asymptotic preserving schemes for highly oscillatory vlasov poisson equations this work is devoted to the numerical simulation of a vlasov poisson model describing a charged particle beam under the action of a rapidly oscillating external field we construct an asymptotic preserving numerical scheme for this kinetic equation in the highly oscillatory limit this scheme enables to simulate the problem without using any time step refinement technique moreover since our numerical method is not based on the derivation of the simulation of asymptotic models it works in the regime where the solution does not oscillate rapidly and in the highly oscillatory regime as well our method is based on a two scale reformulation of the initial equation with the introduction of an additional periodic variable

uniformly accurate numerical schemes for highly oscillatory klein gordon and nonlinear schrodinger equations this work is devoted to the numerical simulation of nonlinear schrodinger and klein gordon equations we present a general strategy to construct numerical schemes which are uniformly accurate with respect to the oscillation frequency this is a stronger feature than the usual so called asymptotic preserving property the last being also satisfied by our scheme in the highly oscillatory limit our strategy enables to simulate the oscillatory problem without using any mesh or time step refinement and the orders of our schemes are preserved uniformly in all regimes in other words since our numerical method is not based on the derivation and the simulation of asymptotic models it works in the regime where the solution does not oscillate rapidly in the highly oscillatory limit regime and in the intermediate regime with the same order of accuracy in the same spirit as in crouseilles et al j comput phys 248 287 308 2013 the method is based on two main ingredients first we embed our problem in a suitable two scale reformulation with the introduction of an additional variable then a link is made with classical strategies based on chapman enskog expansions in kinetic theory despite the dispersive context of the targeted equations allowing to separate the fast time scale from the slow one uniformly accurate schemes are eventually derived from this new formulation and their properties and performances are assessed both theoretically and numerically

a novel robust adaptive fuzzy tracking control for a class of nonlinearmulti input multi output systems robust adaptive fuzzy tracking control of a class of uncertain multi input multi output nonlinear systems with coupled interconnections is considered in this paper takagi sugeno t s fuzzy systems are used to approximate the unknown system functions a novel adaptive control scheme is developed on the basis of the so called dynamic surface control and minimal learning parameters techniques the proposed scheme has following two key features first the number of parameters updated online for each subsystem is reduced to one and both problems of curse of dimension for high dimensional systems and explosion of complexity inherent in the conventional backstepping methods are circumvented second the potential controller singularity problem in some of the existing adaptive control schemes with feedback linearization techniques is overcome it is shown via lyapunov theory that all the signals in the closed loop system are semiglobally uniformly ultimately bounded finally simulation results via two examples are presented to demonstrate the effectiveness and advantages of the proposed scheme

a two level implicit scheme for the numerical solution of the linearized vorticity equation a numerical scheme is developed to study the stability of the linearized vorticity equations the linear growth rates of kelvin helmholtz instabilities resulting from a velocity shear are calculated numerically the theory of neutrally stable waves in two dimensions is extended to include the cases where the stream function is zero or periodic at the boundary and is verified numerically for the case of a velocity profile having the shape of a cosine function the instability growth rates of the oscillations in the neighbourhood of the neutrally stable waves are calculated numerically and are shown to be in very good agreement with the theory the results are also of interest in relation to studies on the instabilities of a two dimensional guiding centre plasma and also in the study of the diocotron instability in electronics

uniformly accurate particle in cell method for the long time solution of the two dimensional vlasov poisson equation with uniform strong magnetic field abstract in this work we focus on the numerical resolution of the four dimensional phase space vlasov poisson system subject to a uniform strong external magnetic field to do so we consider a particle in cell based method for which the characteristics are reformulated by means of the two scale formalism which is well adapted to handle highly oscillatory equations then a numerical scheme is derived for the two scale equations the so obtained scheme enjoys a uniform accuracy property meaning that its accuracy does not depend on the small parameter several numerical results illustrate the capabilities of the method

