co volume methods for degenerate parabolic problems a complementary volume co volume technique is used to develop a physically appealing algorithm for the solution of degenerate parabolic problems such as the stefan problem it is shown that these algorithms give rise to a discrete semigroup theory that parallels the continuous problem in particular the discrete stefan problem gives rise to nonlinear semigroups in both the discretel 1 andh 1 spaces

some properties of the nonlinear semigroup for the problem ut δf u 0 le probleme est de trouver u t l 1 donnee par l equation du d lf u 0 u 0 u 0 r n est un domaine borne a frontiere lisse f r r est une fonction continue de lifschitz non decroissante avec f 0 0

weighted inequalities for commutators of fractional integrals on spaces of homogeneous type abstract let 0 1 b be a bmo function and i b m the commutator of order m for the fractional integral we prove two type of weighted l p inequalities for i b m in the context of the spaces of homogeneous type the first one establishes that for a weights the operator i b m is bounded in the weighted l p norm by the maximal operator m m m where m is the fractional maximal operator and m m is the hardy littlewood maximal operator iterated m times the second inequality is a consequence of the first one and shows that the operator i b m is bounded from l p m p m m 1 p w x d x to l p w x d x where m 1 p is the integer part of m 1 p and no condition on the weight w is required from the first inequality we also obtain weighted l p l q estimates for i b m generalizing the classical results of muckenhoupt and wheeden for the fractional integral operator

robust controller design for stochastic nonlinear systems via convex optimization this paper presents a new nonlinear control design framework called convex optimization based stochastic steady state tracking error minimization cvstem for a class of ito stochastic nonlinear systems including stochastic lagrangian systems this state feedback controller design involves the use of multiple state dependent coefficient sdc models of a nonlinear system equation and computes its controller parameters by solving a convex optimization problem in order to minimize an upper bound of the steady state tracking error this problem is shown to be equivalent to the original nonlinear optimization problem of minimizing the upper bound the exponential stability and robustness properties due to the state dependent riccati inequality are proven using stochastic contraction analysis discrete time stochastic incremental contraction analysis with respect to a state and time dependent metric is also presented along with its explicit connection to continuous time contraction analysis a result of simulation is used to validate the superiority of the proposed controller compared to a known nonlinear controller a pid controller and an h infinity controller

filtering of stochastic nonlinear differential systems via a carleman approximation approach this paper deals with the state estimation problem for stochastic nonlinear differential systems driven by standard wiener processes and presents a filter that is a generalization of the classical extended kalman bucy filter ekbf while the ekbf is designed on the basis of a first order approximation of the system around the current estimate the proposed filter exploits a carleman like approximation of a chosen degree v ges 1 the approximation procedure applied to both the state and the measurement equations allows to define an approximate representation of the system by means of a bilinear system for which a filtering algorithm is available from the literature numerical simulations on an example show the improvement in terms of sample error covariance of the filter based on the first order second order and third order system approximations v 1 2 3

control for a class of second order systems via a state dependent riccati equation approach this study investigates the state dependent riccati equation sdre controller for a class of second order nonlinear systems by fully exploiting the design degree of freedom dof arising from the nonunique state dependent coefficient sdc matrices we explicitly calculate the ranges of control input via the sdre scheme moreover when a permissible control input is determined we also explicitly parameterize the sdc matrices that result in the designated control value in terms of system states and parameters so the engineer can easily implement the scheme notably this is the first analytical result that explores the range of control input using the design dof of sdc matrices in addition by applying the analytical results it is shown that the second order systems are always globally stabilizable without any supplementary assumptions on weighting matrices as extended from existing sdre global results and the corresponding stabilizing sdc matrices are also explicitly presented finally illustr

weighted sobolev morrey estimates for hypoelliptic operators with drift on homogeneous groups abstract let x 0 x 1 x q be left invariant real vector fields on the homogeneous group g and assume that x 1 x q are homogeneous of degree one and x 0 is homogeneous of degree two in this paper we consider the following hypoelliptic operator with drift l i j 1 q a i j x i x j a 0 x 0 where a i j is a constant matrix satisfying the elliptic condition in r q and a 0 0 and obtain weighted sobolev morrey estimates and morrey estimates with two weights of l by establishing boundedness of several singular integrals and interpolation lemmas on g

