globally stable adaptive backstepping fuzzy control for output feedback systems with unknown high frequency gain sign this paper addresses the problem of globally stable adaptive backstepping output feedback tracking control for a class of nonlinear systems with unknown high frequency gain sign the fuzzy systems are used as feedforward compensators to model some system functions depending on the reference signal thus the global stability of closed loop system can be guaranteed under the assumption that the unknown system functions are bounded by partly known nonlinear functions the other advantage of the proposed control scheme is that the designer can determine the approximation domain a priori via the bound of the reference signal which is very important for the choice of the centers and widths of membership functions moreover the nussbaum type function is employed to deal with the unknown high frequency gain sign two simulation examples are provided to illustrate the feasibility of control scheme presented in this paper

asymptotic rejection of general periodic disturbances in output feedback nonlinear systems this note deals with asymptotic rejection of general periodic disturbances in nonlinear systems a novel approach based on integrations over the half of disturbance period is proposed to estimate disturbances which may not be harmonic or even smooth the proposed algorithm uses the period and the knowledge of the basic disturbance patterns while the amplitude and phase of the disturbances are unknown and they are estimated based on the estimated disturbance the disturbance rejection algorithm is then proposed for linear systems and nonlinear systems in the output feedback format which asymptotically rejects the periodical disturbances the proposed algorithm extends asymptotic rejection of unknown disturbances from sinusoidal disturbances to a more general class of periodical disturbances which includes zero mean square waves symmetric triangular waves etc

fuzzy adaptive output feedback fault tolerant tracking control of a class of uncertain nonlinear systems with nonaffine nonlinear faults this paper studies the fuzzy adaptive output feedback fault tolerant control ftc problem for a class of single input and single output uncertain nonlinear systems with time varying nonaffine nonlinear faults in strict feedback form in the design procedure filtered signals are adopted to circumvent algebraic loop problems on implementing the usual controllers by using fuzzy logic systems to approximate the unknown nonlinearity effects and changes in model dynamics due to faults a fuzzy state observer is first presented to estimate the unmeasured states based on the online estimating information from the adaptive mechanism an observer based dynamic output feedback fault tolerant controller is designed via the backstepping technique it is shown that the stability and tracking performances of the closed loop system can be achieved even in the presence of unknown nonlinear faults in comparison with the existing approaches the ftc scheme can handle the nonaffine nonlinear faults effectively finally a simulation example is included to validate the advantages of the proposed approaches

fast polynominal transforms for two dimensional convolution in a recent paper 1 truong et al have presented a new method for computing two dimensional convolutions it is shown that a modification of their algorithm can lead to a slightly more efficient method i e a gain in efficiency of 5 10 percent can be attained

adaptive backstepping fuzzy control for nonlinearly parameterized systems with periodic disturbances a novel function approximator is constructed by combining a fuzzy logic system with a fourier series expansion in order to model unknown periodically disturbed system functions then an adaptive backstepping tracking control scheme is developed where the dynamic surface control approach is used to solve the problem of explosion of complexity in the backstepping design procedure and the time varying parameter dependent integral lyapunov function is used to analyze the stability of the closed loop system the semiglobal uniform ultimate boundedness of all closed loop signals is guaranteed and the tracking error is proved to converge to a small residual set around the origin two simulation examples are provided to illustrate the effectiveness of the control scheme designed in this paper

fuzzy tracking adaptive control of discrete time switched nonlinear systems this paper is concerned with the problem of fuzzy tracking adaptive control for a class of discrete time switched uncertain nonlinear systems with arbitrary switching based on the common lyapunov function method and by utilizing the fuzzy logic systems to approximate the unknown nonlinear functions an adaptive fuzzy controller is firstly constructed for a class of uncertain nonlinear discrete time switched systems meanwhile the proposed adaptive control algorithm reduces the amount of online adjustable parameters based on the above techniques the constructed fuzzy controllers and the adaptive law can guarantee that all the signals are bounded and the system output can converge to a small neighborhood of the reference signal in the closed loop system an illustrative example is provided to demonstrate the effectiveness of the proposed approaches

