small time local controllability for a class of homogeneous systems in this paper we consider the local controllability problem for control affine systems that are homogeneous with respect to a one parameter family of dilations corresponding to time scaling in the control we construct and derive properties of a variational cone that completely characterizes local controllability for these homogeneous systems in the process we are able to give a bound on the order in terms of the integers describing the dilation of perturbations that do not alter the local controllability property our approach uses elementary taylor expansions and avoids unnecessarily complicated open mapping theorems to prove local controllability examples are given that illustrate the main results

controllability and stability analysis of planar snake robot locomotion this paper contributes to the understanding of snake robot locomotion by employing nonlinear system analysis tools for investigating fundamental properties of snake robot dynamics the paper has five contributions 1 a partially feedback linearized model of a planar snake robot influenced by viscous ground friction is developed 2 a stabilizability analysis is presented proving that any asymptotically stabilizing control law for a planar snake robot to an equilibrium point must be time varying 3 a controllability analysis is presented proving that planar snake robots are not controllable when the viscous ground friction is isotropic but that a snake robot becomes strongly accessible when the viscous ground friction is anisotropic the analysis also shows that the snake robot does not satisfy sufficient conditions for small time local controllability stlc 4 an analysis of snake locomotion is presented that easily explains how anisotropic viscous ground friction enables snake robots to locomote forward on a planar surface the explanation is based on a simple mapping from link velocities normal to the direction of motion into propulsive forces in the direction of motion 5 a controller for straight line path following control of snake robots is proposed and a poincare map is investigated to prove that the resulting state variables of the snake robot except for the position in the forward direction trace out an exponentially stable periodic orbit

a necessary condition for feedback stabilization abstract we give a new necessary condition for the existence of a static or dynamic continuous asymptotically stabilizing feedback control for the system x dot f x u we apply our condition to give an example of a system in r 3 which is small time locally controllable satisfies brockett s second and third condition and cannot be locally asymptotically stabilized by employing a static or dynamic continuous feedback law

nilpotent and high order approximations of vector field systems this paper is concerned with the study of structurally stable properties associated with systems described by one or several real analytic vector fields via approximating systems which retain inf

affine and bilinear systems on lie groups abstract in this paper we study affine and bilinear systems on lie groups we show that there is an intrinsic connection between the solutions of both systems such relation allows us to obtain some preliminary controllability results of affine systems on compact and solvable lie groups we also show that the controllability property of bilinear systems is very restricted and may only be achieved if the state space g is an euclidean space

controllability of a planar body with unilateral thrusters investigates the minimal number of unilateral thrusters required for different versions of nonlinear controllability of a planar rigid body for one to three unilateral thrusters one gets a new property with each additional thruster one thruster suffices for small time accessibility on the body s state space tse 2 two thrusters suffice for global controllability on tse 2 and three thrusters suffice for small time local controllability at zero velocity states

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

on the analysis of nonlinear nilpotent switched systems using the hall sussmann system abstract we consider an open problem on the stability of nonlinear nilpotent switched systems posed by daniel liberzon partial solutions to this problem were obtained as corollaries of global nice reachability results for nilpotent control systems the global structure is crucial in establishing stability we show that a nice reachability analysis may be reduced to the reachability analysis of a specific canonical system the nilpotent hall sussmann system furthermore local nice reachability properties for this specific system imply global nice reachability for general nilpotent systems we derive several new results revealing the elegant lie algebraic structure of the nilpotent hall sussmann system

on the global controllability of nonlinear systems fountains recurrence and applications to hamiltonian systems in this paper a form of open local accessibility for nonlinear control systems is introduced called the continuous fountain condition subject to the conditions that i the states of a system are continuous fountains and ii one of various recurrence conditions holds it is established that the system state space is globally controllable it is shown that these controllability results imply the controllability of certain subsets of the state space of hamiltonian control systems called energy slices the relations between the notion of a fountain and i local accessibility and ii the full lie algebra rank condition for control affine systems are investigated finally the results in this paper are shown to have application to hierarchical hybrid control theory in that they give conditions for a finite analytic partition to satisfy the so called in block controllability property this is illustrated with a linear mass spring system example

