direct adaptive nn control of a class of nonlinear systems in this paper direct adaptive neural network nn control is presented for a class of affine nonlinear systems in the strict feedback form with unknown nonlinearities by utilizing a special property of the affine term the developed scheme avoids the controller singularity problem completely all the signals in the closed loop are guaranteed to be semiglobally uniformly ultimately bounded and the output of the system is proven to converge to a small neighborhood of the desired trajectory the control performance of the closed loop system is guaranteed by suitably choosing the design parameters simulation results are presented to show the effectiveness of the approach

distributed memoryless detection and accommodation of unknown time delayed interaction faults in a class of interconnected nonlinear systems this paper addresses a memoryless design problem for the distributed fault detection and accommodation fda of a class of large scale nonlinear systems in the presence of nonlinear interaction faults with unknown time delays existing works designed distributed fda schemes without considering interaction delays however we consider these delays design distributed memoryless detection estimators and time varying thresholds for detecting unknown time delayed interaction faults and analyze the distributed fault detectability then an approximation based distributed fault accommodation scheme which is independent of time delays is constructed via lyapunov stability theorem thus it is shown that all signals of the total controlled closed loop system are uniformly ultimately bounded and tracking errors of subsystems converge to an adjustable neighborhood of the origin finally a simulation example is presented to show the effectiveness of the proposed methodology

a dsc approach to adaptive neural network tracking control for pure feedback nonlinear systems in this paper by incorporating the dynamic surface control technique into a neural network based adaptive control design framework we develop a backstepping based adaptive control design approach for uncertain non affine pure feedback nonlinear systems by using the dynamic surface control technique the problem of explosion of complexity inherent in existing methods are eliminated effectively stability analysis shows that the uniform ultimate boundedness of all the signals in the closed loop system can be guaranteed and the steady state tracking error can be made arbitrarily small by appropriately choosing control parameters simulation results demonstrate the effectiveness of the proposed scheme

direct adaptive controller for nonaffine nonlinear systems using self structuring neural networks a direct adaptive state feedback controller is proposed for highly nonlinear systems we consider uncertain or ill defined nonaffine nonlinear systems and employ a neural network nn with flexible structure i e an online variation of the number of neurons the nn approximates and adaptively cancels an unknown plant nonlinearity a control law and adaptive laws for the weights in the hidden layer and output layer of the nn are established so that the whole closed loop system is stable in the sense of lyapunov moreover the tracking error is guaranteed to be uniformly asymptotically stable uas rather than uniformly ultimately bounded uub with the aid of an additional robustifying control term the proposed control algorithm is relatively simple and requires no restrictive conditions on the design constants for the stability the efficiency of the proposed scheme is shown through the simulation of a simple nonaffine nonlinear system

adaptive fuzzy control of nonlinear systems in pure feedback form based on input to state stability using mean value theorem and backstepping technique a robust adaptive fuzzy control scheme is proposed for a class of pure feedback nonlinear systems with unknown dead zone and disturbances via input to state stability takagi sugeno t s type fuzzy logic systems are used to approximate the uncertain nonlinear functions and fewer learning parameters need to be adjusted online based on small gain theorem the closed loop control system is proven to be semiglobally uniformly ultimately bounded and the tracking error converges to a neighborhood of zero by choosing appropriate parameters simulation results demonstrate the effectiveness of the control scheme

approximation based adaptive fuzzy tracking control for a class of nonstrict feedback stochastic nonlinear time delay systems this paper focuses on the problem of approximation based adaptive fuzzy tracking control for a class of stochastic nonlinear time delay systems with a nonstrict feedback structure a variable separation approach is introduced to overcome the design difficulty from the nonstrict feedback structure mamdani type fuzzy logic systems are utilized to model the unknown nonlinear functions in the process of controller design and an adaptive fuzzy tracking controller is systematically designed by using a backstepping technique it is shown that the proposed controller guarantees that all signals in the closed loop system are fourth moment semiglobally uniformly ultimately bounded and the tracking error eventually converges to a small neighborhood of the origin in the sense of mean quartic value simulation results are provided to demonstrate the effectiveness of our results further developments will consider how to generalize the proposed strategy to nonstrict feedback nonlinear systems with input nonlinearities

adaptive neural control for a class of strict feedback nonlinear systems with state time delays this brief proposes a simple control approach for a class of uncertain nonlinear systems with unknown time delays in strict feedback form that is the dynamic surface control technique which can solve the ldquoexplosion of complexityrdquo problem in the backstepping design procedure is extended to nonlinear systems with unknown time delays the unknown time delay effects are removed by using appropriate lyapunov krasovskii functionals and the uncertain nonlinear terms generated by this procedure as well as model uncertainties are approximated by the function approximation technique using neural networks in addition the bounds of external disturbances are estimated by the adaptive technique from the lyapunov stability theorem we prove that all signals in the closed loop system are semiglobally uniformly bounded finally we present simulation results to validate the effectiveness of the proposed approach

tracking control for nonaffine systems a self organizing approximation approach this paper considers tracking control for single input single output nonaffine dynamic systems a performance dependent self organizing approximation based approach is proposed the designer specifies a positive tracking error criterion the self organizing approximation based controller then monitors the tracking performance and adds basis elements only as needed to achieve the tracking specification even though the system is not affine the approach is defined such that the approximated function is independent of the control variable u stability is proved and the self organization is derived in a lyapunov based methodology to illustrate certain novel aspects of the proposed controller a numerical example is included

fault detection and accommodation of a class of nonlinear systems with unknown multiple time delayed faults this paper investigates a fault detection and accommodation fda problem of a class of nonlinear time delay systems in the presence of unknown multiple time delayed faults compared with existing literature a main contribution of this paper is to design a time delay independent fda scheme namely the exact information on time delays is not required to implement the proposed fda scheme under the assumption that the magnitude and occurrence time of multiple faults are unknown we first design a delay independent fault detection scheme with a detection threshold for time delay systems and analyze the fault detectability then an approximation based fault accommodation design activated after the detection of the first fault is presented for compensating multiple faults the robustness of the fault detection scheme and asymptotic stability of the tracking error are established through lyapunov stability analysis a simulation example is used to illustrate the proposed fda scheme

