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

applications of fuzzy chaos to fuzzy simulation in this paper we wish to use fuzzy chaos to generate fuzzy simulation we first discuss how fuzzy chaos can produce a chaotic sequence of fuzzy numbers we apply this technique to fuzzily simulate a solution to a simple fuzzy optimization problem other applications of fuzzy simulation to fuzzy mathematical programming fuzzy max flow fuzzy regression and tuning a fuzzy controller are also presented

stability of strong travelling waves for a non local time delayed reaction diffusion equation the paper is concerned with a non local time delayed reaction diffusion equation we prove the time asymptotic stability of a travelling wavefront without a smallness assumption on its wavelength i e the so called strong wavefront by means of the technical weighted energy method when the initial perturbation around the wave is small the exponential convergent rate is also given selection of a suitable weight plays a key role in the proof

the projective method for solving linear matrix inequalities numerous problems in control and systems theory can be formulated in terms of linear matrix inequalities lmi since solving an lmi amounts to a convex optimization problem such formulations are known to be numerically tractable however the interest in lmi based design techniques has really surged with the introduction of efficient interior point methods for solving lmis with a polynomial time complexity this paper describes one particular method called the projective method simple geometrical arguments are used to clarify the strategy and convergence mechanism of the projective algorithm a complexity analysis is provided and applications to two generic lmi problems feasibility and linear objective minimization are discussed

stabilization of uncertain systems via linear control this note considers the problem of stabilizing a linear dynamical system whose state equation includes a time varying uncertain parameter vector q cdot given the dynamics dot x t a q t x t b q t u t and a bounding set q for the values q t the objective is to choose a control law u t p x t guaranteeing uniform asymptotic stability for all admissible variations of q cdot our results differ from previous work in one fundamental way that is we show that when working with linear controllers it is possible to dispense with all assumptions on b cdot which have been made by previous authors e g see 1 9 this elimination of hypotheses on b cdot is accomplished roughly as follows the system sigma underline underline delta a q b q is shown to be equivalent to another system sigma underline underline delta a q b as far as stabilization is concerned since b is a constant matrix independent of q the desired result is readily obtained

revisited lq output feedback control minimax controller for a set of initial states a minimax linear quadratic lq output feedback controller is introduced which minimises the maximal value of the performance index over all initial states belonging to some set separated out a priori if the set is an ellipsoid or a polygon such controllers are synthesised in terms of linear matrix inequalities lmis in particular case when a size of this set tends to zero tightening to a point the minimax lq controller approaches the optimal lq output feedback controller for the given initial state while in another extreme case when this size tends to infinity we have the worst case lq output feedback controller numerical results for an inverted pendulum are presented

traveling wavefronts for time delayed reaction diffusion equation ii nonlocal nonlinearity abstract in this paper we study a class of time delayed reaction diffusion equation with local nonlinearity for the birth rate for all wavefronts with the speed c c where c 0 is the critical wave speed we prove that these wavefronts are asymptotically stable when the initial perturbation around the traveling waves decays exponentially as x but the initial perturbation can be arbitrarily large in other locations this essentially improves the stability results obtained by mei so li and shen m mei j w h so m y li s s p shen asymptotic stability of traveling waves for the nicholson s blowflies equation with diffusion proc roy soc edinburgh sect a 134 2004 579 594 for the speed c 2 d m e p d m with small initial perturbation and by lin and mei c k lin m mei on travelling wavefronts of the nicholson s blowflies equations with diffusion submitted for publication for c c with sufficiently small delay time r 0 the approach adopted in this paper is the technical weighted energy method used in m mei j w h so m y li s s p shen asymptotic stability of traveling waves for the nicholson s blowflies equation with diffusion proc roy soc edinburgh sect a 134 2004 579 594 but inspired by gourley s a gourley linear stability of travelling fronts in an age structured reaction diffusion population model quart j mech appl math 58 2005 257 268 and based on the property of the critical wavefronts the weight function is carefully selected and it plays a key role in proving the stability for any c c and for an arbitrary time delay r 0

