a global lower bound for the fundamental solution of kolmogorov fokker planck equations the main result of this paper is a global lower bound for the fundamental solution of the ultraparabolic differential operator

on the stabilization of nonlinear systems we extend the applicability of the global q parametrization method of controller design to a large class of unstable nonlinear plants the main result is a two step compensation theorem analogous to that of zames for unstable linear plants if p l e2 rightarrow l e1 is a nonlinear possibly unstable plant and f 0 is any incrementally stable controller such that p 1 p i f 0 p 1 is incrementally stable then the class of controllers f which yields an f g stable closed loop system in the unity feedback configuration for p is globally parametrized by finite gain stable maps q l e1 rightarrow l e2 with f f 0 q i p 1 q 1

on the trend to global equilibrium in spatially inhomogeneous entropy dissipating systems the linear fokker planck equation we study the long time behavior of kinetic equations in which transport and spatial confinement in an exterior potential or in a box are associated with a degenerate collision operator acting only in the velocity variable we expose a general method based on logarithmic sobolev inequalities and the entropy to overcome the well known problem due to the degeneracy in the position variable of the existence of infinitely many local equilibria this method requires that the solution be somewhat smooth in this paper we apply it to the linear fokker planck equation and prove decay to equilibrium faster than o t 1 for all 0 2001 john wiley sons inc

entire solutions in a time delayed and diffusive epidemic model this paper is concerned with entire solutions in the following time delayed and diffusive epidemic model email protected tu 1 x t d email protected u 1 x t a 1 1u 1 x t a 1 2u 2 x t email protected tu 2 x t d email protected u 2 x t a 2 2u 2 x t gu 1x email protected where d i 0 i 1 2 using comparison arguments we establish the existence and its properties of entire solutions for the above system here an entire solution means a classical solution defined for all email protected r

optimal finite time consensus on fixed and periodic graphs synthesis of optimal controllers achieving finite time consensus for multiagent networks described by fixed or periodic connectivity graphs is considered the solution procedure involves posing a partially nested finite horizon decentralized control problem and converting it to a static convex optimization problem by a quadratic invariance argument the dynamic feedback controller thus synthesized optimizes a transient performance measure and guarantees consensus within a minimal number of steps

bounds on short cylinders and uniqueness in cauchy problem for degenerate kolmogorov equations abstract we consider the cauchy problem for degenerate kolmogorov equations in the form t u i j 1 m a i j x t x i x j u j 1 m a j x t x j u i j 1 n b i j x i x j u x t r n 0 t 1 m n as well as in its divergence form we prove that if u x t m exp a t x 2 for some positive constants a m and 0 1 and u 0 0 then u 0 the proof of the main result is based on some previous uniqueness result and on the application of some estimates in short cylinders previously used by ferretti in the study of uniformly parabolic operators

controllability and observability of coordinated linear systems abstract this paper develops concepts of controllability and observability for the class of coordinated linear systems a special class of linear hierarchical systems with a top to bottom information structure the usual concepts of reachability and indistinguishability for linear systems are refined taking into account the decentralized nature of coordinated linear systems the corresponding controllability and observability decompositions are derived and several concepts of controllability and observability for coordinated linear systems are introduced and discussed these results are then combined to a definition and characterization of stabilizability via dynamic measurement feedback for this class of systems

global attractivity spreading speeds and traveling waves of delayed nonlocal reaction diffusion systems abstract the purpose of this work is to study the spatial dynamics of some delayed nonlocal reaction diffusion systems in whole space we first establish a series of comparison theorems to investigate the global attractivity of the equilibria for a delayed nonlocal reaction diffusion system with and without quasi monotonicity then we show that the spreading speed of a general system without quasi monotone conditions is coincident with the minimal wave speed applying a fluctuation method we further provide some sufficient conditions to ensure the upward convergence of the spreading speed and traveling wave solutions finally we point out the effects of the delay and nonlocality on the spreading speed of the non quasi monotone systems

