speed observation and position feedback stabilization of partially linearizable mechanical systems the problems of speed observation and position feedback stabilization of mechanical systems are addressed in this paper our interest is centered on systems that can be rendered linear in the velocities via a partial change of coordinates it is shown that the class is fully characterized by the solvability of a set of partial differential equations pdes and strictly contains the class studied in the existing literature on linearization for speed observation or control a reduced order globally exponentially stable observer constructed using the immersion and invariance methodology is proposed the design requires the solution of another set of pdes which are shown to be solvable in several practical examples it is also proven that the full order observer with dynamic scaling recently proposed by karagiannis and astolfi obviates the need to solve the latter pdes finally it is shown that the observer can be used in conjunction with an asymptotically stabilizing full state feedback interconnection and damping assignment passivity based controller preserving asymptotic stability

fixed point iterations for asymptotically nonexpansive mappings in banach spaces in this paper we suggest and analyze a three step iterative scheme for asymptotically nonexpansive mappings in banach spaces the new iterative scheme includes ishikawa type and mann type interations as special cases the results obtained in this paper represent an extension as well as refinement of previous known results

three step iterative algorithm for a system of set valued variational inclusions with h η monotone operators abstract in this paper we introduce and study a new system of set valued variational inclusions with h monotone operators we prove the convergence of a new three step iterative algorithm for this system of set valued variational inclusions the results in this paper extend and improve some known results from the literature

new approximation schemes for general variational inequalities in this paper we suggest and consider a class of new three step approximation schemes for general variational inequalities our results include ishikawa and mann iterations as special cases we also study the convergence criteria of these schemes

three step iterations for nonlinear accretive operator equations abstract in this paper we suggest and analyze a three step iterative scheme for solving nonlinear strongly accretive operator equation tx f without continuous condition in a uniformly smooth banach space our results include the ishikawa mann and noor iterations as special cases the results presented in this paper improve and extend almost all the current results in the more general setting

integral input to state stable systems in cascade the integral input to state stability iiss property is studied in the context of nonlinear time invariant systems in cascade some sufficient conditions for the preservation of the iiss property under a cascade interconnection are presented these are first given as growth restrictions on the supply functions of the storage function associated with each subsystem and are then expressed as solutions based requirements a lyapunov based condition guaranteeing that the cascade composed of an iiss system driven by a globally asymptotically stable gas one remains gas is also provided we also show that some of these results extend to cascades composed of more than two subsystems

some results on global and semiglobal stabilization of affine systems in this paper the relations between semiglobal stabilization and global stabilization of affine systems are investigated it is shown that for one dimensional systems the two concepts are equivalent for the n dimensional case we introduce a more restrictive concept the l semiglobal stabilization which implies global stabilization this result is applied to bilinear systems

perturbed proximal point algorithms for generalized quasivariational inclusions abstract in this paper we study a class of generalized quasivariational inclusions by using the properties of the resolvent operator associated with a maximal monotone mapping in hilbert space we have established an existence theorem of solutions for generalized quasivariational inclusions suggesting a new iterative algorithm and a perturbed proximal point algorithm for finding approximate solutions which strongly converge to the exact solution of the generalized quasivariational inclusions as special cases some known results in this field are also discussed

convergence criteria of modified noor iterations with errors for asymptotically nonexpansive mappings in this paper weak and strong convergence theorems of the modified noor iterations with errors are established for asymptotically nonexpansive mappings in banach spaces the results obtained in this paper extend and improve the several recent results in this area

an iterative method for generalized set valued nonlinear mixed quasi variational inequalities this paper presents an iterative method for solving the generalized nonlinear set valued mixed quasi variational inequality a problem class that was introduced by huang et al comp math appl 40 2 3 2000 205 215 the method incorporates step size controls that enable application to problems where certain set valued mappings do not always map to nonempty closed bounded sets

adaptive grid refinement procedures for efficient optical flow computation two approaches are described that improve the efficiency of optical flow computation without incurring loss of accuracy the first approach segments images into regions of moving objects the method is based on a previously defined galerkin finite element method on a triangular mesh combined with a multiresolution segmentation approach for object flow computation images are automatically segmented into subdomains of moving objects by an algorithm that employs a hierarchy of mesh coarseness for the flow computation and these subdomains are reconstructed over a finer mesh on which to recompute flow more accurately the second approach uses an adaptive mesh in which the resolution increases where motion is found to occur optical flow is computed over a reasonably coarse mesh and this is used to construct an optimal adaptive mesh in a way that is different from the gradient methods reported in the literature the finite element mesh facilitates a reduction in computational effort by enabling processing to focus on particular objects of interest in a scene i e those areas where motion is detected the proposed methods were tested on real and synthetic image sequences and promising results are reported

a new system of generalized mixed quasi variational inclusions with h η monotone operators abstract in this paper we introduce and study a new system of generalized mixed quasi variational inclusions with h monotone operators we prove the convergence of a new iterative algorithm for this system of generalized mixed quasi variational inclusions the results in this paper extend and improve some known results in the literature