lqg control with an h sup infinity performance bound a riccati equation approach an lqg linear quadratic gaussian control design problem involving a constraint on h sup infinity disturbance attenuation is considered the h sup infinity performance constraint is embedded within the optimization process by replacing the covariance lyapunov equation by a riccati equation whose solution leads to an upper bound on l sub 2 performance in contrast to the pair of separated riccati equations of standard lqg theory the h sup infinity constrained gains are given by a coupled system of three modified riccati equations the coupling illustrates the breakdown of the separation principle for the h sup infinity constrained problem both full and reduced order design problems are considered with an h sup infinity attenuation constraint involving both state and control variables an algorithm is developed for the full order design problem and illustrative numerical results are given

on travelling wavefronts of nicholson s blowflies equation with diffusion this paper is devoted to the study of nicholson s blowflies equation with diffusion a kind of time delayed reaction diffusion for any travelling wavefront with speed c c c is the minimum wave speed we prove that the wavefront is time asymptotically stable when the delay time is sufficiently small and the initial perturbation around the wavefront decays to zero exponentially in space as x but it can be large in other locations the result develops and improves the previous wave stability obtained by mei et al in 2004 the new approach developed in this paper is the comparison principle combined with the technical weighted energy method numerical simulations are also carried out to confirm our theoretical results

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

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 controller design for stochastic nonlinear systems via convex optimization this paper presents a new nonlinear control design framework called convex optimization based stochastic steady state tracking error minimization cvstem for a class of ito stochastic nonlinear systems including stochastic lagrangian systems this state feedback controller design involves the use of multiple state dependent coefficient sdc models of a nonlinear system equation and computes its controller parameters by solving a convex optimization problem in order to minimize an upper bound of the steady state tracking error this problem is shown to be equivalent to the original nonlinear optimization problem of minimizing the upper bound the exponential stability and robustness properties due to the state dependent riccati inequality are proven using stochastic contraction analysis discrete time stochastic incremental contraction analysis with respect to a state and time dependent metric is also presented along with its explicit connection to continuous time contraction analysis a result of simulation is used to validate the superiority of the proposed controller compared to a known nonlinear controller a pid controller and an h infinity controller

fuzzy input output controllers are universal approximators abstract in this paper we show that a fuzzy input output controller can approximate to any degree of accuracy a continuous fuzzy system this generalizes the known result that fuzzy controllers crisp input output can approximate continuous functions

lagrange stability and performance analysis of discrete time piecewise affine systems with logic states in this paper we consider discrete time piecewise affine systems with boolean inputs outputs and states and show that they can be represented in a logic canonical form where the logic variables influence the switching between different submodels but not the continuous valued dynamics we exploit this representation for studying lagrange stability and developing performance analysis procedures based on linear matrix inequalities moreover by using arguments from dissipativity theory for non linear systems we generalize our approach to solve the h analysis problem

dirichlet problem for the diffusive nicholson s blowflies equation abstract the object of this paper is to consider the asymptotic behavior of solutions of the diffusive nicholson s blowflies equation under dirichlet boundary condition a new approach is developed to study the global attractivity of the positive steady state for a reaction diffusion equation with time delay when monotone or quasi monotone conditions fail to apply this approach should be applicable to other dirichlet problems as well even though our analysis is tailored to the diffusive nicholson s blowflies equation

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

the generalized h 2 control problem abstract in this paper we consider the problem of finding an internally stabilizing controller such that the controlled or regulated signals have a guaranteed maximum peak value in response to arbitrary but bounded energy exogenous inputs more specifically we give a complete solution to the problem of finding a stabilizing controller such that the closed loop gain from l 2 0 to l 0 is below a specified level we consider both state feedback and output feedback problems in the state feedback case it is shown that if this synthesis problem is solvable then a solution can be chosen to be a constant state feedback gain necessary and sufficient conditions for the existence of solutions as well as a formula for a state feedback gain that solves this control problem are obtained in terms of a finite dimensional convex feasibility program after showing the separation properties of this synthesis problem the output feedback case is reduced to a state feedback problem it is shown that in the output feedback case generalized h 2 controllers can be chosen to be observer based controllers the theory is demonstrated with a numerical example

realization of linear outputs by using mixed fuzzy logics abstract the realization of the linear defuzzified output of the fuzzy controller with two inputs is discussed in this paper using the mixed fuzzy logics to evaluate the fuzzy control rule we show that the defuzzified output by an appropriate choice of each component can be precisely equivalent to a linear function of the inputs to the fuzzy controller

