adaptive control of non linear continuous time systems using neural networks general relative degree and mimo cases multilayer neural networks are used in a non linear adaptive control problem the plant is an unknown feedback linearizable continuous time system with relative degree 1 the single input single output system is studied first and then the methodology is extended to control square multi input multi output systems the control objective is for the plant to track a reference trajectory and the control law is defined in terms of the outputs of the neural networks the parameters of the networks are updated on line according to an augmented tracking error and the network derivatives a local convergence theorem is given on the convergence of the tracking error this control algorithm is applied to control a two input two output relative degree two system

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

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

fuzzy control turns 50 in 2015 we celebrate the 50th anniversary of fuzzy sets ten years after the main milestones regarding its applications in fuzzy control in their 40th birthday were reviewed in fss see 1 ten years is at the same time a long period and short time thinking to the inner dynamics of research this paper presented for these 50 years of fuzzy sets is taking into account both thoughts a first part presents a quick recap of the history of fuzzy control from model free design based on human reasoning to quasi lpv linear parameter varying model based control design via some milestones and key applications the second part shows where we arrived and what the improvements are since the milestone of the first 40 years a last part is devoted to discussion and possible future research topics

bicoprime factor stability criteria for linear time varying systems in the nest algebra this paper presents a bicoprime factorisation approach to deal with various stability problems for linear discrete time varying systems within the framework of nest algebra first we show that a s

a connection between state space and doubly coprime fractional representations explicit formulas for a doubly coprime fractional representation of the transfer function of a lumped lti system are given in terms of a stabilizable and detectable state space realization of the transfer function these formulas allow existing computational algorithms to be utilized for the purpose of computing doubly coprime factorizations several additional implications of this result are briefly discussed as are some immediate extensions and future research directions

adaptive control of mimo time varying systems with indicator function based parametrization abstract this paper studies a new solution framework for adaptive control of a class of mimo time varying systems with indicator function based parametrization motivated by a general discrete time mimo takagi sugeno t s fuzzy system model in an input output form with unknown parameters an indicator membership function based parametrization has some favorable capacity to deal with certain large parameter variations a new discrete time mimo system prediction model is derived for approximating a nonlinear dynamic system and its system properties are clarified an adaptive control scheme is developed with desired controller parametrization and stable parameter estimation for control of such uncertain mimo time varying systems a control singularity problem is addressed and the closed loop stability and output tracking properties are analyzed this work provides a new method for multivariable t s fuzzy system modeling and adaptive control an illustrative example and simulation results are presented to demonstrate the proposed novel concepts and to verify the desired adaptive control system performance

a survey of adaptive fuzzy controllers nonlinearities and classifications adaptive fuzzy controllers afcs i e fuzzy controllers using heuristic expert knowledge and equipped with adaption ability are widely used in the industry in the present days as they are capable of dealing with ill formulated nonlinear systems where exact mathematical formulas are not known or partially described nonlinear systems afcs have been widely deployed to control many nonlinear systems with different types of critical nonlinearities over the last two decades many different approaches toward adaptive fuzzy control have been reported in this paper we recapitulate the latest research works related to afcs and provide an up to date survey on the latest development made in adaptive fuzzy control theory and applications based on different types of fuzzy systems considered and nonlinearities associated with the nonlinear system to be controlled we categorize the different approaches based on different types of nonlinearities and consider basic nonlinear systems nonlinear systems with external disturbances nonlinear systems with some special type of nonlinearities nonaffine nonlinear systems and strict feedback nonlinear systems it turns out that many existing methods are subject to various limitations and none of them is capable of controlling a general nonlinear systems hence it is still an open problem to design and develop a universal afc for a general class of nonlinear systems

direct adaptive fuzzy control with a self structuring algorithm this paper presents a direct self structuring adaptive fuzzy control dsafc scheme for affine nonlinear single input single output systems we show that the only restriction on the control gain is that it be positive no upper bound on this gain nor its derivative needs to be known from an initial fuzzy system with a small number of rules the self structuring algorithm adds membership functions and rules when needed to limit the size of the fuzzy system from growing indefinitely the self structuring algorithm replaces old membership functions by new ones instead of adding more membership functions so that the number of rules never exceeds a predefined upper bound the stability of the closed loop system is guaranteed using the lyapunov synthesis approach the proposed control scheme is demonstrated by application to an inverted pendulum and a magnetic levitation system

