proposed approach

on variable structure output feedback controllers in a recent work by zak hui 1993 a sliding mode controller for mimo systems using static output feedback was proposed very nice geometric conditions for how to design sliding surfaces were given however there are two restrictive assumptions in it one is that the uncertainties in the system must be bounded by a known function of outputs which excludes some possible uncertainties in the a matrix if the system is described by the triple a b c the other one requires a matrix equality to be held which may also be very difficult to satisfy in many systems in this paper we propose a modification of the sliding mode controller for a class of single input single output siso systems which can eliminate the above mentioned limitations and under certain conditions guarantee global closed loop stability hence the range of applicability of zak hui s method can be greatly broadened

conditions of output stabilization for nonlinear models in the takagi sugeno s form this paper deals with the control law design with an observer for models in the takagi sugeno s ts form in the general case where the nonlinearities and the variables involved are not measurable the results presented in this paper give sufficient conditions of stabilization for the global loop i e ts model stabilized with a state feedback and a fuzzy observer conditions are given in the form of linear matrix inequalities lmi problem

enumeration and structure of trapezoidal words trapezoidal words are words having at most n 1 distinct factors of length n for every n 0 they therefore encompass finite sturmian words we give combinatorial characterizations of trapezoidal words and exhibit a formula for their enumeration we then separate trapezoidal words into two disjoint classes open and closed a trapezoidal word is closed if it has a factor that occurs only as a prefix and as a suffix otherwise it is open we investigate open and closed trapezoidal words in relation with their special factors we prove that sturmian palindromes are closed trapezoidal words and that a closed trapezoidal word is a sturmian palindrome if and only if its longest repeated prefix is a palindrome we also define a new class of words semicentral words and show that they are characterized by the property that they can be written as uxyu for a central word u and two different letters x y finally we investigate the prefixes of the fibonacci word with respect to the property of being open or closed trapezoidal words and show that the sequence of open and closed prefixes of the fibonacci word follows the fibonacci sequence

output tracking control of mimo fuzzy nonlinear systems using variable structure control approach the output tracking control problem for nonlinear systems in the presence of both parameter perturbations and external disturbances is studied our approach is based on the takagi sugeno t s fuzzy modeling method and a variable structure control vsc technique therefore the systems considered are not and need not be in the triangular and parametric strict feedback form which are prevalent among adaptive model following control for nonlinear systems or in the normal form which pervades almost all existing results in neuro fuzzy model following control approach we first study the problem of stabilization of t s fuzzy systems by using a vsc technique a method for the design of a switching surface based on linear matrix inequalities is developed and a stabilizing controller based on a reaching law concept in the presence of both parameter perturbations and external disturbances is proposed then the method is extended to design controllers for output tracking of t s fuzzy nonlinear systems in two cases i e systems which possess the so called strong passive subsystems and strong stable zero dynamics respectively finally illustrative examples are presented to demonstrate the whole design procedure from the original nonlinear systems to their fuzzification and finally to the realization of the desired controllers simulation results show that the goal of output tracking can be achieved by the proposed controllers

robust control for a class of uncertain nonlinear systems adaptive fuzzy approach based on backstepping a robust adaptive fuzzy control design approach is developed for a class of multivariable nonlinear systems with modeling uncertainties and external disturbances the controller design for the overall systems has been carried out through a number of simpler controller designs for a series of the relevant auxiliary systems based on the backstepping design technique for each auxiliary system an adaptive fuzzy logic system is introduced to learn the behavior of unknown dynamics and then a robust control algorithm is employed to efficiently compensate the approximation error and the external disturbances as well it is shown that the resulting closed loop systems guarantee a satisfactory transient and asymptotic performance a simulation example is also presented to illustrate the design procedure and controller performance

the weyl character formula the half spin representations and equal rank subgroups let b be a reductive lie subalgebra of a semi simple lie algebra f of the same rank both over the complex numbers to each finite dimensional irreducible representation v of f we assign a multiplet of irreducible representations of b with m elements in each multiplet where m is the index of the weyl group of b in the weyl group of f we obtain a generalization of the weyl character formula our formula gives the character of v as a quotient whose numerator is an alternating sum of the characters in the multiplet associated to v and whose denominator is an alternating sum of the characters of the multiplet associated to the trivial representation of f

lmi based nonlinear fuzzy observer controller design for uncertain mimo nonlinear systems based on the variable structure system theory we develop a nonlinear fuzzy observer controller design method for a class of uncertain nonlinear systems that can be represented by a takagi sugeno fuzzy model we use a sliding mode observer and a sliding mode controller as the local state observer and the local controller in terms of linear matrix inequalities lmis we derive sufficient conditions for the existence of the fuzzy observer and the fuzzy controller we also derive lmi conditions for the existence of the fuzzy observer and the fuzzy controller guaranteeing the alpha stability or generalized h2 hinfin performance constraints we show that the observer and the controller can be independently designed i e the separation property holds finally we give simple lmi based design algorithms together with an example

on the combinatorics of finite words in this paper we consider a combinatorial method for the analysis of finite words recently introduced in colosimo and de luca special factors in biological strings preprint 97 42 dipt matematica univ di roma for the study of biological macromolecules the method is based on the analysis of right special factors of a given word a factor u of a word w is special if there exist at least two occurrences of the factor u in w followed on the right by two distinct letters we show that in the combinatorics of finite words two parameters play an essential role the first denoted by r represents the minimal integer such that there do not exist special factors of w of length r the second that we denote by k is the minimal length of a factor of w which cannot be extended on the right in a factor of w some new results are proved in particular a new characterization in terms of special factors and of r and k is given for the set per of all words w having two periods p and q which are coprimes and such that w p q 2