integral hosm semiglobal controller for finite time exact compensation of unmatched perturbations the present technical note studies a class of nonlinear systems with unmatched perturbations the combination of integral high order sliding modes with the hierarchical quasi continuous controller is proposed allowing finite time exact compensation of unmatched perturbations with semiglobal convergence features for both regulation and tracking

efficient asymptotic preserving ap schemes for some multiscale kinetic equations many kinetic models of the boltzmann equation have a diffusive scaling that leads to the navier stokes type parabolic equations as the small scaling parameter approaches zero in practical applications it is desirable to develop a class of numerical schemes that can work uniformly with respect to this relaxation parameter from the rarefied kinetic regimes to the hydrodynamic diffusive regimes an earlier approach in s jin l pareschi and g toscani siam j numer anal 35 1998 pp 2405 2439 reformulates such systems into the common hyperbolic relaxation system by jin and xin for hyperbolic conservation laws used to construct the relaxation schemes and then uses a multistep time splitting method to solve the relaxation system here we observe that the combination of the two time split steps may yield hyperbolic parabolic systems that are more advantageous in both stability and efficiency for numerical computations we show that such an approach yields a class of asymptotic preserving ap schemes which are suitable for the computation of multiscale kinetic problems we use the goldstein taylor and carleman models to illustrate this approach

technical communique quasi continuous hosm control for systems with unmatched perturbations the control of nonlinear systems subject to unmatched perturbations is studied a new design algorithm is proposed based on the block control and quasi continuous higher order sliding modes techniques the proposed method provides for the finite time exact tracking of a smooth desired signal in spite of unmatched perturbations

sampled data fuzzy control for a class of nonlinear systems with missing data and disturbances this paper considers the sampled data fuzzy control of nonlinear systems in strict feedback form with disturbances and random missing input data we propose a novel method in which a state observer and a disturbance observer are combined to construct a sampled data fuzzy output feedback controller the stochastic variables with a bernoulli distributed sequence are used to model missing input data fuzzy logic systems are applied to approximate nonlinearities without requiring prior knowledge the relation between observer gain and sampling period is established the output feedback controller designed guarantees that the nonlinear system is globally stable a simulation example of four degrees of freedom robotic arm is used to demonstrate the effectiveness and applicability of the proposed control scheme

robustness of the tuning functions adaptive backstepping design for linear systems we study robustness of the adaptive backstepping design with tuning functions for linear systems under assumptions on unmodeled dynamics and disturbances equal to those for certainty equivalence schemes we address an adaptive scheme not based on the certainty equivalence principle in the process of redesign for robustness we employ only leakage in the estimator we do not employ normalization neither static nor dynamic a fundamental difference between the tuning functions design and the certainty equivalence designs is that the controller in the former is inherently nonlinear while in the latter it is nonlinear only in the parameter estimate as a result achievable robustness results for the tuning functions scheme are not global but regional with a region of attraction inversely proportional to the size of the unmodeled dynamics the tracking error is proportional to the size of the uncertainties

asymptotically stable particle in cell methods for the vlasov poisson system with a strong external magnetic field this paper deals with the numerical resolution of the vlasov poisson system with a strong external magnetic field by particle in cell pic methods in this regime classical pic methods are subject to stability constraints on the time and space steps related to the small larmor radius and plasma frequency here we propose an asymptotic preserving pic scheme which is not subjected to these limitations our approach is based on first and higher order semi implicit numerical schemes already validated on dissipative systems s boscarino f filbet and g russo j sci comput 2016 doi 10 1007 s10915 016 0168 y additionally when the magnitude of the external magnetic field becomes large this method provides a consistent pic discretization of the guiding center equation that is an incompressible euler equation in vorticity form we propose several numerical experiments which provide a solid validation of the method and its underlying concepts