fuzzy model based control stability robustness and performance issues a nonlinear controller based on a fuzzy model of mimo dynamical systems is described and analyzed the fuzzy model is based on a set of arx models that are combined using a fuzzy inference mechanism the controller is a discrete time nonlinear decoupler which is analyzed both for the adaptive and the fixed parameter cases a detailed stability analysis is carried out and the main result is that the closed loop is globally stable and robust with respect to unstructured uncertainty which may include modeling error and disturbances in addition bounds on the asymptotic and transient performance are given the main assumptions on the system and model are that they must not have strong nonminimum phase effects except time delay and the unstructured uncertainty must not be too large a simulation example illustrates some of the properties of the modeling method and model based control structure

a fuzzy disturbance observer and its application to control in this paper a fuzzy disturbance observer fdo is developed and its application to the control of a nonlinear system under the internal and external disturbances is presented to construct the fdo two parameter tuning methods are proposed and shown to be useful in adjusting the parameters of the fdo the first tuning method employs the disturbance observation error to guarantee that the fdo monitors the unknown disturbance the next one enlarges the concept of error and introduces augmented error to guarantee that the fdo monitors the disturbance and the control objective is achieved in addition the relationships between the suggested fdo based control and the conventional adaptive fuzzy controls reported in the previous literatures are discussed and it is shown in a rigorous manner that the disturbance observation error or the augmented error converges to a region of which size can be kept arbitrarily small finally some examples and computer simulation results are presented to illustrate the effectiveness and the applicability of the fdo

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

selection of a single uniquely specifiable h controller in the chain scattering framework this paper studies the notion of central h controllers in the chain scattering framework since in the chain scattering framework the h control problem is equivalent to a factorisation problem that yields non unique factors it is important to somehow pin down these factors so that the resulting central controller is uniquely defined and corresponds to the central and minimum entropy controller frequently discussed in the literature in so doing we devise a procedure for the selection of a single uniquely specifiable h controller in the chain scattering framework the chain scattering framework is important because it has a distinct advantage over state space based methods for some applications in that it poses and solves the h control problem entirely in an operator theoretic setting thereby allowing us to contemplate direct changes of the frequency domain symbols rather than changes in the corresponding state space matrices

brief paper an adaptive neuro fuzzy tracking control for multi input nonlinear dynamic systems an adaptive neuro fuzzy control design is suggested in this paper for tracking of nonlinear affine in the control dynamic systems with unknown nonlinearities the plant is described by a takagi sugeno t s fuzzy model where the local submodels are realized through nonlinear dynamical input output mappings our approach relies upon the effective approximation of certain terms that involve the derivative of the lyapunov function and the unknown system nonlinearities the above task is achieved locally using linear in the weights neural networks a novel resetting scheme is proposed that assures validity of the control input stability analysis provides the control law and the adaptation rules for the network weights assuring uniform ultimate boundedness of the tracking and the signals appearing in the closed loop configuration illustrative simulations highlight the approach

adaptive fuzzy controller for multivariable nonlinear state time varying delay systems subject to input nonlinearities in this paper an adaptive fuzzy variable structure controller is investigated for a class of uncertain multi input multi output mimo nonlinear time delay systems with both sector nonlinearities and dead zones a decomposition property of the control gain matrix is fully exploited in the controller design and the stability analysis the unknown time varying delay uncertainties are compensated for using an appropriate lyapunov krasovskii functional the boundedness of all signals of the closed loop system as well as the exponential convergence of the underlying tracking errors to an adjustable region are established the effectiveness of the proposed fuzzy adaptive controller is illustrated throughout simulation results

adaptive control of nonlinear systems using neural networks layered networks are used in a nonlinear adaptive control problem the plant is an unknown feedback linearizable discrete time system represented by an input output model a state space model of the plant is obtained to define the zero dynamics which are assumed to be stable a linearizing feedback control is derived in terms of some unknown nonlinear functions to identify these functions it is assumed that they can be modelled by layered neural networks the weights of the networks are updated and used to generate the control a local convergence result is given computer simulations verify the theoretical result