l sub 2 gain analysis of nonlinear systems and nonlinear state feedback h sub infinity control previously obtained results on l2 gain analysis of smooth nonlinear systems are unified and extended using an approach based on hamilton jacobi equations and inequalities and their relation to invariant manifolds of an associated hamiltonian vector field on the basis of these results a nonlinear analog is obtained of the simplest part of a state space approach to linear h sub infinity control namely the state feedback h sub infinity optimal control problem furthermore the relation with h sub infinity control of the linearized system is dealt with

uncertainty principle estimates for vector fields abstract we derive weighted norm estimates for integral operators of potential type and for their related maximal operators these operators are generalizations of the classical fractional integrals and fractional maximal functions the norm estimates are derived in the context of a space of homogeneous type the conditions required of the weight functions involve generalizations of the fefferman phong r bump condition the results improve some earlier ones of the same kind and they also extend to homogeneous spaces some estimates that were previously known to hold only in the classical euclidean setting

simultaneous input and state estimation for nonlinear systems with applications to flow field estimation this paper studies the problem of simultaneous input and state estimation sise for nonlinear dynamical systems with and without direct input output feedthrough we take a bayesian perspective to develop a sequential joint input and state estimation approach our scheme gives rise to a nonlinear maximum a posteriori optimization problem which we solve using the classical gauss newton method the proposed approach generalizes a number of sise methods presented in the literature we illustrate the effectiveness of the proposed scheme for nonlinear systems with direct feedthrough in an oceanographic flow field estimation problem involving submersible drogues that measure position intermittently and acceleration continuously

observer design for a class of mimo nonlinear systems a simple observer is proposed for a large class of mimo nonlinear systems which includes many physical models the main characteristic of the proposed observer lies in the easiness of its implementation and calibration indeed the gain of this observer does not necessitate the resolution of any dynamical system and its expression is given moreover its calibration is achieved through the choice of a single parameter a simulation example is given in order to illustrate the performance of the proposed observer

a contraction theory approach to stochastic incremental stability we investigate the incremental stability properties of ito stochastic dynamical systems specifically we derive a stochastic version of nonlinear contraction theory that provides a bound on the mean square distance between any two trajectories of a stochastically contracting system this bound can be expressed as a function of the noise intensity and the contraction rate of the noise free system we illustrate these results in the contexts of nonlinear observers design and stochastic synchronization

on lmi conditions to design observers for lipschitz nonlinear systems this paper addresses the problem of observer design for lipschitz nonlinear systems via lmi the goal of this note is to clarify some recent results and to propose a new design methodology this is based on the reformulation of the lipschitz property using some mathematical tools this reformulation is a relevant and useful lipschitz condition which leads to less restrictive lmi conditions to show the superiority of this latter two numerical examples are presented

lpestimates for some ultraparabolic operators with discontinuous coefficients we consider a class of ultraparabolic operators of the kind formula z x t rn 1 where the principal part is uniformly elliptic on rq q n and the constant matrixbis upper triangular and such that the operator obtained by freezing the coefficientsaijat any pointz0 rn 1is hypoelliptic we prove local lp estimates for the derivatives xixju i j 1 q of a solution to the equationlu f under the assumption that the coefficientsaijbelong to the space vmo vanishing mean oscillation with respect to a suitable metric related tob

phase synchronization control of complex networks of lagrangian systems on adaptive digraphs this paper presents a formation control and synchronization method that utilizes adaptive network topologies for a class of complex dynamical networks comprised of a large number of highly nonlinear euler lagrange el systems a time varying and switching network topology constructed by the adaptive graph laplacian matrix relaxes the standard requirement of consensus stability even permitting exponential synchronization on an unbalanced digraph or a weakly connected digraph that can sporadically lose connectivity the time varying graph laplacian matrix is adapted by an adaptive control scheme based on relative positions and errors of synchronization and tracking the adaptive graph laplacian is integrated with a phase synchronization controller that synchronizes the relative motions of el systems moving in elliptical orbits thereby yielding a smaller synchronization error than an uncoupled tracking control law in the presence of bounded disturbances and modeling errors an example of reconfiguring hundreds of spacecraft in low earth orbit shows the effectiveness of the proposed phase synchronization controller for a large number of complex el systems moving in periodic elliptical orbits

robust guaranteed cost state estimation for nonlinear stochastic uncertain systems via an iqc approach abstract this paper presents an approach to robust nonlinear state estimation based on the use of integral quadratic constraints and minimax lqg control the approach involves a class of state estimators which includes copies of the system nonlinearities in the state estimator the nonlinearities being considered are those which satisfy a certain global lipschitz condition the linear part of the state estimator is synthesized using minimax lqg control theory which is closely related to h control theory and this leads to a nonlinear state estimator which gives an upper bound on the estimation error cost

