disturbance observer based control for semi markovian jump systems with generally uncertain transition rate and saturation nonlinearity abstract this paper deals with the problem of disturbance observer based control dobc for semi markovian jump systems s mjss with generally uncertain transition rate tr and saturation nonlinearity unlike the existing theories the proposed method considers the external disturbance and saturation nonlinearity in s mjss with more general tr first of all to study this dobc problem the sufficient condition for stochastic stability of the system is derived by the use of lyapunov krasovskii functional then the design methods of the anti disturbance controller and the disturbance observer are proposed based on the given stability condition of the closed loop system furthermore the maximum domain of attraction is estimated by solving an optimization iterative algorithm finally two numerical examples are given to prove the correctness of the proposed results

composite anti disturbance control for markovian jump nonlinear systems via disturbance observer this paper is concerned with the problems of composite disturbance observer based control dobc and control for markovian jump systems with nonlinearity and multiple disturbances our aim is to design a disturbance observer to estimate the disturbance generated by an exogenous system then construct the control scheme by integrating the output of the disturbance observer with state feedback control law such that the closed loop system can be guaranteed to be stochastically stable and different types of disturbances can be attenuated and rejected by constructing a proper stochastic lyapunov krasovskii functional sufficient conditions for the existence of the desired observer and the state feedback controller are established in terms of linear matrix inequalities lmis which can be readily solved by standard numerical software finally a numerical example is provided to show the effectiveness of the proposed approaches

brief paper control for discrete singular hybrid systems the problems of stability state feedback control and static output feedback control for a class of discrete time singular hybrid systems are investigated in this paper a new sufficient and necessary condition for a class of discrete time singular hybrid systems to be regular causal and stochastically stable is proposed in terms of a set of coupled strict linear matrix inequalities lmis sufficient conditions are proposed for the existence of state feedback controller and static output feedback controller in terms of a set of coupled strict lmis respectively finally two illustrative examples are provided to demonstrate the applicability of the proposed approach

on the partial differential equations of electrostatic mems devices iii refined touchdown behavior abstract this paper is a continuation of n ghoussoub y guo on the partial differential equations of electrostatic mems devices stationary case siam j math anal 38 2007 1423 1449 and n ghoussoub y guo on the partial differential equations of electrostatic mems devices ii dynamic case nodea nonlinear differential equations appl 2008 in press where we analyzed nonlinear parabolic problem u t u f x 1 u 2 on a bounded domain of r n with dirichlet boundary conditions this equation models a simple electrostatic micro electromechanical system mems device consisting of a thin dielectric elastic membrane with boundary supported at 0 above a rigid ground plate located at 1 here u is modeled to describe dynamic deflection of the elastic membrane when a voltage represented here by is applied the membrane deflects towards the ground plate and a snap through touchdown must occur when it exceeds a certain critical value pull in voltage creating a so called pull in instability which greatly affects the design of many devices in an effort to achieve better mems design the material properties of the membrane can be technologically fabricated with a spatially varying dielectric permittivity profile f x in this work some a priori estimates of touchdown behavior are established based on which the refined touchdown profiles are obtained by adapting self similar method and center manifold analysis applying various analytical and numerical techniques some properties of touchdown set such as compactness location and shape are also discussed for different classes of varying permittivity profiles

fuzzy control rules and their natural laws abstract we consider the convergence of fuzzy controllers as the number of fuzzy rules tends to infinity we assume that the fuzzy rules are regular and show the existence of limit laws for five different fuzzy control rules

anti disturbance control for nonlinear systems subject to input saturation via disturbance observer this paper is concerned with the problem of the disturbance observer based control for a class of continuous time uncertain systems subject to input saturation and nonlinearity the input of the system includes two parts the control input and the disturbance input the nonlinearity of the system which satisfies a global lipschitz condition is considered as two cases of known nonlinearity and unknown nonlinearity by virtue of the technique of the disturbance observer based controller the anti disturbance controllers are designed respectively with both the polytopic and dead zone representations of the saturation function which ensure that the resulting closed loop systems are asymptotically stable with an estimation of the domain of attraction described by the level set of the lyapunov function further an iterative optimization method is used to obtain the maximum estimation of the domain of the set of initial states an example of application design for a flight control system illustrates the effectiveness of the proposed results