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

a discrete time fuzzy disturbance observer and its application to control in this paper a discrete time fuzzy disturbance observer fdo is developed and its application to the control of a nonlinear system in the presence of the internal and external disturbances is presented to construct the discrete time fdo a novel tuning method is proposed and shown to be useful in adjusting the parameters of the fdo the tuning method uses the augmented error to guarantee that the fdo monitors the disturbance and the control objective is achieved the design parameters such as a learning rate used in constructing the discrete time fdo are determined in a numerical manner by solving a linear matrix inequality it is shown in a rigorous manner that both the disturbance observation error and the control error converge to a compact set of which size can be kept arbitrarily small in addition the relationships between the suggested fdo based control and the conventional adaptive fuzzy controls reported in the previous literatures are discussed finally some examples and computer simulation results are presented to illustrate the effectiveness and the applicability of the fdo

fixed zeros of decentralized control systems considers the notion of decentralized fixed zeros for linear time invariant finite dimensional systems for an n channel plant that is free of unstable decentralized fixed modes an unstable decentralized fixed zero of channel i 1 spl les i spl les n is defined as an element of the closed right half plane which remains as a blocking zero of that channel under the application of every set of n 1 controllers around the other channels which make the resulting single channel system stabilizable and detectable the paper gives a complete characterization of unstable decentralized fixed zeros in terms of system invariant zeros

two mode adaptive fuzzy control with approximation error estimator in this paper we propose a two mode adaptive fuzzy controller with approximation error estimator in the learning mode the controller employs some modified adaptive laws to tune the fuzzy system parameters and an approximation error estimator to compensate for the inherent approximation error in the operating mode the fuzzy system parameters are fixed only the estimator is updated online mathematically we show that the closed loop system is stable in the sense that all the variables are bounded in both modes we also establish mathematical bounds on the tracking error state vector control signal and the rms error using these bounds we show that controller s design parameters can be chosen to achieve desired control performance after that an algorithm to automatically switch the controller between two modes is presented finally simulation studies of an inverted pendulum system and a chua s chaotic circuit demonstrate the usefulness of the proposed controller

stable adaptive fuzzy control for mimo nonlinear systems in this paper an indirect adaptive fuzzy control scheme is presented for a class of multi input and multi output mimo nonlinear systems whose dynamics are poorly understood within this scheme fuzzy systems are employed to approximate the plant s unknown dynamics in order to overcome the controller singularity problem the estimated gain matrix is decomposed into the product of one diagonal matrix and two orthogonal matrices a robustifying control term is used to compensate for the lumped errors and all parameter adaptive laws and robustifying control term are derived based on lyapunov stability analysis the proposed scheme guarantees that all the signals in the resulting closed loop system are uniformly ultimately bounded uub moreover the tracking errors can be made small enough if the designed parameter is chosen to be sufficiently large a simulation example is used to demonstrate the effectiveness of the proposed control scheme

adaptive parameter estimator based on t s fuzzy models and its applications to indirect adaptive fuzzy control design in this paper a new on line parameter estimation methodology for the general continuous time takagi sugeno t s fuzzy model whose parameters are poorly known or uncertain is presented an estimator with an appropriate adaptive law for updating the parameters is designed and analyzed based on the lyapunov theory the adaptive law is designed so that the estimation model follows the parameterized plant model by the proposed estimator the parameters of the t s fuzzy model can be estimated by observing the behavior of the system and it can be a basis for indirect adaptive fuzzy control in order to show the applicability of the proposed estimator indirect adaptive fuzzy control design examples with the proposed estimator are presented

