stability analysis and control of rigid body systems with impacts and friction many critical tasks in robotics such as locomotion or manipulation involve collisions between a rigid body and the environment or between multiple bodies methods based on sums of squares sos for numerical computation of lyapunov certificates are a powerful tool for analyzing the stability of continuous nonlinear systems and can additionally be used to automatically synthesize stabilizing feedback controllers here we present a method for applying sums of squares verification to rigid bodies with coulomb friction undergoing discontinuous inelastic impact events the proposed algorithm explicitly generates lyapunov certificates for stability positive invariance and safety over admissible non penetrating states and contact forces we leverage the complementarity formulation of contact which naturally generates the semialgebraic constraints that define this admissible region the approach is demonstrated on multiple robotics examples including simple models of a walking robot a perching aircraft and control design of a balancing robot

nonlinear decoupling via feedback a differential geometric approach the paper deals with the nonlinear decoupling and noninteracting control problems a complete solution to those problems is made possible via a suitable nonlinear generalization of several powerful geometric concepts already introduced in studying linear multivariable control systems the paper also includes algorithms concerned with the actual construction of the appropriate control laws

consistency of spectral clustering consistency is a key property of all statistical procedures analyzing randomly sampled data surprisingly despite decades of work little is known about consistency of most clustering algorithms in this paper we investigate consistency of the popular family of spectral clustering algorithms which clusters the data with the help of eigenvectors of graph laplacian matrices we develop new methods to establish that for increasing sample size those eigenvectors converge to the eigenvectors of certain limit operators as a result we can prove that one of the two major classes of spectral clustering normalized clustering converges under very general conditions while the other unnormalized clustering is only consistent under strong additional assumptions which are not always satisfied in real data we conclude that our analysis provides strong evidence for the superiority of normalized spectral clustering

on feedback equivalence of nonlinear systems conditions are derived under which a given system can be modified by means of feedback to obtain a new system whose output is influenced only by a linear and controllable dynamics

point set morphological filtering and semantic spatial configuration modeling application to microscopic image and bio structure analysis high level spatial relation and configuration modeling issues are gaining momentum in the image analysis and pattern recognition fields in particular it is deemed important whenever one needs to mine high content images or large scale image databases in a more expressive way than a purely statistically one continuing previous efforts to incorporate structural analysis by developing specific efficient morphological tools performing on mesh representations like delaunay triangulations we propose to formalize spatial relation modeling techniques dedicated to unorganized point sets we provide an original mesh lattice framework which is more convenient for structural representations of large image data by means of interest point sets and their morphological analysis the set of designed numerical operators is based on a specific dilation operator that makes it possible to handle concepts like between or left of over sparse representations of image data such as graphs based on this new theoretical framework for reasoning about images we are able to process high level queries over large histopathological images knowing that digitized histopathology is a new challenge in the field of bio imaging due to the high content nature and large size of these images

path following for the pvtol aircraft this article presents a solution to the path following problem for the planar vertical take off and landing aircraft pvtol which is applicable to a class of smooth jordan curves our path following methodology enjoys the two properties of output invariance of the path i e if the pvtol s centre of mass is initialized on the path and its initial velocity is tangent to the path then the pvtol remains on the path at all future times and boundedness of the roll dynamics further our controller guarantees that after a finite time the time average of the roll angle is zero and the pvtol does not perform multiple revolutions about its longitudinal axis

compensating drift vector fields with gradient vector fields for asymptotic submanifold stabilization we derive sufficient conditions on a drift vector field to let an asymptotically stable invariant submanifold of an input affine system without drift remain asymptotically stable for the system with drift in doing so we use the same feedback laws modulo control gain tuning such that no new feedback laws need to be designed for the system with drift our main assumption is that the vector field of the input affine system without drift assumes the form of a gradient vector field for given feedback laws we show how one can assess the performance of the system with drift only via knowledge about the system without drift finally we find that our results are relevant in synchronization problems and backstepping controllers for mechanical systems

on clusterings good bad and spectral we motivate and develop a natural bicriteria measure for assessing the quality of a clustering that avoids the drawbacks of existing measures a simple recursive heuristic is shown to have poly logarithmic worst case guarantees under the new measure the main result of the article is the analysis of a popular spectral algorithm one variant of spectral clustering turns out to have effective worst case guarantees another finds a good clustering if one exists

