design of fuzzy control systems with guaranteed stability abstract this paper addresses the analysis and design of fuzzy control systems the fuzzy systems are represented by a family of local state space models with aggregation the controller is designed by considering each local state feedback controller and a compensating controller the compensating controller is based on the well known variable structure control theory it is shown that this controller guarantees global stability of the closed loop fuzzy system the issues of a state observer for the fuzzy system is also addressed a numerical example and an example of nonlinear system control are given for demonstration of the performance of the method

design and analysis of optimal controller for fuzzy systems with input constraint in this paper we present a design method of the optimal and robust controller subject to the constraint on control inputs for continuous time takagi sugeno ts fuzzy systems in order to establish this design method we consider an optimal and robust control problem for nonlinear dynamic systems for this problem we present an analytic way which can provide the optimal controller for nonlinear dynamic systems by the dynamic programming approach and the inverse optimal approach moreover we analyze the robustness property of the proposed optimal controller with respect to a class of input uncertainties by the passivity approach then based on the theoretical results presented in this paper we formulate the design problem of the optimal and robust controller with input constraint for continuous time ts fuzzy systems as the semidefinite programming problem and find the controller by solving it the usefulness of the proposed approach is illustrated by considering the three axis attitude stabilization problem of rigid spacecraft

a small gain condition for interconnections of iss systems with mixed iss characterizations we consider interconnected nonlinear systems with external inputs where each of the subsystems is assumed to be input to state stable iss sufficient conditions of small gain type are provided guaranteeing that the interconnection is iss with respect to the external input to this end we extend recently obtained small gain theorems to a more general type of interconnections the small gain theorem provided here is applicable to situations where the iss conditions are formulated differently for each subsystem and are either given in the maximization or the summation sense furthermore it is shown that the conditions are compatible in the sense that it is always possible to transform sum formulations to maximum formulations without destroying a given small gain condition an example shows the advantages of our results in comparison with the known ones

robust self learning fuzzy controller design for a class of nonlinear mimo systems a new learning paradigm that can be applied for the design of a fuzzy logic based learning controller that is robust to external signals such as disturbances and set point changes is proposed in the paper it is well known that the self organizing fuzzy controller proposed by procyk and mamdani is sensitive to external signals such a phenomenon may be observed in other types of direct fuzzy logic based learning controllers that utilize an adaptation scheme in which the locational information of the current error state vector determines the degree of adaptation that should be made in the learning controller to resolve the problem of sensitivity to external signals it is proposed that learning and modification of the controller be made in consideration of the motional trend of the error state vector as well as its locational information this paradigm is adopted in the design of a new robust self learning fuzzy controller for a class of nonlinear mimo systems the well known techniques of sliding mode control and the fuzzy decision making method are utilized to implement the proposed learning scheme in the fuzzy learning controller via simulation study and experimental results the proposed learning controller is verified to be robust in the presence of external disturbances

robustness of fuzzy logic control for an uncertain dynamic system based on the similarity between prevalent fuzzy logic controllers flc and the conventional robust controller i e the variable structure controller control theoretic analysis of a fuzzy control system is presented in the sense of lyapunov as well as the robustness of the fuzzy control system against uncertainties of a controlled process this analysis gives an account of the relationship between control performance and the design parameters of the flc which has been obscure in the theory of fuzzy control

variational methods in relativistic quantum mechanics this review is devoted to the study of stationary solutions of lin ear and nonlinear equations from relativistic quantum mechanics involving the dirac operator the solutions are found as critical points of an energy func tional contrary to the laplacian appearing in the equations of nonrelativistic quantum mechanics the dirac operator has a negative continuous spectrum which is not bounded from below this has two main consequences first the energy functional is strongly indefinite second the euler lagrange equations are linear or nonlinear eigenvalue problems with eigenvalues lying in a spectral gap between the negative and positive continuous spectra moreover since we work in the space domain r 3 the palais smale condition is not satisfied for these reasons the problems discussed in this review pose a challenge in the calculus of variations the existence proofs involve sophisticated tools from nonlinear analysis and have required new variational methods which are now applied to other problems in the first part we consider the fixed eigenvalue problem for models of a free self interacting relativistic particle they allow to describe the localized state of a spin 1 2 particle a fermion which propagates without changing its shape this includes the soler models and the maxwell dirac or klein gordon dirac equations the second part is devoted to the presentation of min max principles al lowing to characterize and compute the eigenvalues of linear dirac operators with an external potential in the gap of their essential spectrum many con sequences of these min max characterizations are presented among them a new kind of hardy like inequalities and a stable algorithm to compute the eigenvalues in the third part we look for normalized solutions of nonlinear eigenvalue problems the eigenvalues are lagrange multipliers lying in a spectral gap we review the results that have been obtained on the dirac fock model which is a nonlinear theory describing the behavior of n interacting electrons in an external electrostatic field in particular we focus on the problematic definition of the ground state and its nonrelativistic limit in the last part we present a more involved relativistic model from quan tum electrodynamics in which the behavior of the vacuum is taken into ac count it being coupled to the real particles the main interesting feature of this model is that the energy functional is now bounded from below providing us with a good definition of a ground state