inverse limit and topological aspects of abstract interpretation we develop abstract interpretation domain construction in terms of the inverse limit construction of denotational semantics and topological principles we define an abstract domain as a structural approximation of a concrete domain if the former exists as a finite approximant in the inverse limit construction of the latter and we extract the appropriate galois connection for sound and complete abstract interpretations the elements of the abstract domain denote basic open sets from the concrete domain s scott topology and we hypothesize that every abstract domain even non structural approximations defines a weakened form of topology on its corresponding concrete domain we implement this observation by relaxing the definitions of topological open set and continuity key results still hold we show that families of closed and open sets defined by abstract domains generate post and pre condition analyses respectively and giacobazzi s forwards and backwards complete functions of abstract interpretation theory are the topologically closed and continuous maps respectively finally we show that smyth s upper and lower topologies for power domains induce the overapproximating and underapproximating transition functions used for abstract model checking

conservative semi lagrangian schemes for vlasov equations conservative methods for the numerical solution of the vlasov equation are developed in the context of the one dimensional splitting in the case of constant advection these methods and the traditional semi lagrangian ones are proven to be equivalent but the conservative methods offer the possibility to add adequate filters in order to ensure the positivity in the non constant advection case they present an alternative to the traditional semi lagrangian schemes which can suffer from bad mass conservation in this time splitting setting

integral sliding mode control for nonlinear systems with matched and unmatched perturbations we consider the problem of designing an integral sliding mode controller to reduce the disturbance terms that act on nonlinear systems with state dependent drift and input matrix the general case of both matched and unmatched disturbances affecting the system is addressed it is proved that the definition of a suitable sliding manifold and the generation of sliding modes upon it guarantees the minimization of the effect of the disturbance terms which takes place when the matched disturbances are completely rejected and the unmatched ones are not amplified a simulation of the proposed technique applied to a dynamically feedback linearized unicycle illustrates its effectiveness even in presence of nonholonomic constraints

3 valued abstraction more precision at less cost this paper investigates both the precision and the model checking efficiency of abstract models designed to preserve branching time logics w r t a 3 valued semantics current abstract models use ordinary transitions to over approximate the concrete transitions while they use hyper transitions to under approximate the concrete transitions in this work we refer to precision measured w r t the choice of abstract states independently of the formalism used to describe abstract models we show that current abstract models do not allow maximal precision we suggest a new class of models and a construction of an abstract model which is most precise w r t any choice of abstract states as before the construction of such models might involve an exponential blowup which is inherent by the use of hyper transitions we therefore suggest an efficient algorithm in which the abstract model is constructed during model checking by need our algorithm achieves maximal precision w r t the given property while remaining quadratic in the number of abstract states to complete the picture we incorporate it into an abstraction refinement framework

nonlinear sliding mode control design an lmi approach abstract this paper presents a novel nonlinear sliding mode control methodology for systems with both matched and unmatched perturbations including parametric uncertainties instead of traditional approaches where uncertainties and nonlinearities are coped with via linear nominal models and linear sliding surfaces the proposed approach incorporates exact convex expressions to represent both the nonlinear surface and the system thus allowing a significant chattering reduction moreover thanks to the convex form of the nonlinear nominal model when combined with the direct lyapunov method it leads to linear matrix inequalities which are efficiently solved via convex optimization techniques illustrative examples are provided

a combination of multiscale time integrator and two scale formulation for the nonlinear schrodinger equation with wave operator abstract in this paper we consider the nonlinear schrodinger equation with wave operator nlsw which contains a dimensionless parameter 0 e 1 as 0 e 1 the solution of the nlsw propagates fast waves in time with wavelength o e 2 and the problem becomes highly oscillatory in time the oscillations come from two parts one part is from the equation and another part is from the initial data for the ill prepared initial data case as described in bao and cai 2014 which brings inconsistency in the limit regime standard numerical methods have strong convergence order reduction in time when e becomes small we review two existing methods to solve the nlsw an exponential integrator and a two scale method we comment on their order reduction issues then we derive a multiscale decomposition two scale method for solving the nlsw by first performing a multiscale decomposition on the nlsw which decomposes it into a well behaved part and an energy unbounded part and then applying an exponential integrator for the well behaved part and a two scale approach for the energy unbounded part numerical experiments are conducted to test the proposed method which shows uniform second order accuracy without significant order reduction for all 0 e 1 comparisons are made with the existing methods

