natural frequencies and mode shapes of deterministic and stochastic non homogeneous rods and beams abstract natural frequencies and mode shapes of non homogeneous deterministic and stochastic rods and beams are studied the solution is based on the functional perturbation method fpm the frequencies and mode shapes are considered as functionals of the non homogeneous properties the natural frequency and mode shape of the k th order is obtained analytically to any desired degree of accuracy once the functional derivatives with respect to the non uniform property have been found the solution for any morphology is obtained by direct integration without resolving the differential equation several examples with different non homogeneous properties are solved and compared with exact solutions as an accuracy check the fpm accuracy range for the frequency and the mode shape is less than 1 even for high heterogeneities in the stochastic case the accuracy of the natural frequencies depends on the stochastic information used given on the correlation distance roughly the grain size on the function around which the perturbation is executed and on whether we are interested in the properties of or of 2 moreover all frequency modes have the same response to heterogeneity as long as their wave length is of the order of the heterogeneity s characteristic distance in addition the heterogeneity effect on the average natural frequencies is minimal for the fundamental mode and may serve as a design tool

semiglobal stabilization of linear discrete time systems subject to input saturation via linear feedback an are based approach we revisit the problem of semiglobal stabilization of linear discrete time systems subject to input saturation and give an algebraic riccati equation are based approach to the proof of a fact established earlier lin and saberi 1995 i e a linear discrete time system subject to input saturation is semiglobally stabilizable via linear feedback as long as the linear system in the absence of the saturation is stabilizable and detectable and all its open loop poles are located inside or on the unit circle moreover we drastically relax the requirements on the characteristic of the saturation elements as imposed in the earlier work

optimization of disturbance rejection in systems with saturating actuators an extension of the lqr lqg methodology to systems with saturating actuators referred to as slqr slqg is obtained the development is based on the method of stochastic linearization using this method and the lagrange multiplier technique a solution to the slqr slqg problem is derived this solution is given by the standard riccati equations coupled with two transcendental equations which define the variance of the signal at the input of the saturation and the lagrange multiplier associated with the quadratic performance index it is shown that under the standard stabilizability and detectability conditions these equations have a unique solution which can be found by a simple bisection algorithm when the saturation is removed these equations reduce to the standard lqr lqg solution

a general result on the stabilization of linear systems using bounded controls we present two constructions of controllers that globally stabilize linear systems subject to control saturation we allow essentially arbitrary saturation functions the only conditions imposed on the system are the obvious necessary ones namely that no eigenvalues of the uncontrolled system have positive real part and that the standard stabilizability rank condition hold one of the constructions is in terms of a neural network type one hidden layer architecture while the other one is in terms of cascades of linear maps and saturations

tight contact structures with no symplectic fillings we exhibit tight contact structures on 3 manifolds that do not admit any symplectic fillings

handlebody construction of stein surfaces the topology of stein surfaces and contact 3 manifolds is studied by means of handle decompositions a simple characterization of homeomorphism types of stein surfaces is obtained they correspond to open handlebodies with all handles of index 2 an uncountable collection of exotic l4 s is shown to admit stein structures new invariants of contact 3 manifolds are produced including a complete and computable set of invariants for determining the homotopy class of a 2 plane field on a 3 manifold these invariants are applicable to seiberg witten theory several families of oriented 3 manifolds are examined namely the seifert fibered spaces and all surgeries on various links in s3 and in each case it is seen that most members of the family are the

semi global stabilization of minimum phase nonlinear systems in special normal forms abstract we semi globally stabilize certain minimum phase nonlinear systems which are in a normal form where the nonlinear subsystem is driven by an output of a linear system that possesses possibly nonzero peaking exponents we eliminate the peaking phenomenon by stabilizing part of the linear system with a high gain linear control and part of the linear system with a small bounded control the interpretation of this approach will be that we are redefining the outputs to add asymptotically stable nonlinear zeros to the system in a manner that allows the new composite zero dynamics to be asymptotically stable on arbitrarily large compact sets