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

robust adaptive neural control for a class of perturbed strict feedback nonlinear systems this paper presents a robust adaptive neural control design for a class of perturbed strict feedback nonlinear system with both completely unknown virtual control coefficients and unknown nonlinearities the unknown nonlinearities comprise two types of nonlinear functions one naturally satisfies the triangularity condition and can be approximated by linearly parameterized neural networks while the other is assumed to be partially known and consists of parametric uncertainties and known bounding functions with the utilization of iterative lyapunov design and neural networks the proposed design procedure expands the class of nonlinear systems for which robust adaptive control approaches have been studied the design method does not require a priori knowledge of the signs of the unknown virtual control coefficients leakage terms are incorporated into the adaptive laws to prevent parameter drifts due to the inherent neural network approximation errors it is proved that the proposed robust adaptive scheme can guarantee the uniform ultimate boundedness of the closed loop system signals the control performance can be guaranteed by an appropriate choice of the design parameters simulation studies are included to illustrate the effectiveness of the proposed approach

adaptive fuzzy control via observer design for uncertain nonlinear systems with unmodeled dynamics in this paper the problems of stability and tracking control for a class of large scale nonlinear systems with unmodeled dynamics are addressed by designing the decentralized adaptive fuzzy output feedback approach because the dynamic surface control technique is introduced the designed controllers can avoid the issue of explosion of complexity which comes from the traditional backstepping design procedure that deals with large scale nonlinear systems with unmodeled dynamics in addition a reduced order observer is designed to estimate those immeasurable states based on the lyapunov stability method it is proven that all the signals in the closed loop system are bounded and the system outputs track the reference signals to a small neighborhood of the origin by choosing the design parameters appropriately the simulation examples are given to verify the effectiveness of the proposed techniques

learning from iss modular adaptive nn control of nonlinear strict feedback systems this paper studies learning from adaptive neural control anc for a class of nonlinear strict feedback systems with unknown affine terms to achieve the purpose of learning a simple input to state stability iss modular anc method is first presented to ensure the boundedness of all the signals in the closed loop system and the convergence of tracking errors in finite time subsequently it is proven that learning with the proposed stable iss modular anc can be achieved the cascade structure and unknown affine terms of the considered systems make it very difficult to achieve learning using existing methods to overcome these difficulties the stable closed loop system in the control process is decomposed into a series of linear time varying ltv perturbed subsystems with the appropriate state transformation using a recursive design the partial persistent excitation condition for the radial basis function neural network nn is established which guarantees exponential stability of ltv perturbed subsystems consequently accurate approximation of the closed loop system dynamics is achieved in a local region along recurrent orbits of closed loop signals and learning is implemented during a closed loop feedback control process the learned knowledge is reused to achieve stability and an improved performance thereby avoiding the tremendous repeated training process of nns simulation studies are given to demonstrate the effectiveness of the proposed method

control of discrete time nonlinear systems with a time varying structure in this paper we present a control methodology for a class of discrete time nonlinear systems that depend on a possibly exogenous scheduling variable this class of systems consists of an interpolation of nonlinear dynamic equations in strict feedback form and it may represent systems with a time varying nonlinear structure moreover this class of systems is able to represent some cases of gain scheduling control takagi sugeno fuzzy systems as well as input output realizations of nonlinear systems which are approximated via localized linearizations we present two control theorems one using what we call a global approach akin to traditional backstepping and a local approach our main result where backstepping is again used but the control law is an interpolation of local control terms an aircraft wing rock regulation problem with varying angle of attack is used to illustrate and compare the two approaches

self organizing approximation based control for higher order systems adaptive approximation based control typically uses approximators with a predefined set of basis functions recently spatially dependent methods have defined self organizing approximators where new locally supported basis elements were incorporated when existing basis elements were insufficiently excited in this paper performance dependent self organizing approximators will be defined the designer specifies a positive tracking error criteria the self organizing approximation based controller then monitors the tracking performance and adds basis elements only as needed to achieve the tracking specification the method of this paper is applicable to general th order input state feedback linearizable systems this paper includes a complete stability analysis and a detailed simulation example

nonlinear adaptive wavelet control using constructive wavelet networks in this paper an adaptive wavelet network based control approach is proposed for highly nonlinear uncertain dynamical systems wavelet network as a kind of universal approximator has two novel properties orthonormality and multiresolution the orthonormal property ensures that adding a new resolution new wavelets does not affect the existing wavelet network that may have been well tuned in the sequel the online adjustment of the structure of the nonlinear adaptive wavelet controller awc can be done in a constructive manner by gradually increasing the network resolution the multiresolution property on the other hand assures a guaranteed improvement of the approximation precision when a new resolution is added in real life problems we are unable to know the adequate size of a network either a neural network nn or a wavelet network to produce the required approximation precision by virtue of the novel wavelet network properties a coarse or very simple structure can be selected first if the system fails to converge after the elapse of a dwell time a new wavelet resolution is considered to be necessary and added directly in this manner the awc can be easily constructed and tuned from the coarse to finer levels until the performance requirement is satisfied the trial and error way of selecting the network structure which may lead to either an inadequate or a highly redundant structure can be avoided in this paper the proposed adaptive wavelet network is applied first to a class of nonlinear dynamical systems with a partially known model and an affine in input structure then the adaptive wavelet network is applied to a class of nonlinear nonaffine dynamical systems

adaptive neural control for a class of stochastic nonlinear systems by backstepping approach this paper addresses adaptive neural control for a class of stochastic nonlinear systems which are not in strict feedback form based on the structural characteristics of radial basis function rbf neural networks nns a backstepping design approach is extended from stochastic strict feedback systems to a class of more general stochastic nonlinear systems in the control design procedure rbf nns are used to approximate unknown nonlinear functions and the backstepping technique is utilized to construct the desired controller the proposed adaptive neural controller guarantees that all the closed loop signals are bounded and the tracking error converges to a sufficiently small neighborhood of the origin two simulation examples are used to illustrate the effectiveness of the proposed approach