epipolar plane image analysis an approach to determining structure from motion we present a technique for building a three dimensional description of a static scene from a dense sequence of images these images are taken in such rapid succession that they form a solid block of data in which the temporal continuity from image to image is approximately equal to the spatial continuity in an individual image the technique utilizes knowledge of the camera motion to form and analyze slices of this solid these slices directly encode not only the three dimensional positions of objects but also such spatiotemporal events as the occlusion of one object by another for straight line camera motions these slices have a simple linear structure that makes them easier to analyze the analysis computes the three dimensional positions of object features marks occlusion boundaries on the objects and builds a three dimensional map of free space in our article we first describe the application of this technique to a simple camera motion and then show how projective duality is used to extend the analysis to a wider class of camera motions and object types that include curved and moving objects

local stabilization of minimum phase nonlinear systems abstract in this note we briefly review the notion of a nonlinear minimum phase system i e a system which when constrained in such a way as to produce zero output evolves with an asymptotically stable dynamics the main purpose of the paper is to show that any minimum phase nonlinear system can always be locally stabilized by smooth state feedback

planar linear systems with single saturated feedback abstract we study planar linear systems with a linear or non linear feedback global stabilizer subjected to saturation the number of open loop unstable eigenvalues characterizes the set of the equilibrium points and the shape of the asymptotic stability region asr some topological bifurcations on the shape of the asr are described

a modified forward backward splitting method for maximal monotone mappings we consider the forward backward splitting method for finding a zero of the sum of two maximal monotone mappings this method is known to converge when the inverse of the forward mapping is strongly monotone we propose a modification to this method in the spirit of the extragradient method for monotone variational inequalities under which the method converges assuming only the forward mapping is lipschitz continuous on some closed convex subset of its domain the modification entails an additional forward step and a projection step at each iteration applications of the modified method to decomposition in convex programming and monotone variational inequalities are discussed

existence of solutions and convergence of iterative algorithms for a system of generalized nonlinear mixed quasi variational inclusions in this paper we introduce and study a new system of generalized nonlinear mixed quasi variational inclusions in q uniformly smooth banach spaces we prove the existence and uniqueness of solutions for this system of generalized nonlinear mixed quasi variational inclusions we also prove the convergence of several new two step iterative algorithms with or without errors for this system of generalized nonlinear mixed quasi variational inclusions the results in this paper extend and improve some known results in the literature

physics based flow estimation of fluids abstract we present a physics based method to compute the optical flow of a fluid in most situations gray level changes in an image do not provide sufficient information to completely ascertain optical flow necessitating the use of a supplementary constraint for this the smoothness constraint is often employed this constraint is however general and does not express well a priori knowledge of a specific object we therefore propose a method in which physical equations describing the object are used as supplementary constraints in this way more accurate flow estimation can be achieved the physical model employed is a combination of the continuity equation and navier stokes equations after describing how we integrate these equations into fluid flow estimation we demonstrate the effectiveness of the proposed method by presenting experimental results of its application to simulated and real karman flows

necessary and sufficient conditions for uniform semiglobal practical asymptotic stability application to cascaded systems it is well established that for a cascade of two uniformly globally asymptotically stable ugas systems the origin remains ugas provided that the solutions of the cascade are uniformly globally bounded while this result has met considerable popularity in specific applications it remains restrictive since in practice it is often the case that the decoupled subsystems are only uniformly semiglobally practically asymptotically stable uspas recently we established that the cascade of uspas systems is uspas under a local boundedness assumption and the hypothesis that one knows a lyapunov function for the driven subsystem the contribution of this paper is twofold 1 we present a converse theorem for uspas and 2 we establish uspas of cascaded systems without the requirement of a lyapunov function compared to other converse theorems in the literature ours has the advantage of guaranteeing a specific relationship between the upper and lower bounds on the generated lyapunov function v and of providing a time invariant bound on the gradient of v which is fundamental to establish theorems for cascades

strong convergence theorems for multi step noor iterations with errors in banach spaces abstract in this paper we established two strong convergence theorems for a multi step noor iterative scheme with errors for mappings of asymptotically nonexpansive in the intermediate sense asymptotically quasi nonexpansive respectively in banach spaces our results extend and improve the recent ones announced by xu and noor b l xu m a noor fixed point iterations for asymptotically nonexpansive mappings in banach spaces j math anal appl 267 2002 444 453 cho zhou and guo y j cho h zhou g guo weak and strong convergence theorems for three step iterations with errors for asymptotically nonexpansive mappings comput math appl 47 2004 707 717 and many others

