computational analysis and improvement of sirt iterative x ray computed tomography ct algorithms have the potential for producing high quality images but are computationally very demanding especially when applied to high resolution problems focusing on simultaneous iterative reconstruction technique sirt we provide an eigenvalue based scheme for automatically determining a near optimal value of the relaxation parameter this accelerates the convergence rate of sirt to the point where only half the number of iterations normally required is needed we also modify the way sirt uses preconditioning to solve a weighted least squares problem the resulting algorithm which we call psirt is associated with a smaller memory footprint and calls for less data to be communicated in a distributed memory implementation experimental residual norm and timing results are provided based on cone beam micro ct mouse data including for an ordered subsets study

nonlinear feedback design for fixed time stabilization of linear control systems two types of nonlinear control algorithms are presented for uncertain linear plants controllers of the first type are stabilizing polynomial feedbacks that allow to adjust a guaranteed convergence time of system trajectories into a prespecified neighborhood of the origin independently on initial conditions the control design procedure uses block control principles and finite time attractivity properties of polynomial feedbacks controllers of the second type are modifications of the second order sliding mode control algorithms they provide global finite time stability of the closed loop system and allow to adjust a guaranteed settling time independently on initial conditions control algorithms are presented for both single input and multi input systems theoretical results are supported by numerical simulations

an improved algorithm for reprojecting rays through pixel images it is often desired to calculate line integrals through a field of reconstructed ct density pixels for the purpose of improving ct image quality two algorithms widely published and discussed in the past are known to either degrade spatial resolution or generate errors in the results due to the discontinuous square pixel modeling of the reconstructed image an algorithm is described based on linear interpolation between pixels which provides superior accuracy without unnecessary loss of resolution it was tested on simulated data for a head section and on a narrow gaussian density distribution the experimental results demonstrated improved performance the method is expected to prove useful for many types of post reconstruction processing including beam hardening missing data and noise supression algorithms

practical output feedback stabilisation for a class of continuous time dynamic systems under sample data outputs this article deals with a class of continuous nonlinear control systems in the presence of sampled outputs the dynamical models under consideration are described by ordinary differential equations with additive bounded uncertainties the linear feedback control design proposed in this article is based on an extended version of the classical invariant ellipsoid method the stability robustness analysis of the resulting closed loop system involves the celebrated descriptor techniques from the extended lyapunov methodology finally the implementability of the proposed control design scheme is illustrated by a computational example a brief discussion on the principal numerical issues is also included

brief paper lyapunov function design for finite time convergence analysis twisting controller for second order sliding mode realization a generalization of the zubov method of a lyapunov function design is presented it is based on the characteristic method application and is related to resolving the first order partial differential equation of a special type a successful resolution of this equation guaranties a finite time convergence for the corresponding dynamics given by an ordinary differential equation with a discontinuous right hand side the suggested method is illustrated by its application to the so called twisting controller stability analysis the constructed lyapunov function as well as its level line sections is graphically illustrated

stability preserving maps for finite time convergence super twisting sliding mode algorithm the super twisting algorithm sta has become the prototype of second order sliding mode algorithm it achieves finite time convergence by means of a continuous action without using information about derivatives of the sliding constraint thus chattering associated to traditional sliding mode observers and controllers is reduced the stability and finite time convergence analysis have been jointly addressed from different points of view most of them based on the use of scaling symmetries homogeneity or non smooth lyapunov functions departing from these approaches in this contribution we decouple the stability analysis problem from that of finite time convergence a nonlinear change of coordinates and a time scaling are used in the new coordinates and time space the transformed system is stabilized using any appropriate standard design method conditions under which the combination of the nonlinear coordinates transformation and the time scaling is a stability preserving map are given provided convergence in the transformed space is faster than o 1 t where t is the transformed time convergence of the original system takes place in finite time the method is illustrated by designing a generalized super twisting observer able to cope with a broad class of perturbations

brief paper global sliding mode observer with adjusted gains for locally lipschitz systems a state observer design procedure is proposed for nonlinear locally lipschitz systems with high relative degree from the available for measurements output to the nonlinearity the possible presence of disturbances is taken into account the solution is based on logic based control and the high order super twisting observer the approach is applicable to nonlinear systems with bounded solutions