observer based adaptive neural network controller for uncertain nonlinear systems with unknown control directions subject to input time delay and saturation abstract this paper addresses the design of an observer based adaptive neural controller for a class of strict feedback nonlinear uncertain systems subject to input delay saturation and unknown direction the input delay has been handled using an integral compensator term in the controller design a neural network observer has been developed to estimate the unmeasured states in the observer design the lipschitz condition has been relaxed to solve the problem of unknown control directions the nussbaum gain function has been applied in the backstepping controller design the explosion of complexity occurred in the traditional backstepping technique has been avoided utilizing the dynamic surface control dsc technique and the designed controller is singularity free it has been shown that all closed loop signals are semi globally uniformly ultimately bounded sguub and the output tracking error converges to a small neighborhood of the origin by choosing the design parameters appropriately the numerical examples illustrate the effectiveness of the proposed control scheme

neural networks based adaptive control for nonlinear time varying delays systems with unknown control direction this paper investigates a neural network nn state observer based adaptive control for a class of time varying delays nonlinear systems with unknown control direction an adaptive neural memoryless observer in which the knowledge of time delay is not used is designed to estimate the system states furthermore by applying the property of the function tanh2 e the function can be defined at 0 and introducing a novel type appropriate lyapunov krasovskii functional an adaptive output feedback controller is constructed via backstepping method which can efficiently avoid the problem of controller singularity and compensate for the time delay it is highly proven that the closed loop systems controller designed by the nn basis function property new kind parameter adaptive law and nussbaum function in detecting the control direction is able to guarantee the semi global uniform ultimate boundedness of all signals and the tracking error can converge to a small neighborhood of zero the characteristic of the proposed approach is that it relaxes any restrictive assumptions of lipschitz condition for the unknown nonlinear continuous functions and the proposed scheme is suitable for the systems with mismatching conditions and unmeasurable states finally two simulation examples are given to illustrate the effectiveness and applicability of the proposed approach

adaptive controller design for tracking and disturbance attenuation in parametric strict feedback nonlinear systems the authors develop a systematic procedure for obtaining robust adaptive controllers that achieve asymptotic tracking and disturbance attenuation for a class of nonlinear systems which are described in the parametric strict feedback form and are subject to additional exogenous disturbance inputs their approach to adaptive control is performance based where the objective for the controller design is not only to find an adaptive controller but also to construct an appropriate cost functional compatible with desired asymptotic tracking and disturbance attenuation specifications with respect to which the adaptive controller is worst case optimal three main issues of the paper are the backstepping methodology worst case identification schemes and singular perturbations analysis closed form expressions have been obtained for an adaptive controller and the corresponding value function a numerical example involving a third order system is given

adaptive neural control of mimo nonlinear state time varying delay systems with unknown dead zones and gain signs in this paper adaptive neural control is proposed for a class of uncertain multi input multi output mimo nonlinear state time varying delay systems in a triangular control structure with unknown nonlinear dead zones and gain signs the design is based on the principle of sliding mode control and the use of nussbaum type functions in solving the problem of the completely unknown control directions the unknown time varying delays are compensated for using appropriate lyapunov krasovskii functionals in the design the approach removes the assumption of linear functions outside the deadband as an added contribution by utilizing the integral lyapunov function and introducing an adaptive compensation term for the upper bound of the residual and optimal approximation error as well as the dead zone disturbance the closed loop control system is proved to be semi globally uniformly ultimately bounded simulation results demonstrate the effectiveness of the approach

on the index integral transformation with nicholson s function as the kernel abstract the integral transformation which is associated with the nicholson function as the kernel is introduced and investigated in the paper this transformation is an integral where integration is with respect to an index of the sum of squares of bessel functions of the first and second kind composition representations and relationships with the meijer k transform the kontorovich lebedev transform the mellin transform and the sine fourier transform are given we also present boundedness properties a parseval type equality and an inversion formula

anderson reverse time modeling optimal control and large deviations abstract a connection between deterministic optimal control and large deviations theory has been known for a number of years whereby the optimal performance index provides information about exit times of stable systems excited by noise and the optimal trajectory provides information about exit trajectories asymptotically as the scalar multiplying the noise tends to zero in this paper a further connection is made to reverse time modeling of stationary diffusions and linear stationary gauss markov discrete time systems in which the drift part of the reverse time model has the same trajectories as the closed loop system resulting from the solution of the same optimal control problem as used for the previous connection

the titchmarsh integral transformation by the index of a bessel function this paper deals with an index integral transformation using bessel functions as kernels it was introduced and studied by titchmarsh in 1946 as an example of a continuous spectrum bessel function expansions in sturm liouville boundary value problems later in the second edition of his book titchmarsh eigenfunction expansions associated with second order differential equations part i 2nd edition clarendon press oxford 1946 in 1962 he corrected his expansion by adding an additional term which contains a combination of an integral and series in this paper the titchmarsh formula is simplified and contains just integrals with bessel and lommel functions as kernels which generate a pair of titchmarsh integral transformations by using the composition properties of the titchmarsh transform and its relationship with the kontorovich lebedev transform lp properties of the titchmarsh transform are investigated and inversion theorems are proved the question of the correctness of titchmarsh s formulas is completely closed by this discussion

adaptive neural output feedback controller design with reduced order observer for a class of uncertain nonlinear siso systems an adaptive output feedback control is studied for uncertain nonlinear single input single output systems with partial unmeasured states in the scheme a reduced order observer roo is designed to estimate those unmeasured states by employing radial basis function neural networks and incorporating the roo into a new backstepping design an adaptive output feedback controller is constructively developed a prominent advantage is its ability to balance the control action between the state feedback and the output feedback in addition the scheme can be still implemented when all the states are not available the stability of the closed loop system is guaranteed in the sense that all the signals are semiglobal uniformly ultimately bounded and the system output tracks the reference signal to a bounded compact set a simulation example is given to validate the effectiveness of the proposed scheme

robust h control of multiple time delay uncertain nonlinear system using fuzzy model and adaptive neural network in this paper a robust control method which combines fuzzy model based control with adaptive neural network control is presented for a class of uncertain nonlinear system with multiple time delay the fuzzy t s model with multiple time delay is adopted for the approximate modeling of the nonlinear system with some unknown uncertainties and fuzzy model based h control law is designed by means of lmi method a full adaptive rbf neural network is added to the fuzzy h control in order to guarantee the robust stability of the controlled system the effect of the unknown uncertainties and the error caused by fuzzy modeling can be overcome by adaptive tuning of the weights centers and widths of the rbf neural network on line and no constraint or matching conditions are required the stability of the designed closed loop system is thus proved the proposed method is applied to a multiple time delay nonlinear chaotic system and the simulation results show that the proposed method cannot only stabilize the chaos systems but has strong robustness against uncertainties and external disturbance

