practical adaptive fuzzy tracking control for a class of perturbed nonlinear systems with backlash nonlinearity abstract this paper addresses the adaptive fuzzy tracking control problem for a class of perturbed nonlinear systems with backlash nonlinearity in the proposed control scheme fuzzy logic systems are used to approximate the unknown nonlinearity in each backstepping design and the classic adaptive technique is employed to deal with some unknown parameters the proposed fuzzy controller is developed by introducing some non negative switching functions and novel parameter adaptation learning laws are designed using the modification method it is emphasized that with the help of novel parameter adaptation laws the high gain phenomenon in the previous work can be avoided in addition by borrowing the property of the introduced non negative functions and the inequality technique an adaptive technique is employed to estimate the norm of the ideal weight vector such that the number of adaptation learning parameters online is reduced by employing barbalat s lemma it can be proved that all the signals in the closed loop system remain semi globally uniformly ultimately bounded and especially that the tracking error converges to an accuracy predefined a priori two simulation examples are provided to verify the effectiveness of the proposed control scheme

adaptive neural network tracking control of mimo nonlinear systems with unknown dead zones and control directions in this paper adaptive neural network nn tracking control is investigated for a class of uncertain multiple input multiple output mimo nonlinear systems in triangular control structure with unknown nonsymmetric dead zones and control directions 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 it is shown that the dead zone output can be represented as a simple linear system with a static time varying gain and bounded disturbance by introducing characteristic function by utilizing the integral type lyapunov function and introducing an adaptive compensation term for the upper bound of the optimal approximation error and the dead zone disturbance the closed loop control system is proved to be semiglobally uniformly ultimately bounded with tracking errors converging to zero under the condition that the slopes of unknown dead zones are equal simulation results demonstrate the effectiveness of the approach

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

technical communique sliding mode control with bounded l 2 gain performance of markovian jump singular time delay systems in this paper we investigate the problem of sliding mode control smc of markovian jump singular time delay systems the aim is to consider the bounded 2 gain performance in the analysis of sliding mode dynamics thus to improve the transient performance of the smc system firstly a delay dependent bounded real lemma is proposed for the underlying system to be stochastically admissible while achieving the prescribed bounded 2 gain performance condition an integral type switching surface function is designed by taking the singular matrix into account thus the resulting sliding mode dynamics is a full order singular markovian jump time delay system then the sliding mode dynamics is analyzed and the solvability condition for the desired switching surface function is derived moreover an smc law is synthesized to drive the system trajectories onto the predefined switching surface in a finite time finally a numerical example is provided to illustrate the effectiveness of the proposed techniques

adaptive control for nonlinear mimo time delay systems based on fuzzy approximation this paper focuses on the problem of adaptive control for a class of nonlinear multi input and multi output mimo systems with time delays a state feedback adaptive controller is constructed by backstepping technique fuzzy logic systems are used to approximate unknown nonlinear functions in the process of the controller design the main advantages of the proposed approach are twofold 1 the controller design is independent of the knowledge of the basis functions of fuzzy logic systems and 2 the suggested approach requires only m adaptive laws to control a nonlinear time delay system with m inputs simulation results illustrate the effectiveness of the proposed approach

attractors synthesis for a lotka volterra like system the aim of this paper is to prove numerically via computer graphic simulations that the synthesis algorithmprovided by danca et al 1 can be utilized to synthesize any attractor of a dynamical system modeling a two predator one prey lotka volterra like system the algorithm switches in a periodic deterministic or a random way the control parameter inside a set of a chosen values the obtained attractor is the same with the attractor obtained for parameter value taken as averaged value of the switched control values this simple and effective algorithm relies on a convex property induced in the set of the attractors corresponding to the chosen switching parameters the algorithm was tested successfully on systems depending linearly on the control parameter like lorenz chen rossler networks and other systems

a performance approach to fuzzy control design for nonlinear systems abstract this paper presents a systematic methodology to the design of a decentralized fuzzy logic controller for large scale nonlinear systems a new method which is based on a performance index of sliding mode control is used to derive fuzzy rules and an adaptive algorithm is used to reduce the chattering phenomenon the simulation results of a two inverted pendulum system and a two link manipulator demonstrate that the attractive features of the proposed approach include a smaller residual error and robustness against nonlinear interactions

dynamic surface control for a class of nonlinear systems a method is proposed for designing controllers with arbitrarily small tracking error for uncertain mismatched nonlinear systems in the strict feedback form this method is another synthetic input technique similar to backstepping and multiple surface control methods but with an important addition spl tau 1 low pass filters are included in the design where spl tau is the relative degree of the output to be controlled it is shown that these low pass filters allow a design where the model is not differentiated thus ending the complexity arising due to the explosion of terms that has made other methods difficult to implement in practice the backstepping approach while suffering from the problem of explosion of terms guarantees boundedness of tracking errors globally however the proposed approach while being simpler to implement can only guarantee boundedness of tracking error semiglobally when the nonlinearities in the system are non lipschitz