an approach to fuzzy control of nonlinear systems stability and design issues presents a design methodology for stabilization of a class of nonlinear systems first the authors represent a nonlinear plant with a takagi sugeno fuzzy model then a model based fuzzy controller design utilizing the concept of the so called parallel distributed compensation is employed the main idea of the controller design is to derive each control rule so as to compensate each rule of a fuzzy system the design procedure is conceptually simple and natural moreover the stability analysis and control design problems can be reduced to linear matrix inequality lmi problems therefore they can be solved efficiently in practice by convex programming techniques for lmis the design methodology is illustrated by application to the problem of balancing and swing up of an inverted pendulum on a cart

comments on robust stabilization of a class of uncertain nonlinear systems via fuzzy control quadratic stabilizability h sup spl infin control theory and linear matrix inequalities this paper presents stability analysis for a class of uncertain nonlinear systems and a method for designing robust fuzzy controllers to stabilize the uncertain nonlinear systems first a stability condition for takagi and sugeno s fuzzy model is given in terms of lyapunov stability theory next new stability conditions for a generalized class of uncertain systems are derived from robust control techniques such as quadratic stabilization h sup spl infin control theory and linear matrix inequalities the derived stability conditions are used to analyze the stability of takagi and sugeno s fuzzy control systems with uncertainty which can be regarded as a generalized class of uncertain nonlinear systems the design method employs the so called parallel distributed compensation important issues for the stability analysis and design are remarked finally three design examples of fuzzy controllers for stabilizing nonlinear systems and uncertain nonlinear systems are presented

fuzzy regulators and fuzzy observers relaxed stability conditions and lmi based designs this paper presents new relaxed stability conditions and lmi linear matrix inequality based designs for both continuous and discrete fuzzy control systems they are applied to design problems of fuzzy regulators and fuzzy observers first takagi and sugeno s fuzzy models and some stability results are recalled to design fuzzy regulators and fuzzy observers nonlinear systems are represented by takagi sugeno s ts fuzzy models the concept of parallel distributed compensation is employed to design fuzzy regulators and fuzzy observers from the ts fuzzy models new stability conditions are obtained by relaxing the stability conditions derived in previous papers lmi based design procedures for fuzzy regulators and fuzzy observers are constructed using the parallel distributed compensation and the relaxed stability conditions other lmi s with respect to decay rate and constraints on control input and output are also derived and utilized in the design procedures design examples for nonlinear systems demonstrate the utility of the relaxed stability conditions and the lmi based design procedures

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

mixed h sub 2 h sub spl infin fuzzy output feedback control design for nonlinear dynamic systems an lmi approach this study introduces a mixed h sub 2 h sub spl infin fuzzy output feedback control design method for nonlinear systems with guaranteed control performance first the takagi sugeno fuzzy model is employed to approximate a nonlinear system next based on the fuzzy model a fuzzy observer based mixed h sub 2 h sub spl infin controller is developed to achieve the suboptimal h sub 2 control performance with a desired h sub spl infin disturbance rejection constraint a robust stabilization technique is also proposed to override the effect of approximation error in the fuzzy approximation procedure by the proposed decoupling technique and two stage procedure the outcome of the fuzzy observer based mixed h sub 2 h sub spl infin control problem is parametrized in terms of the two eigenvalue problems evps one for observer and the other for controller the evps can be solved very efficiently using the linear matrix inequality lmi optimization techniques a simulation example is given to illustrate the design procedures and performances of the proposed method

quaternion based adaptive output feedback attitude control of spacecraft using chebyshev neural networks this paper investigates the problem of output feedback attitude control of an uncertain spacecraft two robust adaptive output feedback controllers based on chebyshev neural networks cnn termed adaptive neural networks nn controller i and adaptive nn controller ii are proposed for the attitude tracking control of spacecraft the four parameter representations quaternion are employed to describe the spacecraft attitude for global representation without singularities the nonlinear reduced order observer is used to estimate the derivative of the spacecraft output and the cnn is introduced to further improve the control performance through approximating the spacecraft attitude motion the implementation of the basis functions of the cnn used in the proposed controllers depends only on the desired signals and the smooth robust compensator using the hyperbolic tangent function is employed to counteract the cnn approximation errors and external disturbances the adaptive nn controller ii can efficiently avoid the over estimation problem i e the bound of the cnns output is much larger than that of the approximated unknown function and hence the control input may be very large existing in the adaptive nn controller i both adaptive output feedback controllers using cnn can guarantee that all signals in the resulting closed loop system are uniformly ultimately bounded for performance comparisons the standard adaptive controller using the linear parameterization of spacecraft attitude motion is also developed simulation studies are presented to show the advantages of the proposed cnn based output feedback approach over the standard adaptive output feedback approach