normalized cuts and image segmentation we propose a novel approach for solving the perceptual grouping problem in vision rather than focusing on local features and their consistencies in the image data our approach aims at extracting the global impression of an image we treat image segmentation as a graph partitioning problem and propose a novel global criterion the normalized cut for segmenting the graph the normalized cut criterion measures both the total dissimilarity between the different groups as well as the total similarity within the groups we show that an efficient computational technique based on a generalized eigenvalue problem can be used to optimize this criterion we applied this approach to segmenting static images as well as motion sequences and found the results to be very encouraging

nonlinear h control around periodic orbits abstract in this paper we study the nonlinear h control of systems with periodic orbits we develop the notion of an induced l 2 gain so called nonlinear h norm for systems where the no disturbance behavior of the system is a periodic orbit and provide conditions under which the induced l 2 gain of the system around the orbit can be made less than a specified value by state feedback this work is a natural extension of results on nonlinear h control of nonlinear systems in a neighborhood of a stable equilibrium point to the periodic orbit case synthesis of a nonlinear h state feedback controller is facilitated by the use of transverse coordinates and in particular the transverse linearization of the system

new analytical derivation of the mean annual water energy balance equation 1 the coupled water energy balance on long term time and catchment scales can be expressed as a set of partial differential equations and these are proven to have a general solution as e p f e0 p c where c is a parameter the state space of p e0 e is a set of curved faces in p e0 e three dimensional space whose projection into e p e0 p two dimensional space is a budyko type curve the analytical solution to the partial differential equations has been obtained as e e0p pn e0n 1 n parameter n representing catchment characteristics using dimensional analysis and mathematic reasoning which is different from that found in a previous study this analytical solution is a useful theoretical tool to evaluate the effect of climate and land use changes on the hydrologic cycle mathematical comparisons between the two analytical equations showed that they were approximately equivalent and their parameters had a perfectly significant linear correlation relationship while the small difference may be a result of the assumption about derivatives in the previous study

a sufficient condition for local controllability of nonlinear systems along closed orbits a computable sufficient condition for determining local controllability of a differential nonlinear control system along a reference closed orbit is presented comparisons to other results on local controllability along a reference trajectory are made

design of coupled harmonic oscillators for synchronization and coordination synchronization and coordination of coupled oscillators are fundamental behaviors in complex dynamical systems this paper considers the design of coupled harmonic oscillators to generate an orbitally stable limit cycle of prescribed oscillation profile based on the floquet theory and averaging techniques necessary and sufficient conditions are obtained for nonlinear coupling functions to achieve local exponential convergence to a desired orbit unlike globally convergent methods based on contraction analysis the result applies to oscillators without flow invariance properties insights into coordination mechanisms are gained through interpretation of the coupling structure as a directed graph the theory is illustrated by simple tutorial examples

transverse linearization for controlled mechanical systems with several passive degrees of freedom this study examines the mechanical systems with an arbitrary number of passive non actuated degrees of freedom and proposes an analytical method for computing coefficients of a linear controlled system solutions of which approximate dynamics transverse to a feasible motion this constructive procedure is based on a particular choice of coordinates and allows explicit introduction of a moving poincare section associated with a nontrivial finite time or periodic motion in these coordinates transverse dynamics admits analytical linearization before any control design if the forced motion of an underactuated mechanical system is periodic then this linearization is an indispensable and constructive tool for stabilizing the cycle and for analyzing its orbital in stability the technique is illustrated with two challenging examples the first one is stabilization of a circular motions of a spherical pendulum on a puck around its upright equilibrium the other one is creating stable synchronous oscillations of an arbitrary number of planar pendula on carts around their unstable equilibria

mean shift spectral clustering in recent years there has been a growing interest in clustering methods stemming from the spectral decomposition of the data affinity matrix which are shown to present good results on a wide variety of situations however a complete theoretical understanding of these methods in terms of data distributions is not yet well understood in this paper we propose a spectral clustering based mode merging method for mean shift as a theoretically well founded approach that enables a probabilistic interpretation of affinity based clustering through kernel density estimation this connection also allows principled kernel optimization and enables the use of anisotropic variable size kernels to match local data structures we demonstrate the proposed algorithm s performance on image segmentation applications and compare its clustering results with the well known mean shift and normalized cut algorithms