an improved fpt algorithm for computing two dimensional cyclic convolutions in this correspondence the fast polynomial transform fpt algorithm for two dimensional cyclic convolutions in 6 7 is improved these improvements result from reduction of the complexity of polynomial products modulo zk 1 and the decomposition and reconstruction by the chinese remainder theorem with these improvements the fpt can be performed with a more regular and modular structure

fuzzy adaptive output feedback control of mimo nonlinear systems with partial tracking errors constrained in this paper a partial tracking error constrained fuzzy output feedback dynamic surface control dsc scheme is proposed for a class of uncertain multi input and multi output mimo nonlinear systems the considered mimo nonlinear systems contain unknown functions and without the requirement of their states being available for the controller design with the help of fuzzy logic systems identifying the mimo unknown nonlinear systems a fuzzy adaptive observer is established to estimate the unmeasured states by transforming the tracking errors into new virtual error variables and based on the dsc backstepping recursive design technique a new adaptive fuzzy output feedback control method is developed it is proved that the proposed control approach can guarantee that all the signals of the resulting closed loop system are bounded and the partial state tracking errors are confined all times within the prescribed bounds the simulation results and comparisons with the previous control approaches confirm the effectiveness and utility of the proposed scheme

convolutions of long integer sequences by means of number theoretic transforms over residue class polynomial rings in a recent paper dubois and venetsanopoulos 6 have derived methods for convolving sequences of numbers belonging to a ring s using number theoretic transforms ntt s over an extension ring r of s in this paper we obtain more explicit expressions for some of their results and more important improve the efficiency of their methods attention is focused on the case r s z p z that is r is the quotient ring of s z modulo the principal ideal generated by a polynomial p z of degree n

robust adaptive fuzzy fault tolerant control for a class of non lower triangular nonlinear systems with actuator failures in this paper the problem of adaptive fuzzy fault tolerant tracking control is studied for a class of non lower triangular nonlinear systems with actuator failures according to the same structure of virtual control inputs and the monotonously increasing property of the bounding functions a variable separation approach is proposed by applying the backstepping technique an adaptive fuzzy control approach is presented which can guarantee the semi global boundedness of all signals within the closed loop system the tracking error using the proposed control scheme eventually converges to a small neighborhood of the origin

on the application of a fast polynomial transform and the chinese remainder theorem to compute a two dimensional convolution in this paper a fast algorithm is developed to compute two dimensional convolutions of an array of d 1 d 2 complex number points where d 2 2mand d 1 2m r 1for some 1 leq r leq m this new algorithm requires fewer multiplications and about the same number of additions as the conventional fft method for computing the two dimensional convolution it also has the advantage that the operation of transposing the matrix of data can be avoided

brief paper asymptotic rejection of asymmetric periodic disturbances in output feedback nonlinear systems this paper deals with asymptotic rejection of periodic disturbances which may have asymmetric basic wave patterns this class of disturbances covers asymmetric wave forms in the half period such as alternating sawtooth wave form some disturbances which are generated from nonlinear oscillation such as van de pol oscillators as well as disturbances with symmetric half period wave forms such as sinusoidal disturbances and triangular disturbances etc the systems considered in this paper can be transformed to the nonlinear output feedback form the amplitude and phase of the disturbances are unknown the novel concept of integral phase shift is introduced together with the newly introduced half period integration operator to investigate the invariant properties of asymmetric periodic disturbances they are used for the estimation of unknown disturbances in the systems together with observer design techniques to deal with nonlinearity the proposed control design with the disturbance estimation asymptotically rejects the unknown disturbance and ensures the overall stability of the system