viscosity solutions of the bellman equation for exit time optimal control problems with vanishing lagrangians we study the hamilton jacobi bellman equation for undiscounted exit time optimal control problems for fully nonlinear systems and fully nonlinear singular lagrangians using the dynamic programming approach we prove a local uniqueness theorem characterizing the value functions for these problems as the unique viscosity solutions of the corresponding hamilton jacobi bellman equations that satisfy appropriate boundary conditions the novelty of this theorem is in the relaxed hypotheses on the lower bound on the lagrangian and the very general assumptions on the target set as a corollary we show that the value function for the fuller problem is the unique viscosity solution of the corresponding hamilton jacobi bellman equation that vanishes at the origin and satisfies certain growth conditions this implies as special cases first that the value function of this problem is the unique proper viscosity solution of the corresponding hamilton jacobi bellman equation in the class of all functions which are continuous in the plane and null at the origin and second that this value function is the unique viscosity solution of that equation in a class which includes functions which are not bounded below we also apply our results to the degenerate eikonal equation of geometric optics and to the shape from shading equations in image processing our theorem also applies to problems with noncompact targets and unbounded control sets whose lagrangians take negative values

an analysis of a new class of integration algorithms for elastoplastic constitutive relations an accuracy analysis of a new class of integration algorithms for finite deformation elastoplastic constitutive relations recently proposed by the authors is carried out in this paper for simplicity attention is confined to infinitesimal deformations the integration rules under consideration fall within the category of return mapping algorithms and follow in a straightforward manner from the theory of operator splitting applied to elastoplastic constitutive relations general rate independent and rate dependent behaviour with plastic hardening or softening associated or non associated flow rules and nonlinear elastic response can be efficiently treated within the present framework isoerror maps are presented which demonstrate the good accuracy properties of the algorithm even for strain increments much larger than the characteristic strains at yielding

single boson realizations of so 3 and so 2 1 realizations of the lie algebras so 3 and so 2 1 are developed which are functions of integer powers of creation and destruction operators for a single boson i e adagger m and a m as well as a function of the associated single boson number operator n identical to adagger a three types of realizations of the lie algebra elements together with the corresponding casimir operators are developed which depend on arbitrary m periodic functions of n a generic form is achieved in terms of devised m quanta operators the boson representation space is infinite dimensional but may contain as many as two imbedded invariant subspaces a distinction is made between irreducible representations of a lie algebra which lead to global group representations and those which lead only to local non integrable group representations it is shown that the two non unitary types of representations developed are equivalent to the unitary one for m 1 specific choices for the m periodic functions lead to realizations known in the literature

sl 2 modules by sl 2 coherent states irreducible sp 4 module with highest weight labeled by the azimuthal and magnetic quantum numbers l and m is split into the direct sums of the irreducible su 2 and su 1 1 submodules in four different ways finite integer unitary irreducible subspaces corresponding to the orbital angular momentum algebra su 2 infinite positive discrete series of su 1 1 with an arbitrary half integer bargmann index and the positive and negative discrete series of su 1 1 with both the bargmann indices 1 4 and 3 4 even and odd coherent states for the positive su 1 1 submodules with the bargmann indices 1 4 and 3 4 are constructed and it is shown that they enjoy the property of completeness by two appropriate positive definite measures we show that the even and odd coherent states themselves form the positive discrete series of su 1 1 with the bargmann indices 1 4 and 3 4 respectively for these even and odd coherent states we consider the uncertainty relations for the x and y components of the angular m

on the positive output controllability of linear time invariant systems this paper considers the output controllability of autonomous linear control systems that are subject to non negative input constraints based on the evaluation of the geometric properties of the system necessary and sufficient conditions are proposed for the positive output controllability of continuous linear time invariant systems to aid in the practical evaluation of positive output controllability additional sufficient conditions are derived for which efficient numerical techniques exist these conditions are evaluated over a set of numerical examples which support the theoretical results

a novel optimal exponential based integration algorithm for von mises plasticity with linear hardening theoretical analysis on yield consistency accuracy convergence and numerical investigations summary in this communication we propose a new exponential based integration algorithm for associative von mises plasticity with linear isotropic and kinematic hardening which follows the ones presented by the authors in previous papers in the first part of the work we develop a theoretical analysis on the numerical properties of the developed exponential based schemes and in particular we address the yield consistency exactness under proportional loading accuracy and stability of the methods in the second part of the contribution we show a detailed numerical comparison between the new exponential based method and two classical radial return map methods based on backward euler and midpoint integration rules respectively the developed tests include pointwise stress strain loading histories iso error maps and global boundary value problems the theoretical and numerical results reveal the optimal properties of the proposed scheme copyright 2006 john wiley sons ltd