convergence of nonlinear observers on bbr n with a riemannian metric part i we study how convergence of an observer whose state lives in a copy of the given system s space can be established using a riemannian metric we show that the existence of an observer guaranteeing the property that a riemannian distance between system and observer solutions is nonincreasing implies that the lie derivative of the riemannian metric along the system vector field is conditionally negative moreover we establish that the existence of this metric is related to the observability of the system s linearization along its solutions moreover if the observer has an infinite gain margin then the level sets of the output function are geodesically convex conversely we establish that if a complete riemannian metric has a lie derivative along the system vector field that is conditionally negative and is such that the output function has a monotonicity property then there exists an observer with an infinite gain margin

observer design for systems with multivariable monotone nonlinearities globally convergent observers are designed for a class of systems with multivariable nonlinearities the approach is to represent the observer error system as the feedback interconnection of a linear system and a state dependent multivariable nonlinearity we first extend an earlier design automatica 37 12 2001 1923 to multivariable nonlinearities satisfying an analog of the scalar nondecreasing property next we exploit the structure of the nonlinearity to relax the positive real restriction on the linear part of the observer error system this relaxed design renders the feasibility conditions less restrictive and widens the applicability of the observer as illustrated with examples finally output nonlinearities are studied and the design is extended to be adaptive in the presence of unknown parameters

dynamic observers as asymptotic limits of recursive filters special cases a method for constructing observers for dynamical systems as asymptotic limits of filters is described the program is carried out in detail for linear systems and in addition an observer is obtai

holder regularity for a kolmogorov equation we study the interior regularity properties of the solutions to the degenerate parabolic equation x u b y u t u f x y t r n r r which arises in mathematical finance and in the theory of diffusion processes

exponentially incremental dissipativity for nonlinear stochastic switched systems in this paper we investigate the exponentially incremental dissipativity for nonlinear stochastic switched systems by using the designed state dependent switching law and multiple lyapunov functio

a tutorial on particle filters for online nonlinear non gaussian bayesian tracking increasingly for many application areas it is becoming important to include elements of nonlinearity and non gaussianity in order to model accurately the underlying dynamics of a physical system moreover it is typically crucial to process data on line as it arrives both from the point of view of storage costs as well as for rapid adaptation to changing signal characteristics in this paper we review both optimal and suboptimal bayesian algorithms for nonlinear non gaussian tracking problems with a focus on particle filters particle filters are sequential monte carlo methods based on point mass or particle representations of probability densities which can be applied to any state space model and which generalize the traditional kalman filtering methods several variants of the particle filter such as sir asir and rpf are introduced within a generic framework of the sequential importance sampling sis algorithm these are discussed and compared with the standard ekf through an illustrative example

on the harnack inequality for a class of hypoelliptic evolution equations we give a direct proof of the harnack inequality for a class of degenerate evolution operators which contains the linearized prototypes of the kolmogorov and fokker planck operators we also improve the known results in that we find explicitly the optimal constant of the inequality

stochastic stability of the discrete time extended kalman filter the authors analyze the error behavior for the discrete time extended kalman filter for general nonlinear systems in a stochastic framework in particular it is shown that the estimation error remains bounded if the system satisfies the nonlinear observability rank condition and the initial estimation error as well as the disturbing noise terms are small enough this result is verified by numerical simulations for an example system

stabilization of stochastic nonlinear systems driven by noise of unknown covariance this paper poses and solves a new problem of stochastic nonlinear disturbance attenuation where the task is to make the system solution bounded by a monotone function of the supremum of the covariance of the noise this is a natural stochastic counterpart of the problem of input to state stabilization in the sense of sontag 1989 our development starts with a set of new global stochastic lyapunov theorems for an exemplary class of stochastic strict feedback systems with vanishing nonlinearities where the equilibrium is preserved in the presence of noise we develop an adaptive stabilization scheme based on tuning functions that requires no a priori knowledge of a bound on the covariance next we introduce a control lyapunov function formula for stochastic disturbance attenuation finally we address optimality and solve a differential game problem with the control and the noise covariance as opposing players for strict feedback systems the resulting isaacs equation has a closed form solution

