stochastic mechanics of reciprocal diffusions the dynamics and kinematics of reciprocal diffusions were examined in a previous paper j math phys 34 1846 1993 where it was shown that reciprocal diffusions admit a chain of conservation laws which close after the first two laws for two disjoint subclasses of reciprocal diffusions the markov and quantum diffusions for the case of quantum diffusions the conservation laws are equivalent to schrodinger s equation the markov diffusions were employed by schrodinger sitzungsber preuss akad wiss phys math kl 144 1931 ann inst h poincare 2 269 1932 nelson dynamical theories of brownian motion princeton university princeton nj 1967 quantum fluctuations princeton university princeton nj 1985 and other researchers to develop stochastic formulations of quantum mechanics called stochastic mechanics we propose here an alternative version of stochastic mechanics based on quantum diffusions a procedure is presented for constructing the quantum diffusion associated to a given wave function it is shown that quantum diffusions satisfy the uncertainty principle and have a locality property whereby given two dynamically uncoupled but statistically correlated particles the marginal statistics of each particle depend only on the local fields to which the particle is subjected however like wigner s joint probability distribution for the position and momentum of a particle the finite joint probability densities of quantum diffusions may take negative values

finite element methods for active contour models and balloons for 2 d and 3 d images the use of energy minimizing curves known as snakes to extract features of interest in images has been introduced by kass witkin and terzopoulos 1987 a balloon model was introduced by cohen 1991 as a way to generalize and solve some of the problems encountered with the original method a 3 d generalization of the balloon model as a 3 d deformable surface which evolves in 3 d images is presented it is deformed under the action of internal and external forces attracting the surface toward detected edgels by means of an attraction potential we also show properties of energy minimizing surfaces concerning their relationship with 3 d edge points to solve the minimization problem for a surface two simplified approaches are shown first defining a 3 d surface as a series of 2 d planar curves then after comparing finite element method and finite difference method in the 2 d problem we solve the 3 d model using the finite element method yielding greater stability and faster convergence this model is applied for segmenting magnetic resonance images

control lyapunov razumikhin functions and robust stabilization of time delay systems motivated by control lyapunov functions and razumikhin theorems on stability of time delay systems we introduce the concept of control lyapunov razumikhin functions clrf the main reason for considering clrfs is construction of robust stabilizing control laws for time delay systems most existing universal formulas that apply to clfs are not applicable to clrfs it turns out that the domination redesign control law applies achieving global practical stability and under an additional assumption global asymptotic stability this additional assumption is satisfied in the practically important case when the quadratic part of a clrf is itself a clrf for the jacobian linearization of the system the clrf based domination redesign possesses robustness to input unmodeled dynamics including an infinite gain margin while in general construction of clrfs is an open problem we show that for several classes of time delay systems a clrf can be constructed in a systematic way

adaptive dynamic surface control a simplified algorithm for adaptive backstepping control of nonlinear systems in this paper we propose a new algorithm for adaptive backstepping control of non linear uncertain systems current backstepping algorithms require repeated differentiations of the modelled non linearities the addition of n first order low pass filters allows the algorithms to be implemented without differentiating any model non linearities the uncertainties are assumed to be linear in the unknown constant parameters the combined adaptive backstepping first order filter system is proven to be semi globally stable for sufficiently fast filters by a singular perturbation approach

approximation based control of nonlinear mimo time delay systems approximation based control is presented for a class of multi input multi output mimo nonlinear systems in block triangular form with unknown state delays neural networks nns are utilized to approximate and compensate for unknown functions in the system dynamics including the unknown bounds of the functions of delayed states the use of a separation technique removes the need for any assumption on the function of delayed states and allows the handling of multiple delays in each function of delayed states by combining the use of lyapunov krasovskii functionals and adaptive nn backstepping the proposed control guarantees that all closed loop signals remain bounded while the outputs converge to a neighborhood of the desired trajectories simulation results demonstrate the effectiveness of the proposed scheme