reduction theorems for stability of closed sets with application to backstepping control design we present a solution to the following reduction problem for asymptotic stability of closed sets in nonlinear systems given two closed positively invariant subsets of the state space of a nonlinear system c 1 c 2 assuming that c 1 is asymptotically stable relative to c 2 find conditions under which c 1 is asymptotically stable we also investigate analogous reduction problems for stability and attractivity we illustrate the implications of our results on the stability of sets for cascade connected systems and on a hierarchical control design problem for upper triangular control systems we present a reduction based backstepping technique that does not require the knowledge of a lyapunov function and mitigates the problem of controller complexity arising in classical backstepping design

global robust stabilization of nonlinear cascaded systems this paper gives a sufficient condition for a class of nonlinear cascaded systems to be globally stabilizable via state feedback in the presence of uncertainty which does not necessarily satisfy the so called matching condition the authors result is an extension of the former stabilization results which treated systems without uncertainty in the sense that the uncertainty is taken into account

computation of 3 d velocity fields from 3 d cine ct images of a human heart a method of computing the three dimensional 3 d velocity field from 3 d cine computer tomographs cts of a beating heart is proposed using continuum theory the authors develop two constraints on the 3 d velocity field generated by a beating heart with these constraints the computation of the 3 d velocity field is formulated as an optimization problem and a solution to the optimization problem is developed using the euler lagrange method the solution is then discretized for computer implementation the authors present the results for both simulated images and clinical cine ct images of a beating heart

on uniform boundedness of parameterized discrete time systems with decaying inputs applications to cascades a framework for controller design of sampled data nonlinear systems via their approximate discrete time models has been established recently within this framework naturally arises the need to investigate stability properties of parameterized discrete time systems further results that guarantee appropriate stability of the parameterized family of discrete time systems that is used within this framework have been also established for systems with cascaded structure a fundamental condition that is required in this framework is uniform boundedness of solutions of the cascade however this is difficult to check in general in this paper we provide a range of sufficient conditions for uniform boundedness that are easier to check these results further contribute to the toolbox for controller design of sampled data nonlinear systems via their approximate discrete time models

stability regions of nonlinear autonomous dynamical systems a topological and dynamical characterization of the stability boundaries for a fairly large class of nonlinear autonomous dynamic systems is presented the stability boundary of a stable equilibrium point is shown to consist of the stable manifolds of all the equilibrium points and or closed orbits on the stability boundary several necessary and sufficient conditions are derived to determine whether a given equilibrium point or closed orbit is on the stability boundary a method for finding the stability region on the basis of these results is proposed the method when feasible will find the exact stability region rather than a subset of it as in the lyapunov theory approach several examples are given to illustrate the theoretical prediction

approximating solutions for the systems of strongly accretive operator equations the purpose of this paper is to study a strong convergence of multi step iterative scheme to a common fixed point for a finite family of strongly pseudo contractive mappings as a consequence the strong convergence theorems for the modified multi step iterative sequence to a solution of systems of strongly accretive operator equations are obtained in real uniformly smooth banach spaces the results presented in this paper improve and extend the corresponding xu y xu ishikawa and mann iterative processes with errors for nonlinear strongly accretive operator equations j math anal appl 224 1998 91 101 and noor rassias and huang m a noor t m rassias z huang three step iterations for nonlinear accretive operator equations j math anal appl 274 2002 59 68 and many others

an iterated estimation of the motion parameters of a rigid body from noisy displacement vectors concerns the estimation of the motion parameters of a rigid body from noisy point matches made on perspective views a minimization problem which permits relatively robust parameter estimation and helps overcome poor zoom estimation when the field of view is small is formulated it is assumed that the motion has a small rotary component interframe differences are small and the errors in the system are due to independently distributed errors in the components of the displacement vectors a fast procedure for minimization is exposited in which the parameter set is partitioned and conditional generalized least squares formulas identified recursive application of these provides the search space for the minimization problem comparative results are presented using simulated data and displacement vectors obtained from an intensity based matching algorithm

stability of cascaded fuzzy systems and observers a large class of nonlinear systems can be well approximated by takagi sugeno ts fuzzy models with linear or affine consequents it is well known that the stability of these consequent models does not ensure the stability of the overall fuzzy system therefore several stability conditions have been developed for ts fuzzy systems we study a special class of nonlinear dynamic systems that can be decomposed into cascaded subsystems which are represented as ts fuzzy models we analyze the stability of the overall ts system based on the stability of the subsystems and prove that the stability of the subsystems implies the stability of the overall system the main benefit of this approach is that it relaxes the conditions imposed when the system is globally analyzed thereby solving some of the feasibility problems another benefit is that by using this approach the dimension of the associated linear matrix inequality lmi problem can be reduced for naturally distributed applications such as multiagent systems the construction and tuning of a centralized observer may not be feasible therefore we also extend the cascaded approach to the observer design and use fuzzy observers to individually estimate the states of these subsystems a theoretical proof of stability and simulation examples are presented the results show that the distributed observer achieves the same performance as the centralized one while leading to increased modularity reduced complexity lower computational costs and easier tuning applications of such cascaded systems include multiagent systems distributed process control and hierarchical large scale systems