on preconditioning newton krylov methods in solidifying flow applications solidifying flow equations can be used to model industrial metallurgical processes such as casting and welding and material science applications such as crystal growth these flow equations contain locally stiff nonlinearities at the moving phase change interface we are developing a three dimensional parallel simulation tool for such problems using a jacobian free newton krylov solver and unstructured finite volume methods a segregated distributed block triangular preconditioning strategy is being developed for the newton krylov solver in this preconditioning approach we are only required to approximately invert matrices coming from a single field variable not matrices arising from a coupled system additionally simple linearizations are used in constructing our preconditioning operators the preconditioning strategy is presented along with the performance of the methods we consider problems in phase change heat transfer and the thermally driven incompressible navier stokes equations separately this is a required intermediate step toward developing a successful preconditioning strategy for the fully coupled physics problem

observers for systems with nonlinearities satisfying incremental quadratic constraints we consider the problem of designing observers to asymptotically estimate the state of a system whose nonlinear time varying terms satisfy an incremental quadratic inequality that is parameterized by a set of multiplier matrices observer design is reduced to solving linear matrix inequalities for the observer gain matrices the proposed observers guarantee exponential convergence of the state estimation error to zero in addition to considering a larger class of nonlinearities than previously considered this paper unifies earlier related results in the literature the results are illustrated by application to several examples

observer design for stochastic nonlinear systems via contraction based incremental stability this paper presents a new design approach to nonlinear observers for ito stochastic nonlinear systems with guaranteed stability a stochastic contraction lemma is presented which is used to analyze incremental stability of the observer a bound on the mean squared distance between the trajectories of original dynamics and the observer dynamics is obtained as a function of the contraction rate and maximum noise intensity the observer design is based on a non unique state dependent coefficient sdc form which parametrizes the nonlinearity in an extended linear form the observer gain synthesis algorithm called linear matrix inequality state dependent algebraic riccati equation lmi sdare is presented the lmi sdare uses a convex combination of multiple sdc parametrizations an optimization problem with state dependent linear matrix inequality sdlmi constraints is formulated to select the coefficients of the convex combination for maximizing the convergence rate and robustness against disturbances two variations of lmi sdare algorithm are also proposed one of them named convex state dependent riccati equation csdre uses a chosen convex combination of multiple sdc matrices and the other named fixed sdare uses constant sdc matrices that are pre computed by using conservative bounds of the system states while using constant coefficients of the convex combination pre computed by a convex lmi optimization problem a connection between contraction analysis and l 2 gain of the nonlinear system is established in the presence of noise and disturbances results of simulation show superiority of the lmi sdare algorithm to the extended kalman filter ekf and state dependent differential riccati equation sddre filter

observers for a class of lipschitz systems with extension to h performance analysis abstract in this paper observer design for a class of lipschitz nonlinear dynamical systems is investigated one of the main contributions lies in the use of the differential mean value theorem dmvt which allows transforming the nonlinear error dynamics into a linear parameter varying lpv system this has the advantage of introducing a general lipschitz like condition on the jacobian matrix for differentiable systems to ensure asymptotic convergence in both continuous and discrete time systems such sufficient conditions expressed in terms of linear matrix inequalities lmis are established an extension to h filtering design is obtained also for systems with nonlinear outputs a comparison with respect to the observer method of gauthier et al a simple observer for nonlinear systems applications to bioreactors ieee trans automat control 37 6 1992 875 880 is presented to show that the proposed approach avoids high gain for a class of triangular globally lipschitz systems in the last section academic examples are given to show the performances and some limits of the proposed approach the last example is introduced with the goal to illustrate good performances on robustness to measurement errors by avoiding high gain

robust nonlinear observer for lipschitz nonlinear systems subject to disturbances this note proposes a robust nonlinear observer for systems with lipschitz nonlinearity the proposed nonlinear observer whose linear part adopts the linear ltr observer design technique has two important advantages over previous designs first the new observer does not impose the small lipschitz constant condition on the system nonlinearity nor other structural conditions on the system dynamics as in the existing observer designs second it is robust in the sense that its state estimation error decays to almost zero even in the face of large external disturbances

nonlinear observers a circle criterion design and robustness analysis globally convergent observers are designed for a class of systems with monotonic nonlinearities the approach is to represent the observer error system as the feedback interconnection of a linear system and a time varying multivariable sector nonlinearity using lmi software observer gain matrices are computed to satisfy the circle criterion and hence to drive the observer error to zero in output feedback design the observer is combined with control laws that ensure input to state stability with respect to the observer error robustness to unmodeled dynamics is achieved with a small gain assignment design as illustrated on a jet engine compressor example