modified neural dynamic surface approach to output feedback of mimo nonlinear systems we report an adaptive output feedback dynamic surface control dsc maintaining the prescribed performance for a class of uncertain nonlinear systems with multiinput and multioutput designing neural network observers and modifying the dsc method achieves several control objectives first to achieve output feedback control the finite time echo state networks esn observer with fast convergence is designed to obtain the online system states thus the immeasurable states in traditional state feedback control are estimated and the unknown functions are approximated by esn then a modified dsc approach is developed by introducing a high order sliding mode differentiator to replace the first order filter in each step thus the effect of filter performance on closed loop stability is reduced furthermore the input to state stability guarantees that all signals of the whole closed loop system are semiglobally uniformly ultimately bounded specifically the performance functions make the tracking errors converge to a compact set around equilibrium two numerical examples illustrated the proposed control scheme with satisfactory results

polynomial filtering for linear discrete time non gaussian systems in this work we propose a new filtering approach for linear discrete time non gaussian systems that generalizes a previous result concerning quadratic filtering a de santis a germani and m raimondi ieee trans automat control 40 1995 pp 1274 1278 a recursive nu th order polynomial estimate of finite memory delta is achieved by defining a suitable extended state which allows one to solve the filtering problem via the classical kalman linear scheme the resulting estimate will be the mean square optimal one among those estimators that take into account nu polynomials of the last delta observations numerical simulations show the effectiveness of the proposed method

dynamic 3d models with local and global deformations deformable superquadrics the authors present a physically based approach to fitting complex three dimensional shapes using a novel class of dynamic models that can deform both locally and globally they formulate the deformable superquadrics which incorporate the global shape parameters of a conventional superellipsoid with the local degrees of freedom of a spline the model s six global deformational degrees of freedom capture gross shape features from visual data and provide salient part descriptors for efficient indexing into a database of stored models the local deformation parameters reconstruct the details of complex shapes that the global abstraction misses the equations of motion which govern the behavior of deformable superquadrics make them responsive to externally applied forces the authors fit models to visual data by transforming the data into forces and simulating the equations of motion through time to adjust the translational rotational and deformational degrees of freedom of the models model fitting experiments involving 2d monocular image data and 3d range data are presented

globally stable adaptive system design for minimum phase siso plants with input saturation model reference adaptive control problem for single input single output time invariant continuous time plants with input saturation is considered with main attention focused on global properties a sufficient condition is presented and a new design method of adaptive control systems is proposed if a priori information about the plant is available to choose the reference model and the reference input so that the sufficient condition holds the closed loop adaptive control system designed by the proposed method can have global stability and globally output tracking property it is shown that the sufficient condition becomes necessary in some cases

bayesian inference for a covariance matrix a flexible class of prior distributions is proposed for the covariance matrix of a multivariate normal distribution yielding much more general hierarchical and empirical bayes smoothing and inference when compared with a conjugate analysis involving an inverted wishart distribution a likelihood approximation is obtained for the matrix logarithm of the covariance matrix via bellman s iterative solution to a volterra integral equation exact and approximate bayesian empirical and hierarchical bayesian estimation and finite sample inference techniques are developed some risk and asymptotic frequency properties are investigated a subset of the project talent american high school data is analyzed applications and extensions to multivariate analysis including a generalized linear model for covariance matrices are indicated

linear estimation of boundary value stochastic processes part i the role and construction of complementary models this paper presents a substantial extension of the method of complementary models for minimum variance linear estimation introduced by weinert and desai in their important paper 1 specifically the method of complementary models is extended to solve estimation problems for both discrete and continuous parameter linear boundary value stochastic processes in one and higher dimensions a major contribution of this paper is an application of green s identity in deriving a differential operator representation of the estimator to clarify the development and to illustrate the range of applications of our approach two brief examples are provided one is a 1 d discrete two point boundary value process and the other is a 2 d process governed by poisson s equation on the unit disk