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

asymptotically stabilizing feedback controls abstract the problem considered is the existence and construction of an asymptotically stabilizing feedback control for a rest solution of an n dimensional single input affine control system the method is to construct high order homogeneous approximations of the vector fields defining the control system which then describe an approximating control system such that an asymptotically stabilizing control of the latter system is a local asymptotically stabilizing control of the original system unlike linear approximations there are many possible nonlinear homogeneous approximations these are constructed from lie algebra filtrations obtained by assigning various weights to the defining vector fields one seeks a weighting hence an approximating system which satisfies the various known necessary conditions for the existence of an asymptotically stabilizing feedback control and for which such a control can be constructed as the solution to a homogeneous hamilton jacobi bellman equation associated with an optimization regulator problem

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

controllability of a class of underactuated mechanical systems with symmetry in this paper we develop results based on geometric mechanics to study the controllability of a class of controlled under actuated left invariant mechanical systems on lie groups we exploit the invariance of the controlled nonlinear dynamics to the group action symmetry to derive a set of reduced dynamics for the system we first present sufficient conditions for the controllability of the reduced dynamics we prove conditions boundedness of coadjoint orbits and existence of a radially unbounded lyapunov function under which the drift vector field of the reduced system is weakly positively poisson stable wpps the wpps nature of the drift vector field along with the lie algebra rank condition is used to show controllability of the reduced system we then extend these results to the unreduced dynamics considering separately the cases when the symmetry group is compact and noncompact in the noncompact case under further assumptions of equilibrium controllability sufficient conditions for controllability of the unreduced dynamics are derived jetpuck hovercraft and underwater vehicles are used as mechanical systems to motivate our work and illustrate our theoretical results

further results on the bellman equation for optimal control problems with exit times and nonnegative lagrangians abstract in a series of papers we proved theorems characterizing the value function in exit time optimal control as the unique viscosity solution of the corresponding bellman equation that satisfies appropriate side conditions the results applied to problems which satisfy a positivity condition on the integral of the lagrangian this positive integral condition assigned a positive cost for remaining outside the target on any interval of positive length in this note we prove a new theorem which characterizes the exit time value function as the unique bounded from below viscosity solution of the bellman equation that vanishes on the target the theorem applies to problems satisfying an asymptotic condition on the trajectories including cases where the positive integral condition is not satisfied our results are based on an extended version of barb lat s lemma we apply the theorem to variants of the fuller problem and other examples where the lagrangian is degenerate

a return mapping algorithm for plane stress elastoplasticity an unconditionally stable algorithm for plane stress elastoplasticity is developed based upon the notion of elastic predictor return mapping plastic corrector enforcement of the consistency condition is shown to reduce to the solution of a simple nonlinear equation consistent elastoplastic tangent moduli are obtained by exact linearization of the algorithm use of these moduli is essential in order to preserve the asymptotic rate of quadratic convergence of newton methods the accuracy of the algorithm is assessed by means of iso error maps the excellent performance of the algorithm for large time steps is illustrated in numerical experiments

a remark on nonlinear accessibility conditions and infinite prolongations the lie rank condition for strong nonlinear accessibility is interpreted via the differential geometry of jets and prolongations of infinite order it yields to a new lie algebraic criterion and to the consideration of first integrals which apply to nonlinear systems in quite general form the latter characterization in particular is valid without distinguishing between the system variables and is independent of time scalings weak accessibility is also considered

a geometric approach to feedback stabilization of nonlinear systems with drift the paper presents an approach to the construction of stabilizing feedback for strongly nonlinear systems the class of systems of interest includes systems with drift which are affine in control and which cannot be stabilized by continuous state feedback the approach is independent of the selection of a lyapunov type function but requires the solution of a nonlinear programming satisficing problem stated in terms of the logarithmic coordinates of flows as opposed to other approaches point to point steering is not required to achieve asymptotic stability instead the flow of the controlled system is required to intersect periodically a certain reachable set in the space of the logarithmic coordinates

configuration controllability of mechanical systems underactuated by one control we investigate local configuration controllability for mechanical control systems within the affine connection formalism we rely on previous results on controllability and series expansions for the evolution of mechanical systems starting from rest extending the work by lewis for the single input case we are able to characterize local configuration controllability for systems with n degrees of freedom and n 1 input forces