fuzzy controls under various fuzzy reasoning methods abstract a fuzzy logic controller consists of linguistic control rules tied together by means of two concepts fuzzy implications and a compositional rule of inference most of the existing fuzzy logic controllers are based on the approximate reasoning method due to mamdani this paper introduces other fuzzy implications such as the arithmetic rule and maximin rule for linguistic control rules and compares control results for a plant model with first order delay under various approximate reasoning methods moreover control results are compared when the widths of fuzzy sets of linguistic control rules are changed

robust h control of descriptor discrete time markovian jump systems this paper considers the stochastic stability and the robust control of descriptor discrete time systems with markovian jumping parameters in terms of linear matrix inequalities a necessary and sufficient condition is proposed which ensures a discrete time descriptor markovian jump system to be regular causal and stochastically stable a robust admissibility condition and a robust bounded real lemma are also developed based on these a sufficient condition on the existence of a state feedback controller which guarantees the robust admissibility and the performance is also given by employing the linear matrix inequality technique a robustly stabilizing state feedback controller can be constructed through the numerical solutions of linear matrix inequalities finally an example is provided to demonstrate the effectiveness of the proposed approach

fault detection filter design for markovian jump singular systems with intermittent measurements this paper addresses the problem of fault detection filter design for discrete time markovian jump singular systems with intermittent measurements the measurement transmission from the plant to the fault detection filter is assumed to be imperfect and a stochastic variable is utilized to model the phenomenon of data missing our attention is focused on the design of a fault detection filter such that the residual system is stochastically markovian jump admissible and satisfies some expected performances a new necessary and sufficient condition for a class of discrete time markovian jump singular systems to be stochastically markovian jump admissible is proposed in the form of strict linear matrix inequalities sufficient conditions are established for the existence of the fault detection filter finally a numerical example is provided to demonstrate the usefulness and applicability of the developed theoretical results

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

analytical structure of a fuzzy controller with linear control rules abstract we prove that a fuzzy controller with linear control rules and mamdani minimum inference is the sum of a global two dimensional multilevel relay and a local nonlinear proportional integral pi controller the properties of the nonlinear gains of the local pi controller are investigated moreover it is proven that as the number of input fuzzy sets approaches the global multilevel relay approaches a global linear pi controller while the local nonlinear pi controller disappears

stabilization of discrete time markovian jump linear systems via time delayed controllers this paper is concerned with the stabilization problem for a class of discrete time markovian jump linear systems with time delays both in the system state and in the mode signal the delay in the system state may be time varying the delay in the mode signal is manifested as a constant mismatch of the modes between the controller and the system we first show that the resulting closed loop system is a time varying delayed markovian jump linear system with extended state space then a sufficient condition is proposed for the design of a controller such that the closed loop system is stochastically stable finally numerical simulation is used to illustrate the developed theory

global bifurcation diagrams and exact multiplicity of positive solutions for a one dimensional prescribed mean curvature problem arising in mems abstract we study global bifurcation diagrams and exact multiplicity of positive solutions for the one dimensional prescribed mean curvature problem arising in mems u x 1 u x 2 1 u p u 1 l x l u l u l 0 where 0 is a bifurcation parameter and p l 0 are two evolution parameters we determine the exact number of positive solutions by the values of p l and moreover for p 1 the bifurcation diagram undergoes fold and splitting bifurcations while for 0 p 1 the bifurcation diagram undergoes fold splitting and segment shrinking bifurcations our results extend and improve those of brubaker and pelesko n d brubaker j a pelesko analysis of a one dimensional prescribed mean curvature equation with singular nonlinearity nonlinear anal 75 2012 5086 5102 and pan and xing h pan r xing exact multiplicity results for a one dimensional prescribed mean curvature problem related to a mems model nonlinear anal rwa 13 2012 2432 2445 by generalizing the nonlinearity 1 u 2 to 1 u p with general p 1 we also answer an open question raised by brubaker and pelesko on the extension of global bifurcation diagram results to general p 0 concerning this open question we find and prove that global bifurcation diagrams for 0 p 1 are different to and more complicated than those for p 1

brief paper sliding mode control for ito stochastic systems with markovian switching this paper deals with the problem of sliding mode control smc for a class of nonlinear uncertain stochastic systems with markovian switching by introducing some specified matrices the connections among the designed sliding surfaces corresponding to every mode are established furthermore the present sliding mode controller including the transition rates of modes can cope with the effect of markovian switching by means of linear matrix inequalities lmis with equality constraint sufficient conditions are derived such that the sliding motions on the specified sliding surfaces are stochastically stable with c disturbance attenuation level finally a numerical example is given to illustrate the applicability of the present method