digitization of nonautonomous control systems abstract methods of the theory of nonautonomous differential equations are used to study the extent to which the properties of local null controllability and local feedback stabilizability are preserved when a control system with time varying coefficients is digitized e g approximated by piecewise autonomous systems on small time subintervals

some new results on closed loop stability in the presence of control saturation some new sufficient conditions for determining global asymptotic stability of an equilibrium point under control saturation are presented for an open loop stable system we show that there exists a class of linear time invariant state feedback matrices which globally stablizes an equilibrium under control saturation in addition we show that for open loop unstable plants an equilibrium can never be globally stabilized using a certain class of saturated linear time invariant state feedback finally we extend the stability results to nonlinear systems whose nonlinearities are globally lipschitz

constrained approximate boundary controllability in this paper constrained approximate boundary controllability for linear disturbed parameter dynamical systems described by partial differential equations of parabolic type with mixed boundary conditions is considered using methods of spectral analysis for linear self adjoint operators and general constrained controllability results given by son 1990 necessary and sufficient conditions for constrained approximate boundary controllability are formulated and proved moreover in illustrative examples the constrained approximate boundary controllability of 1d distributed parameter dynamical systems is investigated the constrained controllability conditions obtained represent an extension of the unconstrained controllability results given by glothin 1974

null controllability of linear systems with constrained controls the paper considers the problem of steering the state of a linear time varying system to the origin when the control is subject to magnitude constraints necessary and sufficient conditions are given for global constrained controllability as well as a necessary and sufficient condition for the existence of a control satisfying the constraints which steers the system to the origin from a specified initial epoch x 0 t 0 the global result does not require zero to be an interior point of the control set omega and the theorem for constrained controllability at x 0 t 0 only requires that omega be compact not that it contain zero the results are compared to those available in the literature furthermore numerical aspects of the problem are discussed as is a technique for determining a steering control

structured and simultaneous lyapunov functions for system stability problems abstract it is shown that many system stability and robustness problems can be reduced to the question of when there is a quadratic lyapunov function of a certain structure which establishes stability of x ax for some appropriate a the existence of such a lyapunov function can be determined by solving a convex program we present several numerical methods for these optimization problems a simple numerical example is given

on the classification of tight contact structures ii we present complete classification results for tight contact structures on two classes of 3 manifolds i torus bundles which fiber over the circle and ii circle bundles which fiber over closed surfaces

on finding the minimum possible peak value of multi input infinite horizon steering controls a computational method for the infinite dimensional optimization problem of finding the minimum possible peak value of a multi input infinite horizon steering control is presented it is shown that the problem is equivalent to a convex program in a finite dimensional euclidean space the convex program is approximated by a sequence of linear programs the objective values of which converge to the objective of the convex program a bound above and below are given for the error between the objective value of the convex program and the objective of any linear program in the approximating sequence the bounds show convergence and are geometric with ratio given by the minimum modulus over all unstable plant poles

approximate analytical solutions for primary chatter in the non linear metal cutting model this paper considers an accepted model of the metal cutting process dynamics in the context of an approximate analysis of the resulting non linear differential equations of motion the process model is based upon the established mechanics of orthogonal cutting and results in a pair of non linear ordinary differential equations which are then restated in a form suitable for approximate analytical solution the chosen solution technique is the perturbation method of multiple time scales and approximate closed form solutions are generated for the most important non resonant case numerical data are then substituted into the analytical solutions and key results are obtained and presented some comparisons between the exact numerical calculations for the forces involved and their reduced and simplified analytical counterparts are given it is shown that there is almost no discernible difference between the two thus confirming the validity of the excitation functions adopted in the analysis for the data sets used these being chosen to represent a real orthogonal cutting process in an attempt to provide guidance for the selection of technological parameters for the avoidance of primary chatter this paper determines for the first time the stability regions in terms of the depth of cut and the cutting speed co ordinates