suboptimal decentralized control over noisy communication channels a b s t r a c t in this paper we present a technique for the design of decentralized controllers for mean square stability of a large scale system with cascaded clusters of subsystems each subsystem is linear and time invariant and both system and measurement are subject to gaussian noise for stability analysis of this system we consider the effects of additive white gaussian noise awgn channels used for exchanging information between subsystems

set valued resolvent equations and mixed variational inequalities in this paper we introduce and study a new class of variational inequalities which is called the generalized set valued mixed variational inequality the resolvent operator technique is used to establish the equivalence among generalized set valued variational inequalities fixed point problems and the generalized set valued resolvent equations this equivalence is used to study the existence of a solution of set valued variational inequalities and to suggest a number of iterative algorithms for solving variational inequalities and related optimization problems the results proved in this paper represent a significant refinement and improvement of the previously known results in this area

common fixed points noor iteration for a finite family of asymptotically quasi nonexpansive mappings in banach spaces in this paper we introduce a general iteration scheme for a finite family of asymptotically quasi nonexpansive mappings the new iterative scheme includes the modified mann and ishikawa iterations three step iterative scheme of xu and noor and khan and takahashi scheme as special cases our results are generalizations as well as refinement of several known results in the current literature

a unifying integral iss framework for stability of nonlinear cascades we analyze nonlinear cascades in which the driven subsystem is integral input to state stable iss and we characterize the admissible integral iss gains for stability this characterization makes use of the convergence speed of the driving subsystem and allows a larger class of gain functions when the convergence is faster we show that our integral iss gain characterization unifies different approaches in the literature which restrict the nonlinear growth of the driven subsystem and the convergence speed of the driving subsystem the result is used to develop a new observer based backstepping design in which the growth of the nonlinear damping terms is reduced

relaxation matching techniques a comparison many different relaxation schemes have been proposed for image analysis tasks we have developed a general matching procedure for comparing semantic network descriptions of images and we have implemented a variety of relaxation techniques an automatic segmentation and description system is used to produce the image representations so that the matching procedures must cope with variations in feature values missing objects and possible multiple matches this environment is used to test different relaxation matching schemes under a variety of conditions the best performance of those we compared in terms of the number of iterations and the number of errors is for the gradient based optimization approach of faugeras and price the related optimization approach of hummel and zucker performed almost as well with differences primarily in difficult matches i e where much of the evidence is against the match for instance poor segmentations the product combination rule proposed by peleg was extremely fast indeed too fast to work when global context is needed the classical rosenfeld hummel and zucker method is included for historical comparisons and performed only adequately producing fewer correct matches and taking more iterations

the frequency structure of one dimensional occluding image signals we present a theoretical investigation of the frequency structure of 1d occluding image signals we show that image signal occlusion contains relevant information which is most easily extractable from its representation in the frequency domain for instance the occluding and occluded signal velocities may be identified as such and translucency phenomena may be understood in the terms of this theoretical investigation in addition it is found that the structure of occluding 1d signals is invariant under constant and linear models of signal velocity this theoretical framework can be used to describe the exact frequency structure of non fourier motion and bridges the gap between such visual phenomena and their understanding in the frequency domain

controller design for nonlinear affine systems by control lyapunov functions abstract this paper addresses the stabilization problems for nonlinear affine systems first of all the explicit feedback controller is developed for a nonlinear multiple input affine system by assuming that there exists a control lyapunov function next based upon the homogeneous property sufficient conditions for the continuity of the derived controller are developed and then the developed control design methodology is applied to stabilize a class of nonlinear affine cascaded systems it is shown that under some homogeneous assumptions on control lyapunov functions and the interconnection term the cascaded system can be globally stabilized finally some interesting results of finite time stabilization for nonlinear affine systems are also obtained

global convergence of nonlinear cascade flows with morse bott zero dynamics abstract we derive a sufficient condition that a flow captures the dynamics on an invariant submanifold this leads to a refinement of the lasalle invariance principle as a consequence we generalize a well known global asymptotic stability result of nonlinear cascade systems to show global convergence to a compact invariant set this includes the case where a globally asymptotically stable system is coupled to a morse bott flow

implicit resolvent dynamical systems for quasi variational inclusions in this paper we suggest and analyze a class of implicit resolvent dynamical systems for quasi variational inclusions by using the resolvent operator technique we show that the trajectory of the solution of the implicit dynamical system converges globally exponentially to the unique solution of the quasi variational inclusions our results can be considered as a significant extension of the previously known results

a lyapunov approach to cascade interconnection of integral input to state stable systems this technical note deals with the stability of cascade interconnection of integral input to state iiss time varying systems a new technique to construct smooth lyapunov functions of cascaded systems is proposed from the construction sufficient conditions for internal stability and stability with respect to external signals are derived one of the derived conditions is a trade off between slower convergence of the driving system and steeper input growth of the driven system the trade off is no more necessary if the speed of convergence of the driven system is not radially vanishing the results are related to trajectory based approaches and small gain techniques for feedback interconnection the difference between the feedback case and the cascade case is viewed from the requirement on convergence speed of autonomous parts

