parameterization and adaptive control of multivariable noncanonical t s fuzzy systems this paper conducts a new study for adaptive takagi sugeno t s fuzzy approximation based control of multi input and multi output mimo noncanonical form nonlinear systems canonical form nonlinear systems have explicit relative degree structures whose approximation models can be directly used to derive desired parameterized controllers noncanonical form nonlinear systems usually do not have such a feature nor do their approximation models which are also in noncanonical forms this paper shows that it is desirable to reparameterize noncanonical form t s fuzzy system models with smooth membership functions for adaptive control and such system reparameterization can be realized using relative degrees a concept yet to be studied for mimo noncanonical form t s fuzzy systems this paper develops an adaptive feedback linearization scheme for control of such general system models with uncertain parameters by first deriving various relative degree structures and normal forms for such systems then a reparameterization procedure is developed for such system models based on which adaptive control designs are derived with desired stability and tracking properties analyzed a detailed example is presented with simulation results to show the new control design procedure and desired control system performance

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

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

adaptive observers for ts fuzzy systems with unknown polynomial inputs a large class of nonlinear systems can be well approximated by takagi sugeno ts fuzzy models with linear or affine consequents however in practical applications the process under consideration may be affected by unknown inputs such as disturbances faults or unmodeled dynamics in this paper we consider the problem of simultaneously estimating the state and unknown inputs in ts systems the inputs considered in this paper are 1 polynomials in time such as a bias in the model or an unknown ramp input acting on the model and 2 unmodeled dynamics the proposed observer is designed based on the known part of the fuzzy model conditions on the asymptotic convergence of the observer are presented and the design guarantees an ultimate bound on the error signal the results are illustrated on a simulation example

adaptive learning control for finite interval tracking based on constructive function approximation and wavelet using a constructive function approximation network an adaptive learning control alc approach is proposed for finite interval tracking problems the constructive function approximation network consists of a set of bases and the number of bases can evolve when learning repeats the nature of the basis allows the continuous adaptive learning of parameters when the network undergoes any structural changes and consequently offers the flexibility in tuning the network structure the expandability of the bases guarantees precision of the function approximation and avoids the trial and error procedure in structure selection for any fixed structure network two classes of unknown nonlinear functions namely either global l2 or local l2 with a known bounding function are taken into consideration using the lyapunov method the existence of solution and the convergence property of the proposed alc system are discussed in a rigorous manner by virtue of the celebrated orthonormal and multiresolution properties wavelet network is used as the universal function approximator with the weights tuned by the proposed adaptive learning mechanism

poincare type inequalities for singular stable like dirichlet forms abstract this paper is concerned with a class of singular stable like dirichlet forms on r d which are generated by d independent copies of a one dimensional symmetric stable process and whose levy jump kernel measure is concentrated on the union of the coordinate axes explicit and sharp criteria for poincare inequality super poincare inequality and weak poincare inequality of such singular dirichlet forms are presented when the reference measure is a product measure on r d we also consider the entropy inequality for the associated dirichlet forms which is similar to the log sobolev inequality for local dirichlet forms and enjoys the tensorisation property

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

polynomial fuzzy models for nonlinear control a taylor series approach classical takagi sugeno t s fuzzy models are formed by convex combinations of linear consequent local models such fuzzy models can be obtained from nonlinear first principle equations by the well known sector nonlinearity modeling technique this paper extends the sector nonlinearity approach to the polynomial case this way generalized polynomial fuzzy models are obtained the new class of models is polynomial both in the membership functions and in the consequent models importantly t s models become a particular case of the proposed technique recent possibilities for stability analysis and controller synthesis are also discussed a set of examples shows that polynomial modeling is able to reduce conservativeness with respect to standard t s approaches as the degrees of the involved polynomials increase

decentralized adaptive tracking control of nonaffine nonlinear large scale systems with time delays this paper addresses the problem of decentralized tracking control of large scale systems with uncertain nonaffine nonlinear isolated subsystems and nonlinear interconnections with time varying delays based on lyapunov krasovskii functional approach and implicit function theorem a delay independent decentralized tracking controller is proposed due to functional approximation capability of fuzzy logic systems fls neither strict structure restrictions on the isolated subsystems nor a priori knowledge of the strong interconnections with time varying delays is required in our control design furthermore transient performance of the resulting closed loop system is also addressed under an analytical framework finally two numerical examples are provided to show the effectiveness of the proposed controller

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

stable fuzzy adaptive control for a class of nonlinear systems abstract in this paper two adaptive fuzzy control schemes for a class of nonlinear systems are proposed each scheme employs a fuzzy control with an adaptive law and a compensation control it is proved that the closed loop system is asymptotically stable based on lyapunov synthesis approach while the identification of the controlled plant is unnecessary finally these schemes are applied to control a chaotic system the simulation results show that our schemes are superior to the scheme of 12

