multimodality image registration by maximization of mutual information a new approach to the problem of multimodality medical image registration is proposed using a basic concept from information theory mutual information mi or relative entropy as a new matching criterion the method presented in this paper applies mi to measure the statistical dependence or information redundancy between the image intensities of corresponding voxels in both images which is assumed to be maximal if the images are geometrically aligned maximization of mi is a very general and powerful criterion because no assumptions are made regarding the nature of this dependence and no limiting constraints are imposed on the image content of the modalities involved the accuracy of the mi criterion is validated for rigid body registration of computed tomography ct magnetic resonance mr and photon emission tomography pet images by comparison with the stereotactic registration solution while robustness is evaluated with respect to implementation issues such as interpolation and optimization and image content including partial overlap and image degradation our results demonstrate that subvoxel accuracy with respect to the stereotactic reference solution can be achieved completely automatically and without any prior segmentation feature extraction or other preprocessing steps which makes this method very well suited for clinical applications

on the synthesis of a stabilizing feedback control via lie algebraic methods let the n dimensional system of differential equations dx dt x x t have p in mathbb r n as a rest solution i e x p 0 even in cases when this rest solution is unstable one can often induce a strong stability asymptotic stability by the inclusion of one or more controls e g via a controlled system a dx dt x x uy x where say u leqq 1 lie theory gives a computable sufficient condition to determine when by use of the control u one can steer a full n dimensional neighborhood of p to p by solutions of a this condition is assumed to hold one prefers a feedback control i e that u u x the main result in this paper is an algorithm which determines a modified stabilizing feedback control specifically for given varepsilon 0 one measures the current state q and the algorithm determines u t q 0 leqq t leqq varepsilon such that the solution x cdot u of a initiating from q and corresponding to this control u satisfies distance x varepsilon u p q p in fact iterates are theoretically shown to converge to p numerical examples computed via a simple fortran program are included these substantiate the strong stability achieved via such a modified feedback control

kernel bundle diffeomorphic image registration using stationary velocity fields and wendland basis functions in this paper we propose a multi scale multi kernel shape compactly supported kernel bundle framework for stationary velocity field based image registration wendland kernel bundle stationary velocity field wkb svf we exploit the possibility of directly choosing kernels to construct a reproducing kernel hilbert space rkhs instead of imposing it from a differential operator the proposed framework allows us to minimize computational cost without sacrificing the theoretical foundations of svf based diffeomorphic registration in order to recover deformations occurring at different scales we use compactly supported wendland kernels at multiple scales and orders to parameterize the velocity fields and the framework allows simultaneous optimization over all scales the performance of wkb svf is extensively compared to the 14 non rigid registration algorithms presented in a recent comparison paper on both mgh10 and cumc12 datasets the accuracy of wkb svf is improved when compared to other registration algorithms in a disease specific application for intra subject registration atrophy scores estimated using the proposed registration scheme separates the diagnostic groups of alzheimer s and normal controls better than the state of the art segmentation technique experimental results show that wkb svf is a robust flexible registration framework that allows theoretically well founded and computationally efficient multi scale representation of deformations and is equally well suited for both inter and intra subject image registration

a general theorem on local controllability we prove a general sufficient condition for local controllability of a nonlinear system at an equilibrium point earlier results of brunovsky hermes jurdjevic crouch and byrnes sussmann and grossmann are shown to be particular cases of this result also a number of new sufficient conditions are obtained all these results follow from one simple general principle namely that local controllability follows whenever brackets with certain symmetries can be neutralized in a suitable way by writing them as linear combinations of brackets of a lower degree both the class of symmetries and the definition of degree can be chosen to suit the problem

brief exponential stabilization of nonholonomic dynamic systems by smooth time varying control a general dynamic model is proposed for describing a large class of nonholonomic systems including extended chained systems extended power systems underactuated surface vessel systems etc by introducing an assistant state variable and a time varying state transformation based on the concept of minimal dilation degree this class of nonholonomic systems is transformed into linear time varying control systems and the asymptotic exponential stability is thus achieved by using a smooth time varying feedback control law the existence and uniqueness of the minimal dilation degree for the discussed systems are also proved under certain conditions

mass concentration phenomena for the l 2 critical nonlinear schrodinger equation in this paper we show that any solution of the nonlinear schr o dinger equation iu t delta u pm u frac 4 n u 0 which blows up in finite time satisfies a mass concentration phenomena near the blow up time our proof is essentially based on the bourgain s one cite mr99f 35184 which has established this result in the bidimensional spatial case and on a generalization of strichartz s inequality where the bidimensional spatial case was proved by moyua vargas and vega cite mr1671214 we also generalize to higher dimensions the results in keraani cite mr2216444 and merle and vega cite mr1628235