optical flow with an intensity weighted smoothing matching algorithms which use image structure such as edges and junctions cannot perform well on unstructured images for such images global gradient based methods may be more appropriate some of the assumptions involved in applying discretized conservation equations such as the optical flow equation are discussed and an intensity weighted method of estimating dense displacement fields is presented which attempts to avoid some of the problems of the standard methods the only derivative required is the intensity gradient and the method includes procedures for automatic parameter evaluation the algorithm is expected to perform better than conventional algorithms on images without strong texture as is demonstrated on the test set of images

strong convergence theorems for three step iterations with errors for non lipschitzian nonself mappings in banach spaces suppose c is a nonempty closed convex subset of a real uniformly convex banach space x with p is a nonexpansive retraction of x onto c let t c x be an asymptotically nonexpansive in the intermediate sense nonself mapping in this paper we introduced the three step iterative sequence for such map with errors moreover we prove that if t is completely continuous then the three step iterative sequences converges strongly to a fixed point of t

on functionals with greyvalue controlled smoothness terms for determining optical flow the modification by h h nagel 1987 of the approach developed by b k p horn and b g schunck 1981 for determining optical flow is generalized to the case where local motion information is given by more than one constraint equation applying this scheme to three constraint equations reported in the literature as a special case a generalization of nagel s approach is obtained an existence and uniqueness result of solutions under very general conditions that in turn ensures the applicability of standard techniques to compute an approximate solution is presented

uniform semiglobal practical asymptotic stability for non autonomous cascaded systems and applications it is due to the modularity they provide that results for cascaded systems have proved their utility in numerous control applications as well as in the development of general control techniques based on adding integrators nevertheless the standing assumptions in most of the present literature on cascaded systems is that when decoupled the subsystems constituting the cascade are uniformly globally asymptotically stable ugas hence existing results fail in the more general case when the subsystems are uniformly semiglobally practically asymptotically stable uspas this situation is often encountered in control practice e g in control of physical systems with external perturbations measurement noise unmodelled dynamics etc after giving a rigorous framework for the analysis of such stability properties this paper generalizes previous results for cascades by establishing that under a uniform boundedness condition on its solutions the cascade of two uspas systems remains uspas an analogous result is derived for uniformly semiglobally asymptotically stable usas systems in cascade furthermore we show the utility of our results in the pid control of mechanical systems affected by unknown non dissipative forces and considering the dynamics of the dc motors

surfaces from stereo integrating feature matching disparity estimation and contour detection an approach is described that integrates the processes of feature matching contour detection and surface interpolation to determine the three dimensional distance or depth of objects from a stereo pair of images integration is necessary to ensure that the detected surfaces are smooth surface interpolation takes into account detected occluding and ridge contours in the scene interpolation is performed within regions enclosed by these contours planar and quadratic patches are used as local models of the surface occluded regions in the image are identified and are not used for matching and interpolation a coarse to fine algorithm is presented that generates a multiresolution hierarchy of surface maps one at each level of resolution experimental results are given for a variety of stereo images

generalized set valued variational inclusions and resolvent equations in this paper we establish the equivalence between the generalized set valued variational inclusions the resolvent equations and the fixed point problem using the resolvent operator technique this equivalence is used to suggest and analyze some iterative algorithms for solving the generalized set valued variational inclusions and related optimization problems

normal maps inducted by linear transformations we study a certain piecewise linear manifold which we call the normal manifold associated with a polyhedral convex set and a family of continuous functions called normal maps that are induced on this manifold by continuous functions from rn to rn these normal maps occur frequently in optimization and equilibrium problems and the subclass of normal maps induced by linear transformations plays a key role our main result is that the normal map induced by a linear transformation is a lipschitzian homeomorphism if and only if the determinant of the map in each n cell of the normal manifold has the same nonzero sign

an investigation of smoothness constraints for the estimation of displacement vector fields from image sequences a mapping between one frame from an image sequence and the preceding or following frame can be represented as a displacement vector field in most situations the mere gray value variations do not provide sufficient information in order to estimate such a displacement vector field supplementary constraints are necessary for example the postulate that a displacement vector field varies smoothly as a function of the image position taken as a general requirement this creates difficulties at gray value transitions which correspond to occluding contours nagel therefore introduced the oriented smoothness requirement which restricts variations of the displacement vector field only in directions with small or no variation of gray values this contribution reports results of an investigation about how such an oriented smoothness constraint may be formulated and evaluated

