regularity of potential functions of the optimal transportation problem the potential function of the optimal transportation problem satisfies a partial differential equation of monge ampere type in this paper we introduce the notion of a generalized solution and prove the existence and uniqueness of generalized solutions of the problem we also prove the solution is smooth under certain structural conditions on the cost function

distributed robust estimation over randomly switching networks using h consensus the paper considers a distributed robust estimation problem over a network with markovian randomly varying topology the objective is to deal with network variations locally by switching observer gains at affected nodes only we propose sufficient conditions which guarantee a suboptimal h level of relative disagreement of estimates in such observer networks when the status of the network is known globally these sufficient conditions enable the network gains to be computed by solving certain lmis when the nodes are to rely on a locally available information about the network topology additional rank constraints are used to condition the gains given this information the results are complemented by necessary conditions which relate properties of the interconnection graph laplacian to the mean square detectability of the plant through measurement and interconnection channels

decentralized measurement feedback stabilization of large scale systems via control vector lyapunov functions abstract this paper studies the problem of decentralized measurement feedback stabilization of nonlinear interconnected systems as a natural extension of the recent development on control vector lyapunov functions the notion of output control vector lyapunov function ocvlf is introduced for investigating decentralized measurement feedback stabilization problems sufficient conditions on local stabilizability are discussed which are based on the proposed notion of ocvlf it is shown that a decentralized controller for a nonlinear interconnected system can be constructed using these conditions under an additional vector dissipation like condition to illustrate the proposed method two examples are given

distributed robust filtering with h consensus of estimates the paper addresses a problem of design of distributed robust filters using the recent vector dissipativity theory the main result is a sufficient condition which guarantees a suboptimal h level of disagreement of estimates in a network of filters it involves solving a convex optimization feasibility problem subject to lmi constraints the special case of balanced interconnection graphs is also considered a gradient descent type algorithm is presented which allows the nodes to compute their estimator parameters in a decentralized manner the proposed approach is applied to the problem of observer based robust synchronization of a nonlinear network to an isolated node

stochastic algorithms for exact and approximate feasibility of robust lmis in this note we discuss fast randomized algorithms for determining an admissible solution for robust linear matrix inequalities lmis of the form f x spl delta spl les 0 where x is the optimization variable and spl delta is the uncertainty which belongs to a given set spl delta the proposed algorithms are based on uncertainty randomization the first algorithm finds a robust solution in a finite number of iterations with probability one if a strong feasibility condition holds in case no robust solution exists the second algorithm computes an approximate solution which minimizes the expected value of a suitably selected feasibility indicator function the theory is illustrated by examples of application to uncertain linear inequalities and quadratic stability of interval matrices

observability through a matrix weighted graph observability of an array of identical linear time invariant systems with incommensurable output matrices is studied where an array is called observable when identically zero relative outputs imply synchronized solutions for the individual systems it is shown that the observability of an array is equivalent to the connectivity of its interconnection graph whose edges are assigned matrix weights moreover to better understand the relative behavior of distant units pairwise observability that concerns with the synchronization of a certain pair of individual systems in the array is studied this milder version of observability is shown to be closely related to certain connectivity properties of the interconnection graph as well pairwise observability is also analyzed using the circuit theoretic tool effective conductance the observability of a certain pair of units is proved to be equivalent to the nonsingularity of the matrix valued effective conductance between the associated pair of nodes of a resistive network with matrix valued parameters whose node admittance matrix is the laplacian of the array s interconnection graph

on the weak continuity of elliptic operators and applications to potential theory in this paper we establish weak continuity results for quasilinear elliptic and subellip tic operators of divergence form acting on corresponding classes of subharmonic functions these results are analogous to our earlier results for fully nonlinear fc hessian operators from the weak continuity we derive various potential theoretic results including capacity estimates potential esti mates and the wiener criterion for regular boundary points our methods make substantial use of harnack inequalities for solutions 1 introduction there are numerous papers on the local behavior of solu tions subsolutions and supersolutions of second order quasilinear elliptic diver gence structure partial differential equations as well as extensions to degenerate elliptic and subelliptic equations in this paper we show that many properties including the quasi continuity of subharmonic functions asymptotic behavior of fundamental solutions removability of singularities wiener criteria for regular boundary points can be derived via harnack inequalities for solutions the two main ingredients in our approach which follow from our treatment of the fully nonlinear hessian operators in 45 46 47 together with that of labutin 30 are a weak convergence result and a pointwise potential estimate for subharmonic functions the weak convergence result is analogous to that for hessian operators 45 46 while the potential estimate extends that found for quasilinear elliptic operators by kilpelainen and maly 27 weak convergence results in the theory of nonlinear partial differential equa tions have been addressed in the survey 13 in this paper we treat nonlinear elliptic divergence structure operators for which harnack type inequalities are available to state our result we need an appropriate notion of subharmonic func tion in the fully nonlinear case 46 we employed the viscosity notion based on differential inequalities for smooth test functions for quasilinear divergence structure equations the traditional definition using the homogeneous equation is more convenient accordingly we shall say that a continuous function w in a domain q in euclidean space ir is harmonic with respect to an operator or c harmonic in short if it is a solution of the homogeneous equation c u 0