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

nonconjugate bayesian estimation of covariance matrices and its use in hierarchical models abstract the problem of estimating a covariance matrix in small samples has been considered by several authors following early work by stein this problem can be especially important in hierarchical models where the standard errors of fixed and random effects depend on estimation of the covariance matrix of the distribution of the random effects we propose a set of hierarchical priors hps for the covariance matrix that produce posterior shrinkage toward a specified structure here we examine shrinkage toward diagonality we then address the computational difficulties raised by incorporating these priors and nonconjugate priors in general into hierarchical models we apply a combination of approximation gibbs sampling possibly with a metropolis step and importance reweighting to fit the models and compare this hybrid approach to alternative markov chain monte carlo methods our investigation involves three alternative hps the first works with the spectral decomposition of the covariance matrix an

brief semi global robust stabilization of mimo nonlinear systems by partial state and dynamic output feedback we study the problem of semi global robust stabilization for a class of multi input multi output mimo uncertain nonlinear systems which cannot be transformed via a change of coordinates and a state feedback into a lower dimensional zero dynamics driven by a set of chains of integrators but more complicated interconnected structures the systems considered here which distinguish from those studied early in the literature possess a new feature that they are non affine in the control inputs sufficient conditions are presented for the existence of a linear high gain partial state controller and or a nonlinear dynamic output compensator achieving robust semi global asymptotic stability both the partial state and output dynamic controllers are also explicitly constructed

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

adaptive output feedback control for nonlinear time delay systems by fuzzy approximation approach in this paper the problem of adaptive fuzzy tracking control via output feedback for a class of uncertain single input single output siso strict feedback nonlinear systems with unknown time delay functions is investigated dynamic surface control technique is used to avoid the problem of explosion of complexity which is caused by repeated differentiation of certain nonlinear functions in the backstepping design process in addition the fuzzy logic systems are utilized to approximate the unknown and desired control input signals directly instead of the unknown nonlinear functions the designed controller can guarantee all the signals in the closed loop system to be semiglobally uniformly ultimately bounded and the tracking error to converge to a small neighborhood of the origin simulations results are provided to demonstrate the effectiveness of the proposed methods

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

snakes active contour models a snake is an energy minimizing spline guided by external constraint forces and influenced by image forces that pull it toward features such as lines and edges snakes are active contour models they lock onto nearby edges localizing them accurately scale space continuation can be used to enlarge the capture region surrounding a feature snakes provide a unified account of a number of visual problems including detection of edges lines and subjective contours motion tracking and stereo matching we have used snakes successfully for interactive interpretation in which user imposed constraint forces guide the snake near features of interest

gaussian conditionally markov sequences singular nonsingular most existing results about modeling and characterizing gaussian markov reciprocal and conditionally markov cm processes assume nonsingularity of the processes this assumption makes the analysis easier but restricts application of these processes this paper studies models and characterizes the general singular nonsingular gaussian cm including reciprocal and markov sequence for example to our knowledge there is no dynamic model for the general singular nonsingular gaussian reciprocal sequence in the literature we obtain two such models from the cm viewpoint as a result the significance of studying reciprocal sequences from the cm viewpoint is demonstrated the results of this paper unify singular and nonsingular gaussian cm including reciprocal and markov sequences and provide tools for their application an application of cm sequences in trajectory modeling with a destination is discussed and illustrative examples are presented

a forgetting property of reciprocal chains reciprocal chains rc are a class of discrete index finite state stochastic processes with a generalized markov nearest neighbour property all markov chains mc are rc but not conversely it is well known that a sufficiently regular mc forgets its initial distribution in a geometric manner this article addresses the issues of forgetting for rc using the properties of inhomogeneous products of nonnegative matrices this article establishes that a rc forget its endpoint distributions in a more complicated manner in particular this article shows that the forgetting function for the initial conditions is bounded by a superposition of increasing and decreasing geometric terms implications for modeling using rc are then discussed the particular case of those rc that are mc with prescribed marginal distributions on the endpoints is considered the tightness of the forgetting bounds is illustrated with numerical examples