on global uniform asymptotic stability of nonlinear time varying systems in cascade abstract in this short paper we deal with the stability analysis problem of nonautonomous nonlinear systems in cascade in particular we give sufficient conditions to guarantee that i a globally uniformly stable gus nonlinear time varying nltv system remains gus when it is perturbed by the output of a globally uniformly asymptotically stable guas nltv system under the assumption that the perturbing signal is absolutely integrable ii if in addition the perturbed system is guas it remains guas under the cascaded interconnection iii two guas systems yield a guas cascaded system under some growth restrictions over the lyapunov function our proofs rely on the second method of lyapunov roughly speaking on a e stability analysis

brief growth rate conditions for uniform asymptotic stability of cascaded time varying systems in the last decade several results on cascaded autonomous systems have appeared in the literature the sufficient conditions for the stability and stabilizability of these systems are often related to certain growth rate conditions on the functions which define the dynamics of the system in this paper we analyze three complementary classes of nonlinear time varying systems according to these growth rates for each case we give further results to guarantee uniform global asymptotic stability of the cascade and relate our contributions to input to state stability and other growth rate conditions previously reported the advantage of this type of analysis is that it is often easier to verify such conditions than to find a lyapunov function with a negative definite derivative

convergence theorem for the common solution for a finite family of ϕ strongly accretive operator equations the purpose of this paper is to study a strong convergence of multi step iterative scheme to a common solution for a finite family of uniformly continuous strongly accretive operator equations in an arbitrary banach space as a consequence the strong convergence theorem for the multi step iterative sequence to a common fixed point for finite family of strongly pseudocontractive mappings is also obtained the results presented in this paper thus improve and extend the corresponding results of inchan 6 kang 8 9 and many others

estimation of optical flow based on higher order spatiotemporal derivatives in interlaced and non interlaced image sequences abstract this contribution 1 investigates local differential techniques for estimating optical flow and its derivatives based on the brightness change constraint by using the tensor calculus representation we build the taylor expansion of the gray value derivatives as well as of the optical flow in a spatiotemporal neighborhood such a formulation provides a unifying framework for all existing local differential approaches and allows to derive new systems of equations for the estimation of the optical flow and of its derivatives we also tested various optical flow estimation approaches on real image sequences recorded by a calibrated camera which was fixed on the arm of a robot by moving the arm of the robot along a precisely defined trajectory we can determine the true displacement rate of scene surface elements projected into the image plane and compare it quantitatively with the results of different optical flow estimators since the optical flow estimators are based on gray value derivatives of up to fourth order we were forced to develop modified gaussian derivative filters to obtain acceptable estimates for the derivatives further we show quantitatively that these filters contribute to a much more robust optical flow estimation in addition successive lines of tv cameras have an offset in time due to the interlace technique we demonstrate the adaptation of filter kernels for estimating higher order spatiotemporal derivatives in interlaced image sequences

variational inequalities for fuzzy mappings ii in this paper we establish the equivalence between the variational inequalities for fuzzy mappings and the wiener hopf equations for fuzzy mappings we use this equivalence to suggest a number of new iterative algorithms for solving the variational inequalities for fuzzy mappings we also study the convergence criteria of these iterative algorithms the auxiliary principle technique is used to study the existence of a solution of the variational inequality for fuzzy mappings and to suggest a novel and innovative iterative algorithm for computing the approximate solution the results proved in this paper represent an improvement of previously known results

generalized multivalued quasi variational inequalities in this paper we introduce and study a new class of variational inequalities known as generalized multivalued quasi variational inequalities this class is the most general and unifying one using essentially the projection technique we establish the equivalence between this class and the implicit wiener hopf equations this equivalence is used to suggest a number of iterative algorithms for solving the generalized multivalued quasi variational inequalities the convergence analysis of these algorithms is also studied the results proved in this paper represent a significant improvement and refinement of the previously known results in this area

global stabilization of nonlinear cascade systems abstract we present sufficient conditions for the global stabilizability of two cascade connected nonlinear systems these are based on general results concerning global asymptotic stability of triangular systems which are proved in the last section for polynomial systems in particular the stabilizing feedback is given explicitly

a correlation relaxation labeling framework for computing optical flow template matching from a new perspective optical flow estimation is discussed based on a model for time varying images more general than that implied by horn and schunk 1981 the emphasis is on applications where low contrast imagery nonrigid or evolving object patterns movement as well as large interframe displacements are encountered template matching is identified as having advantages over point correspondence and the gradient based approach in dealing with such applications the two fundamental uncertainties in feature matching whether template matching or feature point correspondences are discussed correlation template matching procedures are established based on likelihood measurement a method for determining optical flow is developed by combining template matching and relaxation labeling a number of candidate displacements for each template and their respective likelihood measures are determined then relaxation labeling is employed to iteratively update each candidate s likelihood by requiring smoothness within a motion field real cloud images from satellites are used to test the method

sensitivity analysis for quasi variational inclusions in this paper we develop the sensitivity analysis for quasi variational inclusions by using the implicit resolvent equations technique without assuming the differentiability of the given data