efficient graph based image segmentation this paper addresses the problem of segmenting an image into regions we define a predicate for measuring the evidence for a boundary between two regions using a graph based representation of the image we then develop an efficient segmentation algorithm based on this predicate and show that although this algorithm makes greedy decisions it produces segmentations that satisfy global properties we apply the algorithm to image segmentation using two different kinds of local neighborhoods in constructing the graph and illustrate the results with both real and synthetic images the algorithm runs in time nearly linear in the number of graph edges and is also fast in practice an important characteristic of the method is its ability to preserve detail in low variability image regions while ignoring detail in high variability regions

constrained model predictive manifold stabilization based on transverse normal forms the optimization based stabilization of manifolds for nonlinear dynamical systems with constraints is investigated manifolds in the state or output space are considered for which the original system description can be transformed into a so called transverse normal form with this formulation the motion of the system transverse and tangential to the manifold can be separately described the transverse normal form is combined with a tailored model predictive control scheme to achieve the objectives of stabilizing the manifold rendering it invariant and imposing a desired motion on the manifold under due consideration of constraints furthermore the stabilization of the manifold is prioritized over the movement on the manifold convergence of the model predictive control scheme is proven the applicability of the proposed concept is demonstrated by an illustrative simulation example

on local transverse feedback linearization given a control affine system and a controlled invariant submanifold we present necessary and sufficient conditions for local feedback equivalence to a system whose dynamics transversal to the submanifold are linear and controllable a key ingredient used in the analysis is the new notion of transverse controllability indices of a control system with respect to a set

exact and approximate feedback linearization without the linear controllability assumption the feedback linearization problem of nonlinear control systems has been solved in the literature under the assumption that the nonlinear system is linearly controllable in this paper the assumption of linear controllability is removed necessary and sufficient conditions are given through lie orbital symmetries thus giving a geometric characterization of the problem in the analytic case both the exact and the approximate linearization problems are considered in the analytic case

sdp based approximation of stabilising solutions for periodic matrix riccati differential equations numerically finding stabilising feedback control laws for linear systems of periodic differential equations is a nontrivial task with no known reliable solutions the most successful method require

inertia theorems for the periodic liapunov equation and periodic riccati equation the inertia theorems for the time invariant liapunov equation and time invariant riccati equation are generalized to the case were the coefficient matrices are periodically time varying

controlled invariance for affine control systems the paper gives a solution of the disturbance decoupling problem for non linear systems the main difference between this and related works in the field is the construction of a now state dependent basis for the inputs

on the control of complementary slackness juggling mechanical systems studies the feedback control of a class of complementary slackness hybrid mechanical systems roughly the systems we study are composed of an uncontrollable part the object and a controlled one the robot linked by a unilateral constraint and an impact rule a systematic and general control design method for this class of systems is proposed the approach is a nontrivial extension of the one degree of freedom dof juggler control design in addition to the robot control it is also useful to study some intermediate controllability properties of the object s impact poincare mapping which generally takes the form of a nonlinear discrete time system the force input mainly consists of a family of dead beat feedback control laws introduced via a recursive procedure and exploiting the underlying discrete time structure of the system the main goal of the paper is to highlight the role of various physical and control properties characteristic of the system on its stabilizability properties and to propose solutions in certain cases

transverse linearization for impulsive mechanical systems with one passive link a general method for planning and orbitally stabilizing periodic motions for impulsive mechanical systems with underactuation one is proposed for each such trajectory we suggest a constructive procedure for defining a sufficient number of nontrivial quantities that vanish on the orbit after that we prove that these quantities constitute a possible set of transverse coordinates finally we present analytical steps for computing linearization of dynamics of these coordinates along the motion as a result for each such planned periodic trajectory a hybrid transverse linearization for dynamics of the system is computed in closed form the derived impulsive linear system can be used for stability analysis and for design of exponentially orbitally stabilizing feedback controllers a geometrical interpretation of the method is given in terms of a novel concept of a moving poincare section the technique is illustrated on a devil stick example