robust adaptive control of uncertain nonlinear systems in the presence of input saturation and external disturbance in this technical note we consider adaptive control of single input uncertain nonlinear systems in the presence of input saturation and unknown external disturbance by using backstepping approaches two new robust adaptive control algorithms are developed by introducing a well defined smooth function and using a nussbaum function the nussbaum function is introduced to compensate for the nonlinear term arising from the input saturation unlike some existing control schemes for systems with input saturation the developed controllers do not require assumptions on the uncertain parameters within a known compact set and a priori knowledge on the bound of the external disturbance besides showing global stability transient performance is also established and can be adjusted by tuning certain design parameters

adaptive feedback control of nonlinear time delay systems the lasalle razumikhin based approach this note presents a new method to design adaptive feedback controller for nonlinear time delay systems first by using the lasalle razumikhin theorem a sufficient condition is derived that ensures the convergence of a part of the solution with stability for a class of functional differential equations then using this condition the adaptive stabilization problem is solved for nonlinear time delay systems moreover it is shown that for a class of nonlinear time delay systems with triangular structure the adaptive stabilizing controller can be obtained by recursively constructing the lyapunov razumikhin function it will be shown that the provided recursive design approach which is obviously motivated by the typical backstepping method is not a trivial extension of the existing design method

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

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

brief paper novel adaptive neural control design for nonlinear mimo time delay systems in this paper we address the problem of adaptive neural control for a class of multi input multi output mimo nonlinear time delay systems in block triangular form based on a neural network nn online approximation model a novel adaptive neural controller is obtained by constructing a novel quadratic type lyapunov krasovskii functional which not only efficiently avoids the controller singularity but also relaxes the restriction on unknown virtual control coefficients the merit of the suggested controller design scheme is that the number of online adapted parameters is independent of the number of nodes of the neural networks which reduces the number of the online adaptive learning laws considerably the proposed controller guarantees that all closed loop signals remain bounded while the output tracking error dynamics converges to a neighborhood of the origin a simulation example is given to illustrate the design procedure and performance of the proposed method

covariance matrix estimation and classification with limited training data a new covariance matrix estimator useful for designing classifiers with limited training data is developed in experiments this estimator achieved higher classification accuracy than the sample covariance matrix and common covariance matrix estimates in about half of the experiments it achieved higher accuracy than regularized discriminant analysis but required much less computation

discrete time complementary models and smoothing abstract the fact that the smoothing error is a wide sense markov process is somehow surprising since smoothed estimates depend upon both past and future data in this paper we first give a simple and general proof of this fact then we use the so called complementary models introduced by weinert and desai to derive forwards and backwards markovian models for the smoothing error in state space models by exploring the structure of the complementary models we show that under certain restrictions only two simple structured models exist one that runs forwards in time and the other that runs backwards in time the forwards complementary model leads to the forward rauch tung striebel rts smoothing formula and to a backwards markovian model for the error whereas the backwards model leads to the backward rts formula and to a forwards error model the two models for the smoothing error can be derived one from the other by a forward backward transformation that preserves the sample paths finally by using

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

adaptive variable structure control of a class of nonlinear systems with unknown prandtl ishlinskii hysteresis control of nonlinear systems preceded by unknown hysteresis nonlinearities is a challenging task and has received increasing attention in recent years due to growing industrial demands involving varied applications in the literature many mathematical models have been proposed to describe the hysteresis nonlinearities the challenge addressed here is how to fuse those hysteresis models with available robust control techniques to have the basic requirement of stability of the system the purpose of the note is to show such a possibility by using the prandtl ishlinskii pi hysteresis model an adaptive variable structure control approach serving as an illustration is fused with the pi model without necessarily constructing a hysteresis inverse the global stability of the system and tracking a desired trajectory to a certain precision are achieved simulation results attained for a nonlinear system are presented to illustrate and further validate the effectiveness of the proposed approach

robust constraint satisfaction for continuous time nonlinear systems in strict feedback form this work is concerned with the design of feedback control laws that guarantee satisfaction of hard output constraints a recursive procedure is used to derive sufficient conditions for robust constraint satisfaction in input affine nonlinear systems with bounded disturbances or parametric uncertainties the control objective is achieved by a suitable switching between two control modes one responsible for stabilization and one for constraint satisfaction