dynamic surface control using neural networks for a class of uncertain nonlinear systems with input saturation in this paper a dynamic surface control dsc scheme is proposed for a class of uncertain strict feedback nonlinear systems in the presence of input saturation and unknown external disturbance the radial basis function neural network rbfnn is employed to approximate the unknown system function to efficiently tackle the unknown external disturbance a nonlinear disturbance observer ndo is developed the developed ndo can relax the known boundary requirement of the unknown disturbance and can guarantee the disturbance estimation error converge to a bounded compact set using ndo and rbfnn the dsc scheme is developed for uncertain nonlinear systems based on a backstepping method using a dsc technique the problem of explosion of complexity inherent in the conventional backstepping method is avoided which is specially important for designs using neural network approximations under the proposed dsc scheme the ultimately bounded convergence of all closed loop signals is guaranteed via lyapunov analysis simulation results are given to show the effectiveness of the proposed dsc design using ndo and rbfnn

repetitive control system a new type servo system for periodic exogenous signals a control scheme called repetitive control is proposed in which the controlled variables follow periodic reference commands a high accuracy asymptotic tracking property is achieved by implementing a model that generates the periodic signals of period l into the closed loop system sufficient conditions for the stability of repetitive control systems and modified repetitive control systems are derived by applying the small gain theorem and the stability theorem for time lag systems synthesis algorithms are presented by both the state space approach and the factorization approach in the former approach the technique of the kalman filter and perfect regulation is utilized while coprime factorization over the matrix ring of proper stable rational functions and the solution of the hankel norm approximation are used in the latter one

an fpt algorithm with a modularized structure for computing two dimensional discrete fourier transforms the fast polynomial transform fpt for computing two dimensional discrete fourier transforms is modularized into identical modules in this new method only fpts and fast fourier transforms of the same length are required as a consequence the architecture is more regular and naturally suitable for multiprocessor and vlsi implementations the modularized fpt algorithms can simplify the problems of control memory management load balancing etc although more arithmetic operations are needed than with the original ones

improved long convolutions using generalized number theoretic and polynomial transforms generalized number theoretic and polynomial transforms can be used in the computation of a long convolution this will reduce the computation complexity by a factor of two it only requires fewer than 2 real multiplications 45 real additions and 10 data shifts per point for a typical 2048 array

a combined backstepping and stochastic small gain approach to robust adaptive fuzzy output feedback control in this paper an adaptive fuzzy output feedback control approach is investigated for a class of stochastic nonlinear strict feedback systems without the requirement of states measurement the stochastic nonlinear system addressed in this paper is assumed to possess unstructured uncertainties unknown nonlinear functions and in the presence of unmodeled dynamics dynamics disturbances fuzzy logic systems are used to approximate the unstructured uncertainties and a fuzzy state observer is designed to estimate the unmeasured states by combining the backstepping design technique with the stochastic small gain approach a new adaptive fuzzy output feedback control approach is developed it is proved that the proposed control approach can guarantee that the closed loop system is input state practically stability isps in probability and the observer errors and the output of the system converge to a small neighborhood of the origin by appropriate choice of the design parameters simulation results are included to indicate that the proposed adaptive fuzzy control approach has a satisfactory control performance in addition the simulation comparisons with the previous methods show that the proposed adaptive fuzzy control approach has robustness to the dynamical uncertainties

the existence of weak solutions for steady flows of electrorheological fluids with nonhomogeneous dirichlet boundary condition abstract in this paper we show the existence of weak solutions for steady flows of electrorheological fluids with nonhomogeneous dirichlet boundary condition under the condition p x 2 n n 2 n 2 3 in particular we improve a priori estimate for weak solutions to the problem with min p x 2 which is an improvement even for constant p

a new periodic adaptive control approach for time varying parameters with known periodicity a new adaptive control approach is proposed to deal with nonlinear systems with a class of time varying parametric uncertainties which are in an unknown compact set periodic nonvanishing rapid time varying and the only prior knowledge is the periodicity unlike most continuous time adaptation laws which are of differential types in this work a periodic type adaptation law is introduced for continuous time systems the new adaptive controller updates the parameters and the control signal periodically in a pointwise manner over one entire period in the sequel achieves the asymptotic tracking convergence