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

refined and microlocal kakeya nikodym bounds of eigenfunctions in higher dimensions we prove a kakeya nikodym bound on eigenfunctions and quasimodes which sharpens a result of the authors blair and sogge in anal pde 8 747 764 2015 and extends it to higher dimensions as in the prior work the key intermediate step is to prove a microlocal version of these estimates which involves a phase space decomposition of these modes that is essentially invariant under the bicharacteristic geodesic flow in a companion paper blair and sogge in j differ geom 2015 it will be seen that these sharpened estimates yield improved l q m bounds on eigenfunctions in the presence of nonpositive curvature when 2 q frac 2 d 1 d 1

information measures in scale spaces this article investigates renyi s 1976 generalized entropies under linear and nonlinear scale space evolutions of images scale spaces are useful computer vision concepts for both scale analysis and image restoration we regard images as densities and prove monotony and smoothness properties for the generalized entropies the scale space extended generalized entropies are applied to global scale selection and size estimations finally we introduce an entropy based fingerprint description for textures

a few endpoint geodesic restriction estimates for eigenfunctions we prove a couple of new endpoint geodesic restriction estimates for eigenfunctions in the case of general 3 dimensional compact manifolds after a tt argument simply by using the l 2 boundedness of the hilbert transform on mathbb r we are able to improve the corresponding l 2 restriction bounds of burq gerard and tzvetkov duke math j 138 445 486 2007 and hu forum math 6 1021 1052 2009 also in the case of 2 dimensional compact manifolds with nonpositive curvature we obtain improved l 4 estimates for restrictions to geodesics which by holder s inequality and interpolation implies improved l p bounds for all exponents p 2 we do this by using oscillatory integral theorems of hormander ark mat 11 1 11 1973 greenleaf and seeger j reine angew math 455 35 56 1994 and phong and stein int math res notices 4 49 60 1991 along with a simple geometric lemma lemma 3 2 about properties of the mixed hessian of the riemannian distance function restricted to pairs of geodesics in riemannian surfaces we are also able to get further improvements beyond our new results in three dimensions under the assumption of constant nonpositive curvature by exploiting the fact that in this case there are many totally geodesic submanifolds

the structure of locally orderless images we propose a representation of images in which a global but not a local topology is defined the topology is restricted to resolutions up to the extent of the local region of interest roi although the roi s may contain many pixels there is no spatial order on the pixels within the roi the only information preserved is the histogram of pixel values within the roi s this can be considered as an extreme case of a textel texture element image the histogram is the limit of texture where the spatial order has been completely disregarded we argue that locally orderless images are ubiquitous in perception and the visual arts formally the orderless images are most aptly described by three mutually intertwined scale spaces the scale parameters correspond to the pixellation inner scale the extent of the roi s outer scale and the resolution in the histogram tonal scale we describe how to construct locally orderless images how to render them and how to use them in a variety of local and global image processing operations

adaptive output feedback stabilization for nonholonomic systems with strong nonlinear drifts abstract this paper investigates the design of an output feedback adaptive stabilization controller for a nonholonomic chained system with strong nonlinear drifts including modeled nonlinear dynamics unmodeled dynamics and dynamics modeled with unknown parameters also the virtual control directions of the system are unknown the purpose is to design a nonlinear output feedback switching controller such that the closed loop system is globally asymptotically stable a novel observer and estimator are introduced for states and parameter estimates respectively a constructive procedure of design for an output feedback adaptive controller is given by using the integrator backstepping approach and based on the proposed observer and parameter estimator an example is given to show the effectiveness of the proposed scheme