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

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

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

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

an efficient computational scheme for the two dimensional overcomplete wavelet transform we have studied the computational complexity associated with the overcomplete wavelet transform for the commonly used spline wavelet family by deriving general expressions for the computational complexity using the conventional filtering implementation we show that the inverse transform is significantly more costly in computation than the forward transform to reduce this computational complexity we propose a new spatial implementation based on the exploitation of the correlation between the lowpass and the bandpass outputs that is inherent in the overcomplete representation both theoretical studies and experimental findings show that the proposed spatial implementation can greatly simplify the computations associated with the inverse transform in particular the complexity of the inverse transform using the proposed implementation can be reduced to slightly less than that of the forward transform using the conventional filtering implementation we also demonstrate that the proposed scheme allows the use of an arbitrary boundary extension method while maintaining the ease of the inverse transform

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

a global exponential fuzzy observer design for time delay takagi sugeno uncertain discrete fuzzy bilinear systems with disturbance a robust h fuzzy observer is proposed for a class of time delay takagi sugeno t s uncertain discrete fuzzy bilinear systems with disturbance utilizing the lipschitz conditions and some variable transformations a linear matrix inequality lmi approach is developed and a sufficient condition is obtained to design the robust h fuzzy observer the robust h fuzzy observer for time delay t s uncertain discrete fuzzy bilinear systems with disturbance can be obtained directly through the lmis with no preassigned matrices the convergent rate of the error state can be estimated from the initial conditions and the delay time of t s uncertain discrete fuzzy bilinear systems the designed robust h fuzzy observer can guarantee the dynamics of the observer error to be globally exponentially stable and has a prescribed h performance a numerical example is given to demonstrate the feasibility and effectiveness of the proposed observer design method

globally stable direct fuzzy model reference adaptive control abstract in the paper a fuzzy adaptive control algorithm is presented it belongs to the class of direct model reference adaptive techniques based on a fuzzy takagi sugeno model of the plant the plant to be controlled is assumed to be nonlinear and predominantly of the first order consequently the resulting adaptive and control laws are very simple and thus interesting for use in practical applications the system remains stable in the presence of unmodelled dynamics disturbances parasitic high order dynamics and reconstruction errors are treated explicitly the global stability of the overall system is proven in the paper i e it is shown that all signals remain bounded while the tracking error and estimated parameters converge to some residual set that depends on the size of disturbance and high order parasitic dynamics the proposed algorithm is tested on a simulated three tank system its performance is compared to the performance of a classical mrac

h tracking based decentralized hybrid adaptive output feedback fuzzy control for a class of large scale nonlinear systems this paper proposes a novel h tracking based decentralized hybrid adaptive fuzzy controller via output feedback for a class of large scale uncertain nonlinear systems to achieve better adaptation properties the proposed controller is a weighted combination of indirect and direct adaptive fuzzy controls iafc and dafc such that both fuzzy descriptions and control rules can be incorporated at the same time after proper filtering of the observation error dynamics the developed observer based feedback and adaptation mechanisms become implementable indeed by using fuzzy inference systems a state observer and h tracking technique the decentralized combined indirect and direct adaptive fuzzy control algorithm is developed based upon a united h tracking controller design for the modification of the previous work of huang et al the resultant closed loop systems are guaranteed to be stable and a good h tracking performance is obtained simulation results of interrelated inverted pendulums substantiate that the proposed cafc system stands out as being better properties than typical iafc and dafc systems in that the tracking performance is much better while the control effort is even smaller

direct adaptive self structuring fuzzy controller for nonaffine nonlinear system a direct adaptive state feedback controller for highly nonlinear systems is proposed this paper considers uncertain or ill defined nonaffine nonlinear systems and employ a static fuzzy logic system fls with an on line structuring algorithm the fls approximates and adaptively cancels an unknown plant nonlinearity a control law and adaptive laws for unknown fuzzy parameters and bounding constant are established so that the whole closed loop system is stable in the sense of lyapunov the tracking error is guaranteed to be uniformly asymptotically stable rather than uniformly ultimately bounded with the aid of an additional robustifying control term no a priori knowledge of an upper bound on an lumped uncertainty is required

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

relative degrees and adaptive feedback linearization control of t s fuzzy systems this paper presents a new study on the relative degrees of single input and single output t s fuzzy systems in general noncanonical forms and proposes a feedback linearization based control design method for such systems the study extends the system relative degree concepts commonly used for the control of nonlinear systems to general t s fuzzy systems derives various relative degree conditions for general t s fuzzy systems and establishes the relative degree dependent normal forms a feedback linearization based control design framework is developed for general t s fuzzy systems using its normal form to achieve closed loop stability and asymptotic output tracking under relaxed design conditions a new adaptive feedback linearization based control scheme for t s fuzzy systems in general noncanonical forms with parameter uncertainties is designed and analyzed some extensions of relative degrees and their possible application to robust adaptive control for noncanonical form t s fuzzy systems are also demonstrated an illustrative example is presented with simulation results to demonstrate the control system design procedure and to show the effectiveness of the proposed control scheme