the sub harmonic bifurcation of stokes waves steady periodic water waves on the free surface of an infinitely deep irrotational flow under gravity without surface tension stokes waves can be described in terms of solutions of a quasi linear equation which involves the hilbert transform and which is the euler lagrange equation of a simple functional the unknowns are a 2 periodic function w which gives the wave profile and the froude number a dimensionless parameter reflecting the wavelength when the wave speed is fixed and vice versa

variational approach to mems model with fringing field abstract we study semilinear elliptic equations which are called mems model with fringing field using the variational method and dual approach we show the multiple existence of positive solutions

effects of increasing the footprints of uncertainty on analytical structure of the classes of interval type 2 mamdani and ts fuzzy controllers the fundamental difference between an interval type 2 it2 fuzzy controller and a type 1 fuzzy controller is the footprint of uncertainty fou of an it2 fuzzy set in this paper we study how fous affect the analytical structure i e the input output mathematical relationship of a broad class of it2 mamdani and takagi sugeno ts controllers the controllers employ arbitrary fuzzy rules the karnik mendel km or enhanced km type reducer the minimum and operator and the centroid defuzzifier the controllers utilize commonly used it2 fuzzy sets for their input variables and any kind of type 2 fuzzy sets for their output variable we prove that with increase of fous of the input fuzzy sets the mamdani controllers approach constant controllers and the ts controllers approach piecewise linear controllers the resemblance to the constant or pricewise linear controllers increases as the fous increase when all the fous are at their maximum to reflect the highest level of uncertainties the mamdani and ts controllers become the constant controllers and piecewise linear controllers respectively we investigate how change in the resemblance takes place progressively as fous increase we also show that an increase in the resemblance narrows control gain variations for part of the it2 controllers which can worsen control performance these findings implicit controller design too large fous are generally undesirable for the input fuzzy sets because they can make an it2 controller behave like a constant or piecewise linear controller real time control experiment results are provided to illustrate the theoretical analysis

brief paper robust exponential stabilization for markovian jump systems with mode dependent input delay this paper is concerned with the problem of exponential stabilization for uncertain linear systems with markovian jump parameters and mode dependent input delays sufficient stabilization conditions are developed in terms of matrix inequalities which can be solved by a proposed iterative algorithm based on the cone complementarity linearization ccl method memory controllers are also designed such that the closed loop system is exponentially mean square stable for all admissible uncertainties numerical examples are given to show that the developed method is efficient and less conservative

brief nonlinear servocompensation of unknown external disturbances the problem of adaptive compensation of unknown external disturbances is solved for a class of nonlinear systems which have the globally defined normal form when an a priori unknown external disturbance can be accurately modeled as the output of a linear exosystem of the known order but with unknown parameters the proposed adaptive controller provides global asymptotic tracking if the disturbance contains unmodeled components the proposed controller provides boundedness of all the closed loop signals and arbitrarily small tracking error

fuzzy controller theory limit theorems for linear fuzzy control rules abstract for a general fuzzy controller employing linear fuzzy control rules it is shown that as the number of rules grow the defuzzified output becomes a linear function of the input in particular for a sufficiently large number of rules the defuzzified output is approximately the same as the pi pid controller

controllability observability and discrete time markovian jump linear quadratic control this paper is concerned with the controllability and observability of discrete time linear systems that possess randomly jumping parameters described by finite stale markov processes and the relationship between these properties and the solution of the infinite time jump linear quadratic jlq optimal control problem the solution of the markovian jlq problem with finite or infinite time horizons is known necessary and sufficient conditions for the existence of optimal constant control laws that lead to finite optimal expected costs as the time horizon becomes infinite are also known sufficient conditions for these steady state control laws to stabilize the controlled system are also available chizeck et al 1986 these conditions are not easy to test however various definitions of controllability and observability for stochastic systems exist in the literature these definitions are unfortunately not related to the steady state jlq control problem in a manner that is analogous to the role of deter

fixed order robust h sub spl infin filter design for markovian jump systems with uncertain switching probabilities this paper discusses the fixed order robust h sub spl infin filtering problem for a class of markovian jump linear systems with uncertain switching probabilities the uncertainties under consideration are assumed to be norm bounded in the system matrices and to be elementwise bounded in the mode transition rate matrix respectively first a criterion based on linear matrix inequalities is provided for testing the h sub spl infin filtering level of a filter over all the admissible uncertainties then a sufficient condition for the existence of the fixed order robust h sub spl infin filters is established in terms of the solvability of a set of linear matrix inequalities with equality constraints to determine the filter a globally convergent algorithm involving convex optimization is suggested finally a numerical example is used to illustrate that the developed theory is more effective than the existing results