on an output feedback finite time stabilization problem studies the problem of finite time output feedback stabilization for the double integrator system a class of output feedback controllers that can achieve global finite time stability for the double integrator system are constructed based on a finite time separation principle furthermore it is shown that the closed loop system resulting from our control law can maintain its local finite time stability regardless of some nonlinear perturbations thus our control law actually applies to a large class of nonlinear second order systems

the hilbert function of a maximal cohen macaulay module we study hilbert functions of maximal cm modules over cm local rings when a is a hypersurface ring with dimension d 0 we show that the hilbert function of m with respect to open image in new window is non decreasing if a q f for some regular local ring q we determine a lower bound for e0 m and e1 m and analyze the case when equality holds when a is gorenstein a relation between the second hilbert coefficient of m a and sa m syza1 m is found when g m is cm and depthg a d 1 we give bounds for the first hilbert coefficients of the canonical module of a cm local ring and analyze when equality holds we also give good bounds on hilbert coefficients of m when m is maximal cm and g m is cm

sliding order and sliding accuracy in sliding mode control the synthesis of a control algorithm that stirs a nonlinear system to a given manifold and keeps it within this constraint is considered usually what is called sliding mode is employed in such synthesis this sliding mode is characterized in practice by a high frequency switching of the control it turns out that the deviation of the system from its prescribed constraints sliding accuracy is proportional to the switching time delay a new class of sliding modes and algorithms is presented and the concept of sliding mode order is introduced these algorithms feature a bounded control continuously depending on time with discontinuities only in the control derivative it is also shown that the sliding accuracy is proportional to the square of the switching time delay

accuracy of some popular non homogeneous 2 sliding modes asymptotic accuracy of nonsingular terminal sliding modes and 2 sliding modes with prescribed convergence law is calculated in the presence of small sampling periods and measurement errors the controllers are shown to have practically equivalent performance

a fixed time output feedback control scheme for double integrator systems abstract a continuous output feedback control scheme rendering the closed loop double integrator system globally stable in finite time is presented in particular the convergence time is independent of initial conditions the bi limit homogeneous technique is used for controller and observer designs with fixed time convergence then a continuous output feedback control law is proposed for nominal double integrator system and its perturbed version the homogeneity and lyapunov techniques are used to ensure the fixed time stability of the closed loop system under output feedback control framework finally the efficiency of the proposed algorithms is illustrated by numerical simulations

an integral invariance principle for differential inclusions with applications in adaptive control the byrnes martin integral invariance principle for ordinary differential equations is extended to differential inclusions on bbb r n the extended result is applied in demonstrating the existence of adaptive stabilizers and servomechanisms for a variety of nonlinear system classes

euler s discretization effect on a twisting algorithm based sliding mode control in this paper the euler s discretization of the second order sliding mode control system with the twisting algorithm is studied it shows that for all values of discretization steps initial conditions and allowable parameter setting the system trajectories are always bounded it also shows that for the uncertain systems under a mild condition the system trajectories are also bounded further the periodic behaviors and limit cycles of the system trajectories are explored with conditions for the existence of periodic orbits formulated extensive simulation examples are given to show typical trajectories and comparison between the first order and second order sliding mode control systems

on convergence time and disturbance rejection of super twisting control super twisting algorithm is one of the versions of high order sliding mode control the interest to this algorithm is explained by its attractive properties continuous control input finite convergence time disturbance rejection in this paper the upper bound of admissible unknown disturbances and low bound of the convergence time are found and shown that both the values can be achieved with any desired accuracy

a computational framework and an algorithm for the measurement of visual the robust measurement of visual motion from digitized image sequences has been an important but difficult problem in computer vision this paper describes a hierarchical computational framework for the determination of dense displacement fields from a pair of images and an algorithm consist ent with that framework our framework is based on the separation of the image intensity information as well as the process of measuring motion according to scale the large scale intensity information is first used to obtain rough estimates of image motion which are then refined by using intensity information at smaller scales the estimates are in the form of displacement or velocity vectors for pixels and are accompanied by a direction dependent confidence measure a smoothness constraint is employed to propagate the measurements with high confidence to their neigboring areas where the confidences are low at all levels the computations are pixel parallel uniform across the image and based on information from a small neighborhood of a pixel for our algorithm the local displacement vectors are determind by mini mizing the sum of squared differences ssd of intensities the confidence measures are derived from the shape of the ssd surface and the smoothness constraint is cast in the form of energy minimization results of applying our algorithm to pairs of real images are included in addition to our own