pointwise estimates for a class of non homogeneous kolmogorov equations we consider a class of ultraparabolic differential equations that satisfy the hormander s hypoellipticity condition and we prove that the weak solutions to the equation with measurable coefficients are locally bounded functions the method extends the moser s iteration procedure and has previously been employed in the case of operators verifying a further homogeneity assumption here we remove that assumption by proving some potential estimates and some ad hoc sobolev type inequalities for solutions

intractable problems in control theory this paper is an attempt to understand the apparent intractability of problems in decentralized decision making using the concepts and methods of computational complexity we first establish that the discrete version of an important paradigm for this area proposed by witsenhausen is np complete thus explaining the failures reported in the literature to attack it computationally in the rest of the paper we show that the computational intractability of the discrete version of a control problem the team decision problem in our particular example can imply that there is no satisfactory continuous algorithm for the continuous version to this end we develop a theory of continuous algorithms and their complexity and a quite general proof technique which can prove interesting by themselves

moser s estimates for degenerate kolmogorov equations with non negative divergence lower order coefficients abstract we prove l loc estimates for positive solutions to the following degenerate second order partial differential equation of kolmogorov type with measurable coefficients of the form i j 1 m 0 x i a i j x t x j u x t i j 1 n b i j x j x i u x t t u x t i 1 m 0 b i x t i u x t i 1 m 0 x i a i x t u x t c x t u x t 0 where x t x 1 x n t z is a point of r n 1 and 1 m 0 n a i j is a uniformly positive symmetric matrix with bounded measurable coefficients b i j is a constant matrix we apply the moser s iteration method to prove the local boundedness of the solution u under minimal integrability assumption on the coefficients

algebraic resolution of equations of the black scholes type with arbitrary time dependent parameters we examine various forms of the black scholes equation using symmetry analysis and consider the standard problem of a terminal condition namely u t x u the models considered are the standard form of the equation to provide a benchmark the nonhomogeneous form and two variations in which the parameters of the two basic models are explicitly time dependent we find subject to some constraints upon the parameters a remarkable robustness in the results

a characterization of convex problems in decentralized control ast we consider the problem of constructing optimal decentralized controllers we formulate this problem as one of minimizing the closed loop norm of a feedback system subject to constraints on the controller structure we define the notion of quadratic invariance of a constraint set with respect to a system and show that if the constraint set has this property then the constrained minimum norm problem may be solved via convex programming we also show that quadratic invariance is necessary and sufficient for the constraint set to be preserved under feedback these results are developed in a very general framework and are shown to hold in both continuous and discrete time for both stable and unstable systems and for any norm this notion unifies many previous results identifying specific tractable decentralized control problems and delineates the largest known class of convex problems in decentralized control as an example we show that optimal stabilizing controllers may be efficiently computed in the case where distributed controllers can communicate faster than their dynamics propagate we also show that symmetric synthesis is included in this classification and provide a test for sparsity constraints to be quadratically invariant and thus amenable to convex synthesis

sparse stable systems abstract in the design of decentralized networked systems it is important to know whether a given network topology can sustain stable dynamics we consider a basic version of this problem here given a vector space of sparse real matrices does it contain a stable hurwitz matrix said differently is a feedback channel corresponding to a non zero entry necessary for stabilization or can it be done without we provide in this paper a set of necessary conditions and a set of sufficient conditions for the existence of stable matrices in a vector space of sparse matrices we further prove some properties of the set of sparse matrix spaces that contain hurwitz matrices the conditions we exhibit are most easily stated in the language of graph theory which we thus adopt in this paper