automatically finding clusters in normalized cuts normalized cuts is a state of the art spectral method for clustering by applying spectral techniques the data becomes easier to cluster and then k means is classically used unfortunately the number of clusters must be manually set and it is very sensitive to initialization moreover k means tends to split large clusters to merge small clusters and to favor convex shaped clusters in this work we present a new clustering method which is parameterless independent from the original data dimensionality and from the shape of the clusters it only takes into account inter point distances and it has no random steps the combination of the proposed method with normalized cuts proved successful in our experiments

output stabilization and maneuver regulation a geometric approach this paper investigates maneuver regulation for single input control affine systems from a geometric perspective the maneuver regulation problem is converted to output stabilization and necessary and sufficient conditions are provided to solve the latter problem by feedback linearizing the dynamics transverse to a suitable embedded submanifold of the state space when specialized to the linear time invariant setting this work recovers well known results on output stabilization

finding maximum linear subsystems of nonlinear systems with outputs the focus of this paper is to find the maximum input output linearized subsystem necessary and sufficient conditions are presented under which there exist a static state feedback and a coordinate change to input output linearize the system so that the linear subsystem has the largest dimension a systematic method is also developed to compute the desired feedback and coordinate change

feedback linearization of transverse dynamics for periodic orbits in r 3 with points of transverse controllability loss research supported in part by nsf under grant pyi ecs 9396296 by afosr under grant afosr 94nm006 and by a grant from hughes aircraft company

analytical derivation of the budyko curve based on rainfall characteristics and a simple evaporation model the budyko curve is often used to estimate the actual evaporation as a function of the aridity index in a catchment different empirical equations exist to describe this relationship however these equations have very limited physical background the model concept presented in this paper is physically based and uses only measurable parameters it makes use of two types of evaporation interception and transpiration it assumes that interception can be modeled as a threshold process on a daily time scale if multiplied with the rainfall distribution function integrated and multiplied with the expected number of rain days per month the monthly interception is obtained in a similar way the monthly interception can be upscaled to annual interception analogous to the interception process transpiration can be modeled as a threshold process at a monthly time scale and can be upscaled by integration and multiplication with the expected number of rain months the expected rain days permonth are modeled in two ways as a fixed proportion of the monthly rainfall and as a power function based on markov properties of rainfall the latter is solved numerically it appears that on an annual basis the analytical model does not differ much from the numerical solution hence the analytical model is used and applied on 10 locations in different climates this paper shows that the empirical budyko curve can be constructed on the basis of measurable parameters representing evaporation threshold values and the expected number of rain days and rain months and in addition a monthly moisture carryover amount for semiarid zones

image segmentation by a contrario simulation segmenting an image into homogeneous regions generally involves a decision criterion to establish whether two adjacent regions are similar decisions should be adaptive to get robust and accurate segmentation algorithms avoid hazardous a priori and have a clear interpretation we propose a decision process based on a contrario reasoning two regions are meaningfully different if the probability of observing such a difference in pure noise is very low since the existing analytical methods are intractable in our case we extend them to allow a mixed use of analytical computations and monte carlo simulations the resulting decision criterion is tested experimentally through a simple merging algorithm which can be used as a post filtering and validation step for existing segmentation methods

on the largest feedback linearizable subsystem abstract a feedback invariant set of integers is associated with any nonlinear multivariable system which is linear with respect to the inputs it is shown to be the set of controllability indices of the largest feedback linearizable subsystem i e the largest subsystem which can be made locally linear and controllable by means of nonsingular feedback transformations

coordinated path following for unicycles we formulate a coordinated path following problem for n unicycle mobile robots as an instance of a nested set stabilization problem stabilization of the first set corresponds to driving the unicycles to their assigned paths stabilization of the second set a subset of the first corresponds to meeting the coordination specification the first set is stabilized for initial conditions sufficiently close to the set in a decentralized manner using feedback linearization for general coordination tasks we utilize feedback linearization to stabilize the nested set in a centralized manner again for initial conditions sufficiently close to the second set in the special case in which coordination entails making the unicycles maintain a formation along their paths we employ a semi distributed control law under less restrictive communication assumptions experimental results are provided