the time optimal control with constraints of the rectangular type for linear time varying odes in this paper we study a time optimal control problem of some linear time varying ordinary differential equations where the control constraint set is of the rectangular type we derive a necessary and sufficient condition and provide an algorithm for the optimal time as well as the optimal control for this problem the basis consists of an equivalence theorem between the time optimal control problem and an associated norm optimal control problem and the variational characterization of the latter problem

semi global stabilization of linear systems with position and rate limited actuators abstract it is shown that if a linear system is asymptotically null controllable with bounded controls then when subject to both actuator position and rate saturation it is semi globally stabilizable by linear state feedback if in addition the system is also detectable then it is semi global stabilizable via linear output feedback

an algebraic approach to bounded controllability of linear systems in this paper we present an algebraic approach to the proof that a linear system with matrices a b is null controllable using bounded inputs if and only if it is null controllable with unbounde

on the eigenvalues of a uniform cantilever beam carrying any number of spring damper mass systems summary the eigenvalues of a uniform cantilever beam carrying any number of spring damper mass systems with arbitrary magnitudes and locations were determined by means of the analytical and numerical combined method ancm first of all each spring damper mass system was replaced by a massless e ective spring with spring constant k which is the main point that the ancm is available for the present problem next the equation of motion for the constrained beam with spring damper mass systems attached was derived by using the natural frequencies and normal mode shapes of the unconstrained beam without carrying any attachments incorporated with the expansion theorem finally the equation of motion for the constrained beam in complex form is separated into the real and the imaginary parts from either part a set of simultaneous equations were obtained since the simultaneous equations are in real form the eigenvalues of the constrained beam were determined with the conventional numerical methods to con rm the reliability of the presented theory all the numerical results obtained from the ancm were compared with the corresponding ones obtained from the conventional nite element method fem and good agreement was achieved because the order of the property matrices for the equation of motion derived by using the ancm is much lower than that by using the conventional fem the storing memory and the cpu time required by the ancm are much less than those required by the fem besides the solution of the equation of motion derived from the ancm can always be obtained with the general personal computers but that from the fem can sometimes be obtained only with the computers of workstations or main frames when the total degrees of freedom exceeding a certain limit copyright 1999 john wiley sons ltd

semi global stabilizability of linear null controllable systems with input nonlinearities an h sub spl infin based lyapunov proof is provided for a result established by lin and saberi 1993 if a linear system is asymptotically null controllable with bounded controls then when subject to input saturation it is semi globally stabilizable by linear state feedback a new result is that if the system is also detectable then it is semi global stabilizable by completely linear output feedback further an extension which relaxes the requirements on the input characteristic is obtained

tight not semi fillable contact circle bundles extending our earlier results we prove that certain tight contact structures on circle bundles over surfaces are not symplectically semi fillable thus confirming a conjecture of ko honda

an lqr lqg theory for systems with saturating actuators an extension of the lqr lqg methodology to systems with saturating actuators referred to as slqr slqg where s stands for saturating is obtained the development is based on the method of stochastic linearization whereby the saturation is replaced by a gain calculated as a function of the variance of the signal at its input using the stochastically linearized system and the lagrange multiplier technique solutions of the slqr slqg problems are derived these solutions are given by standard riccati and lyapunov equations coupled with two transcendental equations which characterize both the variance of the signal at the saturation input and the lagrange multiplier associated with the constrained minimization problem it is shown that under standard stabilizability and detectability conditions these equations have a unique solution which can be found by a simple bisection algorithm when the level of saturation tends to infinity these equations reduce to their standard lqr lqg counterparts in addition the paper investigates the properties of closed loop systems with slqr slqg controllers and saturating actuators in this regard it is shown that slqr slqg controllers ensure semi global stability by appropriate choice of a parameter in the performance criterion finally the paper illustrates the techniques developed by a ship roll damping problem