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

stable adaptive tracking of uncertain systems using nonlinearly parametrized on line approximators the design of stable adaptive neural controllers for uncertain nonlinear dynamical systems with unknown nonlinearities is considered the lyapunov synthesis approach is used to develop state feedback adaptive control schemes based on a general class of nonlinearly parametrized on line approximation models the key assumptions are that the system uncertainty satisfies a strict feedback condition and that the network reconstruction error and higher order terms of the on line approximator with respect to the network weights satisfy certain bounding conditions an adaptive bounding design is used to show that the overall neural control system guarantees semi global uniform ultimate boundedness within a neighbourhood of zero tracking error the theoretical results are illustrated through a simulation example

robust adaptive fuzzy controller for nonlinear system using estimation of bounds for approximation errors this paper describes the design of the robust adaptive fuzzy controller for uncertain single input single output nonlinear dynamical systems with unknown nonlinearities these unknown nonlinearities are approximated by the fuzzy system with a set of fuzzy if then rules whose parameters are adjusted on line according to some adaptive laws for the purpose of controlling the output of the nonlinear system to track a given trajectory the lyapunov synthesis approach is used to develop a state feedback adaptive control algorithm based on the adaptive fuzzy model the key assumption is that the reconstruction errors satisfy certain bounding conditions the control law consists of two terms one is the certainty equivalent control and the other is the bounding control a bounding parameter adaptive law is used to obtain this bounding control the overall control system guarantees that the tracking error converges in the small neighborhood of zero and that all signals involved are uniformly bounded it is also shown that in the special case the tracking error exponentially converges to zero even though the approximation errors exist

decentralized adaptive output feedback control for a class of nonlinear large scale systems with unknown time varying delayed interactions in this paper the authors investigate a decentralized adaptive output feedback controller design for large scale nonlinear systems with input saturations and time delayed interconnections unmatched in control inputs the interaction terms with unknown time varying delays are bounded by unknown nonlinear bounding functions including all states of subsystems this point is a main contribution of this paper compared with previous output feedback control approaches which assume that the time delayed bounding functions only depend on measurable output variables the bounding functions are compensated by using appropriate lyapunov krasovskii functionals and the function approximation technique based on neural networks the observer dynamic surface design technique is employed to design the proposed memoryless local controller for each subsystem in addition we prove that all signals in the closed loop system are semiglobally uniformly bounded and control errors converge to an adjustable neighborhood of the origin finally an example is provided to illustrate the effectiveness of the proposed control system

direct adaptive fuzzy control for nonlinear systems with time varying delays this paper focuses on the problem of direct adaptive fuzzy control for nonlinear strict feedback systems with time varying delays based on the razumikhin function approach a novel adaptive fuzzy controller is designed the proposed controller guarantees that the system output converges to a small neighborhood of the reference signal and all the signals in the closed loop system remain bounded different from the existing adaptive fuzzy control methodology the fuzzy logic systems are used to model the desired but unknown control signals rather than the unknown nonlinear functions in the systems as a result the proposed adaptive controller has a simpler form and requires fewer adaptation parameters

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

output feedback control of uncertain nonlinear systems using a self structuring adaptive fuzzy observer this paper describes the design of an output feedback controller based on an adaptive fuzzy observer for uncertain single input single output nonlinear dynamical systems we have focused on the realization of a minimal dynamic order for the adaptive fuzzy observer for this purpose we adopt an adaptive fuzzy observer in which no strictly positive real spr condition is needed and we combine a self structuring scheme with an on line estimation of fuzzy parameters by using this proposed scheme we can reduce the dynamic order of the adaptive output feedback fuzzy control system the lyapunov synthesis approach is used to guarantee a global uniform ultimate boundedness property of the state estimation error and tracking error as well as all other signals in the closed loop system no a priori knowledge of an upper limits on the uncertainties including optimal parameters and modeling errors is required the theoretical results are illustrated through simulation examples

adaptive approximation based regulation control for a class of uncertain nonlinear systems without feedback linearizability in this paper for a general class of uncertain nonlinear cascade systems including unknown dynamics which are not feedback linearizable and cannot be solved by existing approaches an innovative adaptive approximation based regulation control aarc scheme is developed within the framework of adding a power integrator api by deriving adaptive laws for output weights and prediction error compensation pertaining to single hidden layer feedforward network slfn from the lyapunov synthesis a series of slfn based approximators are explicitly constructed to exactly dominate completely unknown dynamics by the virtue of significant advancements on the api technique an adaptive api methodology is eventually established in combination with slfn based adaptive approximators and it contributes to a recursive mechanism for the aarc scheme as a consequence the output regulation error can asymptotically converge to the origin and all other signals of the closed loop system are uniformly ultimately bounded simulation studies and comprehensive comparisons with backstepping and api based approaches demonstrate that the proposed aarc scheme achieves remarkable performance and superiority in dealing with unknown dynamics

index integral transformations of titchmarsh type abstract in 1946 titchmarsh 4 introduced the integral transformation g o re j i x f x d x which depends on the index of a bessel function in connection with a continuous spectral bessel function expansion in sturm liouville boundary value problems here we generalize this transformation by using the composition properties and a relationship with the kontorovich lebedev and the mellin type transformations and we give a variety of index transformations with a linear combination depending on a parameter of real and imaginary parts of a bessel function as it is shown the inversion formula consists of the integral over the index of a lommel function