state steering by learning for a class of nonlinear control systems abstract the problem of steering the state of nonlinearly perturbed linear systems by learning is investigated a family of algorithms which compute the steering control by means of successive trials on the real plant is presented convergence in the face of a class of nonlinear plant perturbations is proven state feedback linearizable systems are shown to be addressable by the presented algorithms two examples illustrate the applicability of algorithms

controllability of linear systems on generalized heisenberg groups this paper is devoted to the study of global controllability of linear systems on higher dimensional heisenberg groups hn necessary conditions and sufficient ones are provided they are compared to the known necessary and sufficient conditions on h1 stated in dath and jouan 2016 controllability of linear systems on low dimensional nilpotent and solvable lie groups journal of dynamical and control systems 22 2 207 225 the notion of decoupled systems is introduced in order to get examples and counter examples and more precise controllability criteria are stated for them

local stabilization and controllability of a class of non triangular nonlinear systems this paper considers the problems of local asymptotic stabilization using continuous static state feedback lcfs and small time local controllability stlc of single input nonlinear systems a specific class of nontriangular systems called the essentially triangular form is introduced for this class of systems sufficient conditions for lcfs and necessary and sufficient conditions for stlc are obtained in particular it is shown that stlc implies lcfs a motivating physical example of the etf system is presented

assumed strain nodally integrated hexahedral finite element formulation for elastoplastic applications summary in this work a linear hexahedral element based on an assumed strain finite element technique is presented for the solution of plasticity problems the element stems from the nodally integrated continuum element nice formulation and its extensions assumed gradient operators are derived via nodal integration from the kinematic weighted residual the degrees of freedom are only the displacements at the nodes the adopted constitutive model is the classical associative von mises plasticity model with isotropic and kinematic hardening in particular a double step midpoint integration algorithm is adopted for the integration and solution of the relevant nonlinear evolution equations efficiency of the proposed method is assessed through simple benchmark problems and comparison with reference solutions copyright 2014 john wiley sons ltd

accuracy and stability of integration algorithms for elastoplastic constitutive relations an analysis of accuracy and stability of algorithms for the integration of elastoplastic constitutive relations is carried out in this paper reference is made to a very general internal variable formulation of plasticity and to two families of algorithms that generalize the well known trapezoidal and midpoint rules to fit the present context other integration schemes such as the radial return mean normal and closest point procedures are particular cases of this general formulation the meaning of first and second order accuracy in the presence of the plastic consistency condition is examined in detail and the criteria derived are used to identify two second order accurate members of the proposed algorithms a general methodology is also derived whereby the numerical stability properties of integration schemes can be systematically assessed with the aid of this methodology the generalized midpoint rule is seen to have far better stability properties than the generalized trapezoidal rule finally numerical examples are presented that illustrate the performance of the algorithms

configuration controllability of simple mechanical control systems in this paper we present a definition of configuration controllability for mechanical systems whose lagrangian is kinetic energy with respect to a riemannian metric minus potential energy a computable test for this new version of controllability is derived this condition involves an object that we call the symmetric product of particular interest is a definition of equilibrium controllability for which we are able to derive computable sufficient conditions examples illustrate the theory

integration methods for complex plastic constitutive equations abstract this paper shows new results concerning the finite element computations with complex plastic and viscoplastic constitutive equations the integration procedure then needs special numerical treatments when a large number of internal variables are present or for stiff non linearities implicit and explicit integration methods are compared the general solution proposed can be applied either in plasticity or in viscoplasticity for isotropic or anisotropic materials several options are proposed in the numerical scheme and for the completion step for the semi implicit scheme numerical tests are performed in order to compare the relative performances of the various approaches

high order variations for families of vector fields sufficient conditions involving lie brackets of arbitrarily high order are obtained for local controllability of families of vector fields after providing a general framework for the generation of high order control variations we propose a specific method for generating such variations the theory is applied to a number of nontrivial examples

generalized midpoint integration algorithms for j2 plasticity with linear hardening we consider four schemes based on generalized midpoint rule and return map algorithm for the integration of the classical j2 plasticity model with linear hardening the comparison aiming to establish which is the preferable scheme among the four considered is both theoretical and numerical on one side extending and completing the existing results in the literature we investigate the four schemes from the theoretical viewpoint addressing in particular the existence of solution long term behaviour accuracy and stability on the other hand we develop an extensive set of numerical tests based on pointwise stress strain loading histories iso error maps and initial boundary value problems copyright 2007 john wiley sons ltd

