reduction principles and the stabilization of closed sets for passive systems in this technical note we explore the stabilization of closed invariant sets for passive systems and present conditions under which a passivity based feedback asymptotically stabilizes the goal set our results rely on novel reduction principles allowing one to extrapolate the properties of stability attractivity and asymptotic stability of a dynamical system from analogous properties of the system on an invariant subset of the state space

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

a time domain technique for mechanism extraction the properties of scattered fields from a structure can be better evaluated from the characteristics of the individual scatterers decomposition techniques can be classified either as a matrix or an integral formulation with either formulation aspect pattern or frequency information of a scattering center can be obtained emphasis will be placed on an integral time domain isolation extraction technique to obtain the frequency characteristics of scattering mechanisms this technique has its origins in the time domain interpretation of scattered fields

kyp lemma based stability and control law design for differential linear repetitive processes with applications repetitive processes are a class of two dimensional systems that have physical applications including the design of iterative learning control laws where experimental validation results have been reported this paper uses the kalman yakubovich popov lemma to develop new stability tests for differential linear repetitive processes that are computationally less intensive than those currently available these tests are then extended to allow control law design for stability and performance

a path following problem for a class of non holonomic control systems with noise this paper deals with a path following problem for a system affected by noise and proposes a dynamic inversion based controller that makes use of the error between the real position and a suitable path location an estimate of such error is given in terms of the noise bounds showing the practical stability of the closed loop system the results presented in this article apply to a subclass of chaplygin control systems which includes several common mechanical systems as an example the developed strategy has been applied to maneuver a kinematic model of a system moving in a 3 dimensional space in such a way that a point located at a positive distance from its center of geometry is driven towards a given path

tangent cones to discriminant loci for families of hypersurfaces a deformation of a variety with nonisolated hypersurface singularities such as a projective hypersurface or a theta divisor of an abelian variety determines a rational map of the singular locus to projective space and the resulting projective geometry of the singular locus describes how the singularities propagate in the deformation the basic principle is that the projective model of the singular locus is dual to the tangent cone to the discriminant of the deformation a detailed study of the method which emerged from interpreting andreotti mayer s work on theta divisors in terms of schlessinger s deformation theory of singularities is given along with examples applications and multiplicity formulas introduction this paper is about the geometry associated to deformations of nonisolated hypersurface singularities the basic principle is that a deformation of a hypersurface determines a projective model of the singular locus whose dual variety is the projectivized tangent cone to the discriminant this includes an infinitesimal form of bertini s theorem for a linear system of divisors and a converse to andreotti mayer s condition for double points of theta divisors now we describe the main results more precisely working in the category of complex analytic spaces let x be a space which can locally be written as a hypersurface of a nonsingular space and let x s be a deformation of x ir 1 0 then t1 the sheaf of first order deformations of x is a line bundle on sg x the singular locus of x and ir determines a kodaira spencer linear map to s k h0 t1 i e a linear system on the singular locus if x and s are nonsingular this linear system has no base locus and the corresponding morphism sg x pto s satisfies 0 p ir p tpx for p e sg x hence is called the gauss map of ir for a projective hypersurface of degree d x is the d fold veronese map restricted to the singular locus and for the theta divisor of an abelian variety 0 is the rational map assigning to a double point its quadric tangent cone assuming the restriction of ir to the critical locus c c x is proper consider the discriminant locus d ir c with its reduced analytic structure in addition to the above suppose finally that c is nonsingular of the expected codimension in x duality theorem there is a finite collection of 8ubvarietie8 zz of sg x which is intrinsic to the analytic space sg x and includes the irreducible components received by the editors march 31 1987 the contents of this paper were presented october 18 1986 by the first author in the special session on singularities and algebraic geometry at the charlotte north carolina meeting of the ams 1980 mathematics subject classification 1985 revision primary 14d15 14n05 secondary 32g11 53c57 d1988 american mathematical society 0002 9947 88 1 00 25 per page

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

a validation analysis of huynen s target descriptor interpretations of the mueller matrix elements in polarimetric radar returns using kennaugh s physical optics impulse response formulation by applying correction to kennaugh s impulse response formulation for smooth convex targets huynen s descriptors have been shown to relate to specular geometry at high frequencies a time gating technique has been developed to separate the specular signature from the creeping wave contribution in the total backscattered return this enables approximately equivalent high frequency data to be extracted from bandlimited scattering measurements it is shown that the validation of the target descriptor interpretations of the mueller matrix elements with the isolated specular contribution data is acceptable whereas the validation of these interpretations with the total backscattered data seems doubtful

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

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

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

inverse methods in electromagnetic imaging this nato advanced research workshop on inverse methods in electro magnetic imaging has come at a time of greatly increased interest in using electromagnetic imaging methods as tools for remote sens ing material testing and medical diagnosis spurred by a combina tion of recent advances in sensor and device technology spanning the entire m to sub mm wavelengths the infra red optical ultraviolet and x ray regions of the electromagnetic spectrum the rapid devel opment of radar polarimetry including the deployment of active pas sive sensors on spacecraft platforms it has become evident that these advanced imaging techniques can only then become useful when supported by well developed inverse scattering theories for proper consistent and efficient data interpretation however these data interpretative techniques which are urgently needed in several mil itary and civilian areas are in many aspects not yet completely de veloped thus the main purpose of this nato arw imei 1983 was to bring together internationally renowned key experts of this new scientific discipline of inverse methods in electromagnetic imaging and have them prepare well written overviews treatises on new areas papers on special topics have them deliberate on still unre sovled problems in worki g discussion groups and then report back on their important findings to the entire nato scientific community in dealing with these exciting current developments

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

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

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

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

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

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