lucas kanade meets horn schunck combining local and global optic flow methods differential methods belong to the most widely used techniques for optic flow computation in image sequences they can be classified into local methods such as the lucas kanade technique or bigun s structure tensor method and into global methods such as the horn schunck approach and its extensions often local methods are more robust under noise while global techniques yield dense flow fields the goal of this paper is to contribute to a better understanding and the design of novel differential methods in four ways i we juxtapose the role of smoothing regularisation processes that are required in local and global differential methods for optic flow computation ii this discussion motivates us to describe and evaluate a novel method that combines important advantages of local and global approaches it yields dense flow fields that are robust against noise iii spatiotemporal and nonlinear extensions as well as multiresolution frameworks are presented for this hybrid method iv we propose a simple confidence measure for optic flow methods that minimise energy functionals it allows to sparsify a dense flow field gradually depending on the reliability required for the resulting flow comparisons with experiments from the literature demonstrate the favourable performance of the proposed methods and the confidence measure

time varying feedback for regulation of normal form nonlinear systems in prescribed finite time abstract while non smooth approaches including sliding mode control provide explicit feedback laws that ensure finite time stabilization but in terminal time that depends on the initial condition fixed time optimal control with a terminal constraint ensures regulation in prescribed time but lacks the explicit character in the presence of nonlinearities and uncertainties in this paper we present an alternative to these approaches which while lacking optimality provides explicit time varying feedback laws that achieve regulation in prescribed finite time even in the presence of non vanishing though matched uncertain nonlinearities our approach employs a scaling of the state by a function of time that grows unbounded towards the terminal time and is followed by a design of a controller that stabilizes the system in the scaled state representation yielding regulation in prescribed finite time for the original state the achieved robustness to right hand side disturbances is not accompanied by robustness to measurement noise which is also absent from all controllers that are nonsmooth or discontinuous at the origin

homogeneous high order sliding mode design a lyapunov approach abstract we provide a lyapunov based design of high order sliding mode hosm control of arbitrary order for a class of single input single output uncertain nonlinear systems first we provide a general method to design degree 0 homogeneous controllers based on a homogeneous control lyapunov function clf then for a perturbed chain of integrators we construct a smooth and homogeneous clf and use it to design a family of homogeneous and discontinuous control laws the controller drives in finite time the trajectories of the system to a sliding surface of arbitrary relative degree and keeps the trajectories on this manifold despite persistently acting matched perturbations so that a sliding mode is established we obtain a large and simply parametrized family of usual discontinuous and quasi continuous hosm controllers of nested and polynomial type that share the robustness and accuracy properties of the existing ones

algorithm for the reconstruction of dynamic objects in ct scanning using optical flow abstract computed tomography is a powerful imaging technique that allows non destructive visualisation of the interior of physical objects in different scientific areas in traditional reconstruction techniques the object of interest is mostly considered to be static which gives artefacts if the object is moving during the data acquisition in this paper we present a method that given only scan results of multiple successive scans can estimate the motion and correct the ct images for this motion assuming that the motion field is smooth over the complete domain using optical flow the proposed method is validated on simulated scan data the main contribution is that we show we can use the optical flow technique from imaging to correct ct scan images for motion

finite time stability and robust control synthesis of uncertain switched systems stability analysis is developed for uncertain nonlinear switched systems while being asymptotically stable and homogeneous of degree q 0 these systems are shown to approach the equilibrium point in finite time restricted to second order systems this feature is additionally demonstrated to persist regardless of inhomogeneous perturbations based on this fundamental property switched control algorithms are then developed to globally stabilize uncertain minimum phase systems of uniform m vector relative degree 2 2 t the controllers constructed do not rely on the generation of sliding motions while providing robustness features similar to those possessed by their sliding mode counterparts the proposed synthesis procedure is illustrated via application to a friction servo motor

hilbert coefficients of a cohen macaulay module let a m be a d dimensional noetherian local ring m a finite cohen macaulay a module of dimension r and let i be an ideal of definition for m we define the notion of minimal multiplicity of cohen macaulay modules with respect to i and show that if m has minimal multiplicity with respect to i then the associated graded module gi m is cohen macaulay when a is cohen macaulay m is maximal cohen macaulay and i is m primary we find a relation between the first hilbert coefficient of m a and syz1a m