controllability is harder to decide than accessibility this article compares the difficulties of deciding controllability and accessibility these are standard properties of control systems but complete algebraic characterizations of controllability have proved elusive the article shows in particular that for subsystems of bilinear systems accessibility can be decided in polynomial time but controllability is np hard

solvable potentials generated by sl 2 r canonical transformations are used to build realisations of sl 2 r in terms of the basic quantum mechanical operators q and p the results are used to construct solvable potentials in the framework of one dimensional quantum mechanics

boson and differential realizations of polynomial angular momentum algebra the inhomogeneous multiboson and multivariable differential realizations of the polynomial angular momentum algebra of quadratic type l2 which may be seen as the nonlinear extension of an ordinary angular momentum algebra su 2 or its noncompact form su 1 1 are obtained from fock representations of l2 which are related to master representation of l2 on the space of its universal enveloping algebra u l2 or to induced representations on their respective quotient spaces u l2 ii with different left ideals ii

symmetry adapted wavefunctions and matrix elements the general case the method of symmetry adaptation of wavefunctions with respect to any semisimple symmetry chain originating from a su l 1 algebra for completely symmetrical representations n of su l 1 is extended to the case of arbitrary representations n1 n2 nl 1 of su l 1 with n1 or n2 or or nl 1 and n1 n2 nl 1 n

geometric conditions for local controllability abstract small time local controllability of a c1 affine control system with a generic drift vector field and n 1 linearly independent input vector fields on an n dimensional connected c1 manifold m is studied showing that a necessary condition namely the drift vector field belonging to the convex hull of the control vector fields at the given point is also sufficient on an open dense subset h1 of the set of points where it is verified local controllability at the points in the interior of h 1 is also considered when the input vector fields generate an involutive distribution and a criterion based on the type of contract of h with the hyperplane spanned by the input vector fields is proved an example shows a situation where the sufficient condition for small time local controllability of h sussmann siam j control option 25 1987 158 194 cannot be applied but in which the method now presented distinguishes the possible cases

on the relation between local controllability and stabilizability for a class of nonlinear systems the problem of local stabilizability of locally controllable nonlinear systems is considered it is well known that contrary to the linear case local controllability does not necessarily imply stabilizability a class of nonlinear systems for which local controllability implies local asymptotic stabilizability using continuous static state feedback is described as for this class of systems the well known hermes controllability condition is necessary and sufficient for local controllability

proximal analysis and the minimal time function under general hypotheses on the target set s and the dynamics of the system we show that the minimal time function ts cdot is a proximal solution to the hamilton jacobi equation uniqueness results are obtained with two different kinds of boundary conditions a new propagation result is proven and as an application we give necessary and sufficient conditions for ts cdot to be lipschitz continuous near s a petrov type modulus condition is also shown to be sufficient for continuity of ts cdot near s

local controllability along a reference trajectory abstract local controllability along a reference trajectory of analytic and smooth affine single input control systems without any a priori bounds on the control is considered and a geometric proof of a version of the hermes conjecture is given

steering control of nonholonomic systems with drift the extended nonholonomic double integrator example abstract this paper presents two different kinds of steering control strategies for a system of extended nonholonomic double integrator which is an example of nonholonomic control systems with drift the first strategy presents piece wise constant states dependent feedback control law the method is based on the construction of a cost function v not a lyapunov function which is the sum of two semi positive definite functions v 1 and v 2 the semi positive definite function v 1 is dependent on first m state variables which can be steered along the given vector fields and v 2 is dependent on the remaining n m state variables which can be steered along the missing lie brackets the values of the functions v 1 and v 2 allow determination of a desired direction of system motion and permit to construct a sequence of controls such that the sum of these functions decreases in an average sense the second strategy presents a time varying feedback law based on the model reference approach where the trajectory of the extended system is chosen as the model reference trajectory the controllers are designed in such a way that after each time period t the trajectory of the nonholonomic double integrator intersects the trajectory of the model reference which can be made asymptotically stable the proposed feedback law is as a composition of a standard stabilizing feedback control for a lie bracket extension of the original system and a periodic continuation of a specific solution to an open loop control problem stated for an abstract equation on a lie group this approach does not rely on a specific choice of a lyapunov function and does not require transformations of the model to chained forms