cobordisms of sutured manifolds and the functoriality of link floer homology abstract it has been a central open problem in heegaard floer theory whether cobordisms of links induce homomorphisms on the associated link floer homology groups we provide an affirmative answer by introducing a natural notion of cobordism between sutured manifolds and showing that such a cobordism induces a map on sutured floer homology this map is a common generalization of the hat version of the closed 3 manifold cobordism map in heegaard floer theory and the contact gluing map defined by honda kazez and matic we show that sutured floer homology together with the above cobordism maps forms a type of tqft in the sense of atiyah applied to the sutured manifold cobordism complementary to a decorated link cobordism our theory gives rise to the desired map on link floer homology hence link floer homology is a categorification of the multi variable alexander polynomial we outline an alternative definition of the contact gluing map using only the contact element and handle maps finally we show that a weinstein sutured manifold cobordism preserves the contact element

semi global stabilization of discrete time linear systems with position and rate limited actuators it is shown via explicit construction of feedback laws that if a discrete time linear system is asymptotically null controllable with bounded controls then when subject to both actuator position and rate saturation it is semi globally stabilizable by linear state feedback if in addition the system is also detectable then it is semi globally stabilizable via linear output feedback

on the existence of globally stable actuator saturation compensators although actuator saturation is a common nonlinear problem in practical control systems the condition under which compensators exist that globally stabilize systems subject to actuator saturation is still not well understood in this paper it is shown that actuator saturation compensators exist that globally stabilize systems containing up to one integrator for systems with two integrators it is established that the compensated system can only be lagrange stable the stability result presented in this paper can also be extended to analyse the stability of systems using existing compensation schemes thus providing a much needed justification for the use of these schemes in practice the results presented here are illustrated by examples

null controllability of systems with control constraints and state saturation abstract sufficient conditions for the null controllability of discrete time systems with control constraints and state saturation are presented this is accomplished in two stages first we establish a result for the asymptotic stability of such systems under zero input conditions next we utilize this stability result to obtain a condition for the null controllability of such systems we include specific examples to demonstrate the applicability of the present results

tight contact structures on some small seifert fibered 3 manifolds we classify tight contact structures on the small seifert fibered 3 manifolds m 1 r1 r2 r3 with ri 0 1 q and r1 r2 the result is obtained by combining convex surface theory with computations of contact ozsvath szabo invariants we also show that some of the tight contact structures on the manifolds considered are nonfillable justifying the use of heegaard floer theory

brief stability region for a class of open loop unstable linear systems theory and application a new method to calculate the stability region of scalar systems with one unstable pole subject to control limitations is derived and used to determine the conditions for a maximum stabilizer controller the results are illustrated by means of two numerical examples and experiments on the real compass d tokamak

contact structures on product five manifolds and fibre sums along circles two constructions of contact manifolds are presented i products of s1 with manifolds admitting a suitable decomposition into two exact symplectic pieces and ii fibre connected sums along isotropic circles baykur has found a decomposition as required for i for all closed oriented 4 manifolds as a corollary we can show that all closed oriented 5 manifolds that are cartesian products of lower dimensional manifolds carry a contact structure for symplectic 4 manifolds we exhibit an alternative construction of such a decomposition this gives us control over the homotopy type of the corresponding contact structure in particular we prove that mathbb cp 2 times s 1 admits a contact structure in every homotopy class of almost contact structures the existence of contact structures is also established for a large class of 5 manifolds with fundamental group mathbb z 2

dynamic analysis of a uniform cantilever beam carrying a number of elastically mounted point masses with dampers abstract the free and forced vibration analyses of a uniform cantilever beam carrying a number of spring damper mass systems with arbitrary magnitudes and locations were made by means of the analytical and numerical combined method ancm first of all a method was presented to replace each spring damper mass system by a massless equivalent spring damper system with effective spring constant keffand effective damping coefficient ceffso that the ancm is available for the title problem next the equation of motion for the constrained beam with spring damper mass systems attached was derived by using the natural frequencies and normal mode shapes of the unconstrained beam without carrying any attachments incorporating the expansion theorem finally the eigenvalues and the forced vibration responses of the constrained beam were determined by conventional numerical methods to confirm the reliability of the presented theory all the numerical results obtained from the ancm were compared with the corresponding ones obtained from the conventional finite element method fem and good agreement was achieved the influence of the damping magnitude of each spring damper mass system on the eigenvalues and the forced vibration responses of the constrained beam was studied because the order of the overall property matrices for the equation of motion of the constrained beam derived from the ancm is much lower than that from the conventional fem the storing memory and the cpu time required by the ancm are much less than those required by the fem

