discrete time asymptotic controllability implies smooth control lyapunov function we demonstrate the existence of a smooth control lyapunov function clf for difference equations asymptotically controllable to closed sets we further show that this clf may be used to construct a robust feedback stabilizer the existence of such a clf is a consequence of a more general result on the existence of weak lyapunov function under the assumption of weak asymptotic stability of a closed not necessarily compact set for a difference inclusion

effect of unmodeled actuator dynamics on output feedback stabilization of nonlinear systems the effect of unmodeled fast actuator dynamics on the output feedback stabilization of feedback linearizable systems is studied it is shown that if the actuator dynamics are sufficiently fast the output feedback controller will stabilize the origin of the actual system moreover it is shown that the actuator dynamics need not be faster than the observer dynamics

on brockett s condition for smooth stabilizability and its necessity in a context of nonsmooth feedback the necessity of brockett s condition for stabilizability of nonlinear systems by smooth feedback is shown by an argument based on properties of a degree for set valued maps to persist when the class of controls is enlarged to include discontinuous feedback

asymptotic controllability implies feedback stabilization it is shown that every asymptotically controllable system can be globally stabilized by means of some discontinuous feedback law the stabilizing strategy is based on pointwise optimization of a smoothed version of a control lyapunov function iteratively sending trajectories into smaller and smaller neighborhoods of a desired equilibrium a major technical problem and one of the contributions of the present paper concerns the precise meaning of solution when using a discontinuous controller

convergence of asynchronous iteration with arbitrary splitting form abstract the convergence theorem of asynchronous iteration for solving a system of linear equations presented by d chazan and w miranker is proved with a new method and generalized to splitting iteration with arbitrary form

scattering theory for the schrodinger equation in some external time dependent magnetic fields abstract we study the theory of scattering for a schrodinger equation in an external time dependent magnetic field in the coulomb gauge in space dimension 3 the magnetic vector potential is assumed to satisfy decay properties in time that are typical of solutions of the free wave equation and even in some cases to be actually a solution of that equation that problem appears as an intermediate step in the theory of scattering for the maxwell schrodinger ms system we prove in particular the existence of wave operators and their asymptotic completeness in spaces of relatively low regularity we also prove their existence or at least asymptotic results going in that direction in spaces of higher regularity the latter results are relevant for the ms system as a preliminary step we study the cauchy problem for the original equation by energy methods using as far as possible time derivatives instead of space derivatives

on the existence of euler lagrange orbits satisfying the conormal boundary conditions abstract let m g be a closed connected riemannian manifold l t m r be a tonelli lagrangian given two non empty closed submanifolds q 0 q 1 m and a real number k we study the existence of euler lagrange orbits with energy k connecting q 0 to q 1 and satisfying suitable boundary conditions known as conormal boundary conditions we introduce the mane critical value which is relevant for this problem and discuss existence results for supercritical and subcritical energies we also provide counterexamples showing that all the results are sharp

further results on robustness of possibly discontinuous sample and hold feedback we demonstrate that sample and hold state feedback control possibly discontinuous with respect to the state is robust when the closed loop system possesses an appropriate lyapunov function we first show that if a lyapunov decrease over sampling periods exists for the nominal system this decrease can be maintained with some degradation relative to a sufficiently small additive perturbation we then proceed to catalog several applications of this robustness e g robustness to measurement noise computational delays or fast actuator dynamics

technical communique robust backstepping for the euler approximate model of sampled data strict feedback systems stabilization of uncertain sampled data strict feedback systems is addressed the stability study is carried out on the euler approximation of the exact discretized model of the plant firstly a class of state feedback controllers is developed that guarantees an input to state stability property for the closed loop system additionally assuming some hypotheses on the uncertain terms hold a practical asymptotic stability property is ensured by designing an appropriate class of controllers

epsilon inflation in verification algorithms epsilon inflation is often used in verification numerics to find an interval vector x e such that some interval function f maps x e into itself we recall algorithms which use epsilon inflation to verify this subset property f x e x e and we derive criteria which guarantee that already finitely many inflation steps are sufficient to prove it these criteria require f to be a p contraction we recall results on p contractions and we derive rules to verify them we also introduce local p contractions and we use this concept to guarantee again the subset property above when using epsilon inflation