on controllability of delayed boolean control networks this paper is devoted to studying the trajectory and state controllability of boolean control networks bcns with time delay in contrast to bcns without time delay the dynamics of delayed bcns are determined by a sequence of initial states named here trajectories trajectory controllability means that there exists a control signal steering a system from an initial trajectory to a desired trajectory while state controllability means that there exists a control signal steering an initial state to a given state here both trajectory controllability and state controllability will be studied it should be noted that in this paper trajectory controllability does not mean tracking or following a given trajectory in fact it means to control bcns to a destination trajectory of length mu at the k th step using the semi tensor product of matrices the delayed bcns are first converted into an equivalent algebraic description and then some necessary and sufficient conditions are derived for the trajecto

geometric controllability and stabilization of spherical robot dynamics geometric control of a spherical robot rolling on a horizontal plane with three independent inertia disc actuators is considered in this note the dynamic model of the spherical robot in the geometric framework is used to establish the strong accessibility and small time local controllability properties smooth stabilizability to an equilibrium fails for the nonholonomic spherical robot a novel contribution of this note is a smooth asymptotically stabilizing geometric control law for position and reduced attitude which corresponds to an equilibrium submanifold of dimension one from brockett s condition this is the best possible dimension of a smoothly stabilized equilibrium submanifold we also present a novel smooth global tracking controller for tracking position trajectories

on the controllability of switching linear systems this note presents a necessary and sufficient condition for small time controllability of a linear switching system that is a collection of linear time invariant control systems where a trajectory is any concatenation of trajectories of the individual systems this result extends the controllability condition recently obtained for unconstrained linear switching systems to the case of control which is constrained in a cone

asymptotic model matching for nonlinear systems this paper investigates the problem of designing a compensating control law for a square invertible nonlinear plant so that the response of the closed loop system asymptotically matches that of a prescribed driven nonlinear model a set of necessary conditions for achieving asymptotic model matching is established one of these involves the stability properties for subdynamics which are common to every model matching closed loop these subdynamics called the fixed dynamics are intrinsically characterized based on these results a new set of sufficient conditions for achieving asymptotic model matching is given the interrelation between the minimum phase and vector relative degree properties of a plant and a matchable model are studied

local controllability at critical points and generic systems in 3 space abstract local controllability of genericcktriplets of vector fields in a three dimensional connected manifoldmis studied at a critical point of one of them the results obtained are used to determine local controllability for affine control systems at non relative equilibrium points or with one sided controls it is also proved that the proposed geometric approach is valid for generic affine systems

local controllability for families of diffeomorphisms abstract we study groups and semigroups which are generated by analytic families of diffeomorphisms the central notion is that of local controllability of a family of diffeomorphisms at a given point of the state manifold which generalizes the familiar notion of local controllability of control systems with continuous as well as discrete time lie theory methods are used we systematically exploit the so called fast switching variations and properties of the jet spaces of curves on the state manifold

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

on the application of multi step integration methods to infinitesimal elastoplasticity this article proposes an implicit algorithm for time integration of the differential algebraic equations of small deformation elastoplasticity in strain space the algorithm employs a two step backwards differentiation formula and a standard operator split procedure second order accuracy and non linear stability are established under appropriate constitutive restrictions the algorithm is implemented for the model of j2 plasticity and numerical simulations are conducted that illustrate its applicability and accuracy

reachable sets and controllability of bilinear time invariant systems a qualitative approach this paper is concerned with a qualitative method for the study of reachable sets and controllability of bilinear time invariant systems a nonlinear decomposition technique which reduces the solution of the problem to the analysis of the qualitative behavior of a finite number of linear uncontrolled systems is introduced special consideration is given to the homogeneous bilinear systems with commutative matrices two and three dimensional examples are discussed

motion planning for control affine systems satisfying low order controllability conditions abstractthis paper is devoted to the motion planning problem for control affine systems by using trigonometric polynomials as control functions the class of systems under consideration satisfies the controllability rank condition with the lie brackets up to the second order the approach proposed here allows to reduce a point to point control problem to solving a system of algebraic equations the local solvability of that system is proved and formulas for the parameters of control functions are presented our local and global control design schemes are illustrated by several examples