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

partial tilting modules over m replicated algebras abstract let a be a hereditary algebra over an algebraically closed field k and a m be the m replicated algebra of a given an a m module t we denote by t the number of non isomorphic indecomposable summands of t in this paper we prove that a partial tilting a m module t is a tilting a m module if and only if t a m and that every partial tilting a m module has complements as an application we deduce that the tilting quiver k a m of a m is connected moreover we investigate the number of complements to almost tilting modules over duplicated algebras

stable model reference adaptive fuzzy control of a class of nonlinear systems in this paper we propose a new adaptive fuzzy control scheme called model reference adaptive fuzzy control mrafc the mrafc scheme employs a reference model to provide closed loop performance feedback for generating or modifying a fuzzy controller s knowledge base the mrafc scheme grew from ideas in conventional model reference adaptive control mrac the mrafc scheme is developed to perform adaptive feedback linearization to a class of nonlinear systems a class of fuzzy controllers which can be expressed in an explicit form is used as the primary controller based on lyapunov s second method we have developed mrafc schemes and derived fuzzy rule adaptive laws hence not only the stability of the system can be assured but also the performance such as the issues of robustness and parameter convergence of the mrafc system can be analyzed explicitly we showed that in the case of no modeling error the state error converges to zero asymptotically in the case that persistent excitation is satisfied we showed that the mrafc system is asymptotically stable by considering the periodic signal as reference input signal we showed that the square wave can make the mrafc system be persistently excited the feasibility of applying these techniques has been demonstrated by considering the control of an inverted pendulum in following a reference model response

a j spectral factorization approach to h control it is shown that necessary and sufficient conditions for the existence of sub optimal solutions to the model matching problem associated with h control are that two coupled j spectral factorizations exist the second j spectral factor provides a parameterization of all solutions to the model matching problem the existence of the j spectral factors is then shown to be equivalent to the existence of stabilizing non negative definite solutions to two algebraic riccati equations allowing a state space formula for a linear fractional representation of all controllers to be given

optimal robustness in the gap metric the application of the gap metric to robust stabilization of feedback systems is considered in particular a solution to the problem of robustness optimization in the gap metric is presented the problem of robust stabilization under simultaneous plant controller perturbations is addressed and the least amount of combined plant controller uncertainty measured by the gap metric that can cause instability of a nominally stable feedback system is determined included are a detailed summary of the main properties of the gap metric and the introduction of a dual metric called the t gap metric a key contribution of this study is to show that the problem of robustness optimization in the gap metric is equivalent to robustness optimization for normalized coprime factor perturbations this settles the question as to whether maximizing allowable coprime factor uncertainty corresponds to tolerating the largest ball of uncertainty in a well defined metric

a j spectral factorization approach to control necessary and sufficient conditions for the existence of suboptimal solutions to the standard model matching problem associated with mathcal h infty control j control are derived using j spectral factorization theory the existence of solutions to the model matching problem is shown to be equivalent to the existence of solutions to two coupled j spectral factorization problems with the second factor providing a parametrization of all solutions to the model matching problem the existence of the j spectral factors is then shown to be equivalent to the existence of nonnegative definite stabilizing solutions to two indefinite algebraic riccati equations allowing a state space formula for a linear fractional representation of all controllers to be given a virtue of the approach is that a very general class of problems may be tackled within a conceptually simple framework and no additional auxiliary riccati equations are required

foundations of a bicoprime factorization theory bicoprime factorizations bcfs are a generalization of the well known coprime factorizations commonly used in control theory however they have received negligible attention from the academic community so far this technical note lays the foundations of a bcf theory the theory is built from the ground up starting with the basic characteristics of such factorizations before moving on to state space parameterizations of bcfs and internal stability some advantages of bcfs are outlined including the possibility of reduced dimension internal stability tests an uncertainty structure induced by bcfs is also examined and the associated robust stability analysis tests provided in multiple instances it is shown how coprime factor results have their roots in the more abstract and more general bcfs

adaptive fuzzy control of a class of siso nonaffine nonlinear systems this paper presents a direct adaptive fuzzy control scheme for a class of uncertain continuous time single input single output siso nonaffine nonlinear dynamic systems based on the implicit function theory the existence of an ideal controller that can achieve control objectives is firstly shown since the implicit function theory guarantees only the existence of the ideal controller and does not provide a way for constructing it a fuzzy system is employed to approximate this unknown ideal control law the adjustable parameters in the used fuzzy system are updated using a gradient descent adaptation algorithm this algorithm is designed in order to minimize a quadratic cost function of the error between the unknown ideal implicit controller and the used fuzzy control law the stability analysis of the closed loop system is performed using a lyapunov approach in particular it is shown that the tracking error converges to a neighborhood of zero the effectiveness of the proposed adaptive control scheme is demonstrated through the simulation of a simple nonaffine nonlinear system