integrated design of a linear neuro adaptive controller in the presence of norm bounded uncertainties adaptive neural controllers are often criticised for the lack of clear and easy design methodologies that relate adaptive neural network nn design parameters to performance requirements this study proposes a methodology for the design of an integrated linear adaptive model reference controller that guarantees component wise boundedness of the tracking error within an a priori specified compact domain the approach is based on the design of a robust invariant ellipsoidal set where both the nn reconstruction error and the neuro adaptive control are considered as bounded persistent uncertainties we show that all the performance and control requirements for the closed loop system can be expressed as linear matrix inequality constraints this brings the advantage that feasibility and optimal design parameters can be effectively computed while solving a linear optimisation problem an advantage of the method is that it allows a systematic and quantitative evaluation of the interplay between the design param

exit problem and control theory abstract the first part of the paper is concerned with a version of freidlin wentzell exit theorems suitable for control theoretic applications in the second part the general results are specialized to the case of linear systems and two types of stabilizability questions are considered

adaptive control for a class of nonlinear systems with a time varying structure we present a direct adaptive control method for a class of uncertain nonlinear systems with a time varying structure we view the nonlinear systems as composed of a finite number of pieces which are interpolated by functions that depend on a possibly exogenous scheduling variable we assume that each piece is in strict feedback form and show that the method yields stability of all signals in the closed loop as well as convergence of the state vector to a residual set around the equilibrium whose size can be set by the choice of several design parameters the class of systems considered is a generalization of the class of strict feedback systems traditionally considered in the backstepping literature we also provide design guidelines based on l sub 2 bounds on the transient

optimal adaptive fuzzy ftc design for strict feedback nonlinear uncertain systems with actuator faults abstract in this paper the optimal fault tolerant control ftc design problem is investigated for strict feedback nonlinear systems the considered nonlinear systems contain actuator faults which are bias fault and gain fault the problem of actuator faults is solved by utilizing the adaptive compensation technique applying the backstepping design technique a main fault tolerant controller is established via the designed main fault tolerant control strategy the controlled nonlinear system can be converted to an equivalent nonlinear system in affine form subsequently a fuzzy logic system fls is introduced to approximate the unknown cost function and an adaptive fuzzy feedback optimal controller is developed the whole adaptive fuzzy fault tolerant optimal control scheme consists of a main controller and a feedback optimal controller based on the lyapunov theory it is proved that all the signals in the closed loop system are bounded the system output can track a bounded reference signal in addition the proposed control method can guarantee the cost function is the smallest simulation results are provided to illustrate the effectiveness of the proposed fault tolerant optimal control scheme

robust adaptive neural network control for a class of uncertain mimo nonlinear systems with input nonlinearities in this paper robust adaptive neural network nn control is investigated for a general class of uncertain multiple input multiple output mimo nonlinear systems with unknown control coefficient matrices and input nonlinearities for nonsymmetric input nonlinearities of saturation and deadzone variable structure control vsc in combination with backstepping and lyapunov synthesis is proposed for adaptive nn control design with guaranteed stability in the proposed adaptive nn control the usual assumption on nonsingularity of nn approximation for unknown control coefficient matrices and boundary assumption between nn approximation error and control input have been eliminated command filters are presented to implement physical constraints on the virtual control laws then the tedious analytic computations of time derivatives of virtual control laws are canceled it is proved that the proposed robust backstepping control is able to guarantee semiglobal uniform ultimate boundedness of all signals in the closed loop system finally simulation results are presented to illustrate the effectiveness of the proposed adaptive nn control

adaptive neural control for a class of nonlinearly parametric time delay systems in this paper an adaptive neural controller for a class of time delay nonlinear systems with unknown nonlinearities is proposed based on a wavelet neural network wnn online approximation model a state feedback adaptive controller is obtained by constructing a novel integral type lyapunov krasovskii functional which also efficiently overcomes the controller singularity problem it is shown that the proposed method guarantees the semiglobal boundedness of all signals in the adaptive closed loop systems an example is provided to illustrate the application of the approach

robust adaptive control of strict feedback nonlinear systems with unmodelled dynamics and time varying delays abstractthis paper presents a novel robust adaptive neural control scheme which can be taken as a robustification of the adaptive backstepping design the considered class of uncertainties contains unknown non symmetric dead zone inputs time varying delay uncertainties unknown dynamic disturbances and unmodelled dynamics the radial basis function neural networks rbfnns are employed to approximate the unknown nonlinear functions obtained by young s inequality by constructing exponential lyapunov krasovskii functionals the upper bound functions of the time varying delay uncertainties are compensated for using young s inequality and rbfnns the assumptions with respect to unmodelled dynamics are relaxed it is demonstrated that the proposed controller guarantees that all the signals in the closed loop system are semi globally uniformly ultimately bounded and the tracking error eventually converges to a neighbourhood of zero

preventing bursting in approximate adaptive control when using local basis functions aiming to eliminate the bursting phenomena in low gain approximate adaptive controls that utilize local basis functions this work proposes a new robust adaptation method the bursting phenomena occurs when the approximator s adaptive parameters fuzzy centers or neural weights drift to large values eventually causing a sudden increase in state error the existence of bursting often prevents universal approximators with local functions from controlling non minimum phase systems where bursting is associated with excitation of a natural frequency the proposed solution adds two additional approximators to estimate each nonlinear function one learns the output of the approximator used in the control signal the other stores in memory the best weights found so far in the training these parallel representations of the data guide the stable online training and prevent drift of the adaptive parameters simulation results with a generic nonlinear system illustrate the expected improvement in qualitative behavior over traditional robust methods leakage e modification and deadzone when gains are restricted an experiment with a planar two link flexible joint robot confirms the expected improvement in behavior the new method prevents bursting without large sacrifice in performance

optimal control problems over large time intervals abstract the paper focuses on problems of optimal control over a large time interval with end states prescribed for a wide class of systems and performance indices an approximate solution is characterized by piecing together two solutions for two infinite time problems these solutions exhibit similar transient behaviour