a new theoretical approach to absorbing layers we consider the construction of absorbing boundary layers using asymptotic expansions the small parameter being the width of the layer this allows us to define the order of the layer we compute layers of various orders and analyze their stability properties finally we perform some numerical tests to evaluate the practical utility of our layers

boson operator realizations of su 2 and su 1 1 and unitarization boson operator realizations of su 2 and su 1 1 are obtained scalar products are introduced on fock spaces verma modules spanned by generators of the heisenberg algebra h and by generators of su 2 these scalar products unitarize certain of the representations of h or of su 1 1 it is shown that the gel fand dyson realization of su 1 1 implies a scalar product that unitarizes h while the primakoff holstein realizations imply a scalar product that unitarizes su 1 1 the relationship between the gel fand dyson boson operators a and the primakoff holstein boson operators b is obtained making use of the two distinct scalar products generalized vacuum states are defined that are formed by polynomials in the creation annihilation operator pairs a a a representation of h and su 1 1 on the states a m and an is discussed for this representation a1 a 0 0 but rather a a 0 0 the states of this representation space consist of boson states and boson hole states all the familiar results

on induced scalar products and unitarization infinitesimal unitarity of representations of the simple real lie algebras su 2 su 1 1 and so 4 is discussed with respect to scalar products induced by sesquilinear forms on their universal enveloping algebras sesquilinear forms are explicitly calculated the verma modules their irreducible quotients their irreducible submodules and their infinitesimal unitarizability are discussed

series expansions for the evolution of mechanical control systems this paper presents a series expansion that describes the evolution of a mechanical system starting at rest and subject to a time varying external force mechanical systems are presented as second order systems on a configuration manifold via the notion of affine connections the series expansion is derived by exploiting the homogeneity property of mechanical systems and the variations of constant formula a convergence analysis is obtained using some analytic functions and combinatorial analysis results this expansion provides a rigorous means of analyzing locomotion gaits in robotics and lays the foundation for the design of motion control algorithms for a large class of underactuated mechanical systems

matrix elements for indecomposable representations of complex su 2 indecomposable representations of the simple complex lie algebra a1 are investigated in this article from a general point of view first a master representation is obtained which is defined on the space of the universal enveloping algebra of a1 then from this master representation other indecomposable representations are derived which are induced on quotient spaces or subduced on invariant subspaces finally it is shown that the familiar finite dimensional and infinite dimensional irreducible representations of su 2 and su 1 1 are closely related to certain of the indecomposable representations indecomposable representations of a1 su 2 su 1 1 have found increased applications in physical problems including the unusual finite multiplicity indecomposable representations emphasis is placed in this article on an analysis of the more unfamiliar indecomposable representations the matrix elements are obtained in explicit form for all representations which are discussed in this article th

dynamics and control of a class of underactuated mechanical systems this paper presents a theoretical framework for the dynamics and control of underactuated mechanical systems defined as systems with fewer inputs than degrees of freedom control system formulation of underactuated mechanical systems is addressed and a class of underactuated systems characterized by nonintegrable dynamics relations is identified controllability and stabilizability results are derived for this class of underactuated systems examples are included to illustrate the results these examples are of underactuated mechanical systems that are not linearly controllable or smoothly stabilizable

on the implicit integration of rate dependent inelastic constitutive models although there are many different algorithms for the integration of inelastic constitutive models the fully implicit backward euler method has become the most popular one in this study further investigations on the accuracy of the backward euler method have been carried out also the performance of the discontinuous galerkin family and some implicit runge kutta time integrators is evaluated by using a simple scalar model problem accuracy of some integrators is studied when a single finite time step is applied conclusions drawn from this scalar model problem has been verified to apply also to a full six dimensional strain space formulation by numerical means special emphasis is placed on rate dependent inelastic creep models copyright 2005 john wiley sons ltd

non linear b stability and symmetry preserving return mapping algorithms for plasticity and viscoplasticity a class of second order accurate return mapping algorithms is presented which lead to symmetric algorithmic tangent moduli and contain the classical backward euler return maps as a particular case more importantly it is shown that this class of return maps is contractive relative to the natural norm defined by the complementary helmholz free energy function b stability since the equations of classical plasticity and viscoplasticity are shown to be contractive relative to this natural norm the requirement of b stability furnishes the appropriate notion of unconditionally stable algorithms for plasticity and viscoplasticity the analysis that follows depends critically on the assumption of convexity in particular the models of plasticity and viscoplasticity considered obey the principle of maximum plastic dissipation the proposed algorithms obey the discrete counterpart of this classical principle