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

h_2 analysis of lti systems via conversion to externally positive systems motivated by recent advances in the study of linear time invariant lti positive systems we explore analysis techniques of general not necessarily positive lti systems using positive system theory even though a positive system is characterized by its peculiar property that its impulse response is nonnegative we often deal with nonnegative impulse responses even in general lti system analysis a typical example is the computation of the h 2 norm where we focus on squared impulse responses to deal with such products of impulse responses in a systematic fashion in this paper we first establish a construction technique of an lti system whose impulse response is given by the product of impulse responses of two different lti systems then as the main result we reduce the h 2 norm computation problem of a general lti system into the l infty induced norm computation problem or l 1 problem in short of a positive system by which we can derive various formulas for the h 2 norm computation

conserved quantities of the discrete finite toda equation and lower bounds of the minimal singular value of upper bidiagonal matrices some numerical algorithms are known to be related to discrete time integrable systems where it is essential that quantities to be computed for example eigenvalues and singular values of a matrix poles of a continued fraction are conserved quantities in this paper a new application of conserved quantities of integrable systems to numerical algorithms is presented for an n n n 2 real upper bidiagonal matrix b where all the diagonals and the upper subdiagonals are positive conserved quantities tr btb m 1 m 1 2 of the discrete finite toda equation give a sequence of lower bounds of the minimal singular value of b recurrence relations for computing higher order conserved quantities tr btb m 1 are also derived

pad analysis of fuzzy control stability abstract by means of an index represented rule mapping the response g of a fuzzy controller is decomposed into two parts f the classical component and g f the nonlinear component called pad we intend to analyse the pad in order to know what the relation is between fuzzy and classical pid controllers fuzzy controllers mentioned here are defuzzified by the typical center of gravity method in the 1 input case we get that f g 0 which means that the fuzzy controller is exactly the same as the classical p controller whenever the rule mapping is simple definition 1 2 and the linguistic values are a binary family definition 4 1 in the 2 input case of error and error change for simple rule mapping and for simple linguistic values family 4 7 and perfectly for the wxyz linguistic values family definition 6 1 the fuzzy controller can be viewed as a series connection of a classical pd controller and a 1 pad element the describing function of a 1 pad element is very simple and fine and ensures that such fuzzy controller will be stable if the pd controller is the similar consequences are also obtained for the case of three inputs

constructing nonlinear variable gain controllers via the takagi sugeno fuzzy control we investigated the analytical structure of the takagi sugeno ts type of fuzzy controllers which was unavailable in the literature the ts fuzzy controllers we studied employ a new and simplified ts control rule scheme in which all the rule consequent use a common function and are proportional to one another greatly reducing the number of parameters needed in the rules other components of the fuzzy controllers are general arbitrary input fuzzy sets any type of fuzzy logic and the generalized defuzzifier which contains the popular centroid defuzzifier as a special case we proved that all these ts fuzzy controllers were nonlinear variable gain controllers and characteristics of the gain variation were parametrized and governed by the rule proportionality we conducted an in depth analysis on a class of nonlinear variable gain proportional derivative pd controllers we present the results to show 1 how to analyze the characteristics of the variable gains in the context of control 2 why the nonlinear variable gain pd controllers can outperform their linear counterpart and 3 how to generate various gain variation characteristics through the manipulation of the rule proportionality

fuzzy control of model car this paper discusses fuzzy control of a model car fuzzy control rules are derived by modelling an expert s driving actions experiments are performed using a model car with a sensing unit and a micro computer

accurate singular values and differential qd algorithms in september 1991 j w demmel and w m kahan were awarded the second siam prize in numerical linear algebra for their paper accurate singular values of bidiagonal matrices 1 referred to as dk hereafter among several valuable results was the observation that the standard bidiagonal qr algorithm used in linpack 2 and in many other svd programs can be simplified when the shift is zero and of greater importance no subtractions occur the last feature permits very small singular values to be found with almost all the accuracy permitted by the data and at no extra cost

an improved lmi condition for robust d stability of uncertain polytopic systems a sufficient condition for robust d stability of linear systems with polytope type uncertainties is proposed the result is based on a linear parameter dependent lyapunov function obtained from the feasibility test of a set of linear matrix inequalities lmis defined at the vertices of the polytope this improved lmi condition encompasses previous results based on additional inequalities as well as results based on extra variables