fuzzy controller further limit theorems for linear control rules abstract we consider a fuzzy controller attempting to control a process with multiple outputs and inputs towards some set points we show that for fuzzy controller employing linear control rules as the number of rules grow the defuzzified outputs become linear functions of the inputs to the fuzzy controller this is a type of central limit theorem for fuzzy controllers

analytical structures and analysis of fuzzy pd controllers with multifuzzy sets having variable cross point level this paper deals with fuzzy pd controllers which employ n 3 input fuzzy sets with variable cross point level and 2n 1 output fuzzy sets analytical structures of fuzzy pd controllers are derived using triangular membership functions for fuzzification rule base with four linear control rules two different triangular conorms lukasiewicz or and zadeh or different inference methods such as mamdani s minimum larsen s product and drastic product and center of area method for defuzzification properties of such fuzzy pd controllers are studied influence of variable cross point level on controller performance is demonstrated with an example

structural analysis of fuzzy controllers with nonlinear input fuzzy sets in relation to nonlinear pid control with variable gains the popular linear pid controller is mostly effective for linear or nearly linear control problems nonlinear pid controllers however are needed in order to satisfactorily control highly nonlinear plants time varying plants or plants with significant time delay this paper extends our previous papers in which we show rigorously that some fuzzy controllers are actually nonlinear pi pd and pid controllers with variable gains that can outperform their linear counterparts in the present paper we study the analytical structure of an important class of two and three dimensional fuzzy controllers we link the entire class as opposed to one controller at a time to nonlinear pi pd and pid controllers with variable gains by establishing the conditions for the former to structurally become the latter unlike the results in the literature which are exclusively for the fuzzy controllers using linear fuzzy sets for the input variables this class of fuzzy controllers employs nonlinear input fuzzy sets of arbitrary types our structural results are thus more general and contain the existing ones as special cases two concrete examples are provided to illustrate the usefulness of the new results

decay estimates for some semilinear damped hyperbolic problems let be a bounded open domain in rn g r r a non decreasing continuous function such that g 0 0 and h e lloc1 r l2 under suitable assumptions on g and h the rate of decay of the difference of two solutions is studied for some abstract evolution equations of the general form u lu g u h t x as t the results obtained by use of differential inequalities can be applied to the case of the semilinear wave equation u u delta u g text u t text h text in r times omega text u text 0 on r times partial omega in r u 0 onr for instance if g s c left s right p 1 s d left s right q 1 s with c d 0 and 1 p q n 2 q n 2 then if h in l infty r l 2 omega all solutions are bounded in the energy space for t 0 and if u v are two such solutions the energy norm of u t v t decays like t 1 p 1 as t

adaptive fuzzy logic control of feedback linearizable discrete time dynamical systems under persistence of excitation the objective of this paper is to achieve tracking control of a class of unknown feedback linearizable nonlinear dynamical systems using a discrete time fuzzy logic controller flc discrete time flc design is significant because almost all flcs are implemented on digital computers a repeatable design algorithm and a stability proof for an adaptive fuzzy logic controller is presented that uses basis functions based on the fuzzy system unlike most standard adaptive control approaches which generate basis vectors by computing a regression matrix a new approach to adapt the fuzzy system parameters is attempted with mild assumptions on the class of discrete time nonlinear systems using this adaptive fuzzy logic controller the uniform ultimate boundedness of the closed loop signals is shown under a persistency of excitation pe condition new passivity properties of fuzzy logic systems are described the result is a model free universal fuzzy controller that works for any system in the given class of systems

robust h sub spl infin filtering for stochastic time delay systems with missing measurements in this paper the robust hinfin filtering problem is studied for stochastic uncertain discrete time delay systems with missing measurements the missing measurements are described by a binary switching sequence satisfying a conditional probability distribution we aim to design filters such that for all possible missing observations and all admissible parameter uncertainties the filtering error system is exponentially mean square stable and the prescribed hinfin performance constraint is met in terms of certain linear matrix inequalities lmis sufficient conditions for the solvability of the addressed problem are obtained when these lmis are feasible an explicit expression of a desired robust hinfin filter is also given an optimization problem is subsequently formulated by optimizing the hinfin filtering performances finally a numerical example is provided to demonstrate the effectiveness and applicability of the proposed design approach

some singular equations modeling mems in the past fifteen years mathematical models for microelectromechanical systems mems have been the subject of several studies in particular due to the interesting qualitative properties they feature still most research is devoted to an illustrative but simplified model which is deduced from a more complex model when the aspect ratio of the device vanishes the so called vanishing or small aspect ratio model the analysis of the aforementioned complex model involving a moving boundary has started only recently and an outlook of the results obtained so far in this direction is provided in this survey

convergence of solutions of a nonlocal biharmonic mems equation with the fringing field abstract we study a nonlocal biharmonic mems equation with the fringing field it arises in the micro electro mechanical system mems devices first we establish the local solution and extend it globally in time next we discuss the dynamical properties of omega limit set especially we show that the omega limit set is included in the set of the stationary solution finally we consider the convergence rate to the stationary solution