a new neuro fds definition for indirect adaptive control of unknown nonlinear systems using a method of parameter hopping the indirect adaptive regulation of unknown nonlinear dynamical systems is considered in this paper the method is based on a new neuro fuzzy dynamical system neuro fds definition which uses the concept of adaptive fuzzy systems afss operating in conjunction with high order neural network functions fhonnfs since the plant is considered unknown we first propose its approximation by a special form of an fds and then the fuzzy rules are approximated by appropriate honnfs thus the identification scheme leads up to a recurrent high order neural network rhonn which however takes into account the fuzzy output partitions of the initial fds the proposed scheme does not require a priori experts information on the number and type of input variable membership functions making it less vulnerable to initial design assumptions once the system is identified around an operation point it is regulated to zero adaptively weight updating laws for the involved honnfs are provided which guarantee that both the identification error and the system states reach zero exponentially fast while keeping all signals in the closed loop bounded the existence of the control signal is always assured by introducing a novel method of parameter hopping which is incorporated in the weight updating law simulations illustrate the potency of the method and comparisons with conventional approaches on benchmarking systems are given also the applicability of the method is tested on a direct current dc motor system where it is shown that by following the proposed procedure one can obtain asymptotic regulation

adaptive neural control for output feedback nonlinear systems using a barrier lyapunov function in this brief adaptive neural control is presented for a class of output feedback nonlinear systems in the presence of unknown functions the unknown functions are handled via on line neural network nn control using only output measurements a barrier lyapunov function blf is introduced to address two open and challenging problems in the neuro control area 1 for any initial compact set how to determine a priori the compact superset on which nn approximation is valid and 2 how to ensure that the arguments of the unknown functions remain within the specified compact superset by ensuring boundedness of the blf we actively constrain the argument of the unknown functions to remain within a compact superset such that the nn approximation conditions hold the semiglobal boundedness of all closed loop signals is ensured and the tracking error converges to a neighborhood of zero simulation results demonstrate the effectiveness of the proposed approach

adaptive neural network control for a class of low triangular structured nonlinear systems in this paper a class of unknown perturbed nonlinear systems is theoretically stabilized by using adaptive neural network control the systems with disturbances and nonaffine unknown functions have low triangular structure which generalizes both strict feedback uncertain systems and pure feedback ones there do not exist any effective methods to stabilize this kind of systems with some new conclusions for nussbaum gain functions ngf and the idea of backstepping semiglobal uniformal and ultimate boundedness of all the signals in the closed loop is proved at equilibrium point the two problems control directions and control singularity are well dealt with the effectiveness of proposed scheme is shown by simulation on a proper nonlinear system

residence time control the problem of residence time controllability in dynamical systems with stochastic perturbations is formulated the solution is given for linear systems with small additive white noise perturbation it is shown that the existence of the desired residence time controller depends on the relationship between the column spaces of the control and noise matrices if the former includes the latter any residence time is possible if this inclusion does not occur the achievable residence time is bounded lower and upper estimates of this bound are given for each of these cases controller design techniques are suggested and illustrative examples are considered the development is based on an asymptotic version of the large deviations theory

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

adaptive neural dynamic surface control of strict feedback nonlinear systems with full state constraints and unmodeled dynamics abstract in this paper the problem of adaptive neural network nn dynamic surface control dsc is discussed for a class of strict feedback nonlinear systems with full state constraints and unmodeled dynamics by introducing a one to one nonlinear mapping the strict feedback system with full state constraints is transformed into a novel pure feedback system without state constraints radial basis function rbf neural networks nns are used to approximate unknown nonlinear continuous functions unmodeled dynamics is dealt with by introducing a dynamical signal using modified dsc and introducing integral type lyapunov function adaptive nn dsc is developed using young s inequality only one parameter is adjusted at each recursive step in the design it is shown that all the signals in the closed loop system are semi global uniform ultimate boundedness sguub and the full state constraints are not violated simulation results are provided to verify the effectiveness of the proposed approach

nn based adaptive tracking control of uncertain nonlinear systems disturbed by unknown covariance noise a class of uncertain nonlinear systems that are additionally driven by unknown covariance noise is considered based on the backstepping technique adaptive neural control schemes are developed to solve the output tracking control problem of such systems as it is proven by stability analysis the proposed controller guarantees that all the error variables are bounded with desired probability in a compact set while the tracking error is mean square semiglobally uniformly ultimately bounded m sguub the tracking performance and the effectiveness of the proposed design are evaluated by simulation results

sampled data adaptive nn tracking control of uncertain nonlinear systems in this paper for a class of single input single output siso uncertain nonlinear systems adaptive neural tracking controllers designed for digital computer implementation are proposed the overall scheme can be considered as a sampled data adaptive neural control system as an intermediate result it is proven that for a sufficiently small sampling period the emulated adaptive neural controller i e the discrete implementation of the continuous time adaptive neural network controller ensures semiglobal uniformly ultimate boundedness of the closed loop system then based on the exact discrete time model a controller redesign is proposed that performs efficiently for sampling periods for which the emulation controller fails the redesigned controller consists of two terms the emulated control law and an extra robustness term designed to increase the order of the perturbation with respect to the sampling period in the lyapunov difference in all cases high order neural networks are employed to approximate the unknown nonlinearities using lyapunov techniques it is proven that for a sufficiently small sampling period the proposed redesigned controller ensures the semiglobal boundedness of all the signals in the closed loop while the output of the system converges to a small neighborhood of the desired trajectory simulation results illustrate the superiority of the proposed scheme with respect to the emulation controller and verify the theoretical analysis

locally weighted online approximation based control for nonaffine systems this paper is concerned with tracking control problems for nonlinear systems that are not affine in the control signal and that contain unknown nonlinearities in the system dynamic equations this paper develops a piecewise linear approximation to the unknown functions during the system operation new control and parameter adaptation algorithms are designed and analyzed using lyapunov like methods the objectives are to achieve semiglobal stability of the state accurate tracking of bounded reference signals contained within a known domain and at least boundedness of the function approximator parameter estimates numerical simulations are included to illustrate the effectiveness of the learning algorithm