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

robust regulation with h 2 performance abstract we consider the problem of minimizing the h 2 norm of a feedback system subject to the constraint that the controller robustly regulate against constants and sinusoids we show that for any 0 there exists a controller that both achieves robust regulation and renders the closed loop h 2 norm within of the optimal norm the norm achievable without the robust regulation constraint we also provide conditions that are both necessary and sufficient for there to exist a robustly regulating controller that achieves the optimal h 2 norm all proofs are constructive

expert fuzzy controller abstract we describe a fuzzy controller based on our general purpose fuzzy expert system shell flops we take a decision theoretic view in designing an optimal fuzzy controller the variables in the decision problem are 1 the defuzzification rules 2 the fuzzification rules and 3 the fuzzy control rules the objective function is composed of fuzzy goals specified for each system output we differentiate between decision making under certainty risk or uncertainty depending whether or not random elements are present in the system an example is presented illustrating varying the defuzzification rules to improve system performance

numerical steady state and hopf bifurcation analysis on the diffusive nicholson s blowflies equation1research partially supported by natural sciences and engineering research council of canada 1 for the dirichlet boundary value problem of the diffusive nicholson s blowflies equation it was shown in ref 17 that in a certain range of the parameter space there is a unique positive steady state solution in this paper we propose a scheme to compute this steady state numerically in addition we describe an iterative procedure to locate the critical values of the delay where a hopf bifurcation of time periodic solutions takes place near the steady state some numerical simulations of both schemes are given

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

a duality based approach to the multiobjective h 2 h optimisation problem in this article a duality approach to multiobjective h 2 h problems is pursued in which real rational para hermitian multipliers and real valued ones are associated to h and as usual h 2 constraints respectively it is shown that the maximisation of a dual functional over all such multipliers yields the optimal value of the original multiobjective h 2 h problem to compute lower bounds on the latter and the corresponding approximate solutions to the original problem the maximisation of the dual functional over linearly parameterised finite dimensional classes of real rational multipliers is shown to be equivalent to semi definite linear programming problems once the optimal multipliers in such a class are obtained the corresponding approximate solutions can be computed from an unconstrained h 2 problem iterative modification of such classes is discussed to obtain increasing sequences of lower bounds on the optimal value of the original problem this is done on the basis of locally incr

continuous time analysis eigenstructure assignment and h sub 2 synthesis with enhanced linear matrix inequalities lmi characterizations this note describes a new framework for the analysis and synthesis of control systems which constitutes a genuine continuous time extension of results that are only available in discrete time in contrast to earlier results the proposed methods involve a specific transformation on the lyapunov variables and a reciprocal variant of the projection lemma in addition to the classical linearizing transformations on the controller data for a wide range of problems including robust analysis and synthesis multichannel h sub 2 stateand output feedback syntheses the approach leads to potentially less conservative linear matrix inequality lmi characterizations this comes from the fact that the technical restriction of using a single lyapunov function is to some extent ruled out in this new approach moreover the approach offers new potentials for problems that cannot be handled using earlier techniques an important instance is the eigenstructure assignment problem blended with lyapunov type constraints which is given a simple and tractable formulation

asymptotic behavior and traveling wave solutions for parabolic functional differential equations on presente une generalisation de la theorie des equations kpp et de diffusion bistables non lineaires on montre que des solutions onde de propagation existent pour des equations fonctionnelles paraboliques non lineaires

fuzzy control theory the linear case abstract a linear fuzzy proportional integral pi controller with one input and one output is defined in terms of piecewise linear membership functions for fuzzification control rules and defuzzification algorithm it is shown that a linear fuzzy controller is not equivalent to a linear non fuzzy pi controller if the rules are evaluated using the zadeh probability or lukasiewicz fuzzy logic alone however the linear fuzzy controller is precisely equivalent to a linear non fuzzy pi controller if mixed fuzzy logic is used to evaluate the control rules when the fuzzy logics used are selected with due regard to prior associations implied by the control rule operands themselves this finding has relevance to the selection of fuzzy logics in fuzzy expert systems and for fuzzy logics in general