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

observer based adaptive neural network control for nonlinear stochastic systems with time delay this paper considers the problem of observer based adaptive neural network nn control for a class of single input single output strict feedback nonlinear stochastic systems with unknown time delays dynamic surface control is used to avoid the so called explosion of complexity in the backstepping design process radial basis function nns are directly utilized to approximate the unknown and desired control input signals instead of the unknown nonlinear functions the proposed adaptive nn output feedback controller can guarantee all the signals in the closed loop system to be mean square semi globally uniformly ultimately bounded simulation results are provided to demonstrate the effectiveness of the proposed methods

a novel approach to filter design for t s fuzzy discrete time systems with time varying delay in this paper the problem of l2 l filtering for a class of discrete time takagi sugeno t s fuzzy time varying delay systems is studied our attention is focused on the design of full and reduced order filters that guarantee the filtering error system to be asymptotically stable with a prescribed h performance sufficient conditions for the obtained filtering error system are proposed by applying an input output approach and a two term approximation method which is employed to approximate the time varying delay the corresponding full and reduced order filter design is cast into a convex optimization problem which can be efficiently solved by standard numerical algorithms finally simulation examples are provided to illustrate the effectiveness of the proposed approaches

adaptive fuzzy control for full states constrained systems with nonstrict feedback form and unknown nonlinear dead zone this paper addresses the problem of direct adaptive fuzzy tracking control design for a class of uncertain nonstrict feedback systems with nonlinear dead zone and full state constraints fuzzy logic systems are used to approximate some unknown nonlinear functions and less adjustable parameters are adopted in each backstepping design process this advantage is first to take into account the full state constrained nonstrict feedback systems with input dead zone nonlinearity to guarantee that the full state constraints are not violated a novel adaptive fuzzy controller is developed by introducing barrier lyapunov function with the error variables furthermore it is proved that all the closed loop signals remain semi globally uniformly ultimately bounded and the tracking error converges to a small neighborhood of the origin two simulation examples are provided to verify the effectiveness of the proposed control method

observer based adaptive fuzzy tracking control of mimo stochastic nonlinear systems with unknown control directions and unknown dead zones in this paper an adaptive fuzzy backstepping output feedback tracking control approach is proposed for a class of multi input and multi output mimo stochastic nonlinear systems the mimo stochastic nonlinear systems under study are assumed to possess unstructured uncertainties unknown dead zones and unknown control directions by using a linear state transformation the unknown control coefficients and the unknown slopes characteristic of the dead zones are lumped together and the original system is transformed to a new system on which the control design becomes feasible fuzzy logic systems are used to approximate the unstructured uncertainties and a fuzzy state observer is designed to estimate the unmeasured states by introducing a special nussbaum gain function into the backstepping control design a stable adaptive fuzzy output feedback tracking control scheme is developed the main features of the proposed adaptive control approach are that it can guarantee the stability of the closed loop system and the tracking errors converge to a small neighborhood of zero moreover it can solve the problems of unknown control direction unknown dead zone and unmeasured states simultaneously two simulation examples are provided to show the effectiveness of the proposed approach

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

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

numerical shadowing using componentwise bounds and a sharper fixed point result shadowing provides a means of obtaining global error bounds for approximate solutions of nonlinear differential equations with interesting dynamics in particular for initial value problems with positive lyapunov exponents shadowing breaks down in the presence of zero lyapunov exponents although some results such as shadowing with rescaling of time have been obtained using a reformulation of the original differential equations and an improved fixed point result we take advantage of componentwise local error bounds to use relatively smaller error tolerances in nonhyperbolic and contractive directions i e in directions corresponding to zero and negative lyapunov exponents the result is a decrease in the shadowing global error

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

robust adaptive control of a class of nonlinear systems with unknown dead zone this paper deals with the adaptive control of a class of continuous time nonlinear dynamic systems preceded by an unknown dead zone by using a new description of a dead zone and by exploring the properties of this dead zone model intuitively and mathematically a robust adaptive control scheme is developed without constructing the dead zone inverse the new control scheme ensures global stability of the adaptive system and achieves desired tracking precision simulations performed on a typical nonlinear system illustrate and clarify the validity of this approach

decentralized adaptive output feedback controller design for stochastic nonlinear interconnected systems in this paper the controller design for a class of stochastic interconnected systems with both parametric uncertainties and unknown nonlinear interactions is presented the diffusion terms considered are dependent on the outputs of local subsystems and allowed to be unbounded first by employing decentralized state observers totally decentralized adaptive tracking controllers with suitable parameter adaptive laws are designed to ensure the boundedness in probability of all the signals in the closed loop system it is shown that the tracking errors converge to small residual sets around the origin then for systems with relaxed diffusion vector fields a decentralized adaptive stabilizing scheme is proposed to ensure the boundedness in probability of all signals in the closed loop 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

shadowing orbits of ordinary differential equations abstract a new notion of shadowing of a pseudo orbit an approximate solution of an autonomous system of ordinary differential equations by an associated nearby true orbit is introduced then a general shadowing theorem for finite time which guarantees the existence of shadowing in ordinary differential equations and provides error bounds for the distance between the true and the pseudo orbit in terms of computable quantities is proved the use of this theorem in numerical computations of orbits is outlined