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

general analytical structure of typical fuzzy controllers and their limiting structure theorems abstract the fuzzy controllers studied in this paper have r input variables error rate change of error of process output etc n members of input fuzzy sets are employed to fuzzify the inputs nr nonlinear control rules represented by an arbitrary function f are used which are evaluated by any type of fuzzy logic in conjunction with any inference method the center of gravity algorithm is utilized for defuzzification the author proves that the general analytical structure of the fuzzy controllers is the sum of a global f dependent nonlinear controller and a local nonlinear controller which locally adjusts control action of the global controller as n the global nonlinear controller approaches a global f dependent nonlinear controller while the local nonlinear controller disappears a necessary and sufficient condition is obtained for judging convergence of limiting structure of the fuzzy controllers if linear control rules are used the global controller is a global r dimensional multilevel relay which approaches a global linear controller as n two illustrative examples which deal with linear product maximum and minimum control rules are given

a nonlinear fuzzy controller with linear control rules is the sum of a global two dimensional multilevel relay and a local nonlinear proportional integral controller abstract the author analytically proves that a nonlinear fuzzy controller with linear control rules and n members for input fuzzy sets is the sum of a global two dimensional multilevel relay and a local nonlinear proportional integral pi controller which adjusts the control action generated by the global multilevel relay as n increases the resolution of the global multilevel relay is enhanced but the role of the local nonlinear pi controller in total control action is decreased as n approaches the global multilevel relay approaches a regular linear pi controller while the control action from the local nonlinear pi controller approaches zero the role of the global multilevel relay and the local nonlinear pi controller in total control action is quantitatively described as is the degree of nonlinearity of the fuzzy controllers with different n

analytical structure of the typical fuzzy controllers employing trapezoidal input fuzzy sets and nonlinear control rules fuzzy controllers are generally nonlinear controllers and as such it is important toreveal analytical structure of fuzzy controllers relative to conventional nonlinear controllers so that the well developed nonlinear control theory can be utilized to effectively analyze and design fuzzy control systems in our previous papers we have shown that the analytical structure of the fuzzy controllers using triangular input fuzzy sets and linear fuzzy control rules is the sum of a global two dimensional multilevel relay and a local nonlinear pi controller in this paper we present the analytical structure of much more general and typical fuzzy controllers the ones that employ trapezoidal input fuzzy sets and arbitrary nonlinear control rules we analytically prove that the structure of such controllers is the sum of a global nonlinear controller and a local nonlinear pi like controller whose proportional gain and integral gain vary both globally and locally with change of the controllers inputs this result significantly generalizes our previous ones and contains them only as special cases analytical results are presented which reveal the characteristics and properties of the fuzzy controllers we show that the global nonlinear controller is characterized solely by fuzzy control rules that is different nonlinear control rules result in different types of global nonlinear controllers when the number of input fuzzy sets approaches oo the global nonlinear controller approaches a control rules dependent nonlinear controller whereas the local nonlinear pi like controller disappears the results presented in this paper can directly be used to generate analytical structure of any specific fuzzy controllers and we demonstrate how by illustrative examples

on designing of sliding mode control for stochastic jump systems in this note we consider the problems of stochastic stability and sliding mode control for a class of linear continuous time systems with stochastic jumps in which the jumping parameters are modeled as a continuous time discrete state homogeneous markov process with right continuous trajectories taking values in a finite set by using linear matrix inequalities lmis approach sufficient conditions are proposed to guarantee the stochastic stability of the underlying system then a reaching motion controller is designed such that the resulting closed loop system can be driven onto the desired sliding surface in a limited time it has been shown that the sliding mode control problem for the markovian jump systems is solvable if a set of coupled lmis have solutions a numerical example is given to show the potential of the proposed techniques