exponential stabilization of an underactuated autonomous surface vessel this paper studies the problem of controlling the planar position and orientation of an autonomous surface vessel using two independent thrusters it is first shown that although the system is not asymptotically stabilizable to a given configuration using a time invariant continuous feedback it is strongly accessible and small time locally controllable at any equilibrium time invariant discontinuous feedback laws are then constructed to asymptotically stabilize the system to the desired configuration with exponential convergence rates a simulation example is included to demonstrate the results

steering for a class of dynamic nonholonomic systems we derive control algorithms for a class of dynamic nonholonomic steering problems characterized as mechanical systems with nonholonomic constraints and symmetries we use a simplified geometric framework in developing two types of control algorithms for such systems the first targets local configuration controllability using a perturbation approach to establish results similar to steering using sinusoids the second method builds on this approach by utilizing kinematic steering algorithms for mobile robots in generating more nonlocal motion plans for this class of systems

optimization of mutual information for multiresolution image registration we propose a new method for the intermodal registration of images using a criterion known as mutual information our main contribution is an optimizer that we specifically designed for this criterion we show that this new optimizer is well adapted to a multiresolution approach because it typically converges in fewer criterion evaluations than other optimizers we have built a multiresolution image pyramid along with an interpolation process an optimizer and the criterion itself around the unifying concept of spline processing this ensures coherence in the way we model data and yields good performance we have tested our approach in a variety of experimental conditions and report excellent results we claim an accuracy of about a hundredth of a pixel under ideal conditions we are also robust since the accuracy is still about a tenth of a pixel under very noisy conditions in addition a blind evaluation of our results compares very favorably to the work of several other researchers

riemannian manifolds with maximal eigenfunction growth on any compact riemannian manifold m g of dimension n the l sp 2 normalized eigenfunctions phi sb lambda satisfy lvert rvert phi sb lambda lvert rvert sb infty leq c lambda sp n 1 2 where delta phi sb lambda lambda sp 2 phi sb lambda the bound is sharp in the class of all m g since it is obtained by zonal spherical harmonics on the standard n sphere s sp n but of course it is not sharp for many riemannian manifolds for example for flat tori mathbb r sp n gamma we say that s sp n but not mathbb r sp n gamma is a riemannian manifold with maximal eigenfunction growth the problem that motivates this paper is to determine the m g with maximal eigenfunction growth our main result is that such an m g must have a point x where the set mathscr l sb x of geodesic loops at x has positive measure in s sp ast sb xm we show that if m g is real analytic this puts topological restrictions on m for example only m s sp 2 or m mathbb r p sp 2 topologically in dimension 2 can possess a real analytic metric of maximal eigenfunction growth we further show that generic metrics on any m fail to have maximal eigenfunction growth in addition we construct an example of m g for which mathscr l sb x has positive measure for an open set of x but which does not have maximal eigenfunction growth thus it disproves a naive converse to the main result

l p norms nodal sets and quantum ergodicity abstract for small range of p 2 we improve the l p bounds of eigenfunctions of the laplacian on negatively curved manifolds our improvement is by a power of logarithm for a full density sequence of eigenfunctions we also derive improvements on the size of the nodal sets our proof is based on a quantum ergodicity property of independent interest which holds for families of symbols supported in balls whose radius shrinks at a logarithmic rate

on trajectory and force tracking control of constrained mobile manipulators with parameter uncertainty this paper studies the trajectory and force tracking control problem of mobile manipulators subject to holonomic and nonholonomic constraints with unknown inertia parameters adaptive controllers are proposed based on a suitable reduced dynamic model the defined reference signals and the mixed tracking errors the proposed controllers not only ensure the entire state of the system to asymptotically converge to the desired trajectory but also ensure the constraint force to asymptotically converge to the desired force a detailed numerical example is presented to illustrate the developed methods

bifurcation and chaotic behavior of a discrete singular biological economic system abstract in this paper the complex dynamics of a discrete singular biological economic system are first investigated firstly we establish a discrete singular biological economic system which is based on the discretization of a differential algebraic equations that is described by a ratio dependent predator prey system with harvesting and economic factor then it is shown that the system undergoes flip bifurcation and neimark sacker bifurcation in the interior of r 3 by using the new normal form of discrete singular systems the center manifold theorem and the bifurcation theory as varying the economic profit in some range numerical simulations are presented not only to illustrate our results with the theoretical analysis but also to exhibit the complex dynamic behaviors such as cascades of period doubling bifurcation in orbits of period 2 4 8 and chaotic sets these results reveal far richer dynamics of the discrete model compared with the continuous model the lyapunov exponents are numerically computed to confirm further the complexity of the dynamical behaviors