decentralized adaptive fuzzy output feedback control of stochastic nonlinear large scale systems with dynamic uncertainties in this paper centralized and decentralized adaptive fuzzy output feedback control schemes are investigated for a class of stochastic nonlinear interconnected large scale systems with dynamic uncertainties and unmeasured states fuzzy systems are used to approximate the unknown nonlinear functions decentralized k filters are designed to estimate the unmeasured states an available dynamic signal is introduced to dominate the unmodeled dynamics by combining dynamic surface control dsc technique with backstepping design the condition in which the approximation errors are assumed to be bounded is avoided using the defined compact set in the stability analysis the unknown smooth interconnections and black box functions are effectively dealt with using it o formula and chebyshev s inequality it is shown that all the signals in the closed loop system are bounded in probability and the error signals are semi globally uniformly ultimately bounded in mean square or the sense of four moment simulation results demonstrate the effectiveness of the proposed approach

nonlinear quantum dynamical semigroups for many body open systems the notion of a nonlinear quantum dynamical semigroup is introduced and the existence and uniqueness of solutions of the corresponding nonlinear evolution equations are studied in a more abstract framework the construction of nonlinear quantum dynamical semigroups is carried out for two different mean field models first a mean field coupling between a system of noninteracting subsystems and the bath is investigated as examples a nonlinear frictional schrodinger equation and a model for a quantum boltzmann equation are discussed second a many body system with mean field interaction coupled to a bath is considered here again the form of the generator is derived however it cannot be obtained rigorously except for some particular examples finally the quantum ising weiss model is briefly studied

output feedback stabilization for a class of stochastic time delay nonlinear systems this note focuses on a class of stochastic time delay nonlinear systems the problem we address is to design a controller such that the closed loop system is exponentially stable it is shown that the stabilization via output feedback can be solved by a lyapunov based recursive design method

a shadowing lemma approach to global error analysis for initial value odes the authors show that for dynamical systems that possess a type of piecewise hyperbolicity in which there is no decrease in the number of stable modes the global error in a numerical approximation may be obtained as a reasonable magnification of the local error in particular under certain conditions the authors prove the existence of a trajectory on an infinite time interval of the given ordinary differential equation uniformly close to a given numerically computed orbit of the same differential equation by allowing for different initial conditions for finite time intervals a general result is proved for obtaining a posteriori bounds on the global error based on computable quantities and on finding and bounding the norm of a right inverse of a particular matrix two methods for finding and bounding estimating the norm of a right inverse are considered one method is based upon the choice of the pseudo or generalized inverse the other method is based upon solving multipoint boundary value problems bv

design of a unified adaptive fuzzy observer for uncertain nonlinear systems this paper presents an adaptive fuzzy observer for a class of uncertain nonlinear systems more precisely we propose a unified approach for designing such an observer with some design flexibility so that it can be easily adaptable and employed either as a high gain or a sliding mode observer by selecting its gain appropriately additionally we derive a suitable parameter adaptation law so that the proposed observer is robust with respect to ubiquitous fuzzy approximation errors and external disturbances we also show that the observation error is ultimately bounded using a lyapunov approach without having recourse to the usual strictly positive real spr condition or a suitable observation error filtering the effectiveness of the proposed observers is illustrated through two simulation case studies taken from the adaptive fuzzy control literature

discrete time adaptive backstepping nonlinear control via high order neural networks this paper deals with adaptive tracking for discrete time multiple input multiple output mimo nonlinear systems in presence of bounded disturbances in this paper a high order neural network honn structure is used to approximate a control law designed by the backstepping technique applied to a block strict feedback form bsff this paper also includes the respective stability analysis on the basis of the lyapunov approach for the whole controlled system including the extended kalman filter ekf based nn learning algorithm applicability of the scheme is illustrated via simulation for a discrete time nonlinear model of an electric induction motor

stochastic nonlinear stabilization i a backstepping design while the current robust nonlinear control toolbox includes a number of methods for systems affine in deterministic bounded disturbances the problem when the disturbance is unbounded stochastic noise has hardly been considered we present a control design which achieves global asymptotic lyapunov stability in probability for a class of strict feedback nonlinear continuous time systems driven by white noise in a companion paper we develop inverse optimal control laws for general stochastic systems affine in the noise input and for strict feedback systems a reader of this paper needs no prior familiarity with techniques of stochastic control

adaptive backstepping controller design using stochastic small gain theorem a more general class of stochastic nonlinear systems with unmodeled dynamics and uncertain nonlinear functions are considered in this paper with the concept of input to state practical stability isps and nonlinear small gain theorem being extended to stochastic case by combining stochastic small gain theorem with backstepping design technique an adaptive output feedback controller is proposed it is shown that the closed loop system is practically stable in probability a simulation example demonstrates the control scheme

classical and quantum probability we follow the development of probability theory from the beginning of the last century emphasizing that quantum theory is really a generalization of this theory the great achievements of probability theory such as the theory of processes generalized random fields estimation theory and information geometry are reviewed their quantum versions are then described