three step iterative algorithms for multivalued quasi variational inclusions in this paper we suggest and analyze some new classes of three step iterative algorithms for solving multivalued quasi variational inclusions by using the resolvent equations technique new iterative algorithms include the ishikawa mann and noor iterations for solving variational inclusions inequalities and optimization problems as special cases the results obtained in this paper represent an improvement and a significant refinement of previously known results

strong convergence of three step relaxed hybrid steepest descent methods for variational inequalities in this paper we prove the strong convergence of a three step relaxed hybrid steepest descent method for solving variational inequalities under some suitable conditions our result can be considered as an improvement and refinement of the previously known results

a nonlinear small gain theorem for the analysis of control systems with saturation a nonlinear small gain theorem is presented that provides a formalism for analyzing the behavior of certain control systems that contain or utilize saturation the theorem is used to show that an iterative procedure can be derived for controlling systems in a general nonlinear feedforward form this result in turn is applied to the control of 1 linear systems stable and unstable with inputs subject to magnitude and rate saturation and time delays 2 the cascade of globally asymptotically stable nonlinear systems with certain linear systems those that are stabilizable right invertible and such that all of their invariant zeros have nonpositive real part 3 the inverted pendulum on a cart and 4 the planar vertical takeoff and landing aircraft

some developments in general variational inequalities general variational inequalities provide us with a unified natural novel and simple framework to study a wide class of equilibrium problems arising in pure and applied sciences in this paper we present a number of new and known numerical techniques for solving general variational inequalities using various techniques including projection wiener hopf equations updating the solution auxiliary principle inertial proximal penalty function dynamical system and well posedness we also consider the local and global uniqueness of the solution and sensitivity analysis of the general variational inequalities as well as the finite convergence of the projection type algorithms our proofs of convergence are very simple as compared with other methods our results present a significant improvement of previously known methods for solving variational inequalities and related optimization problems since the general variational inequalities include quasi variational inequalities and quasi implicit complementarity problems as special cases results presented here continue to hold for these problems several open problems have been suggested for further research in these areas

some aspects of variational inequalities abstract in this paper we provide an account of some of the fundamental aspects of variational inequalities with major emphasis on the theory of existence uniqueness computational properties various generalizations sensitivity analysis and their applications we also propose some open problems with sufficient information and references so that someone may attempt solution s in his her area of special interest we also include some new results which we have recently obtained

comments on the stabilization of nonlinear systems by adding an integrator we present a new proof of the result that static stabilizability implies dynamic stabilizability the goal is to show how to compute explicitly the stabilizing feedback in some cases when the classical proof shows only the existence new results on dynamic feedback stabilization are proposed

on multivalued complementarity problems in banach spaces in this paper we prove a new existence result for multivalued complementarity problems in banach spaces our result represents a refinement and improvement of the previously known results

reliable control of nonlinear systems in this paper we extend veillette s results 1995 to the study of reliable linear quadratic regulator problem for nonlinear systems this is achieved by employing the hamilton jacobi inequality in the nonlinear case instead of algebraic riccati equation in the linear one the proposed state feedback controllers are shown to be able to tolerate the outage of actuators within a prespecified subset of actuators both the gain margins of guaranteeing system stability and retaining a performance bound are estimated

design of linear systems with saturating linear control and bounded states a theorem is developed based on the circle criterion which gives sufficient conditions for the stability of a saturating linear control for a linear system with bounded states this theorem can be applied to determine a range of gains for the linear control which ensures stability it is shown by example that this approach results in an increased speed of response over that obtained by previous methods which do not account for state bounds

strongly nonlinear generalized equations we study a class of generalized equations which includes as a special case various classes of quasi variational inequalities introduced by noor isac siddiqi and ansari such problems occur in mathematical programming and in various other branches of pure and applied mathematics we also propose two iterative schemes for the numerical solution of the problems considered

permanent magnet synchronous motors are globally asymptotically stabilizable with pi current control this note shows that the industry standard desired equilibrium for permanent magnet synchronous motors i e maximum torque per ampere can be globally asymptotically stabilized with a pi control around the current errors provided some viscous friction possibly small is present in the rotor dynamics and the proportional gain of the pi is suitably chosen instrumental to establish this surprising result is the proof that the map from voltages to currents of the incremental model of the motor satisfies some passivity properties the analysis relies on basic lyapunov theory making the result available to a wide audience

existence of periodic orbits of stable saturated systems the saturation of linear controllers produces the undesirable existence of equilibrium points or periodic orbits of the closed loop system this typical nonlinear behavior has been observed in real systems or by means of simulation of certain examples however there are only a few studies in which the properties of saturated systems have been examined rigorously and a proof of the existence of periodic orbits created by the saturation of the controller is lacking in this paper we choose an example of an open loop stable linear control system with an stabilizing saturated linear feedback to prove rigorously the existence of a periodic orbit