concerning the lp norm of spectral clusters for second order elliptic operators on compact manifolds in this paper we study the lp l2 mapping properties of a spectral projection operator for riemannian manifolds this operator is a generalization of the harmonic projection operator for spherical harmonics on s see c d sogge duke math j 53 1986 43 65 among other things we generalize the l2 restriction theorems of c fefferman e m stein and p tomas bull amer math sot 81 1975 477478 for the fourier transform in r to the setting of riemannian manifolds we obtain these results for the spectral projection operator as a corollary of a certain sobolev inequality involving d r2 for large r this sobolev inequality generalizes certain results for r of c kenig a ruiz and the author duke math j 55 1987 329 347 the main tools in the proof of the sobolev inequalities for riemannian manifolds are the hadamard parametrix cf l hbrmander acta mad 88 1968 341 370 and the analysis of linear partial differential equations vol iii springer verlag new york 1985 and oscillatory integral theorems of l carleson and p sjolin studia math 44 19x 287 299 and stein arm math stud 112 1986 307 357 0 1988 academic pnss iw

approximating pointwise products of laplacian eigenfunctions abstract we consider laplacian eigenfunctions on a d dimensional bounded domain m or a d dimensional compact manifold m with dirichlet conditions these operators give rise to a sequence of eigenfunctions e l l n we study the subspace of all pointwise products a n span e i x e j x 1 i j n l 2 m clearly that vector space has dimension dim a n n n 1 2 we prove that products e i e j of eigenfunctions are simple in a certain sense for any e 0 there exists a low dimensional vector space b n that almost contains all products more precisely denoting the orthogonal projection b n l 2 m b n we have 1 i j n e i e j b n e i e j l 2 e and the size of the space dim b n is relatively small for every 0 dim b n m e n 1 we obtain the same sort of bounds for products of arbitrary length as well for approximation in h 1 norm pointwise products of eigenfunctions are low rank this has implications among other things for the validity of fast algorithms in electronic structure computations

a patchy dynamic programming scheme for a class of hamilton jacobi bellman equations in this paper we present a new algorithm for the solution of hamilton jacobi bellman equations related to optimal control problems the key idea is to divide the domain of computation into subdomains which are shaped by the optimal dynamics of the underlying control problem this can result in a rather complex geometrical subdivision but it has the advantage that every subdomain is invariant with respect to the optimal dynamics and then the solution can be computed independently in each subdomain the features of this dynamics dependent domain decomposition can be exploited to speed up the computation and for an efficient parallelization since the classical transmission conditions at the boundaries of the subdomains can be avoided for their properties the subdomains are patches in the sense introduced by ancona and bressan esaim control optim calc var 4 1999 pp 445 471 several examples in two and three dimensions illustrate the properties of the new method

locally orderless registration this paper presents a unifying approach for calculating a wide range of popular but seemingly very different similarity measures our domain is the registration of n dimensional images sampled on a regular grid and our approach is well suited for gradient based optimization algorithms our approach is based on local intensity histograms and built upon the technique of locally orderless images histograms by locally orderless images are well posed and offer explicit control over the three inherent and unavoidable scales the spatial resolution intensity levels and spatial extent of local histograms through locally orderless images we offer new insight into the relations between these scales we demonstrate our unification by developing a locally orderless registration algorithm for two quite different similarity measures namely normalized mutual information and sum of squared differences and we compare these variations both theoretically and empirically finally using our algorithm we explain the empirically observed differences between two popular joint density estimation techniques used in registration parzen windows and generalized partial volume

probability density estimation using isocontours and isosurfaces applications to information theoretic image registration we present a new geometric approach for determining the probability density of the intensity values in an image we drop the notion of an image as a set of discrete pixels and assume a piecewise continuous representation the probability density can then be regarded as being proportional to the area between two nearby isocontours of the image surface our paper extends this idea to joint densities of image pairs we demonstrate the application of our method to affine registration between two or more images using information theoretic measures such as mutual information we show cases where our method outperforms existing methods such as simple histograms histograms with partial volume interpolation parzen windows etc under fine intensity quantization for affine image registration under significant image noise furthermore we demonstrate results on simultaneous registration of multiple images as well as for pairs of volume datasets and show some theoretical properties of our density estimator our approach requires the selection of only an image interpolant the method neither requires any kind of kernel functions as in parzen windows which are unrelated to the structure of the image in itself nor does it rely on any form of sampling for density estimation