global error analysis and inertial manifold reduction four types of global error for initial value problems are considered in a common framework they include classical forward error analysis and shadowing error analysis together with extensions of both to include rescaling of time to determine the amplification of the local error that bounds the global error we present a linear analysis similar in spirit to condition number estimation for linear systems of equations we combine these ideas with techniques for dimension reduction of differential equations via a boundary value formulation of numerical inertial manifold reduction these global error concepts are exercised to illustrate their utility on the lorenz equations and inertial manifold reductions of the kuramoto sivashinsky equation

a novel control design on discrete time takagi sugeno fuzzy systems with time varying delays this paper focuses on analyzing a new model transformation of discrete time takagi sugeno t s fuzzy systems with time varying delays and applying it to dynamic output feedback dof controller design a new comparison model is proposed by employing a new approximation for time varying delay state and then a delay partitioning method is used to analyze the scaled small gain of this comparison model a sufficient condition on discrete time t s fuzzy systems with time varying delays which guarantees the corresponding closed loop system to be asymptotically stable and has an induced l2 disturbance attenuation performance is derived by employing the scaled small gain theorem then the solvability condition for the induced l2 dof control is also established by which the dof controller can be solved as linear matrix inequality optimization problems finally examples are provided to illustrate the effectiveness of the proposed approaches

sliding mode control for stochastic systems subject to packet losses this paper investigates the problem of sliding mode control for stochastic system under the effect of packet dropout in this work a new sliding function dependent on the probability of packet dropout is constructed by means of a lyapunov function involved in sliding mode variable and system state both the reachabiltiy and the stability are analyzed simultaneously and the sufficient condition is derived via linear matrix inequalities finally numerical simulation results are given

transversal connecting orbits from shadowing a rigorous numerical method for establishing the existence of a transversal connecting orbit from one hyperbolic periodic orbit to another of a differential equation in mathbb r n is presented as the first component of this method a general shadowing theorem that guarantees the existence of such a connecting orbit near a suitable pseudo connection orbit given the invertibility of a certain operator is proved the second component consists of a refinement procedure for numerically computing a pseudo connecting orbit between two pseudo periodic orbits with sufficiently small local errors so as to satisfy the hypothesis of the theorem the third component consists of a numerical procedure to verify the invertibility of the operator and obtain a rigorous upper bound for the norm of its inverse using this method existence of chaos is demonstrated on examples with transversal homoclinic orbits and with cycles of transversal heteroclinic orbits

convergence of the quantum boltzmann map we consider a non linear map on the space of density matrices which we call the boltzmann map it is the composition of a doubly stochastic mapt on the space ofn body states and the conditional expectation onto the one body space whent is ergodic then the iterates of take any initial state to the uniform distribution if the energy levels are equally spaced andt conserves energy and is ergodic on each energy shell then iterates of take any initial state of finite energy to a canonical distribution

rigorous computational shadowing of orbits of ordinary differential equations the existence of a true orbit near a numerically computed approximate orbit shadowing of autonomous system of ordinary differential equations is investigated a general shadowing theorem for finite time which guarantees the existence of shadowing in ordinary differential equations and provides error bounds for the distance between the true and the approximate orbit in terms of computable quantities is proved the practical use and the effectiveness of this theorem is demonstrated in the numerical computations of chaotic orbits of the lorenz equations

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

stabilization of stochastic nonlinear systems driven by noise of unknown covariance this paper poses and solves a new problem of stochastic nonlinear disturbance attenuation where the task is to make the system solution bounded by a monotone function of the supremum of the covariance of the noise this is a natural stochastic counterpart of the problem of input to state stabilization in the sense of sontag 1989 our development starts with a set of new global stochastic lyapunov theorems for an exemplary class of stochastic strict feedback systems with vanishing nonlinearities where the equilibrium is preserved in the presence of noise we develop an adaptive stabilization scheme based on tuning functions that requires no a priori knowledge of a bound on the covariance next we introduce a control lyapunov function formula for stochastic disturbance attenuation finally we address optimality and solve a differential game problem with the control and the noise covariance as opposing players for strict feedback systems the resulting isaacs equation has a closed form solution

fuzzy adaptive decentralized output feedback control for large scale nonlinear systems with dynamical uncertainties in this paper an adaptive fuzzy decentralized robust output feedback control approach is proposed for a class of large scale strict feedback nonlinear systems with the unmeasured states the large scale nonlinear systems in this paper are assumed to possess the unstructured uncertainties unmodeled dynamics and unknown high frequency gain sign fuzzy logic systems are used to approximate the unstructured uncertainties k filters are designed to estimate the unmeasured states and a dynamical signal and a special nussbaum gain function are introduced into the control design to solve the problem of unknown high frequency gain sign and dominate unmodeled uncertainties respectively based on the backstepping design and adaptive fuzzy control methods an adaptive fuzzy decentralized robust output feedback control scheme is developed it is proved that the proposed adaptive fuzzy control approach can guarantee that all the signals in the closed loop system are uniformly and ultimately bounded and the tracking errors converge to a small neighborhood of the origin the effectiveness of the proposed approach is illustrated by using simulation results