low order controllability and kinematic reductions for affine connection control systems controllability and kinematic modeling notions are investigated for a class of mechanical control systems first low order controllability results are given for the class of mechanical control systems second a precise connection is made between those mechanical systems which are dynamic i e have forces as inputs and those which are kinematic i e have velocities as inputs interestingly and surprisingly these two subjects are characterized and linked by a certain intrinsic vector valued quadratic form that can be associated to an affine connection control system

new inhomogeneous boson realizations and inhomogeneous differential realizations of lie algebras the inhomogeneous boson realizations ihbr and the corresponding inhomogeneous differential realizations ihdr of lie algebras which play an important role in the search of quasi exactly solvable problems qesp of quantum mechanics are studied all possible ihdr of semisimple lie algebras can be obtained in this way as examples the ihbr and the corresponding ihdr of lie algebras su 2 and su 3 are studied in detail

a global steering method for nonholonomic systems abstract in this paper we present an iterative steering algorithm for nonholonomic systems also called driftless control affine systems and we prove its global convergence under the sole assumption that the lie algebraic rank condition larc holds true everywhere that algorithm is an extension of the one introduced in jean et al 2005 21 for regular systems the first novelty here consists in the explicit algebraic construction starting from the original control system of a lifted control system which is regular the second contribution of the paper is an exact motion planning method for nilpotent systems which makes use of sinusoidal control laws and which is a generalization of the algorithm described in murray and sastry 1993 29 for chained form systems

local controllability in 3 manifolds small time local controllability of a two input ck affine control system on a 3 dimesional connected ck manifold m is studied showing that in general a necessary condition is also sufficient on an open dense subset of the set of points where it is verified an example shows a situation where the sufficient condition for small time local controllability of sussmann 8 cannot be applied but in which the method now presented distinguishes the possible cases

minimum time with bounded energy minimum energy with bounded time necessary and sufficient conditions for the regularity of the minimum time function and minimum energy function for a control system with controls in l p 0 infty bbb r m and p ge 1 are given in terms of topological properties of the reachable sets in particular standard local controllability assumptions are sufficient to yield the continuity of both value functions for linear systems and p ge1 and the holder continuity of the minimum time function for nonlinear systems and p 1

a polynomial approach to discrete time non linear system controllability this paper uses a polynomial approach to present a necessary and sufficient condition for local controllability of single input single output siso discrete time non linear systems the condition is presented in terms of common factors of a non commutative polynomial expression this extends the result on controllability of linear systems and the recent result on controllability of continuous time non linear systems to expose controllability of discrete time non linear systems in the input output framework the controllability condition yields a finite step computing procedure for examining controllability of discrete time input output non linear systems

accessibility of switched linear systems this note considers the controllability of switched linear systems the structure of accessibility lie algebra is revealed some accessibility properties are proved certain necessary and sufficient conditions for local or global weak or normal controllability of a large class of switched linear systems are obtained

collectivity and geometry iv sp 6 sp 2 o 3 basis states for open shells using generating function methods branching rules for sp 6 sp 2 o 3 are derived the branching rules suggest an integrity basis or set of elementary permissible diagrams in terms of which the subgroup basis states are defined they correspond to vibrational or bohr mottelson type states in the nuclear symplectic model

configuration controllability of simple mechanical control systems in this paper we present a definition of configuration controllability for mechanical systems whose lagrangian is kinetic energy with respect to a riemannian metric minus potential energy a computable test for this new version of controllability is derived this condition involves an object which we call the symmetric product of particular interest is a definition of equilibrium controllability for which we are able to derive computable sufficient conditions examples illustrate the theory

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

controllability distributions and systems approximations a geometric approach given a nonlinear system we determine a relation at an equilibrium between controllability distributions defined for a nonlinear system and a taylor series approximation of it the value of such a relation is appreciated if we recall that the solvability conditions as well as the solutions to some control synthesis problems can be stated in terms of geometric concepts like controlled invariant controllability distributions the relation between these distributions at the equilibrium will help us to decide when the solvability conditions of this kind of problems are equivalent for the nonlinear system and its approximation

the complexity of deciding controllability abstract it is shown that the problem of deciding whether a control system is small time locally controllable or not is np hard this is an extension of a recent paper by sontag to single input systems and to bounded controls