controllability and the nature of quasi frequencies abstract using methods of dynamical systems we construct an example of a time dependent linear control process with quasi periodic coefficients for which the controllability properties of the system are very sensitive to the diophantine properties of the quasi frequencies

infinitely many universally tight torsion free contact structures with vanishing ozsvath szabo contact invariants ozsvath szabo contact invariants are a powerful way to prove tightness of contact structures but they are known to vanish in the presence of giroux torsion in this paper we construct on infinitely many manifolds infinitely many isotopy classes of universally tight torsion free contact structures whose ozsvath szabo invariant vanishes we also discuss the relation between these invariants and an invariant on t3 and construct other examples of new phenomena in heegaard floer theory along the way we prove two conjectures of k honda w kazez and g matic about their contact topological quantum field theory almost all the proofs in this paper rely on their gluing theorem for sutured contact invariants

commuting matrices equilibrium points for control systems with single saturated input in this paper commutative matrices of multiple input multiple output mimo linear systems are considered the existence of the feedback matrices of a commutative state matrix set in the mimo closed loops is reduced to the existence of an invariant subspace of a matrix a the existence of feedback matrices in systems in open loop is equivalent to the existence of the solution of matrix equations denoted by kronecker products by defining new equilibrium points the relationship between equilibrium points are discussed for a linear system with a single saturated input four criteria for equilibrium points are outlined for such linear systems finally four interesting examples including their corresponding simulink plots are shown to illustrate the above results

semi global exponential stabilization of linear systems subject to input saturation via linear feedbacks abstract it is known that a linear time invariant system subject to input saturation can be globally asymptotically stabilized if it has no eigenvalues with positive real parts it is also shown by fuller 1997 and sussmann and yang 1991 that in general one must use nonlinear control laws and only some special cases can be handled by linear control laws in this paper we show the existence of linear state feedback and or output feedback control laws for semi global exponential stabilization rather than global asymptotic stabilization of such systems we explicitly construct linear static state feedback laws and or linear dynamic output feedback laws that semi globally exponentially stabilize the given system our results complement the negative result of fuller 1977 and sussmann and yang 1991

simultaneous quadratic stabilization for a class of non linear systems with input saturation using dynamic surface control in this paper a new method to estimate the initial condition set which guarantees the quadratic stability for a class of non linear systems via dynamic surface control dsc in the presence of input saturation has been proposed the estimated set is enlarged to allow some degree of input saturation while achieving the simultaneous quadratic stability of the system in the domain a convex optimization problem to obtain ellipsoidal initial condition sets via a linear matrix inequality lmi approach as well as an illustrative example will be presented

on the output regulation for linear systems in the presence of input saturation some results on the problem of achieving output regulation in the presence of sinusoidal constant exogenous signals for linear systems subject to input saturation are presented in particular the issue of enlarging the set of initial conditions for which the problem has solutions is addressed