observer based adaptive fuzzy decentralized control for stochastic large scale nonlinear systems with unknown dead zones this paper studies the problem of adaptive fuzzy decentralized output feedback control for a class of uncertain stochastic large scale nonlinear systems the considered systems have unknown nonlinear functions unknown dead zones unmodeled dynamics and unmeasurable state variables therefore fuzzy logic systems are utilized to approximate the unknown nonlinear functions and a fuzzy state observer is established to estimate the unmeasurable states based on the backstepping design and the supply changing function technique a robust adaptive fuzzy decentralized output feedback control approach is developed the proposed control approach can ensure the closed loop system to be input state practically stable isps in probability and accommodate the unmodeled dynamics and unknown dead zones as well the effectiveness of the proposed control approach is illustrated by a simulation example

technical communique sliding mode control of singular stochastic hybrid systems this paper is concerned with the sliding mode control smc of nonlinear singular stochastic systems with markovian switching an integral sliding surface function is designed and the resulting sliding mode dynamics is a full order markovian jump singular stochastic system by introducing some specified matrices a new sufficient condition is proposed in terms of strict linear matrix inequality lmi which guarantees the stochastic stability of the sliding mode dynamics then a smc law is synthesized for reaching motion moreover when there exists an external disturbance the 2 disturbance attenuation performance is analyzed for the sliding mode dynamics some related sufficient conditions are also established

shadowing orbits of ordinary differential equations on invariant submanifolds a finite time shadowing theorem for autonomous ordinary differential equations is presented under consideration is the case were there exists a twice continuously differentiable function g mapping phase space into lrtm with the property that for a particular regular value c of g the submanifold g 1 c is invariant under the flow the main theorem gives a condition which implies that an approximate solution lying close to g1 c is uniformly close to a true solution lying in g 1 c applications of this theorem to computer generated approximate orbits are discussed

fuzzy filter design for ito stochastic systems with application to sensor fault detection the paper deals with the robust fault detection problem for takagi sugeno t s fuzzy ito stochastic systems our aim is to develop a robust fault detection approach to the t s fuzzy systems with brownian motion by using a general observer based fault detection filter as a residual generator the robust fault detection is formulated as a filtering problem attention is focused on the design of both the fuzzy rule independent and the fuzzy rule dependent fault detection filters guaranteeing a prescribed noise attenuation level in an hinfin sense sufficient conditions are proposed to guarantee the mean square asymptotic stability with an hinfin performance for the fault detection system the corresponding solvability conditions for the desired fuzzy rule independent and fuzzy rule dependent fault detection filters are also established finally a numerical example is provided to illustrate the effectiveness of the proposed theory

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

stabilization for t s model based uncertain stochastic systems this paper considers the stabilization problem of a class of uncertain ito stochastic fuzzy systems driven by a multidimensional wiener process the uncertainty modeled in the systems is of the linear fractional type which includes the norm bounded uncertainty as a special case the objective is to design a state feedback fuzzy controller such that the closed loop system is robustly asymptotically stable under a stochastic setting by using a stochastic lyapunov approach sufficiency conditions for the stability and stabilization of this class of systems are established based on a novel matrix decomposition technique the derived stability conditions are then employed to design controllers which stabilize the uncertain ito stochastic fuzzy systems two simulation examples are given to illustrate the effectiveness of the approaches proposed

optimal adaptive solution of piecewise regular systems of ivps with unknown switching hypersurface we study the solution of piecewise regular systems of ivps with a switching hypersurface defined by an unknown event function our aim is to design an algorithm that is not based on heuristic steps it does not use information on the event function and preserves the order known for regular systems the algorithm is based on the adaptive mesh which differs from the equidistant mesh only by a single point we provide a rigorous that is independent of heuristic arguments analysis of its error and cost

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

brief paper output feedback stabilization for stochastic nonlinear systems whose linearizations are not stabilizable this brief paper investigates the problem of output feedback stabilization for a class of high order stochastic nonlinear systems which are neither necessarily feedback linearizable nor affine in the control input based on the ideas of the homogeneous systems theory and the adding a power integrator technique an output feedback controller is constructed to ensure that the equilibrium at the origin of the closed loop system is globally asymptotically stable gas in probability the efficiency of the output feedback controller is demonstrated by a simulation example

feedback stabilization of affine in the control stochastic differential systems by the control lyapunov function method the purpose of this paper is to study the asymptotic stability in probability of affine in the control stochastic differential systems sufficient conditions for the existence of control lyapunov functions leading to the existence of stabilizing feedback laws which are smooth except possibly at the equilibrium point of the system are provided

a numerical c 1 shadowing result for retarded functional differential equations the aim of the present paper is to give a numerical c1 shadowing between the exact solutions of a functional differential equation and its numerical approximations the shadowing result is obtained by comparing exact solutions with numerical approximation which do not share the same initial value behavior of stable manifolds of functional differential equations under numerics will follow from the shadowing result

stable adaptive fuzzy sliding mode control of interconnected systems the problem of stable adaptive fuzzy control for a class of interconnected systems with unknown control gains is studied in this paper by using fuzzy modeling method a design scheme of an adaptive fuzzy controller is proposed the design is capable of incorporating linguistic and numerical information into controllers by theoretical analysis the closed loop adaptive fuzzy control system is proved to be globally stable in the sense that all signals involved are bounded with tracking errors converging to a neighborhood of zero