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

h tracking based adaptive fuzzy neural control for mimo uncertain robotic systems with time delays in this paper a novel adaptive fuzzy neural control afnc scheme for multi input multi output uncertain robotic systems is proposed for h tracking performance and to suppress the effects caused by multiple time delayed state uncertainties unmodeled dynamics and disturbances each delayed uncertainty is assumed to be bounded by an unknown gain a reference model with the desired amplitude and phase properties is given to construct an error model a fuzzy neural fn system is used to approximate an unknown controlled system from the strategic manipulation of the model following tracking errors the proposed afnc scheme uses two on line estimations which allows for the inclusion of identifying the gains of the delayed state uncertainties and training the weights of the fn system simultaneously stability and robustness of the afnc scheme is analyzed in lyapunov sense it is shown that the proposed control scheme can guarantee parameter estimation convergence and stability robustness of the closed loop system with h tracking performance for the overall system without a priori knowledge on the upper bounds of the delayed state uncertainties the performance of the proposed scheme is evaluated through the simulation results simulations are given to show the validity and confirm the performance of the proposed scheme

stable adaptive control using fuzzy systems and neural networks stable direct and indirect adaptive controllers are presented which use takagi sugeno fuzzy systems conventional fuzzy systems or a class of neural networks to provide asymptotic tracking of a reference signal for a class of continuous time nonlinear plants with poorly understood dynamics the indirect adaptive scheme allows for the inclusion of a priori knowledge about the plant dynamics in terms of exact mathematical equations or linguistics while the direct adaptive scheme allows for the incorporation of such a priori knowledge in specifying the controller we prove that with or without such knowledge both adaptive schemes can learn how to control the plant provide for bounded internal signals and achieve asymptotically stable tracking of a reference input in addition for the direct adaptive scheme a technique is presented in which linguistic knowledge of the inverse dynamics of the plant may be used to accelerate adaptation the performance of the indirect and direct adaptive schemes is demonstrated through the longitudinal control of an automobile within an automated lane

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

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

perspectives of fuzzy systems and control although fuzzy control was initially introduced as a model free control design method based on the knowledge of a human operator current research is almost exclusively devoted to model based fuzzy control methods that can guarantee stability and robustness of the closed loop system state of the art techniques for identifying fuzzy models and designing model based controllers are reviewed in this article attention is also paid to the role of fuzzy systems in higher levels of the control hierarchy such as expert control supervision and diagnostic systems open issues are highlighted and an attempt is made to give some directions for future research

adaptive fuzzy control of a class of mimo nonlinear systems this paper presents two indirect adaptive fuzzy control schemes for a class of uncertain continuous time multi input multi output nonlinear dynamic systems within these schemes fuzzy systems are employed to approximate the plant s unknown nonlinear functions and robustifying control terms are used to compensate for approximation errors by using a regularized matrix inverse a stable well defined adaptive controller is firstly investigated then in order to obtain an adaptive controller not depending upon any parameter initialization conditions and to relax the requirement of bounding parameter values a second adaptive controller is proposed all parameter adaptive laws and robustifying control terms are derived based on lyapunov stability analysis so that under appropriate assumptions semi global stability and asymptotic convergence to zero of tracking errors can be guaranteed simulations performed on a two link robot manipulator illustrate the approach and exhibit its performance

bicoprime factorizations of the plant and their relation to right and left coprime factorizations in a general algebraic framework starting with a bicoprime factorization p n sub pr d sup 1 n sub pl a right coprime factorization n sub p d sub p sup 1 a left coprime factorization d sup 1 sub p n sub p and the generalized bezout identities associated with the pairs n sub p d sub p and d sub p n sub p are obtained the set of all h stabilizing compensators for p in the unity feedback configuration s p c are expressed in terms of n sub pr d n sub pt and the elements of the bezout identity the state space representation p c si a sup 1 b is included as an example