reinforcement learning design based adaptive tracking control with less learning parameters for nonlinear discrete time mimo systems based on the neural network nn approximator an online reinforcement learning algorithm is proposed for a class of affine multiple input and multiple output mimo nonlinear discrete time systems with unknown functions and disturbances in the design procedure two networks are provided where one is an action network to generate an optimal control signal and the other is a critic network to approximate the cost function an optimal control signal and adaptation laws can be generated based on two nns in the previous approaches the weights of critic and action networks are updated based on the gradient descent rule and the estimations of optimal weight vectors are directly adjusted in the design consequently compared with the existing results the main contributions of this paper are 1 only two parameters are needed to be adjusted and thus the number of the adaptation laws is smaller than the previous results and 2 the updating parameters do not depend on the number of the subsystems for mimo systems and the tuning rules are replaced by adjusting the norms on optimal weight vectors in both action and critic networks it is proven that the tracking errors the adaptation laws and the control inputs are uniformly bounded using lyapunov analysis method the simulation examples are employed to illustrate the effectiveness of the proposed algorithm

new delay dependent stability criteria for neural networks with time varying delay in this letter a new method is proposed for stability analysis of neural networks nns with a time varying delay some less conservative delay dependent stability criteria are established by considering the additional useful terms which were ignored in previous methods when estimating the upper bound of the derivative of lyapunov functionals and introducing the new free weighting matrices numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method

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

robust stability analysis and fuzzy scheduling control for nonlinear systems subject to actuator saturation takagi sugeno ts fuzzy models can provide an effective representation of complex nonlinear systems in terms of fuzzy sets and fuzzy reasoning applied to a set of linear input output submodels in this paper the ts fuzzy modeling approach is utilized to carry out the stability analysis and control design for nonlinear systems with actuator saturation the ts fuzzy representation of a nonlinear system subject to actuator saturation is presented in our ts fuzzy representation the modeling error is also captured by norm bounded uncertainties a set invariance condition for the system in the ts fuzzy representation is first established based on this set invariance condition the problem of estimating the domain of attraction of a ts fuzzy system under a constant state feedback law is formulated and solved as a linear matrix inequality lmi optimization problem by viewing the state feedback gain as an extra free parameter in the lmi optimization problem we arrive at a method for designing state feedback gain that maximizes the domain of attraction a fuzzy scheduling control design method is also introduced to further enlarge the domain of attraction an inverted pendulum is used to show the effectiveness of the proposed fuzzy controller

adaptive fuzzy output feedback tracking backstepping control of strict feedback nonlinear systems with unknown dead zones in this paper an adaptive fuzzy backstepping control approach is considered for a class of nonlinear strict feedback systems with unknown functions unknown dead zones and immeasurable states fuzzy logic systems are utilized to approximate the unknown nonlinear functions and a fuzzy filters state observer is designed to estimate the immeasurable states by using the adaptive backstepping recursive design technique and constructing the dead zone inverse a new adaptive fuzzy backstepping output feedback control approach is developed it is mathematically proved that all the signals of the resulting closed loop adaptive control system are semiglobally uniformly ultimately bounded and the tracking error converges to a small neighborhood of the origin by appropriate choice of design parameters the proposed approach cannot only solve the problem of the dead zones but also cancel the restrictive assumption in the previous literature that the states are all available for measurement two simulation examples are provided to show the effectiveness of the proposed approach

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

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

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

decentralized adaptive stabilization in the presence of unknown backlash like hysteresis due to the difficulty of handling both hysteresis and interactions between subsystems there is still no result available on decentralized stabilization of unknown interconnected systems with hysteresis even though the problem is practical and important in this paper we provide solutions to this challenging problem by proposing two new schemes to design decentralized output feedback adaptive controllers using backstepping approach for each subsystem a general transfer function with arbitrary relative degree is considered the interactions between subsystems are allowed to satisfy a nonlinear bound with certain structural conditions in the first scheme no knowledge is assumed on the bounds of unknown system parameters in case that the uncertain parameters are inside known compact sets we propose an alternative scheme where a projection operation is employed in the adaptive laws in both schemes the effects of the hysteresis and the effects due to interactions are taken into consideration in devising local control laws it is shown that the designed local adaptive controllers can ensure all the signals in the closed loop system bounded a root mean square type of bound is obtained for the system states as a function of design parameters this implies that the transient system performance can be adjusted by choosing suitable design parameters with scheme ii the proposed control laws allow arbitrarily strong interactions provided their upper bounds are available in the absence of hysteresis perfect stabilization is ensured and the l 2 norm of the system states is also shown to be bounded by a function of design parameters when the second scheme is applied