adaptive learning control of nonlinear systems by output error feedback this paper addresses the problem of designing an output error feedback control for single input single output nonlinear systems with uncertain smooth output dependent nonlinearities whose local lipschitz constants are known the considered systems are required to be observable minimum phase with known relative degree and known high frequency gain sign linear systems are included the reference output signal is assumed to be smooth and periodic with known period by developing in fourier series expansion a suitable periodic input reference signal an output error feedback adaptive learning control is designed which ldquolearnsrdquo the input reference signal by identifying its fourier coefficients bounded closed loop signals and exponential tracking of both input and output reference signals are obtained when the fourier series expansion is finite while arbitrary small tracking errors are exponentially achieved otherwise the resulting control is not model based is independent of the system order and depends only on the relative degree the reference signal period and the high frequency gain sign

an fpt algorithm with a modularized structure for computing 2 d cyclic convolutions the fast polynomial transform fpt for computing 2 d cyclic convolutions is modularized into identical modules in the new method the 1 d cyclic polynomial convolution is decomposed into cycle convolutions of polynomials all of the same length thus only fpts and fft s of the same length are required as a consequence the architecture is more regular and naturally suitable for a vlsi implementation

direct adaptive fuzzy tracking control for a class of perturbed strict feedback nonlinear systems in this paper a novel direct adaptive fuzzy tracking control scheme is presented for a class of perturbed strict feedback nonlinear systems with unknown virtual control coefficients based on the mamdani type fuzzy logic system online approximation capability a direct adaptive fuzzy tracking controller is developed by using the backstepping approach the proposed design scheme guarantees that all the signals in the resulting closed loop system are uniform ultimate bounded and the tracking error converges to an arbitrarily small neighborhood of the origin in addition the number of the online adaptive parameters is not more than the order of the considered system and the possible controller singularity problem is removed by introducing the modified integral lyapunov functions finally two simulation examples are used to demonstrate the effectiveness of the proposed control scheme

fuzzy approximate disturbance decoupling of mimo nonlinear systems by backstepping and application to chemical processes fuzzy approximate disturbance decoupling concept is introduced for a class of multiple input multiple output mimo nonlinear systems with completely unknown nonlinearities based on backstepping technique a fuzzy almost disturbance decoupling control scheme is proposed the fuzzy controllers guarantee internal uniform ultimate boundedness of the closed loop adaptive systems and render a bounded approximate l sub 2 gain from the disturbance input to the output the developed design scheme is applied to control a two continuous stirred tank reactor process the simulation results illustrate the effectiveness of the method proposed in this paper

brief robust learning control for a class of nonlinear systems with periodic and aperiodic uncertainties this paper addresses the robust learning control problem for a class of nonlinear systems with structured periodic and unstructured aperiodic uncertainties a recursive technique is proposed which extends the backstepping idea to the robust repetitive learning control systems a learning evaluation function instead of a lyapunov function is formulated as a guideline for derivation of the control strategy which guarantees the asymptotic stability of the tracking system a design example is given

adaptive tracking for periodically time varying and nonlinearly parameterized systems using multilayer neural networks this brief addresses the problem of designing adaptive neural network tracking control for a class of strict feedback systems with unknown time varying disturbances of known periods which nonlinearly appear in unknown functions multilayer neural network mnn and fourier series expansion fse are combined into a novel approximator to model each uncertainty in systems dynamic surface control dsc approach and integral type lyapunov function ilf technique are combined to design the control algorithm the ultimate uniform boundedness of all closed loop signals is guaranteed the tracking error is proved to converge to a small residual set around the origin two simulation examples are provided to illustrate the feasibility of control scheme proposed in this brief

adaptive neural output feedback control of output constrained nonlinear systems with unknown output nonlinearity this paper addresses the problem of adaptive neural output feedback control for a class of special nonlinear systems with the hysteretic output mechanism and the unmeasured states a modified bouc wen model is first employed to capture the output hysteresis phenomenon in the design procedure for its fusion with the neural networks and the nussbaum type function two key lemmas are established using some extended properties of this model to avoid the bad system performance caused by the output nonlinearity a barrier lyapunov function technique is introduced to guarantee the prescribed constraint of the tracking error in addition a robust filtering method is designed to cancel the restriction that all the system states require to be measured based on the lyapunov synthesis a new neural adaptive controller is constructed to guarantee the prescribed convergence of the tracking error and the semiglobal uniform ultimate boundedness of all the signals in the closed loop system simulations are implemented to evaluate the performance of the proposed neural control algorithm in this paper