observer based fuzzy adaptive control for multi input multi output nonlinear systems with a nonsymmetric control gain matrix and unknown control direction in this study we present an observer based fuzzy adaptive control scheme for a class of uncertain multi input multi output nonlinear systems with a nonsymmetric control gain matrix unknown control direction and unmeasured states in this scheme fuzzy systems are used to approximate the unknown nonlinear functions and an adaptive fuzzy state observer is designed to estimate the unmeasured states the parameter adaptive laws are designed by fuzzy basis functions rather than by its filtering and a robust control term is used to compensate for the lumped errors the proposed method solves the problem of the nonsymmetric control gain matrix and it requires no a priori knowledge of the control direction for the states that are unmeasured we prove that all of the signals in the resulting closed loop systems are bounded and that the tracking errors converge asymptotically to zero two simulation examples are used to demonstrate the effectiveness of the proposed scheme

gaussian networks for direct adaptive control a direct adaptive tracking control architecture is proposed and evaluated for a class of continuous time nonlinear dynamic systems for which an explicit linear parameterization of the uncertainty in the dynamics is either unknown or impossible the architecture uses a network of gaussian radial basis functions to adaptively compensate for the plant nonlinearities under mild assumptions about the degree of smoothness exhibit by the nonlinear functions the algorithm is proven to be globally stable with tracking errors converging to a neighborhood of zero a constructive procedure is detailed which directly translates the assumed smoothness properties of the nonlinearities involved into a specification of the network required to represent the plant to a chosen degree of accuracy a stable weight adjustment mechanism is determined using lyapunov theory the network construction and performance of the resulting controller are illustrated through simulations with example systems

dynamic structure adaptive neural fuzzy control for mimo uncertain nonlinear systems this paper proposes a novel dynamic structure neural fuzzy network dsnfn to address the adaptive tracking problems of multiple input multiple output mimo uncertain nonlinear systems the proposed control scheme uses a four layer neural fuzzy network nfn to estimate system uncertainties online the main feature of this dsnfn is that it can either increase or decrease the number of fuzzy rules over time based on tracking errors projection type adaptation laws for the network parameters are derived from the lyapunov synthesis approach to ensure network convergence and stable control a hybrid control scheme that combines the sliding mode control and the adaptive bound estimation control with different weights improves system performance by suppressing the influence of external disturbances and approximation errors as the employment of the dsnfn high quality tracking performance could be achieved in the system furthermore the trained network avoids the problems of overfitting and underfitting simulations performed on a two link robot manipulator demonstrate the effectiveness of the proposed control scheme

fuzzy model reference adaptive control this paper investigates a fuzzy model reference adaptive controller fmrac for continuous time multiple input multiple output mimo nonlinear systems the proposed adaptive scheme uses a takagi seguno ts fuzzy adaptive system which allows for the inclusion of a priori information in terms of qualitative knowledge about the plant operating points or analytical regulators e g state feedback for those operating points a proportional integral update law is used to obtain a fast parameters adaptation stability and robustness of this adaptive scheme are established using lyapunov stability tools the simulation results for a two link robot confirm the performance of the proposed approach

fuzzy adaptive observer backstepping control for mimo nonlinear systems in this paper a fuzzy adaptive backstepping output feedback control approach is developed for a class of multi input and multi output mimo nonlinear systems with unmeasured states using fuzzy logic systems to approximate the unknown nonlinear functions a fuzzy adaptive observer is designed for state estimation as well as system identification combining with the backstepping design techniques a fuzzy adaptive output feedback control is constructed recursively it is proved that the proposed fuzzy adaptive control approach can guarantee the semi global uniform ultimate boundedness for all the signals and the tracking error to a small neighborhood of the origin simulation studies illustrate the effectiveness of the proposed approach