optimal smoothing for finite state hidden reciprocal processes this technical note addresses modelling and estimation of a class of finite state random processes called hidden reciprocal chains hrc a hidden reciprocal chain consists of a finite state reciprocal process together with an observation process conditioned on the reciprocal process much as in the case of a hidden markov model hmm the key difference between markov models and reciprocal models is that reciprocal models are non causal the technical note presents a characterization of a hrc by a finite set of hidden markov bridges which are hmms with the final state fixed the technical note then uses this characterization to derive the optimal fixed interval smoother for a hrc performance of linear and optimal smoothers derived for both hmm and hrc are compared using simulations for a class of hrc derived from underlying markov transitions these experiments suggest that not surprisingly the performance of the optimal hmm and hrc smoothers are signifcantly better than their linear counterparts and that some performance improvement is obtained using the hrc smoothers compared to the hmm smoothers the technical note concludes by mentioning some ongoing and future work which exploits this new markov bridge characterization of a hrc

modeling and estimation of discrete time gaussian reciprocal processes discrete time gaussian reciprocal processes are characterized in terms of a second order two point boundary value nearest neighbor model driven by a locally correlated noise whose correlation is specified by the model dynamics this second order model is the analog for reciprocal processes of the standard first order state space models for markov processes the model is used to obtain a solution to the smoothing problem for reciprocal processes the resulting smoother obeys second order equations whose structure is similar to that of the kalman filter for gauss markov processes it is shown that the smoothing error is itself a reciprocal process

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

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

modelling and estimation for finite state reciprocal processes a reciprocal equation is a kind of descriptor linear discrete index stochastic system which is well known be satisfied pathwise by all gaussian reciprocal processes from a system theoretic point of view it is a kind of noncausal linear system in the sense that the solution of it cannot be determined by only an initial condition indeed requiring the terminal state as well besides all the input function between initial and terminal states also nice properties are known of a reciprocal equation such as the equivalence of it with a couple of ordinary causal dynamic systems running in opposite directions for these reasons here we assume a reciprocal equation as the target of stochastic realization for the class of finite state reciprocal processes also named reciprocal chains the central result of the present paper is showing that any canonical reciprocal chain i e valued in the canonical base of realrn n being the cardinality of the set of chain s states satisfies pathwise a reciprocal equation in a n2 dimensional canonical variable or in other word a quadratic reciprocal equation named augmented state reciprocal model asrm also for a partially observed reciprocal chain a linear optimal smoother is derived all the results here presented are based upon the idea that a reciprocal chain is a combination of markov bridges to this purpose other forms besides the asrm are presented in order to make clear the meaning of this combination as well as to prove that the linear smoother can be actually implemented as n smoothers all operating independently on each markov bridge component

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

robust adaptive control of a class of nonlinear systems with unknown backlash like hysteresis deals with adaptive control of a class of nonlinear dynamic systems preceded by unknown backlash like hysteresis nonlinearities where the hysteresis is modeled by a differential equation by exploiting solution properties of the differential equation and combining those properties with adaptive control techniques a robust adaptive control algorithm is developed without constructing a hysteresis inverse the new control law ensures global stability of the adaptive system and achieves both stabilization and tracking to within a desired precision simulations performed on a nonlinear system illustrate and clarify the approach