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

studies on the output of fuzzy controller with multiple inputs abstract in this paper we discuss the output of a fuzzy controller in which an arbitrary number of fuzzy control inputs and an arbitrary number of fuzzy sets employed to fuzzify every linguistic variable are considered in the fuzzy control rules a rule base with a rule mapping concept is considered a defuzzifier with the general t norm and t conorm operators is formulated a triangular family is adopted so that the defuzzifier of the complete rule mapping is represented by a formula consisting of only some rules using a specific logic pair to evaluate values we derive that the output of the fuzzy controller can be simply represented by a linear parametric function of the inputs to the 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

travelling wave fronts in reaction diffusion systems with spatio temporal delays this paper deals with the existence of travelling wave fronts in reaction diffusion systems with spatio temporal delays our approach is to use monotone iterations and a nonstandard ordering for the set of profiles of the corresponding wave system new iterative techniques are established for a class of integral operators when the reaction term satisfies different monotonicity conditions following this the existence of travelling wave fronts for reaction diffusion systems with spatio temporal delays is established finally we apply the main results to a single species diffusive model with spatio temporal delay and obtain some existence criteria of travelling wave fronts by choosing different kernels

nonlinear fuzzy controller abstract we consider a fuzzy controller with two inputs triangular fuzzy numbers zadeh logic to evaluate linear control rules and a center of gravity defuzzifier we derive a closed form expression for the defuzzified output and show it is a nonlinear controller we then analyze the nonlinearities of the fuzzy controller with respect to the pi controller

regular paper the takagi sugeno fuzzy controllers using the simplified linear control rules are nonlinear variable gain controllers takagi sugeno ts for short fuzzy controllers have been used and treated as black box controllers and there exists no explicit structure of any ts fuzzy controller in the literature in this paper we investigate the analytical structure of the ts fuzzy controllers that use our newly introduced simplified ts control rule scheme our scheme requires that all the rule consequent employ a common linear function and be proportional to one another the scheme drastically reduces the number of adjustable parameters required by the original ts rule scheme product fuzzy logic and was employed in the rule antecedents we theoretically proved that the ts controllers using the simplified rule scheme were nonlinear variable gain controllers the proportionality of the rule consequent parameterized the gain variation characteristics as special cases the ts controllers with three or two input variables and the simplified linear rule consequent were nonlinear variable gain pid pi or pd controllers as an illustration we mathematically analyzed the nonlinear variable gain pi controllers and revealed that the gain variation empowered the controllers to outperform their linear counterparts stability of the nonlinear pi control systems was also addressed a practical example is given to show how to achieve the desired characteristics of the gain variation by properly designing the simplified rules

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

mixed spl hscr sub 2 and spl hscr sub spl infin performance objectives ii optimal control this paper considers the analysis and synthesis of control systems subject to two types of disturbance signals white signals and signals with bounded power the resulting control problem involves minimizing a mixed spl hscr sub 2 and spl hscr sub spl infin norm of the system it is shown that the controller shares a separation property similar to those of pure spl hscr sub 2 or spl hscr sub spl infin controllers necessary conditions and sufficient conditions are obtained for the existence of a solution to the mixed problem explicit state space formulas are also given for the optimal controller

numerical relationships between neural networks continuous functions and fuzzy systems abstract in this survey paper we first discuss computational equivalence between continuous functions regular neural nets fuzzy controllers and discrete fuzzy expert systems we also discuss how to build hybrid neural nets numerically identical to a fuzzy controller or a discrete fuzzy expert system we then discuss computational equivalence between continuous fuzzy functions regular fuzzy neural nets and fuzzy systems we also discuss how to construct hybrid fuzzy neural nets to approximate continuous fuzzy functions

a primal dual potential reduction method for problems involving matrix inequalities we describe a potential reduction method for convex optimization problems involving matrix inequalities the method is based on the theory developed by nesterov and nemirovsky and generalizes gonzaga and todd s method for linear programming a worst case analysis shows that the number of iterations grows as the square root of the problem size but in practice it appears to grow more slowly as in other interior point methods the overall computational effort is therefore dominated by the least squares system that taust be solved in each iteration a type of conjugate gradient algorithm can be used for this purpose which results in important savings for two reasons first it allows us to take advantage of the special structure the problems often have e g lyapunov or algebraic riccati inequalities second we show that the polynomial bound on the number ofiterations remains valid even if the conjugate gradient algorithm is not run until completion which in practice can greatly reduce the computational effort per iteration we describe in detail how the algorithm works for optimization problems with l lyapunov inequaliues each of size m we prove an overall worst case operation count of o mssll5 the average case complexity appears to be closer to o m4ll5 this estimate is justified by extensive numerical experimentation and is consistent with other researchers experience with the practical performance of interior point algorithms for linear programming this result means that the computational cost of extending current control theory based on the solution of lyapunov or riccati equations to a theory that is based on the solution of multiple coupled lyapunov or riccati inequalities is modest