rapidly exponentially stabilizing control lyapunov functions and hybrid zero dynamics this paper addresses the problem of exponentially stabilizing periodic orbits in a special class of hybrid models systems with impulse effects through control lyapunov functions the periodic orbit is assumed to lie in a c1 submanifold z that is contained in the zero set of an output function and is invariant under both the continuous and discrete dynamics the associated restriction dynamics are termed the hybrid zero dynamics the orbit is furthermore assumed to be exponentially stable within the hybrid zero dynamics prior results on the stabilization of such periodic orbits with respect to the full order dynamics of the system with impulse effects have relied on input output linearization of the dynamics transverse to the zero dynamics manifold the principal result of this paper demonstrates that a variant of control lyapunov functions that enforce rapid exponential convergence to the zero dynamics surface z can be used to achieve exponential stability of the periodic orbit in the full order dynamics thereby significantly extending the class of stabilizing controllers the main result is illustrated on a hybrid model of a bipedal walking robot through simulations and is utilized to experimentally achieve bipedal locomotion via control lyapunov functions

a canonical expansion for nonlinear systems the importance of differential geometry in particular lie brackets of vector fields in the study of nonlinear systems is well established under very mild assumptions we show that a real analytic nonlinear system has an expansion in which the coefficients are computed in terms of lie brackets this expansion occurs in a special coordinate system we also explain the concept of a pure feedback system for control design involving a nonlinear system one approach is to put the system in its canonical expansion and approximate by that part having only feedback paths

nonlinear control of mechanical systems with an unactuated cyclic variable numerous robotic tasks associated with underactuation have been studied in the literature for a large number of these in the plane the mechanical models have a cyclic variable the cyclic variable is unactuated and all shape variables are independently actuated this paper formulates and solves two control problems for this class of models if the generalized momentum conjugate to the cyclic variable is not conserved conditions are found for the existence of a set of outputs that yields a system with a one dimensional exponentially stable zero dynamics i e an exponentially minimum phase system along with a dynamic extension that renders the system locally input output decouplable if the generalized momentum conjugate to the cyclic variable is conserved a reduced system is constructed and conditions are found for the existence of a set of outputs that yields an empty zero dynamics along with a dynamic extension that renders the system feedback linearizable a common element in these two feedback problems is the construction of a scalar function of the configuration variables that has relative degree three with respect to one of the input components the function arises by partially integrating the conjugate momentum the results are illustrated on two balancing tasks and on a ballistic flip motion

weighted graph cuts without eigenvectors a multilevel approach a variety of clustering algorithms have recently been proposed to handle data that is not linearly separable spectral clustering and kernel k means are two of the main methods in this paper we discuss an equivalence between the objective functions used in these seemingly different methods in particular a general weighted kernel k means objective is mathematically equivalent to a weighted graph clustering objective we exploit this equivalence to develop a fast high quality multilevel algorithm that directly optimizes various weighted graph clustering objectives such as the popular ratio cut normalized cut and ratio association criteria this eliminates the need for any eigenvector computation for graph clustering problems which can be prohibitive for very large graphs previous multilevel graph partitioning methods such as metis have suffered from the restriction of equal sized clusters our multilevel algorithm removes this restriction by using kernel k means to optimize weighted graph cuts experimental results show that our multilevel algorithm outperforms a state of the art spectral clustering algorithm in terms of speed memory usage and quality we demonstrate that our algorithm is applicable to large scale clustering tasks such as image segmentation social network analysis and gene network analysis

nonlinear model predictive control for constrained output path following we consider the tracking of geometric paths in output spaces of nonlinear systems subject to input and state constraints without pre specified timing requirements commonly referred to as constrained output path following problems specifically we propose a predictive control approach to constrained path following problems with and without velocity assignments we present sufficient convergence conditions based on terminal regions and end penalties furthermore we analyze the geometric nature of constrained output path following problems and thereby provide insight into the computation of suitable terminal control laws and terminal regions we draw upon an example from robotics to illustrate our findings