dynamics and kinematics of reciprocal diffusions this paper examines the dynamics and kinematics of reciprocal diffusions reciprocal processes were introduced by bernstein in 1932 and were later studied in detail by jamison the reciprocal diffusions are constructed here by specifying their finite joint densities in terms of the green s function of a general heat operator and an end point density a path integral interpretation of the heat operator green s function is provided which is used to derive a stochastic form of newton s law as well as a conditional distribution for the velocity of a diffusing particle given its position these results are then employed to derive two conservation laws expressing the conservation of mass and momentum the conservation laws do not form a closed system of equations in general except for two subclasses of reciprocal diffusions the markov and quantum diffusions

some matrix variate distribution theory notational considerations and a bayesian application summary we introduce and justify a convenient notation for certain matrix variate distributions which by its emphasis on the important underlying parameters and the theory on which it is based eases greatly the task of manipulating such distributions important examples include the matrix variate normal t f and beta and the wishart and inverse wishart distributions the theory is applied to compound matrix distributions and to bayesian prediction in the multivariate linear model

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

maximum likelihood sequence estimation for hidden reciprocal processes this paper addresses the problem of maximum likelihood sequence estimation mlse based on a hidden reciprocal chain hrc as the underlying target model hrcs are non causal discrete time finite state stochastic processes which can be regarded as the one dimensional version of a markov random field although they are not in general markov processes this paper describes a procedure for evaluating the mlse for hrc and compares the resultant estimator with its markov model equivalent the viterbi algorithm in addition the performance of the newly proposed reciprocal mlse is compared to a hrc based optimal smoother

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

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

a unified version of cauchy schwarz and wielandt inequalities abstract let a be an n n positive definite symmetric real matrix with n eigenvalues 1 2 n and let x and y be two n 1 vectors with the angle this paper proves the following inequality x t ay 2 max i j i cos 2 2 j sin 2 2 i cos 2 2 j sin 2 2 2 x t ax y t ay it is a unified version of the cauchy schwarz inequality and the wielandt one

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

direct filtering a new approach to optimal filter design for nonlinear systems optimal filters for nonlinear systems are in general difficult to derive or implement the common approach is to use approximate solutions such as extended kalman filters ensemble filters or particle filters however no optimality properties can be guaranteed by these approximations and even the stability of the estimation error cannot often be ensured another relevant issue is that in most practical situations the system whose variables have to be estimated is not known and a two step procedure is adopted based on model identification from data and filter design from the identified model however the designed filter may display large performance deteriorations in the case of modeling errors in this paper a new approach overcoming these issues is proposed allowing the design of optimal filters for nonlinear systems in both the cases of known and unknown system the approach is based on the direct filter design from a set of data generated by the system either experimental or simulated data can be used for design a bound on the number of data necessary to ensure a given filter accuracy is also provided showing that the proposed approach is not affected by the curse of dimensionality

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

adaptive fuzzy tracking control based barrier functions of uncertain nonlinear mimo systems with full state constraints and applications to chemical process an adaptive control approach based on the fuzzy systems for a class of uncertain nonlinear multi input multi output mimo systems is presented in this paper this class of systems is in the nested multiple coupling structure and their states are constrained in the corresponding compact sets the properties of the system structure are inevitable to bring about a complicated design and a difficult task the fuzzy logic systems are employed to approximate the unknown functions of systems and the decoupling backstepping way is proposed to design the stability controller and adaptation laws barrier lyapunov functions blfs are constructed in the backstepping design to guarantee that the constraint bounds are not violated based on lyapunov analysis in barrier form we can prove the stability of the closed loop system two simulation examples are viewed to verify the feasibility of the approach

robust observer design for unknown inputs takagi sugeno models this paper deals with the observer design for takagi sugeno t s fuzzy models subject to unknown inputs and disturbance affecting both states and outputs of the system sufficient conditions to design an unknown input t s observer are given in linear matrix inequality lmi terms both continuous time and discrete time cases are studied relaxations are introduced by using intermediate variables extension to the case of unmeasured decision variables is also given a numerical example is given to illustrate the effectiveness of the given results

adaptive backstepping control of a class of uncertain nonlinear systems with unknown backlash like hysteresis in this note we consider the same class of systems as in a previous paper i e a class of uncertain dynamic nonlinear systems preceded by unknown backlash like hysteresis nonlinearities where the hysteresis is modeled by a differential equation in the presence of bounded external disturbances by using backstepping technique robust adaptive backstepping control algorithms are developed unlike some existing control schemes for systems with hysteresis the developed backstepping controllers do not require the uncertain parameters within known intervals also no knowledge is assumed on the bound of the disturbance like term a combination of the external disturbances and a term separated from the hysteresis model it is shown that the proposed controllers not only can guarantee global stability but also transient performance