the regularity of mappings with a convex potential in this work we apply the techniques developed in cl to the problem of mappings with a convex potential between domains that is given two bounded domains q q2 of rn and two nonnegative real functions fi defined in qi that are bounded away from zero and infinity we want to study the map vf v w for a lipschitz convex v such that v maps ql onto q 2 in the a e sense and in some weak sense 1 f2 vyv det dij v f1 x in recent work y brenier showed existence and uniqueness of such a map provided that jaqil 0 under the obvious compatibility condition

a note on distributed finite time observers the robust distributed estimation for a class of time invariant plants is achieved via a finite time observer its error reaching zero after a finite time in the absence of perturbation two types of robustness are also shown first input to state stability with respect to measurement noises and additive perturbations is proven second we demonstrate that the estimation error stays bounded in the presence of known transmission delays

distributed control design for systems interconnected over an arbitrary graph we consider the problem of synthesizing a distributed dynamic output feedback controller achieving h sub spl infin performance for a system composed of different interconnected sub units when the topology of the underlying graph is arbitrary first using tools inspired by dissipativity theory we derive sufficient conditions in the form of finite dimensional linear matrix inequalities when the interconnections are assumed to be ideal these inequalities are coupled in a way that reflects the spatial structure of the problem and can be exploited to design distributed synthesis algorithms we then investigate the case of lossy interconnection links and derive similar results for systems whose interconnection relations can be captured by a class of integral quadratic constraints that includes constant delays

design of distributed decentralized estimators for formations with fixed and stochastic communication topologies this paper proposes a solution to the problem of synthesizing distributed decentralized estimators for a formation of agents the collected dynamics of the formation are modeled by a discrete lti system in the considered estimation structure each agent of the formation carries an estimate of the entire formation state agents of the formation can communicate information between each other through unidirectional links modeled with a fixed or a stochastic communication topology the design procedures are based on a set of convex optimization problems with linear matrix inequalities and result in the suboptimal choice of estimator gains which stabilize the estimation error dynamics and minimize a norm of the estimation error correlation matrix

on distributed pinning observers for a network of dynamical systems in this technical note a distributed observer structure is proposed to estimate the states of a large scale network of semi linear systems interconnected by a positive time varying coupling strength the distributed observer comprises distinct sub observers which require only local node level information and exchange their local state estimates with their neighboring observers the key idea here is to use a minimum number or at least relatively few measurements from the network being monitored to reduce the sensor requirements the problem is formulated as a two stage lmi optimization problem

local condition based consensus filtering with stochastic nonlinearities and multiple missing measurements this paper is concerned with the distributed h infty consensus filtering problem for a class of discrete time varying systems with stochastic nonlinearities and multiple missing measurements the stochastic nonlinearities are formulated by statistical means and the missing measurements are characterized by a set of random variables obeying bernoulli distribution a novel h infty consensus performance index is proposed to measure both the filtering accuracy of every node and the consensus among neighbor nodes then a new concept called stochastic vector dissipativity is proposed wherein the dissipation matrix is formulated by a nonsingular substochastic matrix which is skillfully constructed by a new defined interval function on the out degree a set of local sufficient conditions in terms of the recursive linear matrix inequalities is presented for each node such that the proposed h infty consensus performance can be guaranteed for the local augmented dynamics over the finite horizon furthermore a novel algorithm proposed here can be implemented on each node finally an illustrative simulation is presented to demonstrate the effectiveness and applicability of the proposed algorithm

on the regularity of solutions of optimal transportation problems we give a necessary and sufficient condition on the cost function so that the map solution of monge s optimal transportation problem is continuous for arbitrary smooth positive data this condition was first introduced by ma trudinger and wang 24 30 for a priori estimates of the corresponding monge ampere equation it is expressed by a socalled cost sectional curvature being non negative we show that when the cost function is the squared distance of a riemannian manifold the cost sectional curvature yields the sectional curvature as a consequence if the manifold does not have non negative sectional curvature everywhere the optimal transport map cannot be continuous for arbitrary smooth positive data the non negativity of the cost sectional curvature is shown to be equivalent to the connectedness of the contact set between any cost convex function the proper generalization of a convex function and any of its supporting functions when the cost sectional curvature is uniformly positive we obtain that optimal maps are continuous or holder continuous under quite weak assumptions on the data compared to what is needed in the euclidean case this case includes the quadratic cost on the round sphere

homogeneous networks of non introspective agents under external disturbances h almost synchronization this paper addresses the problem of h almost synchronization for homogeneous networks of general linear agents subject to external disturbances and under directional communication links agents are presumed to be non introspective i e agents are not aware of their own states or outputs and the only available information for each agent is a network measurement that is a linear combination of relative outputs under a certain set of conditions a family of dynamic protocols is developed such that the impact of disturbances on the synchronization error dynamics expressed in terms of the h norm of the corresponding closed loop transfer function is reduced to any arbitrarily small value