fuzzy control theory a nonlinear case abstract sources of nonlinearity in a fuzzy controller include the fuzzification algorithm used for the controller inputs fuzzy control rules type of fuzzy logic used for evaluating the fuzzy control rules and the defuzzification algorithm used for the controller output we analyze the performance of a simple fuzzy controller with linear and nonlinear defuzzification algorithms we prove theoretically that such a fuzzy controller the smallest possible with two inputs error and rate change of error and a nonlinear defuzzification algorithm is equivalent to a nonfuzzy nonlinear proportional integral pi controller with proportional gain and integral gain changing with error and rate change of error about a setpoint furthermore this fuzzy controller is precisely equivalent to a conventional linear pi controller if a linear defuzzification algorithm is employed computer simulation showed that the performance of the fuzzy controller was almost the same as that of the pi controller when first order and second order linear processes were used furthermore the fuzzy controller was significantly better when a first order with a time delay model was used more importantly the simulated result illustrated that the fuzzy controller was stable when a nonlinear process model was controlled but the pi controller was unstable

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

solution to the positive real control problem for linear time invariant systems in this paper we study the problem of synthesizing an internally stabilizing linear time invariant controller for a linear time invariant plant such that a given closed loop transfer function is extended strictly positive real necessary and sufficient conditions for the existence of a controller are obtained state space formulas for the controller design are given in terms of solutions to algebraic riccati equations or inequalities the order of the constructed controller does not exceed that of the plant

lmi based reset mathcal h _ infty design for linear continuous time plants in this technical note an optimization based synthesis of a multi objective reset controller for linear plants is presented the result allows designing via convex tools with a line search a multi objective reset controller optimizing both the exponential converging rate and the mathcal l 2 gain a novel peculiarity of our scheme is that the underlying linear flow dynamics is not necessarily stabilizing this last property is the consequence of taking into account where the flowing trajectories lay and lead to improved performance especially in terms of decay rate some simulations illustrate the usefulness of our techniques

h sub spl infin design with pole placement constraints an lmi approach this paper addresses the design of state or output feedback h sub spl infin controllers that satisfy additional constraints on the closed loop pole location sufficient conditions for feasibility are derived for a general class of convex regions of the complex plane these conditions are expressed in terms of linear matrix inequalities lmis and the authors formulation is therefore numerically tractable via lmi optimization in the state feedback case mixed h sub 2 h sub spl infin synthesis with regional pole placement is also discussed finally the validity and applicability of this approach are illustrated by a benchmark example

method of centers for minimizing generalized eigenvalues abstract we consider the problem of minimizing the largest generalized eigenvalue of a pair of symmetric matrices each of which depends affinely on the decision variables although this problem may appear specialized it is in fact quite general and includes for example all linear quadratic and linear fractional programs many problems arising in control theory can be cast in this form the problem is nondifferentiable but quasiconvex so methods such as kelley s cutting plane algorithm or the ellipsoid algorithm of shor nemirovsky and yudin are guaranteed to minimize it in this paper we describe relevant background material and a simple interior point method that solves such problems more efficiently the algorithm is a variation on huard s method of centers using a self concordant barrier for matrix inequalities developed by nesterov and nemirovsky nesterov and nemirovsky have also extended their potential reduction methods to handle the same problem since the problem is quasiconvex but not convex devising a nonheuristic stopping criterion i e one that guarantees a given accuracy is more difficult than in the convex case we describe several nonheuristic stopping criteria that are based on the dual of a related convex problem and a new ellipsoidal approximation that is slightly sharper in some cases than a more general result to nesterov and nemirovsky the algorithm is demonstrated on an example determining the quadratic lyapunov function that optimizes a decay rate estimate for a differential inclusion