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

technical communique null controllable region of lti discrete time systems with input saturation we present a formula for the extremes of the null controllable region of a general lti discrete time system with bounded inputs for an nth order system with only real poles not necessarily distinct the formula is simplified to an elementary matrix function which in turn shows that the set of the extremes coincides with a set of trajectories of the time reversed system under bang bang controls with n 2 or less switches

existence and classification of overtwisted contact structures in all dimensions we establish a parametric extension h principle for overtwisted contact structures on manifolds of all dimensions which is the direct generalization of the 3 dimensional result from 12 it implies in particular that any closed manifold admits a contact structure in any given homotopy class of almost contact structures

global null controllability of perturbed linear periodic systems in this note we study the global null controllability with bounded controls of perturbed linear periodic systems in rn more explicitly a globally null controllable periodic system is perturbed by suitably small terms v t and c t to obtain a system of the form dot x a t v t x b t c t u and sufficient conditions are given to ensure the global null controllability of the resulting perturbed system

numerical approach to the non linear diofantic equations with applications to the controllability of infinite dimensional dynamical systems the article is devoted to the analysis of the approximate controllability of a given type of second order infinite dimensional system defined by the hyperbolic type partial differential equation with dirichlet like type zero boundary conditions defined in the n dimensional rectangular prism following this aim spectral theory for linear unbounded operators is involved new numerical algorithms for solving some kind of non linear diofantic equations corresponding with the spectral properties of the unbounded operators are presented and proved an algorithm is optimized for eliminating the symmetrical solutions not interesting in the scope of verification of the controllability next the limit which shows that the direct application of the analytical methods of verifying the controllability in the numerical approach is impossible is proved finally so called partial approximate controllability is defined and the numerical algorithm for its verification is presented finally proven theorems are applied

global and point controllability of uncertain dynamical systems this paper analyzes the problem of controllability in the presence of additive uncertainty unlike the stochastic controllability problem the uncertain parameters here are described in a set theoretic manner i e no a priori statistics are assumed for the uncertainty q cdot only a bounding set q is taken as given loosely speaking the state x cdot of a dynamical system s is said to be omega q controllable to a given target x if one can guarantee by choice of a measurable control u t in omega the transfer of x cdot to x in finite time this guarantee above must hold for all measurable q t in q known results on constrained controllability of deterministic systems are derived as a special case by setting q 0 the finite dimensional nature of the omega q controllability criteria is perhaps the most salient feature of the results given here instead of searching over the function space of controls one can decide on the question of controllability by solving an equivalent problem in r where n is the state dimension the generation of this equivalent problem involves artificially inducing a saddle point via a certain enveloping operation a number of examples are given to illustrate the method of computing numerical solutions

constrained approximate controllability in the paper constrained approximate controllability for linear dynamical systems described by abstract differential equations with unbounded control operator is considered using methods of spectral analysis for linear self adjoint operators and general constrained controllability results given by son 1990 necessary and sufficient conditions of the constrained approximate controllability for the piecewise polynomial controls with values in a given cone are formulated and proved moreover as illustrative examples constrained approximate boundary controllability of one dimensional distributed parameter dynamical systems described by partial differential equations of parabolic type with dirichlet and neumann boundary conditions are investigated the constrained controllability conditions obtained in the paper represent an extension of the unconstrained controllability results given by glothin 1974 and klamka 1991

a necessary algebraic condition for controllability and observability of linear time varying systems in this note we give an algebraic condition which is necessary for the system x t a t x t b t u t y t c t x t either to be totally controllable or to be totally observable where x spl isin spl ropf sup d u spl isin spl ropf sup p y spl isin spl ropf sup q and the matrix functions a b and c are d 2 d 1 and d 1 times continuously differentiable respectively all conditions presented here are in terms of known quantities and therefore easily verified our conditions can be used to rule out large classes of time varying systems which cannot be controlled and or observed no matter what the nonzero time varying coefficients are this work is motivated by the deep result of silverman and meadows

a general variational approach to constrained null controllability for multi variable systems and application to switching control we consider the problem of null controllability with switching constrained control for the multi variable system y t ay t bu t the study is focused on the canonical saturation constraints on t