finite horizon estimation of randomly occurring faults for a class of nonlinear time varying systems this paper is concerned with the finite horizon estimation problem of randomly occurring faults for a class of nonlinear systems whose parameters are all time varying the faults are assumed to occur in a random way governed by two sets of bernoulli distributed white sequences the stochastic nonlinearities entering the system are described by statistical means that can cover several classes of well studied nonlinearities the aim of the problem is to estimate the random faults over a finite horizon such that the influence from the exogenous disturbances onto the estimation errors is attenuated at the given level quantified by an h norm in the mean square sense by using the completing squares method and stochastic analysis techniques necessary and sufficient conditions are established for the existence of the desired finite horizon h fault estimator whose parameters are then obtained by solving coupled backward recursive riccati difference equations rdes a simulation example is utilized to illustrate the effectiveness of the proposed fault estimation method

analytical structure of a two input two output fuzzy controller and its relation to pi and multilevel relay controllers abstract this study investigates the analytical structure of a two input two output fuzzy controller which employs triangular shaped input fuzzy sets trapezoidal shaped output fuzzy sets linear control rules probabilistic and fuzzy logic ukasiewicz or fuzzy logic mamdani s minimum inference method and the center of gravity defuzzification algorithm we analytically prove that the structure of the fuzzy controller is the sum of global four dimensional multilevel relays and local nonlinear proportional integral pi controllers with variable gains continuously changing with process outputs the global multilevel relays play a major role in determining control action of the fuzzy controller while the local pi controllers locally fine tune the control action of the relays properties of the fuzzy controller structure are analytically and quantitatively investigated moreover it is proved that as the number of control rules approaches each global four dimensional multilevel relay becomes the sum of two global linear pi controllers while the local pi controllers disappear

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

deriving analytical input output relationship for fuzzy controllers using arbitrary input fuzzy sets and zadeh fuzzy and operator a fuzzy controller uses either zadeh or product fuzzy and operator with the former being more frequently used than the latter we have recently published a novel technique for deriving analytical input output relation for the fuzzy controllers that use zadeh and operator and arbitrary trapezoidal input fuzzy sets including triangular ones as special cases in this paper we have developed a general technique based on that technique to cover arbitrary types of input fuzzy sets moreover we have established some necessary and sufficient conditions to characterize general relationship between shape of input fuzzy sets and shape of input space divisions an important and integral issue because analytical relationship differs in different regions of input space the new technique and the shape relations are applicable to any type of fuzzy controllers e g mamdani type or takagi sugeno type the analytical structures that we have derived provide an unprecedented opportunity to insightfully and rigorously examine the advantages and shortcomings of different design choices available for various components of the fuzzy controllers we have focused on type selection for input fuzzy sets of mamdani fuzzy controllers our preliminary analysis indicates that the fuzzy controllers using trapezoidal fuzzy sets may be understood and possibly analyzed and designed more sensibly and easily in the context of conventional control theory than the fuzzy controllers using any other types of fuzzy sets our proposition is that trapezoidal fuzzy sets should be the first choice and used most of time possible implication for automatic learning of input fuzzy sets via neural networks or genetic algorithms is briefly discussed

a new model for electrostatic mems with two free boundaries abstract a moving boundary problem with two free boundaries modeling a two dimensional idealized mems device with pull in instability is discussed we use a fixed point argument to show that the model possesses stationary solutions for small source voltages we also give a rigorous evidence that solutions of the model converge towards solutions of the associated small aspect ratio equation in the vanishing aspect ratio limit

disturbance attenuation and rejection for stochastic markovian jump system with partially known transition probabilities in this paper the problem of disturbance attenuation and rejection is investigated for stochastic markovian jump system with multiple disturbances which include white noises and disturbances with partially known information a disturbance observer is designed to estimate the disturbances with partially known information based on the estimation value a disturbance observer based attenuation and rejection controller is constructed such that the closed loop system is asymptotically bounded in mean square or asymptotically stable in probability under different conditions finally a numerical example is given to illustrate the effectiveness of the proposed approach

theoretical analysis of crisp type fuzzy logic controllers using various t norm sum gravity inference methods the input output parametric relationship of a class of crisp type fuzzy logic controllers flcs using various t norm sum gravity inference methods is studied four most important t norms are used to calculate the matching level of each control rule and the explicit mathematical forms of reasoning surfaces obtained by using these four t norms are addressed reasoning surfaces of these crisp type flcs are proved to be composed of a two dimensional multilevel relay no matter which t norm is used and a local position dependent nonlinear compensator with output pattern influenced by the t norms is selected by analyzing the intrinsic operation of the four t norms the authors find that both standard intersection and algebraic product are suitable operators to perform the inference of the flc however bounded difference and drastic intersection are disqualified because they cannot satisfy some important criteria a measure of relative degree of nonlinearity is defined to examine the output figures of these crisp type flcs the ultimate behavior of these crisp type flcs as the number of linguistic terms approaches infinity is also explored the local stability criteria for the proportional integral pi type fuzzy control systems and the natural global stability characteristic for the proportional derivative pd type fuzzy control systems are also examined