modified noor iterations for nonlinear equations in banach spaces the purpose of this paper is to analyze the modified three step iterative scheme for solving nonlinear operator equations in real banach spaces our results can be viewed as an extension of three step and two step iterative schemes of glowinski and le tallec r glowinski p le tallec augemented lagrangian and operator splitting methods in nonlinear mechanics siam publishing co philadelphia 1989 noor m a noor three step iterative algorithms for multivalued quasi variational inclusions j math anal appl 255 2001 589 604 m a noor some predictor corrector algorithms for multivalued variational inequalities j optim theory appl 108 3 2001 659 670 m a noor t m rassias z huang three step iterations for nonlinear accretive operator equations j math anal appl 274 2002 59 68 and ishikawa s ishikawa fixed points by a new iteration method proc amer math soc 44 1974 147 150

stabilization of exponentially unstable linear systems with saturating actuators we study the problem of stabilizing exponentially unstable linear systems with saturating actuators the study begins with planar systems with both poles exponentially unstable for such a system we show that the boundary of the domain of attraction under a saturated stabilizing linear state feedback is the unique stable limit cycle of its time reversed system a saturated linear state feedback is designed that results in a closed loop system having a domain of attraction that is arbitrarily close to the null controllable region this design is then utilized to construct state feedback laws for higher order systems with two exponentially unstable poles

estimation of the velocity field of two dimensional deformable motion abstract for a deformable motion the velocities of neighboring points are different in general the traditional smoothness constraints which minimize the spatial derivatives of the velocity are not applicable a new way is proposed to integrate the motion fundamental constraint and the deformation linear constraint an iterative algorithm based on the maximum a posteriori map estimation criterion is proposed to estimate the velocity field of a two dimensional 2d deformable motion based on the statistical approach the relative weights of the two constraints used in the estimation process can be represented by a single parameter methods to avoid the critical problem of determining the region size for which the linear constraint holds are discussed the constraint propagation property is also used to overcome this problem by assuming that the flow field is analytic a promising application for optical flow techniques is to visualize the 2d heart motion quantitatively the 2d echocardiographic images taken by the short axis view are used in the experiments to study the performance of the proposed algorithm the results of using the method proposed by horn and schunck are also given for comparison

lyapunov functions for stable cascades and applications to global stabilization generalizes lyapunov constructions for a cascade of two nonlinear systems one of which is stable rather than asymptotically stable a new cross term construction in the lyapunov function allows us to replace earlier growth conditions by a necessary boundedness condition this method is instrumental in the global stabilization of feedforward systems and new stabilization results are derived from the generalized construction

on a new system of generalized mixed quasi variational like inclusions with h η accretive operators in real q uniformly smooth banach spaces abstract in this paper we introduce and study a new system of generalized mixed quasi variational like inclusions with h accretive operators which contains variational inequalities variational inclusions systems of variational inequalities and systems of variational inclusions in the literature as special cases by using the resolvent technique for the h accretive operators we prove the existence of solutions and the convergence of a new p step iterative algorithm for this system of generalized mixed quasi variational like inclusions in real q uniformly smooth banach spaces the results in this paper unify extend and improve some known results from the literature

optimal brightness functions for optical flow estimation of deformable motion estimation accuracy of horn and schunck s 1981 classical optical flow algorithm depends on many factors including the brightness pattern of the measured images since some applications can select brightness functions with which to paint the object it is desirable to know what patterns will lead to the best motion estimates the paper presents a method for determining this pattern a priori using mild assumptions about the velocity field and imaging process the method is based on formulating horn and schunck s algorithm as a linear smoother and rigorously deriving an expression for the corresponding error covariance function the authors then specify a scalar performance measure and develop an approach to select an optimal brightness function which minimizes this performance measure from within a parametrized class conditions for existence of an optimal brightness function are also given the resulting optimal performance is demonstrated using simulations and a discussion of these results and potential future research is given

the modified noor iterations with errors for non lipschitzian mappings in banach spaces in this paper weak and strong convergence theorems are established for the modified noor iterations with errors for asymptotically nonexpansive mappings in the intermediate sense in a uniformly convex banach space mann type and ishikawa type iterations are included by the modified noor iterations with errors the results obtained in this paper extend and improve the recent ones announced by schu j schu iterative construction of fixed points of asymptotically nonexpansive mappings j math anal appl 158 1991 407 413 j schu weak and strong convergence to fixed points of asymptotically nonexpansive mappings bull austral math soc 43 1991 153 159 xu and noor b l xu m a noor fixed point iterations for asymptotically nonexpansive mappings in banach spaces j math anal appl 267 2002 444 453 cho et al y j cho h y zhou g guo weak and strong convergence theorems for three step iterations with errors for asymptotically nonexpansive mappings comput math appl 47 2004 707 717 suantai s suantai weak and strong convergence criteria of noor iterations for asymptotically nonexpansive mappings j math anal appl 311 2005 506 517 nammanee et al k nammanee m a noor s suantai convergence criteria of modified noor iterations with errors for asymptotically nonexpansive mappings j math anal appl 314 2006 320 334 and many others