controllability results for systems with a nonconvex target this paper considers the problem of steering the state x t of the system dot x t a t x t f t u t to a prescribed target x the input u t is restricted to lie in a prespecified set which is assumed compact unlike the results of previous authors we allow x to be any set and do not require x to be convex or closed necessary conditions and sufficient conditions for the existence of a control which steers the system to the target from a specified initial condition are given conditions for global controllability to the target are also derived an additional concept of controllability that we investigate is that of complete controllability complete controllability is concerned with the ability to steer the system from any initial point to any final point one of the most important results of this paper is that we develop a technique for constructing a steering control previous work on the constrained controllability problem has dealt with methods for determining a steering control in only a limited way finally numerical techniques for checking controllability and for constructing a steering control are described and the results obtained from the application of our algorithm to several examples are presented

on the contact geometry of nodal sets in the 3 dimensional riemannian geometry contact structures equipped with an adapted riemannian metric are divergence free nondegenerate eigenforms of the laplace beltrami operator we trace out a 2 d analogue of this fact there is a close relationship between the topology of the contact structure on a convex surface in the 3manifold the dividing curves and the nodal curves of laplacian eigenfunctions on that surface motivated by this relationship we consider a topological version of payne s conjecture for the free membrane problem we construct counterexamples to payne s conjecture for closed riemannian surfaces in light of the correspondence between the nodal lines and dividing curves we interpret payne s conjecture in terms of the tight versus overtwisted dichotomy for contact structures

boundary value control of isotropic elastodynamic systems with constrained controls abstract admissible controllability of isotropic elastodynamic systems when the boundary value controls are constrained in some sets is given as a realistic example the case is considered where the controls are constrained to be exercised by means of pushing the boundary with small forces

a unified approach to constrained approximate controllability for the heat equations and the retarded equations abstract the aim of this paper is to study controllability of the linear infinite dimensional system x ax bu where a is the infinitesimal generator of a c 0 semigroup of linear bounded operators in the banach space x the control u is restricted to lie in a subset of the banach space u need not assumed to be convex or to contain 0 in its interior some necessary and sufficient conditions for approximate controllability to the whole space x are given the proof of the main result is based on the spectral decomposition method developed by fattorini and the generalized open mapping theorem due to robinson the obtained results are used to consider some controllability problems with constrained controls for the class of linear systems described by partial differential equations of parabolic type with bounded domain and for the class of retarded functional differential equations in the state space m p particularly in the case of the heat equation with positive scalar controls and in the case of the retarded equation with finite discrete delays the general result leads to easily verifiable tests for approximate controllability expressed in terms of the system matrices

an explicit description of null controllable regions of linear systems with saturating actuators we give simple exact descriptions of the null controllable regions for general linear systems with saturating actuators the description is in terms of a set of extremal trajectories of the anti stable subsystem for lower order systems or systems with only real eigenvalues this description is further simplified to result in explicit formulae for the boundaries of the null controllable regions

rationally convex domains and singular lagrangian surfaces in mathbb c 2 we give a complete characterization of those disk bundles over surfaces which embed as rationally convex strictly pseudoconvex domains in mathbb c 2 we recall some classical obstructions and prove some deeper ones related to symplectic and contact topology we explain the close connection to lagrangian surfaces with isolated singularities and develop techniques for constructing such surfaces our proof also gives a complete characterization of lagrangian surfaces with open whitney umbrellas answering a question first posed by givental in 1986

dynamical properties of the reaction diffusion type model of fast synaptic transport abstract the modulation of a signal that is transmitted in the nerve system takes place in chemical synapses this article focuses on the phenomena undergone in the presynaptic part of the synapse a diffusion reaction type model based on the partial differential equation is proposed through an averaging procedure this model is reduced to a model based on ordinary differential equations with control which is then analyzed according to its dynamical properties controllability observability and stability the system is strongly connected to the one introduced by aristizabal and glavinovic 2004 13 the biological implications of the obtained mathematical results are also discussed

an index for closed orbits in beltrami fields abstract we consider the class of beltrami fields eigenfields of the curl operator on three dimensional riemannian solid tori such vector fields arise as steady incompressible inviscid fluids and plasmas using techniques from contact geometry we construct an integer valued index for detecting closed orbits in the flow which are topologically inessential they have winding number zero with respect to the solid torus the most important feature of the index is its computability it can be rigorously determined from a c 1 approximation to the vector field on any meridional disc of the solid torus as a result we obtain a test for detecting the non existence of a global cross section to the 3d flow via purely 2d information