the wave group on asymptotically hyperbolic manifolds abstract we show that the wave group on asymptotically hyperbolic manifolds belongs to an appropriate class of fourier integral operators then we use now standard techniques to analyze its regularized trace we prove that as in the case of compact manifolds without boundary the singularities of the regularized wave trace are contained in the set of periods of closed geodesics we also obtain an asymptotic expansion for the trace at zero

generalized strichartz inequalities for the wave equation strichartz inequalities for the wave equation u f are estimates of the solution u of the cauchy problem for that equation in the form of space time integral norms in terms of similar norms of the inhomogeneity f and of suitable norms of the initial data

feedback stabilization and lyapunov functions given a locally defined nondifferentiable but lipschitz lyapunov function we employ it in order to construct a discontinuous feedback law which stabilizes the underlying system to any given tolerance a converse result shows that suitable lyapunov functions of this type exist under mild assumptions we also establish that the feedback in question possesses a robustness property relative to measurement error despite the fact that it may not be continuous

asynchronous parallel methods for enclosing solutions of nonlinear equations we consider interval arithmetic based parallel methods for enclosing solutions of nonlinear systems of equations where processors are allowed to proceed asynchronously we present a general study on the convergence of asynchronous iterations in interval spaces and apply them to a variety of methods for the nonlinear equations case the convergence results turn out to be very similar to those known for synchronous methods several practical examples on shared memory architectures are included the asynchronous methods sometimes perform substantially better than their synchronous counterparts

weak converse lyapunov theorems and control lyapunov functions given a weakly uniformly globally asymptotically stable closed not necessarily compact set cal a for a differential inclusion that is defined on mathbb r n is locally lipschitz on mathbb r n backslash cal a and satisfies other basic conditions we construct a weak lyapunov function that is locally lipschitz on mathbb r n using this result we show that uniform global asymptotic controllability to a closed not necessarily compact set for a locally lipschitz nonlinear control system implies the existence of a locally lipschitz control lyapunov function and from this control lyapunov function we construct a feedback that is robust to measurement noise

uniqueness of continuous solutions for bv vector fields we consider a vector field whose coefficients are functions of bounded variation with a bounded divergence we prove the uniqueness of continuous solutions for the cauchy problem

robust global stabilisability by means of sampled data control with positive sampling rate this work proposes a notion of robust reachability of one set from another set under constant control this notion is used to construct a control strategy involving sequential set to set reachability which guarantees robust global stabilisation of non linear sampled data systems with positive sampling rate sufficient conditions for robust reachability of one set from another under constant control are also provided the proposed method is illustrated through a number of examples including the study of the sampled data stabilisation problem of the chemostat

on asynchronous iterations asynchronous iterations arise naturally on parallel computers if one wants to minimize idle times this paper reviews certain models of asynchronous iterations using a common theoretical framework the corresponding convergence theory and various domains of applications are presented these include nonsingular linear systems nonlinear systems and initial value problems

global existence and asymptotic behavior of solutions for the maxwell schrodinger equations in three space dimensions in this paper we study the global existence and asymptotic behavior of solutions for the maxwell schrodinger equations under the coulomb gauge condition in three space dimensions with the final states given att this leads to the construction of the modified wave operator for certain scattered data it is also shown that for the initial data in the range of the modified wave operator the initial value problem of the maxwell schrodinger equations has the global solutions in time

distributed asynchronous computation of fixed points we present an algorithmic model for distributed computation of fixed points whereby several processors participate simultaneously in the calculations while exchanging information via communication links we place essentially no assumptions on the ordering of computation and communication between processors thereby allowing for completely uncoordinated execution we provide a general convergence theorem for algorithms of this type and demonstrate its applicability to several classes of problems including the calculation of fixed points of contraction and monotone mappings arising in linear and nonlinear systems of equations optimization problems shortest path problems and dynamic programming