adaptive tracking control for stochastic uncertain non linear systems satisfying short and long term cost criteria the tracking control problem for a class of stochastic and uncertain non linear systems is addressed the proposed controller uses suitable radial basis function neural network designs for the approximation of the unknown non linearities while it is arbitrarily regulated in order to effectively penalize the tracking error this regulation is implemented through a risk sensitivity parameter a stability analysis based on lyapunov functions obtained by the backstepping technique proves that all the error variables are bounded in probability simultaneously for any given risk sensitivity parameter the system performance is regulated with respect to both a desired small average tracking error and low long term average cost in accordance to a risk sensitive cost criterion moreover the larger this parameter is the mean square tracking error becomes semiglobally uniformly ultimately bounded in a smaller area while a lower level of a long term average cost is achieved the effectiveness of the design approac

feedback linearization using neural networks abstract for a class of single input single output continuous time nonlinear systems a multilayer neural network based controller that feedback linearizes the system is presented control action is used to achieve tracking performance for a state feedback linearizable but unknown nonlinear system the control structure consists of a feedback linearization portion provided by two neural networks plus a robustifying portion that keeps the control magniture bounded a stability proof is given in the sense of lyapunov it is shown that all the signals in the closed loop system are uniformly ultimately bounded no off line learning phase is needed initialization of the network weights is straightforward

takagi sugeno fuzzy model based indirect adaptive fuzzy observer and controller design this paper proposes the design scheme of the alternative adaptive observer and controller based on the takagi sugeno t s fuzzy model the t s fuzzy modeling and the state feedback control technique are adopted for the simple structure the proposed method maintains consistent performance in the presence of parameter uncertainties and incorporates linguistic fuzzy information from human operators in addition with the simple adaptive state feedback controller it solves the singularity problem which occurs in the inverse dynamics based on the feedback linearization method using lyapunov theory and lipschitz condition the stability analysis is conducted and the adaptive law is derived the proposed method is applied to the stabilization problem of a flexible joint manipulator in order to guarantee its performance

brief paper localized adaptive bounds for approximation based backstepping recent research has established the utility of adaptive bounds on model uncertainty in adaptive approximation based control such bounds have utility both for robust control law design and for self organizing approximators that could adjust the number of basis elements n by adding additional approximation resources in the regions where the approximation error bound is large existing adaptive bounding methods utilize algorithms with global forgetting in this article we investigate methods to develop bounds on approximation accuracy that involve local forgetting the importance of local versus global forgetting is motivated in the text and illustrated with an example

globally stable adaptive backstepping neural network control for uncertain strict feedback systems with tracking accuracy known a priori this paper addresses the problem of globally stable direct adaptive backstepping neural network nn tracking control design for a class of uncertain strict feedback systems under the assumption that the accuracy of the ultimate tracking error is given a priori in contrast to the classical adaptive backstepping nn control schemes this paper analyzes the convergence of the tracking error using barbalat s lemma via some nonnegative functions rather than the positive definite lyapunov functions thus the accuracy of the ultimate tracking error can be determined and adjusted accurately a priori and the closed loop system is guaranteed to be globally uniformly ultimately bounded the main technical novelty is to construct three new n th order continuously differentiable functions which are used to design the control law the virtual control variables and the adaptive laws finally two simulation examples are given to illustrate the effectiveness and advantages of the proposed control method

distributed consensus tracking for multiple uncertain nonlinear strict feedback systems under a directed graph in this brief we study the distributed consensus tracking control problem for multiple strict feedback systems with unknown nonlinearities under a directed graph topology it is assumed that the leader s output is time varying and has been accessed by only a small fraction of followers in a group the distributed dynamic surface design approach is proposed to design local consensus controllers in order to guarantee the consensus tracking between the followers and the leader the function approximation technique using neural networks is employed to compensate unknown nonlinear terms induced from the controller design procedure from the lyapunov stability theorem it is shown that the consensus errors are cooperatively semiglobally uniformly ultimately bounded and converge to an adjustable neighborhood of the origin

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

global stabilization of the generalized mimo triangular systems with singular input output links this work is devoted to the problem of global stabilization for a class of the general multi input and multi output mimo triangular systems which are not feedback linearizable to solve the problem we develop a specific backstepping procedure and generalize some existing results since we deal with the global stabilization for the singular and mimo case the technique of the proof differs from the standard backstepping algorithms

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

adaptive control for output feedback nonlinear systems in the presence of modeling errors the paper is extending output feedback nonlinear control and backstepping approaches to a class of systems approximately diffeomorphic to output feedback systems that include unknown functions the unknown functions are addressed via online function approximation which results in two types of uncertainty parametric uncertainty due to online function approximation and non parametric uncertainty the non parametric uncertainty results from the inability of any function approximator to perfectly model an unknown function and from terms unmodeled by the output feedback form the non parametric terms are assumed to be bounded by unknown constants the backstepping procedure is applied to adapt with respect to both parametric uncertainties and the upper bound on the non parametric uncertainties

stable neural controller design for unknown nonlinear systems using backstepping we propose from an adaptive control perspective a neural controller for a class of unknown minimum phase feedback linearizable nonlinear system with known relative degree the control scheme is based on the backstepping design technique in conjunction with a linearly parametrized neural network structure the resulting controller however moves the complex mechanics involved in a typical backstepping design from off line to online with appropriate choice of the network size and neural basis functions the same controller can be trained online to control different nonlinear plants with the same relative degree with semi global stability as shown by the simple lyapunov analysis meanwhile the controller also preserves some of the performance properties of the standard backstepping controllers simulation results are shown to demonstrate these properties and to compare the neural controller with a standard backstepping controller

prescribed performance distributed consensus control for nonlinear multi agent systems with unknown dead zone input in this paper the problem of prescribed performance distributed output consensus for higher order non affine nonlinear multi agent systems with unknown dead zone input is investigated fuzzy logic

adaptive fuzzy tracking control of nonlinear time delay systems with unknown virtual control coefficients in this paper a novel adaptive fuzzy control scheme is proposed for a class of uncertain single input and single output siso nonlinear time delay systems with the lower triangular form fuzzy logic systems are used to approximate unknown nonlinear functions then the adaptive fuzzy tracking controller is constructed by combining lyapunov krasovskii functionals and the backstepping approach the proposed controller guarantees uniform ultimate boundedness of all the signals in the closed loop system while the tracking error converges to a small neighborhood of the origin an advantage of the proposed control scheme lies in that the number of adaptive parameters is not more than the order of the systems under consideration finally simulation studies are given to demonstrate the effectiveness of the proposed design scheme