monte carlo td λ methods for the optimal control of discrete time markovian jump linear systems in this paper we present an iterative technique based on monte carlo simulations for deriving the optimal control of the infinite horizon linear regulator problem of discrete time markovian jump linear systems for the case in which the transition probability matrix of the markov chain is not known we trace a parallel with the theory of td l algorithms for markovian decision processes to develop a td l like algorithm for the optimal control associated to the maximal solution of a set of coupled algebraic riccati equations care it is assumed that either there is a sample of past observations of the markov chain that can be used for the iterative algorithm or it can be generated through a computer program our proofs rely on the spectral radius of the closed loop operators associated to the mean square stability of the system being less than 1

towards a paradigm for fuzzy logic control the purpose of this paper is to lay a foundation for fuzzy logic control flc design constructing a class of fuzzy logic controllers that is suitable for a broad range of controls applications some scalar definitions in flc are extended to the n dimensional case including vector fuzzy number and membership vector a rigorous mathematical expression is given for the function g x called the reasoning surface manufactured by a fuzzy associative memory fam for the existence and uniqueness of solutions in any closed loop system with a fuzzy logic controller it is shown that the fam function g x must be lipschitz this places restrictions on the allowed rules in the flc it is argued that for effective control design the membership functions should not be uniformly spaced the triangular membership functions generally suffice and product inferencing should be used under these conditions the flc manufactures a piecewise multilinear lipschitz fam function g x that is a generalized proportional plus derivative plus offset controller the scalar and two dimensional cases are studied in detail

necessary conditions for some typical fuzzy systems as universal approximators abstract we investigate necessary conditions for general single input single output fuzzy systems and a class of typical multiple input single output fuzzy systems as universal approximators for continuous functions defined on compact domains with arbitrarily small uniform approximation error bounds considering the case where the only available data about the continuous function to be approximated are a finite set of its extrema we have established some necessary conditions for the fuzzy systems to be universal approximators of the function the conditions can be used practically to determine input fuzzy sets output fuzzy sets and fuzzy rules of the fuzzy systems furthermore these necessary conditions provide a basis for insightful analysis of the strengths as well as the limitations of the fuzzy systems the main strength is that only a small number of fuzzy rules may be needed to uniformly approximate continuous functions that have a complicated formulation but a relatively small number of extrema the limitation is that in order to approximate highly oscillatory continuous functions the number of fuzzy rules must be large 1997 elsevier science ltd

theorectical analysis of a fuzzy logic controller with unequally spaced triangular membership functions abstract the mathematical analysis concerning the explicit input output relation of the fuzzy logic controller flc is addressed in this article under the assumption of simple rule mapping and the use of arbitrarily located triangular fuzzy partitions as the membership functions the inferred output of the flc can be decomposed into two terms the global multilevel relay and the local nonlinear compensator the ultimate control behavior of this flc and the equivalence to nonlinear proportional integral pi controller as the number of linguistic terms are approaching to infinity are also investigated the local stability criteria for pi type flcs are derived and the global stability properties for pd type flcs are established this analysis is a generalization to previous related research works where the flc is characterized by equally spaced triangular fuzzy partitions on the universal sets

optimal control of a singular pde modeling transient mems with control or state constraints abstract a particular feature of certain microelectromechanical systems mems is the appearance of a so called pull in instability corresponding to a singularity in the underlying pde model we here consider a transient mems model and its optimal control via the dielectric properties of the membrane and or the applied voltage in contrast to the static case the control problem suffers from low dimensionality of the control compared to the state and hence requires different techniques for establishing first order optimality conditions for this purpose we here use a relaxation approach combined with a localization technique