pseudo linear scale space theory it has been observed that linear gaussian scale space and nonlinear morphological erosion and dilation scale spaces generated by a quadratic structuring function have a lot in common indeed far reaching analogies have been reported which seems to suggest the existence of an underlying isomorphism however an actual mapping appears to be missing in the present work a one parameter isomorphism is constructed in closed form which encompasses linear and both types of morphological scale spaces as non uniform limiting cases the unfolding of the one parameter family provides a means to transfer known results from one domain to the other moreover for any fixed and non degenerate parameter value one obtains a novel type of pseudo linear multiscale representation that is in a precise way in between the familiar ones this is of interest in its own right as it enables one to balance pros and cons of linear versus morphological scale space representations in any particular situation

stabilizability of nonholonomic control systems abstract we consider here the problem of stabilization of nonlinear hamiltonian control systems with nonholonomic constraints such systems are of interest in various applications including the control of robotic systems we discuss the formulation of hamiltonian systems with nonholonomic constraints in particular considering the differences between the dirac theory of constraints the classical theory of nonholonomic constraints and weber s theory of generalized nonholonomic constraints stabilization of systems with these constraints is discussed using the theory of hamiltonian control systems and a reduced stabilization criterion is given

isoholonomic problems and some applications we study the problem of finding the shortest loops with a given holonomy we show that the solutions are the trajectories of particles in yang mills potentials theorem 4 or equivalently the projections of kaluza klein geodesics theorem 2 applications to quantum mechanics berry s phase sect 3 and the optimal control of deformable bodies sect 6 are touched upon

deformable templates using large deformation kinematics a general automatic approach is presented for accommodating local shape variation when mapping a two dimensional 2 d or three dimensional 3 d template image into alignment with a topologically similar target image local shape variability is accommodated by applying a vector field transformation to the underlying material coordinate system of the template while constraining the transformation to be smooth globally positive definite jacobian smoothness is guaranteed without specifically penalizing large magnitude deformations of small subvolumes by constraining the transformation on the basis of a stokesian limit of the fluid dynamical navier stokes equations this differs fundamentally from quadratic penalty methods such as those based on linearized elasticity or thin plate splines in that stress restraining the motion relaxes over time allowing large magnitude deformations kinematic nonlinearities are inherently necessary to maintain continuity of structures during large magnitude deformations and are included in all results after initial global registration final mappings are obtained by numerically solving a set of nonlinear partial differential equations associated with the constrained optimization problem automatic regridding is performed by propagating templates as the nonlinear transformations evaluated on a finite lattice become singular application of the method to intersubject registration of neuroanatomical structures illustrates the ability to account for local anatomical variability

linear and bilinear estimates for oscillatory integral operators related to restriction to hypersurfaces abstract we obtain bilinear estimates for oscillatory integral operators which are variable coefficient generalizations of bilinear restriction estimates for hypersurfaces as applications we improve the known estimates for oscillatory integrals

output feedback adaptive stabilization control design for non holonomic systems with strong non linear drifts this paper investigates the problem of output feedback adaptive stabilization control design for non holonomic chained systems with strong non linear drifts including modelled non linear dynamics unmodelled dynamics and those modelled but with unknown parameters an observer and an estimator are introduced for state and parameter estimates respectively by using the integrator backstepping approach and based on the observer and parameter estimator a constructive design procedure for output feedback adaptive stabilization control is given it is shown that under some conditions the control design ensures the closed loop system is globally asymptotically stable when there is no non linear drift in the first subsystem and semiglobally asymptotically stable otherwise an example is given to show the effectiveness of the theory