periodic motion planning for virtually constrained euler lagrange systems the paper suggests an explicit form of a general integral of motion for some classes of dynamical systems including n degrees of freedom euler lagrange systems subject to n 1 virtual holonomic

on the linear equivalents of nonlinear systems this paper studies feedback equivalence of nonlinear systems an equivalence relation is established for the systems x f x u a complete characterization of the class of nonlinear systems which are equivalent to controllable linear systems is obtained

on the largest input output linearizable subsystem feedback input output linearization is considered in this paper the main result provides the necessary and sufficient conditions to determine the largest dimension of a linear subsystem achievable by a suitable coordinate change after an input output linearization feedback has been applied a systematic method to find the desired coordinate change is also given in this paper

stable synchronization of mechanical system networks in this paper we address stabilization of a network of underactuated mechanical systems with unstable dynamics the coordinating control law stabilizes the unstable dynamics with a term derived from the method of controlled lagrangians and synchronizes the dynamics across the network with potential shaping designed to couple the mechanical systems the coupled system is lagrangian with symmetry and energy methods are used to prove stability and coordinated behavior two cases of asymptotic stabilization are discussed one yields convergence to synchronized motion staying on a constant momentum surface and the other yields convergence to a relative equilibrium we illustrate the results in the case of synchronization of n carts each balancing an inverted pendulum

on regionalizing the turc mezentsev water balance formula 1 the turc mezentsev water balance formula is a simple and efficient mathematical formulation relating long term average streamflow to long term average precipitation and potential evaporation usually it is applied in its original form i e without parameterization this paper aims to assess the possibilities of regionalizing this formula for improved efficiency on ungaged catchments four regionalization options are compared based on i the relative error ii the arithmetic difference iii the correcting factor of the aridity index and iv the shape factor the four alternatives are assessed in terms of efficiency and robustness on a large set of 609 french catchments we show that introducing a correcting factor of the aridity index provides the best regionalization solution

design of orbitally stable zero dynamics for a class of nonlinear systems a method for the generation of globally attractive limit cycles for nonlinear systems is presented it consists in designing an output that when regulated through a suitable feedback forces a limit cycle in the zero dynamics conditions are then given to ensure that a globally attractive limit cycle in the zero dynamics results in a globally attractive limit cycle in the whole system the method is illustrated on the torque control of an induction motor

worst case analysis of set union algorithms this paper analyzes the asymptotic worst case running time of a number of variants of the well known method of path compression for maintaining a collection of disjoint sets under union we show that two one pass methods proposed by van leeuwen and van der weide are asymptotically optimal whereas several other methods including one proposed by rein and advocated by dijkstra are slower than the best methods

the minimum description length principle in coding and modeling we review the principles of minimum description length and stochastic complexity as used in data compression and statistical modeling stochastic complexity is formulated as the solution to optimum universal coding problems extending shannon s basic source coding theorem the normalized maximized likelihood mixture and predictive codings are each shown to achieve the stochastic complexity to within asymptotically vanishing terms we assess the performance of the minimum description length criterion both from the vantage point of quality of data compression and accuracy of statistical inference context tree modeling density estimation and model selection in gaussian linear regression serve as examples

a mathcal b invariant distributions and disturbance decoupling of nonlinear systems the concept of a b invariant subspaces has resulted in a unified approach to many of the basic structural properties of time invariant linear systems w m wonham lecture notes in economics and mathematical systems vol 101 springer verlag new york 1974 the purpose of this paper is to introduce the more general notion of a mathcal b invariant distributions on differentiable manifolds and to use this idea to study the disturbance decoupling problem for a class of nonlinear systems which evolve on real analytic manifolds

nonlinear control of a swinging pendulum we propose a nonlinear controller to regulate the swinging energy of the pendulum for a cart and pendulum system roughly speaking the controller is designed to regulate an output the swing energy while providing internal stability regulating the cart position it is difficult to apply many of the standard nonlinear control design techniques since the output zeroing manifold does not contain any equilibrium points and the relative degree of the system is not constant in contrast to controllers that use a command generator and possibly a time varying feedback our control law is a simple autonomous nonlinear controller we analyze the stability of the closed loop system using an lv small gain approach on a transverse linearization of the system about the desired periodic orbit one can easily extend this approach to analyze the robustness of the control system with respect to disturbances and parameter variations experimental results demonstrate the effectiveness of the nonlinear controller