the analysis of partial differential operators i hormander springer 1985 vol 1 391 pp vol 2 390 pp vol 3 525 pp vol 4 351 pp

models of parallel chaotic iteration methods abstract we consider two models of parallel multisplitting chaotic iterations for solving large nonsingular systems of equations ax b in the first model each processor can carry out an arbitrary number of local iterations before the next global approximation to the solution is formed in the second model any processor can update the global approximation which resides in the central processor at any time this model is a generalization of a sequential iterative scheme due to ostrowski called the free steering group jacobi iterative scheme and a chaotic relaxation point iterative scheme due to chazan and miranker we show that when a is a monotone matrix and all the splittings are weak regular both models lead to convergent schemes

quantum classical correspondence using projection operators classical properties associated with a large phase space domain with a smooth boundary as compared to the planck constant are shown to be expressed quantum mechanically by a family of quantum projection operators with the help of known theorems in microlocal analysis under the conditions of egorov s theorem the conservation of this correspondence under classical quantum dynamics is asserted

a quadratically convergent krawczyk like algorithm in this paper we introduce a method for computing a solution of a nonlinear system which is similar to that proposed by r krawczyk computing 4 1969 pp 187 201 our method however needs considerably less work per step starting with an interval vector we give a criterion under which the method is convergent to the solution of the system if a solution is contained in the interval vector if the starting vector contains no solution then the method will break down after a finite number of steps

interval slopes for rational functions and associated centered forms for an arithmetic expression f x involving n rational operations an o n algorithm is given which computes an interval enclosure for the set of slopes f x z where x ranges over an interval x applications to real and complex centered forms are given resulting in improvements over previous results by ratschek siam j numer anal 17 1980 pp 656 662 and petkovic freiburger intervall berichte 83 2 1983 pp 33 50

regular articlegeneralized strichartz inequalities for the wave equation we make a synthetic exposition of the generalized strichartz inequalities for the wave equation obtained in 6 together with the limiting cases recently obtained in 13 with as simple proofs as possible the proofs combine stationary phase estimates dyadic decompositions the hardy littlewood inequality or the holder inequality in time and abstract duality and interpolation arguments

convergence of sequential and asynchronous nonlinear paracontractions we establish the convergence of sequential and asynchronous iteration schemes for nonlinear paracontracting operators acting in finite dimensional spaces applications to the solution of linear systems of equations with convex constraints are outlined a first generalization of one of our convergence results to an infinite pool of asymptotically paracontracting operators is also presented

comparison theorems for iterative methods based on strong splittings by means of strong splittings of an n times n interval m matrix mathcal a one can construct iterative methods to enclose the solution set x x ax b a in a b in mathfrak b where mathfrak b is an interval vector and x in mathbb r n we derive comparison theorems for an upper bound of the asymptotic convergence factor and for the fixpoints resulting from those methods

ordinary differential equations transport theory and sobolev spaces we obtain some new existence uniqueness and stability results for ordinary differential equations with coefficients in sobolev spaces these results are deduced from corresponding results on linear transport equations which are analyzed by the method of renormalized solutions

on the r order of newton like methods for enclosing solutions of nonlinear equations a class of newton like methods for enclosing solutions of nonlinear equations is considered given q in 1 2 criteria that yield an r order of convergence of at least q are derived in particular it is shown that under certain circumstances this r order can reach 2 the results are illustrated on a discretized version of chandrasekhar s h equation

krawczyk like algorithms for the solution of systems of nonlinear equations in this paper we present interval arithmetic methods for the solution of systems of nonlinear equations these methods are based on the algorithm of r krawczyk 5 and a modification introduced in 3 starting with an interval vector containing a solution of the given system these methods converge to that solution under relatively weak conditions i e it can be said that the convergence is almost global