distance measures for uncertain linear systems a general theory in this paper we propose a generic notion of distance between systems that can be used to measure discrepancy between open loop systems in a feedback sense under several uncertainty structures when the uncertainty structure is chosen to be four block or equivalently normalized coprime factor uncertainty then this generic distance measure reduces to the well known nu gap metric associated with this generic distance notion we also define a generic stability margin notion that allows us to give the distance measure a feedback interpretation by deriving generic robust stability and robust performance results the proposed distance notion and the corresponding results exploit a powerful generalization of the small gain theorem which handles perturbations in rfrl infin rather than only in rfrh infin when the uncertainty structure is fixed to one of the standard structures e g additive multiplicative inverse multiplicative coprime factor four block or any mixtures of the above we give a step by step procedure based on model validation ideas that shows how the generic notion of distance and the correspondingly generic winding number conditions can be reduced to simple formulae this work provides a unified framework that captures and embeds previous results in this area and also completes the picture by showing how other results of a similar nature can be obtained from the same framework the techniques used involve only basic linear algebra so they also provide a simplification of previous advanced proofs furthermore the various distance measures so created can be used for non conservative model embedding into the smallest uncertain family an illustrative example is also given that demonstrates the superior qualities above the nu gap metric of a particular distance measure obtained from this work in situations where the plant is lightly damped all systems considered in this paper are linear time invariant

fuzzy adaptive controller for mimo nonlinear systems with known and unknown control direction this paper investigates fuzzy adaptive control schemes for a class of multi input multi output mimo unknown nonlinear systems with known and unknown sign of the control gain matrix three fuzzy adaptive control schemes are developed in the design of the second and third controller we will exploit a decomposition of the control gain matrix into a symmetric positive definite matrix a diagonal matrix with diagonal entries 1 or 1 and a unity upper triangular matrix the nussbaum type function is used to deal with the unknown control direction i e the unknown sign of the control gain matrix for updating the parameters of the fuzzy system an adaptation proportional integral pi law is proposed theoretical results are illustrated through two simulation examples

adaptive fuzzy control for mimo nonlinear systems with nonsymmetric control gain matrix and unknown control direction in this paper an indirect adaptive fuzzy control scheme is developed for a class of uncertain multi input multi output nonlinear systems with nonsymmetric control gain matrix and unknown control direction the nonsymmetric control gain matrix is expressed as the sum of a symmetric matrix and a skew symmetric matrix and the symmetric matrix as well as the skew symmetric matrix is approximated by fuzzy systems by using the symmetric matrix decomposition technique the estimated symmetric matrix is decomposed into the product of one diagonal matrix and two orthogonal matrixes based on the decomposition results the adaptive fuzzy controller is developed to avoid the possible singularity problem and the parameter initialization problem a robust control term is employed to compensate for the lumped errors and a nussbaum type function is incorporated in the robust control term to deal with the unknown control direction the proposed scheme guarantees that all the signals in the resulting closed loop system are bounded and that the tracking errors converge asymptotically to zero two simulation examples are used to demonstrate the effectiveness of the proposed scheme

robust output feedback consensus for networked negative imaginary systems a robust output feedback consensus problem for networked homogeneous negative imaginary ni systems is investigated in this technical note by virtue of ni systems theory a set of reasonable yet elegant conditions are derived for output consensus under fraktur l 2 external disturbances as well as ni model uncertainty as a byproduct this technical note also reaffirms a previous result by li et al which shows the robustness of networked systems is always worse than that of single agent systems furthermore the eventual convergence sets are also characterized for several special ni systems that are commonly studied in the literature it is shown how the results in this work embed and generalize earlier results for these classes of systems we show that the natural convergence set boils down to the centroid of the initial pattern when the initial conditions of the controllers are zero numerical examples are given to showcase the main results

robust stabilization of normalized coprime factor plant descriptions with h sub infinity bounded uncertainty the problem of robustly stabilizing a family of linear systems is explicitly solved in the case where the family is characterized by h sub infinity bounded perturbations to the numerator and denominator of the normalized left coprime factorization of a nominal system this problem can be reduced to a nehari extension problem directly and gives an optimal stability margin all controllers satisfying a suboptimal stability margin are characterized and explicit state space formulas are given