output feedback stabilization and estimation of the region of attraction for nonlinear systems a vector control lyapunov function perspective this technical note deals with local asymptotic stabilization of uncertain nonlinear systems by output feedback control our study provides a new design technique from a vector control lyapunov function perspective a comparison principle is developed and as a major consequence an effective estimation method of the region of attraction roa is established application to a class of minimum phase strict feedback nonlinear systems gives rise to a constructive stabilization design as well as an estimate of the resulting roa

on the regularity of reflector antennas where is the outer normal to a at the point where the light ray hits a suppose that we have a light source located at o and are two domains in the sphere sn 1 f x is a positive function for x input illumination intensity and g x is a positive function for x output illumination intensity if light emanates from o with intensity f x for x the far field reflector antenna problem is to find a perfectly reflecting surface a parametrized by z x x for x such that all reflected rays by a fall in the directions in and the output illumination received in the direction x is g x that is t where t is given by 1 1 assuming there is no loss of energy in the reflection then by the law of conservation of energy

on the reflector shape design in this paper we study the problem of recovering the reflecting surface in a reflector system which consists of a point light source a reflecting surface and an object to be illuminated this problem involves a fully nonlinear partial differential equation of monge

on strict convexity and continuous differentiability of potential functions in optimal transportation this note concerns the relationship between conditions on cost functions and domains the convexity properties of potentials in optimal transportation and the continuity of the associated optimal mappings in particular we prove that if the cost function satisfies the condition a3 introduced in our previous work with xinan ma the densities and their reciprocals are bounded and the target domain is convex with respect to the cost function then the potential is continuously differentiable and its dual potential strictly concave with respect to the cost function our results extend by different and more direct proof similar results of loeper proved by approximation from our earlier work on regularity

common lyapunov functions and gradient algorithms this note is concerned with the problem of finding a quadratic common lyapunov function for a large family of stable linear systems we present gradient iteration algorithms which give deterministic convergence for finite system families and probabilistic convergence for infinite families

kullback leibler average consensus on probability densities and distributed state estimation with guaranteed stability this paper addresses distributed state estimation over a sensor network wherein each node equipped with processing communication and sensing capabilities repeatedly fuses local information with information from the neighbors estimation is cast in a bayesian framework and an information theoretic approach to data fusion is adopted by formulating a consensus problem on the kullback leibler average of the local probability density functions pdfs to be fused exploiting such a consensus on local posterior pdfs a novel distributed state estimator is derived it is shown that for a linear system the proposed estimator guarantees stability i e mean square boundedness of the state estimation error in all network nodes under the minimal requirements of network connectivity and system observability and for any number of consensus steps finally simulation experiments demonstrate the validity of the proposed approach

robust h control for a class of uncertain nonlinear switched systems with average dwell time this paper focuses on the robust h control problem for a class of nonlinear switched systems containing neutral uncertainties with average dwell time adt switching uncertainties are considered to be nonlinearly dependent on state and state derivative and allowed to appear in channels of state control input and disturbance input the robust h control problem of the switched system with stabilisable and unstabilisable subsystems is solvable if the stabilisable and unstabilisable subsystems satisfy certain conditions and admissible switching strategy among them adt and piecewise lyapunov function approaches are applied to achieve the control design a numerical example is provided to illustrate the effectiveness of the proposed approach

global existence and maximal regularity of solutions of gradient systems abstract in this article we use a galerkin method to prove a maximal regularity result for the following abstract gradient system u t g t e u t f t for a e t 0 t u 0 u 0 this abstract result is applied to nonlinear diffusion equations and to nondegenerate quasilinear parabolic equations with nonlocal coefficients

mean square state estimation for sensor networks this paper deals with mean square state estimation over sensor networks with a fixed topology attention is focused on designing local stationary state estimators with a general structure while accounting for the network communication topology two estimator design approaches are proposed one is based on the observability gramian and the other on the controllability gramian the computation of the estimator state space matrices is recast as off line convex optimization problems and requires the system asymptotic stability and global knowledge of the network topology convergence of the estimation error variance is ensured at each network node and a guaranteed performance in the mean square sense is achieved the proposed approaches are also extended for designing robust filters to handle polytopic type parameter uncertainty

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

probabilistic robust design with linear quadratic regulators in this paper we study robust design of uncertain systems in a probabilistic setting by means of linear quadratic regulators lqr we consider systems affected by random bounded nonlinear uncertainty so that classical optimization methods based on linear matrix inequalities cannot be used without conservatism the approach followed here is a blend of randomization techniques for the uncertainty together with convex optimization for the controller parameters in particular we propose an iterative algorithm for designing a controller which is based upon subgradient iterations at each step of the sequence we first generate a random sample and then we perform a subgradient step for a convex constraint defined by the lqr problem the main result of the paper is to prove that this iterative algorithm provides a controller which quadratically stabilizes the uncertain system with probability one in a finite number of steps in addition at a fixed step we compute a lower bound of the probability that a quadratically stabilizing controller is found