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

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

hyperbolic trajectories of time discretizations abstract the problem of persistence of trajectories of time discretizations is addressed analogues of essential concepts in the theory of hyperbolic flows are formulated for time discretizations we show these are appropriate by proving that the underlying flow inherits a hyperbolic trajectory of the time discretization approximation properties and inherited hyperbolicity properties are analyzed here explicit estimates in terms of the key problem parameters are provided an auxiliary result on roughness of exponential dichotomies for time discretizations may be of independent interest directions of future research are indicated

optimal solution of a class of non autonomous initial value problems with unknown singularities in this paper we are interested in a rigorous analysis of the solution of a class of initial value problems with singularities we consider scalar non autonomous ivps with separated variables and one unknown singularity in each variable which leads to four unknown events in the two dimensional space many algorithms proposed in the literature for singular ivps are practically oriented they do not avoid heuristic arguments and are often checked for efficiency by numerical experiments we design an adaptive algorithm with no heuristic steps for solving the considered problems and provide rigorous bounds on the error we show that in spite of the presence of singularities the algorithm preserves the optimal error known for the regular case lower bounds on the error of any algorithm in the case of a larger number of singularities are also discussed

decentralized adaptive output feedback stabilization for large scale stochastic nonlinear systems in this paper the problem of decentralized adaptive output feedback stabilization is investigated for large scale stochastic nonlinear systems with three types of uncertainties including parametric uncertainties nonlinear uncertain interactions and stochastic inverse dynamics under the assumption that the inverse dynamics of the subsystems are stochastic input to state stable an adaptive output feedback controller is constructively designed by the backstepping method it is shown that under some general conditions the closed loop system trajectories are bounded in probability and the outputs can be regulated into a small neighborhood of the origin in probability in addition the equilibrium of interest is globally stable in probability and the outputs can be regulated to the origin almost surely when the drift and diffusion vector fields vanish at the origin the contributions of the work are characterized by the following novel features 1 even for centralized single input single output systems this paper presents a first result in stochastic nonlinear adaptive output feedback asymptotic stabilization 2 the methodology previously developed for deterministic large scale systems is generalized to stochastic ones at the same time novel small gain conditions for small signals are identified in the setting of stochastic systems design 3 both drift and diffusion vector fields are allowed to be dependent not only on the measurable outputs but some unmeasurable states 4 parameter update laws are used to counteract the parametric uncertainty existing in both drift and diffusion vector fields which may appear nonlinearly 5 the concept of stochastic input to state stability and the method of changing supply functions are adapted for the first time to deal with stochastic and nonlinear inverse dynamics in the context of decentralized control

adaptive fuzzy output feedback control for output constrained nonlinear systems in the presence of input saturation abstract in this paper the problem of adaptive fuzzy output feedback control is investigated for a class of output constrained uncertain nonlinear systems with input saturation and unmeasured states to address output constraint and input constraint a barrier lyapunov function and an auxiliary design system are employed respectively fuzzy logic systems are utilized to approximate the unknown nonlinear functions and a fuzzy state observer is designed to estimate the unmeasured states by utilizing the fuzzy state observer and combining the adaptive backstepping technique with adaptive fuzzy control design an observer based adaptive fuzzy output feedback control approach is developed it is proved that the proposed control approach can guarantee that all the signals in the closed loop system are bounded and the input and output constraints are circumvented simultaneously a numerical example is provided to illustrate the effectiveness of the proposed approach

global adaptive neural control for strict feedback time delay systems with predefined output accuracy this paper focuses on the stabilization problem for a class of nonlinear strict feedback systems with disturbances and time delay by constructing some nonnegative functionals a multiswitching based adaptive backstepping neural state feedback controller is designed compared with all the existing control methodologies for the uncertain time delay systems the outstanding merits of the proposed control scheme are presented as follows first the controller guarantees that all the signals in the closed loop system remain globally bounded meanwhile the system output achieves an accuracy that is given a priori according to the practical requirements second in contrast to the classical adaptive backstepping neural control schemes we analyze the convergence of the tracking error by using barbalat s lemma instead of lyapunov stability theory third the main technical novelty is to construct three new nth order continuously differentiable functions which are used to design the actual controller the virtual control variables and the adaptive laws two simulation examples are provided to illustrate the effectiveness and advantage of the proposed control scheme