a bilinear approach to the restriction and kakeya conjectures the purpose of this paper is to investigate bilinear variants of the restriction and kakeya conjectures to relate them to the standard formulations of these conjectures and to give applications of this bilinear approach to existing conjectures the methods used are based on several observations and results of bourgain see 2 6 together with some refinements by moyua vargas and vega 17 18 this paper is organized as follows in the first section we discuss bilinear restriction estimates and show how one can pass back and forth between these estimates and the standard restriction estimates we also generalize the 12 7 bilinear restriction estimate of 18 to higher dimensions in the second section we give analogues of the above results for the kakeya operator in particular we give a bilinear improvement to wolff s kakeya theorem in arbitrary dimension in the third section we give applications of these bilinear estimates in three dimensions for example we are able to improve the 42 11 exponent in wolff s restriction theorem to 34 9 we are also able to prove a sharp lp lq restriction theorem which improves on the classical l2 l4 tomas stein theorem and also give some concrete progress on a bilinear restriction conjecture of klainerman and machedon we also give a non bilinear approach to these estimates which gives weaker results but is more direct and probably has a wider range of application

discontinuous control of nonholonomic systems the problem of asymptotic convergence for a class of nonholonomic control systems via discontinuous control is addressed and solved from a new point of view it is shown that control laws which ensures asymptotic exponential convergence of the closed loop system can be easily designed if the system is described in proper coordinates in such coordinates the system is discontinuous hence the problem of local asymptotic stabilization for a class of discontinuous nonholonomic control systems is dealt with and a general procedure to transform a continuous system into a discontinuous one is presented moreover a general strategy to design discontinuous control laws yielding asymptotic convergence for a class of nonholonomic control systems is proposed the enclosed simulation results show the effectiveness of the method

logarithmic improvements in l p bounds for eigenfunctions at the critical exponent in the presence of nonpositive curvature we consider the problem of proving l p bounds for eigenfunctions of the laplacian in the high frequency limit in the presence of nonpositive curvature and more generally manifolds without conjugate points in particular we prove estimates at the critical exponent p c frac 2 d 1 d 1 where a spectrum of scenarios for phase space concentration must be ruled out our work establishes a gain of an inverse power of the logarithm of the frequency in the bounds relative to the classical l p bounds of the second author

control and stabilization of nonholonomic dynamic systems a class of inherently nonlinear control problems has been identified the nonlinear features arising directly from physical assumptions about constraints on the motion of a mechanical system models are presented for mechanical systems with nonholonomic constraints represented both by differential algebraic equations and by reduced state equations control issues for this class of systems are studied and a number of fundamental results are derived although a single equilibrium solution cannot be asymptotically stabilized using continuous state feedback a general procedure for constructing a piecewise analytic state feedback which achieves the desired result is suggested

adaptive tracking control of uncertain nonholonomic dynamic system this note considers the tracking problem of nonholonomic dynamic systems with unknown inertia parameters a new controller is proposed relying on newly defined tracking errors and the passivity property of the nonholonomic dynamic system the proposed controller ensures that the entire state of the system asymptotically tracks the desired trajectory simulation results show effectiveness of the proposed controller

nonholonomic mechanical systems with symmetry this work develops the geometry and dynamics of mechanical systems with nonholonomic constraints and symmetry from the perspective of lagrangian mechanics and with a view to control theoretical applications the basic methodology is that of geometric mechanics applied to the formulation of lagrange d alembert generalizing the use of connections and momentum maps associated with a given symmetry group to this case we begin by formulating the mechanics of nonholonomic systems using an ehresmann connection to model the constraints and show how the curvature of this connection enters into lagrange s equations unlike the situation with standard configuration space constraints the presence of symmetries in the nonholonomic case may or may not lead to conservation laws however the momentum map determined by the symmetry group still satisfies a useful differential equation that decouples from the group variables this momentum equation which plays an important role in control problems involves parallel transport operators and is computed explicitly in coordinates an alternative description using a body reference frame relates part of the momentum equation to the components of the euler poincar e equations along those symmetry directions consistent with the constraints one of the purposes of this paper is to derive this evolution equation for the momentum and to distinguish geometrically and mechanically the cases where it is conserved and those where it is not an example of the former is a ball or vertical disk rolling on a flat plane and an example of the latter is the snakeboard a modified version of the skateboard which uses momentum coupling for locomotion generation we construct a synthesis of the mechanical connection and the ehresmann connection defining the constraints obtaining an important new object we call the nonholonomic connection when the nonholonomic connection is a principal connection for the given symmetry group we show how to perform lagrangian reduction in the presence of nonholonomic constraints generalizing previous results which only held in special cases several detailed examples are given to illustrate the theory september 1994 revised march 1995 revised june 1995