robust regulation in the presence of norm bounded uncertainty we consider robust regulation against steps and sinusoids in the presence of unstructured uncertainty the unstructured uncertainty is norm bounded by a constant that is given a priori this problem is equivalent to a certain multiobjective problem where one objective is robust regulation and the other is the standard objective of h sub spl infin suboptimal control it is shown that a solution to this problem exists if and only if the standard h sub spl infin problem admits a solution and certain matrix inequalities are satisfied these solvability conditions are readily computable controller synthesis is also addressed

explicit controller formulas for lmi based h synthesis the set of h controllers with closed loop performance c can be implicitly parametrized by the solutions r s of a system of linear matrix inequalities lmi the matrices r and s play a role analogous to that of the riccati solutions x and y in classical riccati based h control useful applications include lmi based h synthesis mixed h 2h design and h design with a pole placement constraint this paper is concerned with the reliable computation of h controllers given a solution r s of the characteristic system of lmis explicit formulas are derived for both the regular and singular cases remarkably these formulas are extensions of the usual central controller formulas where the lmi solutions r and s replace the riccati solutions x and y simple and numerically appealing new formulas for discrete time h controllers are also derived

universal fuzzy controllers a collection b of fuzzy controllers is a universal fuzzy controller if and only if given any controllable process p it can also be controlled by some fuzzy controller in b this paper identifies a new type of universal fuzzy controller

fuzzy modeling and control of multilayer incinerator abstract a method to design a fuzzy controller based on a fuzzy model is suggested the identification method of a fuzzy model is also discussed the suggested method is applied for the modelling and control of a multilayer incinerator the performance of the designed fuzzy controller is tested by computer simulation using the identified process model the results are satisfactory

stability of traveling waves in a population dynamics model with spatio temporal delay abstract in this paper we are concerned with the stability of all traveling waves for a population dynamics model with spatio temporal delay by the weighted energy method combining comparison principle the global exponential stability of all traveling waves for the model is established even including the slower waves whose wave speed is close to the critical speed

the orthogonal qd algorithm the orthogonal qd algorithm is presented to compute the singular value decomposition of a bidiagonal matrix this algorithm represents a modification of rutishauser s qd algorithm and it is capable of determining all the singular values and their corresponding singular vectors to high relative accuracy a generalization of the givens transformation which has applications besides the orthogonal qd algorithm is also introduced the shift strategy of the orthogonal qd algorithm is based on laguerre s method which is used to compute a lower bound on the smallest singular value of the bidiagonal matrix special attention is devoted to the numerically stable evaluation of this shift

sliding mode design via quadratic performance optimization with pole clustering constraint we consider a novel method for designing the sliding mode that minimizes the quadratic performance while keeping a pole clustering constraint our approach is based on the manipulations of linear matrix inequalities lmis imposed by the design objectives for this purpose we newly propose lmi conditions for the quadratic performance optimization and the pole clustering problem respectively in a full order state then they are combined in the lmi framework that is typically devised for the sliding mode design in the convex form an effort is made to reduce the generic conservatism by allowing different lyapunov matrices in addition a class of polytope uncertain systems is addressed to illustrate the advantages of the proposed method

theory of the fuzzy controller abstract we first introduce notation in an attempt to standardize the description of a basic fuzzy controller if r 1 r 2 r n are the real number inputs to the fuzzy controller and is its defuzzified output then f r 1 r n for some function f by the theory of the fuzzy controller we mean in this paper the study of the structure of f for elementary fuzzy controllers using this standardized notation we first survey the known results on the theory of the fuzzy controller and then discuss important future research topics in this area

mixed h sub 2 h sub infinity control a convex optimization approach the problem of finding an internally stabilizing controller that minimizes a mixed h sub 2 h sub infinity performance measure subject to an inequality constraint on the h sub infinity norm of another closed loop transfer function is considered this problem can be interpreted and motivated as a problem of optimal nominal performance subject to a robust stability constraint both the state feedback and output feedback problems are considered it is shown that in the state feedback case one can come arbitrarily close to the optimal even over full information controllers mixed h sub 2 h sub infinity performance measure using constant gain state feedback moreover the state feedback problem can be converted into a convex optimization problem over a bounded subset of n n and n q where n and q are respectively the state and input dimensions real matrices using the central h sub infinity estimator it is shown that the output feedback problem can be reduced to a state feedback problem in this case the dimension of the resulting controller does not exceed the dimension of the generalized plant