global solutions of singular parabolic equations arising from electrostatic mems abstract we study dynamic solutions of the singular parabolic problem p u t u x 1 u 2 x t b 0 u x 0 u 0 x 0 x b u x t 0 x b where 0 and 0 are two parameters and b is the unit ball x r n x 1 with n 2 our interest is focussed on p with 2 3 n 4 9 for which p admits a singular stationary solution in the form s x 1 x 2 3 this equation models dynamic deflection of a simple electrostatic micro electro mechanical system mems device under the assumption u 0 s x we address the existence uniqueness regularity stability or instability and asymptotic behavior of weak solutions for p given 4 6 n 3 6 n 2 4 in particular we show that if either n 8 and or 2 n 7 then the minimal compact stationary solution u of p is stable and while s x is unstable however for n 8 and 0 p has no compact minimal solution and s x is an attractor from below not from above furthermore the refined asymptotic behavior of global solutions for p is also discussed for the case where n 8 and 0 which is given by a certain matching of different asymptotic developments in the large outer region closer to the boundary and the thin inner region near the singularity

the critical dimension for a fourth order elliptic problem with singular nonlinearity we study the regularity of the extremal solution of the semilinear biharmonic equation delta 2 u frac lambda 1 u 2 which models a simple micro electromechanical system mems device on a ball b subset mathbb r n under dirichlet boundary conditions u partial nu u 0 on partial b we complete here the results of lin and yang 14 regarding the identification of a pull in voltage 0 such that a stable classical solution u with 0 our main result asserts that the extremal solution u lambda is regular rm sup b u lambda 1 provided n leqq 8 while u lambda is singular rm sup b u lambda 1 for n geqq 9 in which case 1 c 0 x 4 3 leqq u lambda x leqq 1 x 4 3 on the unit ball where c 0 left frac lambda overline lambda right frac 1 3 and bar lambda frac 8 9 left n frac 2 3 right left n frac 8 3 right

a general technique for deriving analytical structure of fuzzy controllers using arbitrary trapezoidal input fuzzy sets and zadeh and operator deriving the analytical structure of fuzzy controllers is very important as it creates a solid foundation for better understanding insightful analysis and more effective design of fuzzy control systems we previously developed a technique for deriving the analytical structure of the fuzzy controllers that use zadeh fuzzy and operator and the symmetric identical trapezoidal or triangular input fuzzy sets many fuzzy controllers use arbitrary trapezoidal triangular input fuzzy sets that are asymmetric at present there exists no technique capable of deriving the analytical structure of these fuzzy controllers extending our original technique we now present a novel method that can accomplish rigorously the structure derivation for any fuzzy controller mamdani type or ts type that employs the arbitrary trapezoidal input fuzzy sets and zadeh fuzzy and operator the new technique contains our original technique as a special case given the importance of pid control we focus on mamdani fuzzy pi and pd controllers in this paper and show in detail how to use the new technique for different configurations of the fuzzy pi pd controllers the controllers use two arbitrary trapezoidal fuzzy sets for each input variable four arbitrary singleton output fuzzy sets four fuzzy rules zadeh fuzzy and operator and the centroid defuzzifier this configuration is more general and complicated than the mamdani fuzzy pi pd controllers in the current literature it actually contains them as special cases we call this configuration the generalized fuzzy pi pd controller

global existence for nonlocal mems we prove the existence of solutions for a nonlocal equation arising from the mathematical modeling of microelectromechanicalsystems mems the existence result obtained within a suitable implicit function theorem framework is established under rather general boundary conditions and for bounded domains whose diameter is fairly small

positivity and almost positivity of biharmonic green s functions under dirichlet boundary conditions in general for higher order elliptic equations and boundary value problems like the biharmonic equation and the linear clamped plate boundary value problem neither a maximum principle nor a comparison principle or equivalently a positivity preserving property is available the problem is rather involved since the clamped boundary conditions prevent the boundary value problem from being reasonably written as a system of second order boundary value problems it is shown that on the other hand for bounded smooth domains omega subset mathbb r n the negative part of the corresponding green s function is small when compared with its singular positive part provided n geqq 3 moreover the biharmonic green s function in balls b subset mathbb r n under dirichlet that is clamped boundary conditions is known explicitly and is positive it has been known for some time that positivity is preserved under small regular perturbations of the domain if n 2 in the present paper such a stability result is proved for n geqq 3

robust h sub spl infin control of uncertain markovian jump systems with time delay this paper is concerned with the robust stochastic stabilizability and robust h sub spl infin disturbance attenuation for a class of uncertain linear systems with time delay and randomly jumping parameters the transition of the jumping parameters is governed by a finite state markov process sufficient conditions on the existence of a robust stochastic stabilizing and spl gamma suboptimal h sub spl infin state feedback controller are presented using the lyapunov functional approach it is shown that a robust stochastically stabilizing h sub spl infin state feedback controller can be constructed through the numerical solution of a set of coupled linear matrix inequalities