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

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

adaptive fuzzy tracking control for stochastic nonlinear systems with unknown time varying delays an adaptive fuzzy controller is presented for a class of stochastic nonlinear systems an quadratic function is constructed to give the condition of the stability of systems the scheme guarantees the stability of closed loop system in the mean square sense the drawback of the quartic moment approach is overcome and the method is simplified this paper addresses the problem of adaptive tracking control for a class of stochastic strict feedback nonlinear time varying delays systems using fuzzy logic systems fls in this paper quadratic functions are used as lyapunov functions to analyze the stability of systems other than the fourth moment approach proposed by h deng and m krstic and the hyperbolic tangent functions are introduced to deal with the hessian terms this approach overcomes the drawback of the traditional quadratic moment approach and reduce the complexity of design procedure and controller based on the backstepping technique the appropriate lyapunov krasovskii functionals and the fls the adaptive fuzzy controller is well designed the proposed adaptive fuzzy controller guarantees that all the signals in the closed loop system are bounded in probability and the tracking error can converge to a small residual set around the origin in the mean square sense

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

a novel robust adaptive fuzzy tracking control for a class of nonlinearmulti input multi output systems robust adaptive fuzzy tracking control of a class of uncertain multi input multi output nonlinear systems with coupled interconnections is considered in this paper takagi sugeno t s fuzzy systems are used to approximate the unknown system functions a novel adaptive control scheme is developed on the basis of the so called dynamic surface control and minimal learning parameters techniques the proposed scheme has following two key features first the number of parameters updated online for each subsystem is reduced to one and both problems of curse of dimension for high dimensional systems and explosion of complexity inherent in the conventional backstepping methods are circumvented second the potential controller singularity problem in some of the existing adaptive control schemes with feedback linearization techniques is overcome it is shown via lyapunov theory that all the signals in the closed loop system are semiglobally uniformly ultimately bounded finally simulation results via two examples are presented to demonstrate the effectiveness and advantages of the proposed scheme

stochastic adaptive backstepping controller design by introducing dynamic signal and changing supply function a more general class of stochastic non linear systems with unmodelled dynamics and uncertain non linear functions are considered in this paper with the concept of isps being extended to stochastic case by combining changing supply function technique with backstepping design technique an adaptive output feedback controller is proposed it is shown that all the solutions of the closed loop system are uniformly bounded in probability and the output can be regulated to an arbitrarily small neighbourhood of the origin in probability a simulation example demonstrates the control scheme

single parameter learning based fuzzy fault tolerant output feedback dynamic surface control of constrained input nonlinear systems abstract this paper addresses the problem of adaptive fuzzy fault tolerant dynamic surface control for a class of constrained input nonlinear systems to resolve this problem the design of an observer based single parameter learning spl control method using output feedback is proposed the takagi sugeno t s fuzzy system is used to identify and approximate online the uncertain nonlinear dynamics requiring no knowledge the barriers that restrict the applications of the traditional backstepping and approximation based approach including the explosion of complexity and the dimension curse problems are circumvented via dynamic surface control and spl techniques the merit of the proposed method lies in that only one parameter in the entire control scheme requires online adjustment regardless of the number of parameters in the t s fuzzy system that characterizes the fuzzy rules the calculation burden in this sense is reduced to the extent of the minimum value the truncated adaptation method is used to avoid the chattering and instability caused by constrained input it is shown with rigorous proof using the lyapunov and invariant set theorems that all the closed loop signals are guaranteed semi globally uniformly ultimately bounded the output tracking error is adjustable by means of design parameters in an explicit form and can be adjusted to an arbitrarily small value around zero by appropriately chosen control parameters even under faulty and constrained actuators simulation and comparative results are provided to demonstrate the effectiveness of the proposed control approach

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

output feedback regulation of stochastic nonlinear systems with stochastic iiss inverse dynamics this paper develops a unifying framework for output feedback regulation of stochastic nonlinear systems with more general stochastic inverse dynamics the contributions of this work are characterized by the following novel features 1 motivated by the concept of integral input to state stability iiss in deterministic systems and stochastic input to state stability siss using lyapunov function in stochastic systems a concept of stochastic integral input to state stability siiss using lyapunov function is first introduced two important properties of siiss are obtained i siiss is strictly weaker than siss using lyapunov function ii siiss is stronger than the minimum phase property however only under the minimum phase assumption there is no dynamic output feedback control law for global stabilization in probability 2 almost sure boundedness a reasonable and stronger concept than boundedness in probability is introduced the purpose of introducing the concept is to prove the boundedness and convergence of some signals in the closed loop control system 3 some important mathematical tools which play an essential role in the boundedness and convergence analysis of the closed loop system are established 4 a unifying framework is proposed to design a dynamic output feedback control law which drives the states to the origin almost surely while maintaining all the closed loop signals bounded almost surely

adaptive fuzzy output feedback control of mimo nonlinear systems with unknown dead zone inputs this paper is concerned with the problem of adaptive fuzzy tracking control for a class of multi input and multi output mimo strict feedback nonlinear systems with both unknown nonsymmetric dead zone inputs and immeasurable states in this research fuzzy logic systems are utilized to evaluate the unknown nonlinear functions and a fuzzy adaptive state observer is established to estimate the unmeasured states based on the information of the bounds of the dead zone slopes as well as treating the time varying inputs coefficients as a system uncertainty a new adaptive fuzzy output feedback control approach is developed via the backstepping recursive design technique it is shown that the proposed control approach can assure that all the signals of the resulting closed loop system are semiglobally uniformly ultimately bounded it is also shown that the observer and tracking errors converge to a small neighborhood of the origin by selecting appropriate design parameters simulation examples are also provided to illustrate the effectiveness of the proposed approach