a probabilistic and statistical view of fuzzy methods fuzzy set theory has primarily been associated with control theory and with the representation of uncertainty in applications in artificial intelligence more recently fuzzy methods have been proposed as alternatives to traditional statistical methods in statistical quality control linear regression and forecasting among other areas we review some basic concepts of fuzzy methods point out some philosophical and practical problems and offer simpler alternatives based on traditional probability and statistical theory applications in control theory and statistical quality control serve as our primary examples

fuzzy nash equilibriums in crisp and fuzzy games in this paper we introduce fuzzy nash equilibrium to determine a graded representation of nash equilibriums in crisp and fuzzy games this interpretation shows the distribution of equilibriums in the matrix form of a game and handles uncertainties in payoffs in addition a new method to rank fuzzy values with the user s viewpoint is investigated by this means the definition of satisfaction function which provides the result of comparison in the form of real value is developed when users have preferences regarding the payoffs

travelling waves in the nicholson s blowflies equation with spatio temporal delay abstract in this paper nicholson s blowflies equation with diffusion and delay is investigated by taking four different kinds of delay kernels and defining four corresponding characteristic equations the existence of travelling wave solutions for nicholson blowflies equation is obtained by employing the monotone iteration technique as well as the upper and lower solution method

fuzzy adaptive control of a first order process abstract fuzzy adaptive control of a first order process with a varying gain and time constant is demonstrated the fuzzy adaptive controller is based on a fuzzy model based controller that uses an explicit fuzzy model of the process adaptation is achieved by the addition of on line identification of the fuzzy process model starting with a crude initial model the adaptive controller matches the model to the process to self tune the controller the model is further modified when the operating point is changed to adapt the controller to the new process conditions two different fuzzy identification algorithms are both shown to provide a successful fuzzy adaptive controller the robustness of the algorithms in the presence of process noise is investigated and improved by the addition of weighting factors

on the linear static output feedback problem the annihilating polynomial approach abstract one of the fundamental open problems in control theory is that of the stabilization of a linear time invariant dynamical system through static output feedback we are given a linear dynamical system defined through w a w b u y c w the problem is to find if it exists a feedback u k y such that the matrix a b k c has all its eigenvalues in the complex left half plane and if such a feedback does not exist to prove that it does not substantial progress has not been made on the computational aspect of the solution to this problem in this paper we consider instead which annihilating polynomials can a matrix of the form a b k c possess we give a simple solution to this problem when the system has either a single input or a single output for the multi input multi output case we use these ideas to characterize the annihilating polynomials when k has rank one and suggest possible computational solutions for general k we also present some numerical evidence for the plausibility of this approach for the general case as well as for the problem of shifting the eigenvalues of the system

a stability approach to fuzzy control design for nonlinear systems abstract by the application of fuzzy set theory a method for feedback control of nonlinear systems based on the principle of sliding mode control is developed called fuzzy sliding mode control the control method provides a simple way to achieve asymptotic stability of the systems other attractive features of the method include a minimal realization of the fuzzy controller and robustness against model uncertainties and external disturbances in addition the method is capable of handling the chattering problem inherent to sliding mode control simply and effectively a simulation study of an inverted pendulum system is presented to demonstrate these features of the method also it is indicated that the method is easy to use for practicing control engineers

traveling waves for the diffusive nicholson s blowflies equation we consider traveling wave front solutions for the diffusive nicholson s blowflies equation on the real line the existence of such solutions is proved using the technique developed by j wu and x zou j dyn differ equations 13 3 2001 some numerical simulation using the iteration formula of wu and zou 7 is also provided

fuzzy i o controller abstract we describe a fuzzy controller which accepts and produces fuzzy data linguistic variables as well as crisp data real numbers for the control of man machine systems

linear quadratic uncertain differential game with application to resource extraction problem uncertain differential game investigates interactive decision making of players over time and the system dynamics is described by an uncertain differential equation this paper goes further to study the two player zero sum uncertain differential game in order to guarantee the saddle point nash equilibrium a max min theorem is provided furthermore when the system dynamics is described by a linear uncertain differential equation and the performance index function is quadratic the existence of saddle point nash equilibrium is obtained via the solvability of a corresponding riccati equation finally a resource extraction problem is analyzed by using the theory proposed in this paper