making abstract interpretations complete completeness is an ideal although uncommon feature of abstract interpretations formalizing the intuition that relatively to the properties encoded by the underlying abstract domains there is no loss of information accumulated in abstract computations thus complete abstract interpretations can be rightly understood as optimal we deal with both pointwise completeness involving generic semantic operations and least fixpoint completeness completeness and fixpoint completeness are shown to be properties that depend on the underlying abstract domains only our primary goal is then to solve the problem of making abstract interpretations complete by minimally extending or restricting the underlying abstract domains under the weak and reasonable hypothesis of dealing with continuous semantic operations we provide constructive characterizations for the least complete extensions and the greatest complete restrictions of abstract domains as far as fixpoint completeness is concerned for merely monotone semantic operators the greatest restrictions of abstract domains are constructively characterized while it is shown that the existence of least extensions of abstract domains cannot be in general guaranteed even under strong hypotheses these methodologies which in finite settings give rise to effective algorithms provide advanced formal tools for manipulating and comparing abstract interpretations useful both in static program analysis and in semantics design a number of examples illustrating these techniques are given

observation and output adaptive tracking for a class of nonlinear non minimum phase systems abstractin this paper the output tracking problem for a class of systems with unstable zero dynamics is addressed the state is assumed not measurable the output of the dynamical system to be controlled has to track a signal which is the sum of a known number of sinusoids with unknown frequencies amplitudes and phases the non minimum phase nature of the considered systems prevents the direct tracking by standard sliding mode methods which are known to generate unstable behaviours of the internal dynamics the proposed method relies on the availability of a flat output and its time derivatives which are functions of the unavailable state therefore a nonlinear observer is needed due to the uncertainty in the frequencies and in the parameters defining the relationship between the output of the system and the flat states adaptive indirect methods are applied

exact tracking using backstepping control design and high order sliding modes in this technical note a controller ensuring exponential exact tracking in the presence of matched and unmatched disturbances for the nonlinear systems in the block controllable form is proposed the controller is designed using the backstepping procedure and combines the feedback linearization technique with the high order sliding modes the matched and unmatched disturbances are compensated by the injection of a continuous term generated by the robust exact high order sliding modes differentiator the obtained control law is differentiable and can be applied directly to the system simulations verify the performance of the proposed controller

dynamic switching surfaces for output sliding mode control the robustness properties of sliding mode and h controllers are exploited to produce a dynamic output feedback controller that is insensitive to matched perturbations and attenuates the unmatched ones the assumptions on the plant differ from the standard assumptions of the riccati state space approach to h control the sliding mode controller drives the state into a reduced order manifold for which the equivalent system does satisfy the standard assumptions and hence the standard theory can be applied the resulting riccati equations are of reduced order

global properties of the triangular systems in the singular case we introduce a new class of the triangular multi input and multi output control systems of o d e which are not feedback linearizable and investigate its global behavior the triangular form introduced is a generalization of the classes of triangular systems considered before for our class we solve the problem of global robust controllability combining our main result with that of f h clarke yu s ledyaev e d sontag a i subbotin asymptotic controllability implies feedback stabilization ieee trans automat control 42 1997 1394 1407 we obtain a corollary on the global discontinuous sampled stabilization an example showing that global smooth stabilization can be irrelevant to the singular case is considered to prove our main result we apply a certain back stepping algorithm and combine the technique proposed in v i korobov s s pavlichkov w h schmidt global robust controllability of the triangular integro differential volterra systems j math anal appl 309 2005 743 760 with solving a specific problem of global practical stabilization by means of a discontinuous time varying feedback law

adaptive dynamic surface control a simplified algorithm for adaptive backstepping control of nonlinear systems in this paper we propose a new algorithm for adaptive backstepping control of non linear uncertain systems current backstepping algorithms require repeated differentiations of the modelled non linearities the addition of n first order low pass filters allows the algorithms to be implemented without differentiating any model non linearities the uncertainties are assumed to be linear in the unknown constant parameters the combined adaptive backstepping first order filter system is proven to be semi globally stable for sufficiently fast filters by a singular perturbation approach