cabling and transverse simplicity we study legendrian knots in a cabled knot type specifically given a topological knot type c we analyze the legendrian knots in knot types ob tained from k by cabling in terms of legendrian knots in the knot type k as a corollary of this analysis we show that the 2 3 cable of the 2 3 torus knot is not transversely simple and moreover classify the transverse knots in this knot type this is the first classification of transverse knots in a non transversely simple knot type we also classify legendrian knots in this knot type and exhibit the first example of a legendrian knot that does not destabi lize yet its thurston bennequin invariant is not maximal among legendrian representatives in its knot type in this paper we continue the investigation of legendrian knots in tight contact 3 manifolds using 3 dimensional contact topological methods in eh1 the authors introduced a general framework for analyzing legendrian knots in tight contact 3 manifolds there we streamlined the proof of the classification of legendrian unknots originally proved by eliashberg eraser in ef and gave a complete classification of legendrian torus knots and figure eight knots in eh2 we gave the first structure theorem for legendrian knots namely the reduction of the analysis of connected sums of legendrian knots to that of the prime summands this yielded a plethora of non legendrian simple knot types a topological knot type is legendrian simple if legendrian knots in this knot type are determined by their thurston bennequin invariant and rotation number moreover we exhibited pairs of legendrian knots in the same topological knot type with the same thurston bennequin and rotation numbers which required arbitrarily many stabilizations before they became legendrian isotopic see eh2

ozsvath szabo invariants and fillability of contact structures recently ozsvath and szabo defined an invariant of contact structures with values in the heegaard floer homology groups they also proved that a version of the invariant with twisted coefficients is non trivial for weakly symplectically fillable contact structures in this article we show that their non vanishing result does not hold in general for the contact invariant with untwisted coefficients as a consequence of this fact heegaard floer theory can distinguish between weakly and strongly symplectically fillable contact structures

semi global exponential stabilization of linear discrete time systems subject to input saturation via linear feedbacks abstract in this paper we show that a linear discrete time system subject to input saturation is semi globally exponentially stabilizable via linear state and or output feedback laws as long as the system in the absence of input saturation is stabilizable and detectable and has all its poles located inside or on the unit circle furthermore the semi globally stabilizing feedback laws are explicitly constructed the results presented here are parallel to our earlier results on the continuous time counterpart lin and saberi 1993

chatter resistance of non uniform turning bars with attached dynamic absorbers analytical approach abstract forced harmonic vibration of a non uniform elastic beam with attached dynamic vibration absorbers dva is studied analytical approximation of the solution is obtained by the functional perturbation method fpm the problem has application to cutting tools operations where the resistance of the tool holder against regenerative chatter can be enhanced by optimizing the real part of the frequency response function frf a test case of a beam with step like heterogeneity and single dva at the tip shows that the fpm solution is very accurate for up to 40 percent deviation in both stiffness and mass density using the analytical results and sims approach optimal dva tuning is found for each set of beam heterogeneity parameters by solving a set of nonlinear algebraic equations numerically it is found that the optimum can be further improved by searching for the best step location the system optimization is then expanded to a general heterogeneous beam with a dva at its tip the mass and stiffness distribution is optimized by applying the lagrange variation method on the fpm solution yielding fredholm integral equations the optimized morphology is found to be approximately linear and far from the intuitive step like one rivin and kang 1992 and yields better chatter resistance

nonlinear static state feedback for saturated linear plants via a polynomial approach the technical note revisits the local exponential stabilization and global asymptotic stabilization problems of saturated linear systems using nonlinear control laws the proposed nonlinear control law has rational dependence on a parameter sigma which is computed by solving an implicit equation depending on the state constructive solutions are obtained based on a sum of squares formulation of the proposed conditions