2 d recursive modelling of homogeneous discrete gaussian markov fields a 2 d stochastic realization is obtained for an homogeneous discrete gaussian markov field in two dimensions in specific it is shown that such markov fields can be represented as the unique pathwise solution of a 2 d recursive system of equations with a locally correlated forcing noise the idea of stochastic dynamic system in two dimensions gets realized this way two types of domain are considered spheric and rectangular

a bayesian framework for noise covariance estimation using the facet model in image processing literature thus far researchers have assumed the perturbation in the data to be white or uncorrelated having a covariance matrix spl sigma sup 2 i i e assumption of equal variance for all the data samples and that no correlation exists between the data samples however there have been very few attempts to estimate noise characteristics under the assumption that there is a correlation between data samples in this work we propose a new and a novel approach for the simultaneous bayesian estimation of the unknown colored or correlated noise population covariance matrix and the hyperparameters of the covariance model using the well known facet model we also estimate the facet model coefficients we use the facet model because of its simple yet elegant mathematical formulation we use the generalized inverted wishart density as the prior model for the noise covariance matrix we place a structure on the covariance matrix using the parameters of a correlation filter these hyperparameters are estimated by a new extension of the expectation maximization algorithm called the generalized constrained expectation maximization algorithm that we developed

adaptive fuzzy control for a class of nonlinear discrete time systems with backlash an adaptive fuzzy controller design is studied for uncertain nonlinear systems in this paper the considered systems are of the discrete time form in a triangular structure and include the backlash and the external disturbance by using the prediction function of future states the systems are transformed into an n step ahead predictor the fuzzy logic systems flss are used to approximate the unknown functions unknown backlash and backlash inversion respectively a discrete time tuning algorithm is developed to estimate the optimal fuzzy parameters compared with the previous works for the discrete time systems with backlash the main contributions of the paper are that 1 the rigorous restriction for the functional estimation error is removed and 2 the external disturbance is bounded but the bound is not required to be known a novel controller and the adaptation laws are constructed by using the discrete taylor series expansion and the difference lyapunov analysis and thus those limitations in the previous works are overcome it is proven that all the signals in the closed loop system are bounded and that the system output can be to follow the reference signal to a bounded compact set a simulation example is provided to illustrate the effectiveness of the proposed approach

sufficient condition for the existence of the compact set in the rbf neural network control in this brief sufficient conditions are proposed for the existence of the compact sets in the neural network controls first we point out that the existence of the compact set in a classical neural network control scheme is unsolved and its result is incomplete next as a simple case we derive the sufficient condition of the existence of the compact set for the neural network control of first order systems finally we propose the sufficient condition of the existence of the compact set for the neural network based backstepping control of high order nonlinear systems the theoretic result is illustrated through a simulation example

barrier lyapunov functions for the control of output constrained nonlinear systems in this paper we present control designs for single input single output siso nonlinear systems in strict feedback form with an output constraint to prevent constraint violation we employ a barrier lyapunov function which grows to infinity when its arguments approach some limits by ensuring boundedness of the barrier lyapunov function in the closed loop we ensure that those limits are not transgressed besides the nominal case where full knowledge of the plant is available we also tackle scenarios wherein parametric uncertainties are present asymptotic tracking is achieved without violation of the constraint and all closed loop signals remain bounded under a mild condition on the initial output furthermore we explore the use of an asymmetric barrier lyapunov function as a generalized approach that relaxes the requirements on the initial conditions we also compare our control with one that is based on a quadratic lyapunov function and we show that our control requires less restrictive initial conditions a numerical example is provided to illustrate the performance of the proposed control