asymptotic expansion of the trace of the heat kernel associated to the dirichlet to neumann operator abstract for a given bounded domain with smooth boundary in a smooth riemannian manifold m g by decomposing the dirichlet to neumann operator into a sum of the square root of the laplacian and a pseudodifferential operator and by applying grubb s method of symbolic calculus for the corresponding pseudodifferential heat kernel operators we establish a procedure to calculate all the coefficients of the asymptotic expansion of the trace of the heat kernel associated to dirichlet to neumann operator as t 0 in particular we explicitly give the first four coefficients of this asymptotic expansion these coefficients provide precise information regarding the area and curvatures of the boundary of the domain in terms of the spectrum of the steklov problem

long range scattering for the maxwell schrodinger system in the lorenz gauge without any restriction on the size of data abstract this paper concerns the scattering theory for the maxwell schrodinger ms system in the lorenz gauge or more precisely the existence of the modified wave operators for this system in r 3 1 space time we construct solutions to the ms system which behave as free maxwell and schrodinger waves with prescribed asymptotic states when t without any restriction on the size thereof since this system belongs to the borderline between the short range case and the long range case we need modification of phase for the schrodinger function

asynchronous two stage iterative methods parallel block two stage iterative methods for the solution of linear systems of algebraic equations are studied convergence is shown for monotone matrices and for h matrices two different asynchronous versions of these methods are considered and their convergence investigated

m functions and parallel asynchronous algorithms the solution of nonlinear systems of equations fx z via parallel asynchronous algorithms is considered it is shown that when f is continuous off diagonally antitone and strictly diagonally isotone then point asynchronous iterations converge monotonically to a solution of the problem from supersolutions and subsolutions a global convergence result for asynchronous iterations when f is a continuous surjective m function is also presented

a real time framework for model predictive control of continuous time nonlinear systems a new formulation of model predictive control mpc for continuous time nonlinear systems is developed which allows for the use of ldquoreal timerdquo rt optimization techniques in which the solution to the finite horizon optimal control problem opc evolves within the same timescale as the process dynamics the computational savings of the rt solver are enhanced by the unique framework within which the opc is posed enabling significant reduction in the dimensionality of the search for situations where computational speed takes priority over optimality of the solutions this framework and its associated proof of stability encompasses results on sampled data sd nonlinear model predictive control nmpc implementation as a special case

some convergence results for asynchronous algorithms nous presentons dans cet article des resultats de convergence des algorithmes asynchrones bases essentiellement sur la notion classique de contraction nous generalisons en particulier tous les resultats de convergence de ces algorithmes qui font l hypothese de contraction en norme vectorielle qui recemment a ete tres souvant utilisee par ailleurs l hypothese de contraction en norme vectorielle peut se trouver difficile voire impossible a verifier pour certains problemes qui peuvent etre cependant abordes dans le cadre de la contraction classique que nous adoptons in this paper we present convergence results for the asynchronous algorithms based essentially on the notion of classical contraction we generalize in particular all convergence results for those algorithms which are based on the vectorial norm hypothesis in wide spread use recently certain problems for which the vectorial norm hypothesis can be difficult or even impossible to verify can nontheless be tackled within the scope of the classical contraction that we adopte

gevrey regularity for a class of sums of squares of monomial vector fields abstract analytic or gevrey hypoellipticity is proved for a class of sums of squares of vector fields having a symplectic characteristic manifold of dimension 2 and arbitrary even codimension we note that this class contains examples for which the treves stratification seems to work as well as examples for which the treves stratification does not identify properly the non symplectic stratum

on the convergence of asynchronous paracontractions with application to tomographic reconstruction from incomplete data abstract convergence of iterative processes in c k of the form x i r i j i x 1 r i 1 1 p j i x i where j i 1 2 n i 1 2 is analyzed it is shown that if the matrices p 1 p n are paracontracting in the same smooth strictly convex norm and if the sequence j i i 1 has certain regularity properties then the above iterates converge this result implies the convergence of a parallel asynchronous implementation of the algebraic reconstruction technique art algorithm often used in tomographic reconstruction from incomplete data