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

optimal fuzzy controller design local concept approach in this paper we present a global optimal and stable fuzzy controller design method for both continuous and discrete time fuzzy systems under both finite and infinite horizons first a sufficient condition is proposed which indicates that the global optimal effect can be achieved by the fuzzily combined local optimal controllers based on this sufficient condition we derive a local concept approach to designing the optimal fuzzy controller by applying traditional linear optimal control theory the stability of the entire closed loop continuous fuzzy system can be ensured by the designed optimal fuzzy controller the optimal feedback continuous fuzzy system can not only be guaranteed to be exponentially stable but also be stabilized to any desired degree also the total energy of system output is absolutely finite moreover the resultant feedback continuous fuzzy system possesses an infinite gain margin that is its stability is guaranteed no matter how large the feedback gain becomes two examples are given to illustrate the proposed optimal fuzzy controller design approach and to demonstrate the proved stability properties

input to state stability of rate controlled biochemical networks in this paper the study of the class of biochemical systems known as zero deficiency networks is extended to the case of time varying kinetic parameters we show that the resulting class of nonlinear systems with inputs satisfies a notion of input to state stability uniformly over a set of parameters in particular the input to state stability estimates allow us to characterize the robustness of zero deficiency networks with respect to perturbations in the parameters as well as study their stability when the reaction rates are controlled by an independent process

brief paper a degree of flexibility in lyapunov inequalities for establishing input to state stability of interconnected systems in this paper a novel approach to constructing flexible lyapunov inequalities is developed for establishing input to state stability iss of interconnection of nonlinear time varying systems it aims at a useful tool for using nonlinear small gain conditions by allowing some flexibility in lyapunov inequalities each subsystem is to satisfy in the application of the iss small gain theorem achieving a lyapunov inequality conforming to a nonlinear small gain condition is not a straightforward task the proposed technique provides us with many lyapunov inequalities with which a single trade off condition between subsystems gains can establish the iss property of the interconnected system proofs are based on explicit construction of lyapunov functions

lmi based design of stabilizing fuzzy controllers for nonlinear systems described by takagi sugeno fuzzy model abstract there have been several recent studies concerning the stability of fuzzy control systems and the synthesis of stabilizing fuzzy controllers this paper reports on a related study of the takagi sugeno ts fuzzy systems and it is shown that the controller synthesis problems for the nonlinear systems described by the ts fuzzy model can be reduced to convex problems involving linear matrix inequalities lmis after classifying the ts fuzzy systems into three families based on how diverse their input matrices are a unique controller synthesis procedure is given for each of the families a numerical example is presented to illustrate the synthesis procedures developed in this paper

general siso takagi sugeno fuzzy systems with linear rule consequent are universal approximators takagi sugeno ts fuzzy systems have been employed as fuzzy controllers and fuzzy models in successfully solving difficult control and modeling problems in practice virtually all the ts fuzzy systems use linear rule consequent at present there exist no results qualitative or quantitative to answer the fundamentally important question that is especially critical to ts fuzzy systems as fuzzy controllers and models are ts fuzzy systems with linear rule consequent universal approximators if the answer is yes then how can they be constructed to achieve prespecified approximation accuracy and what are the sufficient renditions on systems configuration in this paper we provide answers to these questions for a general class of single input single output siso fuzzy systems that use any type of continuous input fuzzy sets ts fuzzy rules with linear consequent and a generalized defuzzifier containing the widely used centroid defuzzifier as a special case we first constructively prove that this general class of siso ts fuzzy systems can uniformly approximate any polynomial arbitrarily well and then prove by utilizing the weierstrass approximation theorem that the general ts fuzzy systems can uniformly approximate any continuous function with arbitrarily high precision furthermore we have derived a formula as part of sufficient conditions for the fuzzy approximation that can compute the minimal upper bound on the number of input fuzzy sets and rules needed for any given continuous function and prespecified approximation error bound an illustrative numerical example is provided

resolvent estimates and bounds on eigenvalues for dirac operators on the half line estimates for the eigenvalues of non self adjoint 1d dirac operators considered on the half line are obtained in terms of the l p norms of the potentials the proofs are based on the resolvent est

inverse optimal stabilization of a rigid spacecraft the authors present an approach for constructing optimal feedback control laws for regulation of a rotating rigid spacecraft they employ the inverse optimal control approach which circumvents the task of solving a hamilton jacobi equation and results in a controller optimal with respect to a meaningful cost functional the inverse optimality approach requires the knowledge of a control lyapunov function and a stabilizing control law of a particular form for the spacecraft problem they are both constructed using the method of integrator backstepping the authors give a characterization of nonlinear stability margins achieved with the inverse optimal control law

stable and optimal fuzzy control of linear systems a number of stable and optimal fuzzy controllers are developed for linear systems based on some classical results in control theory we design the structure and parameters of fuzzy controllers such that the closed loop fuzzy control systems are stable provided that the process under control is linear and satisfies certain conditions it turns out that if stability is the only requirement there is much freedom in choosing the fuzzy controller parameters therefore a performance criterion is set to optimalize the parameters using the pontryagin minimum principle we design an optimal fuzzy controller for linear systems with quadratic cost function finally the optimal fuzzy controller is applied to a ball and beam system