global stabilizing near optimal control design for nonholonomic chained systems it is well known that a nonlinear optimal control requires the solution to a two point boundary value problem or to a nonlinear partial differential equation and that such a solution can only be obtained off line by numerical iteration in this paper a new and near optimal control design framework is proposed for controlling any nonholonomic system in the chained form the proposed design is based upon thorough study of uniform complete controllability of the corresponding linear time varying nominal system it is shown that no matter whether the first component u1d t of reference input vector is uniformly nonvanishing or simply nonconvergent to zero or vanishing or identically zero uniform complete controllability of the nominal system can be recovered by employing the proposed time folding unfolding technique upon establishing the common property of uniform complete controllability the proposed framework can be used to design both trajectory tracking control and regulation control in a systematic and unified manner using duality uniform complete observability can also be established a closed form and exponentially convergent observer can be synthesized and the controls designed using the proposed framework can be either state feedback or output feedback the tracking controls are designed using the same three step process that is design of the proposed controls starts with optimal control solutions to two linear nominal subsystems one time invariant and the other time varying the two solutions combined together render a globally stabilizing suboptimal control for the overall system then the optimality condition is invoked to determine the distance between the suboptimal control and the optimal one consequently an improved control can be obtained by introducing a nonlinear additive control term in such a way that the distance aforementioned is minimized as much as possible in closed form an example is used to show that regulation control can be designed similarly all the controls designed are in simple closed forms and hence real time implementable they are time varying and smooth globally and exponentially asymptotically stabilizing and they are near optimal since their closeness to the optimal control attainable only offline can be measured monitored on line and has been minimized

control problems in super articulated mechanical systems control of super articulated mechanical systems sams controlled mechanical system in which the dimension of the configuration space exceeds the dimension of the control input space is studied as a starting point a graphical characterization of general sams is developed in which a so called control flow diagram cfd is constructed to represent the interaction forces among the degrees of freedom of the system three types of structure namely the chain structure the tree structure and isolated points are identified degree of complexity of the system is defined based on the structure of the system a systematic backstepping type controller design is proposed for systems with a chain structure to achieve global asymptotic stability and trajectory tracking such a controller design itself illustrates the sufficient conditions for the existence of smooth feedback control such that the systems with a chain structure can be globally asymptotically stabilized the connection of the authors control algorithm with existing results is discussed

local equilibrium controllability of multibody systems controlled via shape change we study local equilibrium controllability of shape controlled multibody systems the multibody systems are defined on a trivial principal fiber bundle by a lagrangian that characterizes the base body motion and shape dynamics a potential dependent on an advected parameter e g uniform gravitational potential is considered this potential breaks base body symmetries but a symmetry subgroup is assumed to exist symmetric product formulas are derived and important properties are obtained for symmetric products of horizontal shape control vector fields and a potential vector field that is dependent on an advected parameter based on these properties sufficient conditions for local equilibrium controllability and local fiber equilibrium controllability are developed these results are applied to two classes of shape controlled multibody systems in a uniform gravitational field multibody attitude systems and neutrally buoyant multibody underwater vehicles

variational methods for multimodal image matching matching images of different modalities can be achieved by the maximization of suitable statistical similarity measures within a given class of geometric transformations handling complex nonrigid deformations in this context turns out to be particularly difficult and has attracted much attention in the last few years the thrust of this paper is that many of the existing methods for nonrigid monomodal registration that use simple criteria for comparing the intensities e g ssd can be extended to the multimodal case where more complex intensity similarity measures are necessary to this end we perform a formal computation of the variational gradient of a hierarchy of statistical similarity measures and use the results to generalize a recently proposed and very effective optical flow algorithm l alvarez j weickert and j sanchez 2000 technical report and ijcv 39 1 41 56 to the case of multimodal image registration our method readily extends to the case of locally computed similarity measures thus providing the flexibility to cope with spatial non stationarities in the way the intensities in the two images are related the well posedness of the resulting equations is proved in a complementary work o d faugeras and g hermosillo 2001 technical report 4235 inria using well established techniques in functional analysis we briefly describe our numerical implementation of these equations and show results on real and synthetic data