asymptotic stability and smooth lyapunov functions abstract we establish that differential inclusions corresponding to upper semicontinuous multifunctions are strongly asymptotically stable if and only if there exists a smooth lyapunov function since well known concepts of generalized solutions of differential equations with discontinuous right hand side can be described in terms of solutions of certain related differential inclusions involving upper semicontinuous multifunctions this result gives a lyapunov characterization of asymptotic stability of either filippov or krasovskii solutions for differential equations with discontinuous right hand side in the study of weak as opposed to strong asymptotic stability the existence of a smooth lyapunov function is rather exceptional however the methods employed in treating the strong case of asymptotic stability are applied to yield a necessary condition for the existence of a smooth lyapunov function for weakly asymptotically stable differential inclusions this is an extension to the context of lyapunov functons of brockett s celebrated covering condition from continuous feedback stabilization theory

complete determination of the singularity structure of zeta functions series of extended epstein type provide examples of non trivial zeta functions with important physical applications the regular part of their analytic continuation is seen to be a convergent or an asymptotic series their singularity structure is completely determined in terms of the wodzicki residue in its generalized form which is proven to yield the residua of all the poles of the zeta function and not just that of the rightmost pole obtainable from the dixmier trace the calculation is a very down to earth application of these powerful functional analytical methods in physics

feedback control of linear systems by multirate pulse width modulation in this note sampled data methods for modeling and control design of pulse width modulated systems are examined both single rate and multirate approaches are considered local controllability and observability analyses of the sampled data models are performed and feedback linearizability conditions for the sampled data models are derived multirate nonlinear state and output feedback designs are presented that permit asymptotic regulation or tracking

continuous control lyapunov functions for asymptotically controllable time varying systems this paper shows that for time varying systems global asymptotic controllability to a given closed subset of the state space is equivalent to the existence of a continuous control lyapunov function with respect to the set

asymptotic controllability and observability imply semiglobal practical asymptotic stabilizability by sampled data output feedback it is shown for general nonlinear systems that asymptotic controllability and observability are sufficient for semiglobal practical asymptotic stabilization by output feedback indeed as previously shown in the literature asymptotic controllability implies the existence of a discontinuous in general state feedback that when implemented by sample and hold is semiglobally practically stabilizing and robust to measurement disturbance moreover a weak form of observability allows reconstruction of the state with arbitrary precision in an arbitrarily short amount of time so we can build an output feedback that operates periodically in two modes an initial small fraction of a sampling period is used to estimate the state and the remainder of the sampling period is used to implement the state feedback control using the state estimate our stabilization results are presented not only for compact target sets e g the origin but also for noncompact target sets

generalized nonlinear diagonal dominance and applications to asynchronous iterative methods abstract we introduce a concept of generalized diagonal dominance for nonlinear functions as in the linear case this brings together several apparently different classes of nonlinear functions such as strictly diagonally dominant functions and certain m functions with our concept we easily obtain a quite far reaching result on the global convergence of asynchronous iterative methods for finding zeros of nonlinear functions special cases include some known and several new convergence results for special iterative methods such as the nonlinear jor sor and ssor method

algorithmes mixtes asynchrones etude de convergence monotone nous introduisons dans cet article deux classes d algorithmes iteratifs que nous appelons algorithmes mixtes asynchrones et nous en etudierons la convergence selon un ordre partiel ces algorithmes sont implementables aussi bien sur les monoprocesseurs que sur les multiprocesseurs et avec leur etude de convergence constituent une generalisation des algorithmes mixtes classiques newton relaxation in this paper we introduce two classes of iterative algorithms which we call asynchronous mixed algorithms and we study their convergence under partial ordering these algorithms can be implemented just as well on monoprocessors as on multiprocessors and along with their convergence study constitute a generalization of the mixed classical newton relaxation algorithms

a new class of asynchronous iterative algorithms with order intervals this paper deals with a new class of parallel asynchronous iterative algorithms for the solution of nonlinear systems of equations the main feature of the new class of methods preseted here is the possibility of flexible commmunication between processors in particular partial updates can be exchanged approximation of the asssociated fixed point mapping is also considered a detailed convergengence study is presented a connection with the schwarz alternating method is made for nonlinear boundary value problems computational results on a shared memory multiprocessotr ibm 3090 are presented