virtual holonomic constraints for euler lagrange systems this technical brief investigates virtual holonomic constraints for euler lagrange systems with n degrees of freedom and n 1 controls in our framework a virtual holonomic constraint is a relation specifying n 1 configuration variables in terms of a single angular configuration variable the enforcement by feedback of such a constraint induces a desired repetitive behavior in the system we give conditions under which a virtual holonomic constraint is feasible i e it can be made invariant by feedback and it is stabilizable we provide sufficient conditions under which the dynamics on the constraint manifold correspond to an euler lagrange system these ideas are applied to the problem of swinging up an underactuated pendulum while guaranteeing that the second link does not fall over

an automatic shape independent clustering technique this article describes a clustering technique that can automatically detect any number of well separated clusters which may be of any shape convex and or non convex this is in contrast to most other techniques which assume a value for the number of clusters and or a particular cluster structure the proposed technique is based on an iterative partitioning of the relative neighborhood graph coupled with a post processing step for merging small clusters techniques for improving the efficiency of the proposed scheme are implemented the clustering scheme is able to detect outliers in data it is also able to indicate the inherent hierarchical nature of the clusters present in a data set moreover the proposed technique is also able to identify the situation when the data do not have any natural clusters at all results demonstrating the effectiveness of the clustering scheme are provided for several data sets

feedback linearization of transverse dynamics for periodic orbits in this paper we give necessary and sufficient conditions for feedback linearization of the transverse dynamics tfl of a nonlinear affine single input system in a neighborhood of a periodic orbit the tfl procedure provides a means of finding coordinates that are tuned to the structure of the control system with respect to the periodic orbit an autonomous feedback control providing exponential stability of the periodic orbit is easily designed in the transverse coordinate system

generating self excited oscillations via two relay controller a tool for the design of a self excited oscillation of a desired amplitude and frequency in linear plants by means of the variable structure control is proposed an approximate approach based on the describing function method is given which requires that the mechanical plant should be a low pass filter the hypothesis that usually holds when the oscillations are relatively fast the proposed approach is demonstrated via the controller design and experiments on the furuta pendulum

asymptotic stabilization of submanifolds embedded in riemannian manifolds we study control problems in which systems whose states spaces are riemannian manifolds must be steered towards embedded submanifolds of their state spaces in a stable fashion i e feedback laws rendering the given submanifold asymptotically stable are sought bringing the closed loop to the form of a gradient system with drift we find that the gradient part can be scaled in a fashion so as to guarantee asymptotic stability of the desired submanifold under this circumstance we show that solutions of the system can be brought to an arbitrarily small neighborhood of the submanifold in arbitrary time thereafter we derive an algebraic condition under which the control vector fields can be brought to the desired form lastly we recast our algebraic condition in terms of vertical and horizontal spaces for the case that the submanifold is an equivalence class

spatial proximity physical similarity regression and ungaged catchments a comparison of regionalization approaches based on 913 french catchments 1 given the contradictory results from recent studies this paper compares classical regionalization schemes of catchment model parameters over the wide range of hydroclimates found in france to ensure the generality of the conclusions we used two lumped rainfall runoff models applied to daily data over a large set of 913 french catchments three types of approaches were considered regionalization using regression regionalization based on spatial proximity and regionalization based on physical similarity this comparison shows that in france where a dense network of gauging stations is available spatial proximity provides the best regionalization solution the regression approach is the least satisfactory with results very close to those obtained using one median parameter set for the whole country the physical similarity approach is intermediary however the results obtained with these three methods lag far behind those obtained by full model calibration our results also show that some improvement could be made by combining spatial proximity and physical similarity and that there is still considerable room for progress in the field of ungaged catchment modeling

converse lyapunov functions for exponentially stable periodic orbits abstract in this paper we present a technique for constructing a class of quadratic lyapunov functions for exponentially stable periodic orbits this construction is facilitated by the use of a special set of local coordinates that serve to highlight the tangential and transverse dynamics of the system