adaptive neural control of nonlinear mimo systems with time varying output constraints in this paper adaptive neural control is investigated for a class of unknown multiple input multiple output nonlinear systems with time varying asymmetric output constraints to ensure constraint satisfaction we employ a system transformation technique to transform the original constrained in the sense of the output restrictions system into an equivalent unconstrained one whose stability is sufficient to solve the output constraint problem it is shown that output tracking is achieved without violation of the output constraint more specifically we can shape the system performance arbitrarily on transient and steady state stages with the output evolving in predefined time varying boundaries all the time a single neural network whose weights are tuned online is used in our design to approximate the unknown functions in the system dynamics while the singularity problem of the control coefficient matrix is avoided without assumption on the prior knowledge of control input s bound all the signals in the closed loop system are proved to be semiglobally uniformly ultimately bounded via lyapunov synthesis finally the merits of the proposed controller are verified in the simulation environment

learning from neural control of nonlinear systems in normal form a deterministic learning theory was recently proposed which states that an appropriately designed adaptive neural controller can learn the system internal dynamics while attempting to control a class of simple nonlinear systems in this paper we investigate deterministic learning from adaptive neural control anc of a class of nonlinear systems in normal form with unknown affine terms the existence of the unknown affine terms makes it difficult to achieve learning by using previous methods to overcome the difficulties firstly an extension of a recent result is presented on stability analysis of linear time varying ltv systems then with a state transformation the closed loop control system is transformed into a ltv form for which exponential stability can be guaranteed when a partial persistent excitation pe condition is satisfied accurate approximation of the closed loop control system dynamics is achieved in a local region along a recurrent orbit of closed loop signals consequently learning of control system dynamics i e closed loop identification from adaptive neural control of nonlinear systems with unknown affine terms is implemented

a novel alleviating fuzzy control algorithm for a class of nonlinear stochastic systems in pure feedback form abstract in this paper a novel alleviating computation adaptive fuzzy control scheme is presented for a class of uncertain stochastic nonlinear pure feedback systems different from the existing results that are based on traditional back stepping schemes as well as approximation technique of fuzzy logic systems flss for stochastic nonlinear systems this new approach assumes that the norm of optimal approximation parameter vector of flss is bounded by unknown parameter at each design step of this new approach fewer bounded adaptive parameters need to be adjusted thus this new approach can alleviate the online computation burden and improve the robust control performance meanwhile combining lyapunov theorem analysis it is proven that all the signals in the closed loop system are uniformly ultimately bounded uub and the tracking error can converge to a small neighborhood of zero the good performance of this approach is well demonstrated in a simulation example

adaptive output feedback fuzzy tracking control for a class of nonlinear systems this paper is concerned with the problem of adaptive fuzzy tracking control via output feedback for a class of uncertain single input single output siso strict feedback nonlinear systems the dynamic feedback strategy begins with an input driven filter by utilizing fuzzy logic systems to approximate unknown and desired control input signals directly instead of the unknown nonlinear functions an output feedback fuzzy tracking controller is designed via a backstepping approach it is shown that the proposed fuzzy adaptive output controller can guarantee that all the signals remain bounded and that the tracking error converges to a small neighborhood of the origin simulations results are presented to demonstrate the effectiveness of the proposed methods

distributed adaptive containment control of uncertain nonlinear multi agent systems in strict feedback form abstract this paper presents a distributed containment control approach for uncertain nonlinear strict feedback systems with multiple dynamic leaders under a directed graph topology where the leaders are neighbors of only a subset of the followers the strict feedback followers with nonparametric uncertainties are considered and the local adaptive dynamic surface controller for each follower is designed using only neighbors information to guarantee that all followers converge to the dynamic convex hull spanned by the dynamic leaders where the derivatives of leader signals are not available to implement controllers i e the position information of leaders is only required the function approximation technique using neural networks is employed to estimate nonlinear uncertainty terms derived from the controller design procedure for the followers it is shown that the containment control errors converge to an adjustable neighborhood of the origin

learning from adaptive neural dynamic surface control of strict feedback systems learning plays an essential role in autonomous control systems however how to achieve learning in the nonstationary environment for nonlinear systems is a challenging problem in this paper we present learning method for a class of n th order strict feedback systems by adaptive dynamic surface control dsc technology which achieves the human like ability of learning by doing and doing with learned knowledge to achieve the learning this paper first proposes stable adaptive dsc with auxiliary first order filters which ensures the boundedness of all the signals in the closed loop system and the convergence of tracking errors in a finite time with the help of dsc the derivative of the filter output variable is used as the neural network nn input instead of traditional intermediate variables as a result the proposed adaptive dsc method reduces greatly the dimension of nn inputs especially for high order systems after the stable dsc design we decompose the stable closed loop system into a series of linear time varying perturbed subsystems using a recursive design the recurrent property of nn input variables is easily verified since the complexity is overcome using dsc subsequently the partial persistent excitation condition of the radial basis function nn is satisfied by combining a state transformation accurate approximations of the closed loop system dynamics are recursively achieved in a local region along recurrent orbits then the learning control method using the learned knowledge is proposed to achieve the closed loop stability and the improved control performance simulation studies are performed to demonstrate the proposed scheme can not only reuse the learned knowledge to achieve the better control performance with the faster tracking convergence rate and the smaller tracking error but also greatly alleviate the computational burden because of reducing the number and complexity of nn input variables

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

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 neural control for strict feedback nonlinear systems without backstepping in this brief a new adaptive neurocontrol algorithm for a single input single output siso strict feedback nonlinear system is proposed most of the previous adaptive neural control algorithms for strict feedback nonlinear systems were based on the backstepping scheme which makes the control law and stability analysis very complicated the main contribution of the proposed method is that it demonstrates that the state feedback control of the strict feedback system can be viewed as the output feedback control problem of the system in the normal form as a result the proposed control algorithm is considerably simpler than the previous ones based on backstepping depending heavily on the universal approximation property of the neural network nn only one nn is employed to approximate the lumped uncertain system nonlinearity the lyapunov stability of the nn weights and filtered tracking error is guaranteed in the semiglobal sense