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

adaptive fuzzy output feedback control of uncertain nonlinear systems with unknown backlash like hysteresis in this paper the problem of adaptive fuzzy output feedback control is investigated for a class of uncertain nonlinear systems with unknown backlash like hysteresis and unmeasured states the fuzzy logic systems are used to approximate the nonlinear system functions and a fuzzy state observer is designed to estimate the unmeasured states by utilizing the fuzzy state observer and combining the adaptive backstepping technique with adaptive fuzzy control design an observer based adaptive fuzzy output feedback control approach is developed it is proved that the proposed control approach can guarantee that all the signals in the closed loop system are semi globally uniformly ultimately bounded suub and both observer error and tracking error can converge to a small neighborhood of the origin two simulations are included to illustrate the effectiveness of the proposed approach

on designing of sliding mode control for stochastic jump systems in this note we consider the problems of stochastic stability and sliding mode control for a class of linear continuous time systems with stochastic jumps in which the jumping parameters are modeled as a continuous time discrete state homogeneous markov process with right continuous trajectories taking values in a finite set by using linear matrix inequalities lmis approach sufficient conditions are proposed to guarantee the stochastic stability of the underlying system then a reaching motion controller is designed such that the resulting closed loop system can be driven onto the desired sliding surface in a limited time it has been shown that the sliding mode control problem for the markovian jump systems is solvable if a set of coupled lmis have solutions a numerical example is given to show the potential of the proposed techniques

robust control on saturated markov jump systems with missing information in this paper a robust h controller is designed for saturated markov jump systems with uncertainties and time varying transition probabilities the time varying transition probability uncertainty is described as a polytope set stochastic stability is analyzed for the underlying systems by lyapunov function approach and a sufficient condition is derived to design controllers such that the resulting closed loop system is stochastically stable and a prescribed h performance is also achieved furthermore the attraction domain of this markov jump system is estimated and evaluated a simulation example is given to show the effectiveness of the developed techniques

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 adaptive quantized output feedback tracking control for switched nonlinear systems with input quantization in this paper the problem of adaptive fuzzy quantized output feedback control is investigated for a class of uncertain switched nonlinear systems in strict feedback form the considered switched systems contain unknown nonlinearities hysteretic quantized input and without requiring the system states being available for measurement fuzzy logic systems are utilized to approximate the unknown nonlinear functions and a switched fuzzy state observer is designed to estimate the unmeasured states the hysteretic quantized input is implemented to avoid the oscillation caused by logarithmic quantizer and decomposed into two bounded nonlinear functions based on the estimated states and using the backstepping design principle an adaptive fuzzy quantized output feedback control scheme is developed it is proved that whole adaptive fuzzy quantized control scheme can guarantee that all the variables in the closed loop system are bounded under a class of switching signals with average dwell time and also that the system output can track a given reference signal as closely as possible the simulation results are given to check the effectiveness of the proposed approach

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

quantum dynamical semigroups for diffusion models with hartree interaction we consider a class of evolution equations in lindblad form which model the dynamics of dissipative quantum mechanical systems with mean field interaction particularly this class includes the so called quantum fokker planck poisson model the existence and uniqueness of global in time mass preserving solutions is proved thus establishing the existence of a nonlinear conservative quantum dynamical semigroup the mathematical difficulties stem from combining an unbounded lindblad generator with the hartree nonlinearity

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

rigorous shadowing of numerical solutions of ordinary differential equations by containment an exact trajectory of a dynamical system lying close to a numerical trajectory is called a shadow we present a general purpose method for proving the existence of finite time shadows of numerical ode integrations of arbitrary dimension in which some measure of hyperbolicity is present and there are either 0 or 1 expanding modes or 0 or 1 contracting modes much of the rigor is provided automatically by interval arithmetic and validated ode integration software that is freely available the method is a generalization of a previously published containment process that was applicable only to two dimensional maps we extend it to handle maps of arbitrary dimension with the above restrictions and finally to odes the method involves building n cubes around each point of the discrete numerical trajectory through which the shadow is guaranteed to pass at appropriate times the proof consists of two steps first the rigorous computational verification of a simple geometric property which we call the inductive containment property and second a simple geometric argument showing that this property implies the existence of a shadow the computational step is almost entirely automated and easily adaptable to any ode problem the method allows for the rescaling of time which is a necessary ingredient for successfully shadowing odes finally the method is local in the sense that it builds the shadow inductively requiring information only from the most recent integration step rather than more global information typical of several other methods the method produces shadows of comparable length and distance to all currently published results finally we conjecture that the inductive containment property implies the existence of a shadow without restriction on the number of expanding and contracting modes although proof currently eludes us