comments on adaptive fuzzy h_ infty stabilization for strict feedback canonical nonlinear systems via backstepping and small gain approach for original paper see y s yang c j zhou ibid vol 13 no 1 p 104 114 2005 in this note we point out some mistakes in a 2005 paper by yang and zhou

multidimensional cyclic convolution algorithms with minimal multiplicative complexity this paper presents novel multidimensional cyclic convolution algorithms which achieve the theoretically minimum number of multiplications the proposed algorithms are compared to the well known and used polynomial transform and split nesting convolution algorithms

robust control for a class of uncertain nonlinear systems adaptive fuzzy approach based on backstepping a robust adaptive fuzzy control design approach is developed for a class of multivariable nonlinear systems with modeling uncertainties and external disturbances the controller design for the overall systems has been carried out through a number of simpler controller designs for a series of the relevant auxiliary systems based on the backstepping design technique for each auxiliary system an adaptive fuzzy logic system is introduced to learn the behavior of unknown dynamics and then a robust control algorithm is employed to efficiently compensate the approximation error and the external disturbances as well it is shown that the resulting closed loop systems guarantee a satisfactory transient and asymptotic performance a simulation example is also presented to illustrate the design procedure and controller performance

adaptive fuzzy tracking control for a class of perturbed strict feedback nonlinear time delay systems this paper is concerned with the problem of adaptive fuzzy output tracking for a class of perturbed strict feedback nonlinear systems with time delays and unknown virtual control coefficients fuzzy logic systems in mamdani type are used to approximate the unknown nonlinear functions then the adaptive fuzzy tracking controller is designed by using the backstepping technique and lyapunov krasovskii functionals the proposed adaptive fuzzy controller guarantees that all the signals in the closed loop system are bounded and the system output eventually converges to a small neighborhood of the desired reference signal an advantage of the proposed control scheme lies in that the number of the online adaptive parameters is not more than the order of the original system finally two examples are used to demonstrate the effectiveness of our results proposed in this paper

decentralized adaptive fuzzy output feedback control of switched large scale nonlinear systems in this paper a decentralized adaptive fuzzy output feedback control problem is discussed for a class of switched large scale nonlinear systems without the measurements of the system states fuzzy logic systems are used to approximate the unknown nonlinear functions and a switched observer is designed to avoid the conservativeness caused by adoption of a common observer for all subsystems a common coordinate transformation of all subsystems is constructed to get rid of individual coordinate transformations for subsystems that are required when applying the backstepping recursive design scheme meanwhile since the exponential decline property of lyapunov functions for individual subsystems is no longer satisfied in this paper the classical average dwell time method cannot be directly applied based on this a switched observer based decentralized adaptive fuzzy output feedback control technique is set up by exploiting the average dwell time method and backstepping it is proved that all the signals of the resulting closed loop system are semiglobally uniformly ultimately bounded under a class of switching signals with average dwell time while the tracking errors converge to a small neighborhood of the origin the effectiveness of the proposed control scheme is illustrated by its applications to a two inverted pendulum system and a quadruple tank process system

fuzzy adaptive control of nonlinear uncertain plants with unknown dead zone output this paper focuses on a tracking problem for a class of strict feedback nonlinear systems with unknown dead zone output and unmeasurable states based on the adaptive backstepping technique a new adaptive fuzzy control scheme is proposed it is shown that the proposed control scheme guarantees that all the signals in the closed loop system are semi globally uniformly ultimately bounded the tracking error converges to a small neighborhood of the origin moreover the proposed control method requires only one adaptive law for an nth order system and the structure of the controllers is very simple so they are easy to be implemented the main advantage of this paper is that the unknown dead zone nonlinearity in the output mechanism of strict feedback systems is considered by introducing a nussbaum function the problem of unknown virtual control coefficient is resolved which is caused by the nonlinearity in the output mechanism finally simulation results are provided to show the effectiveness of the proposed approach