a convex characterization of multidimensional linear systems subject to sqi constraints this technical note proposes a convex characterization of the set of all stable closed loop linear systems that are obtained from a given plant which may be multidimensional by interconnecting it in feedback with controllers that satisfy a certain pre selected constraint we take an approach that is particularly useful when a doubly coprime factorization of the plant is difficult to obtain and a stable stabilizing controller may not exist the plant is not strongly stabilizable or when one may be difficult to find most related work requires one of these we adopt the so called coordinate free approach which unlike youla s parametrization does not rely on a doubly coprime factorization of the plant we show that if constraints which satisfy a condition called strong quadratic invariance sqi are imposed on the controllers then the set of all stable closed loop multidimensional linear systems has a convex representation and norm optimal control problems can be cast in convex form although the sqi condition is in general slightly stronger than quadratic invariance qi which was developed in related work they are equivalent for common classes of problems arising in decentralized control

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

entire solutions for a multi type sis nonlocal epidemic model in r or z abstract in this paper we study entire solutions for a multi type sis nonlocal epidemic model in r or z the existence and asymptotic behavior of spatially independent solutions are first established some new entire solutions are then constructed by combining traveling wave fronts with different speeds and a spatially independent solution from the viewpoint of epidemiology the results provide some new spread ways of the epidemic

optimal multivariable controller design using an itse performance index this article deals with the design of optimal controllers and as an embedded problem with the computation of achievable performance bounds in the control of non minimum phase unstable multi input multi output systems the cost function comprises a time weighted measure of the tracking error itse and an incremental quadratic penalisation of the control effort the proposed methodology relies on the properties of a frequency domain generalisation of the itse index the solution to the optimisation problem can be computed using orthonormal basis function expansions and a closed form expression is found for the optimal coefficients of the expansion numerical examples are presented to illustrate the results

lp compactness of inhomogeneous kinetic equation with rough force abstract we are concerned with the inhomogeneous kinetic equations with rough force l p compactness of the inhomogeneous kinetic equation with rough force is constructed by using phase space analysis and the fourier multiplier method

hardy littlewood sobolev inequalities for a class of non symmetric and non doubling hypoelliptic semigroups in his seminal 1934 paper on brownian motion and the theory of gases kolmogorov introduced a second order evolution equation which displays some challenging features in the opening of his 1967 hypoellipticity paper hormander discussed a general class of degenerate ornstein uhlenbeck operators that includes kolmogorov s as a special case in this note we combine semigroup theory with a nonlocal calculus for these hypoelliptic operators to establish new inequalities of hardy littlewood sobolev type in the situation when the drift matrix has nonnegative trace our work has been influenced by ideas of e stein and varopoulos in the framework of symmetric semigroups one of our objectives is to show that such ideas can be pushed to successfully handle the present degenerate non symmetric setting

centralized and decentralized solutions of the linear exponential gaussian problem a particular class of stochastic control problems constrained to different information patterns is considered this class consists of minimizing the expectation of an exponential cost criterion with quadratic argument subject to a discrete time gauss markov dynamic system i e the linear exponential gaussian leg control problem besides the one step delayed information pattern previously considered the classical and the one step delayed information sharing osdis patterns are assumed after determining the centralized controller based upon the classical information pattern the optimal decentralized controller based upon the osdis pattern and the solution to a static team problem is found to be affine a unifying approach to determine controllers based upon these three information patterns is obtained by noting that the value of a quadratic exponent of an exponential function is independent of the information structure both necessary and sufficient conditions for the controllers to be minimizing are obtained regardless of the exponential form the negative exponential form is included which is unimodal but not convex

feedback and optimal sensitivity model reference transformations multiplicative seminorms and approximate inverses in this paper the problem of sensitivity reduction by feedback is formulated as an optimization problem and separated from the problem of stabilization stable feedback schemes obtainable from a given plant are parameterized salient properties of sensitivity reducing schemes are derived and it is shown that plant uncertainty reduces the ability of feedback to reduce sensitivity the theory is developed for input output systems in a general setting of banach algebras and then specialized to a class of multivariable time invariant systems characterized by n times n matrices of h infty frequency response functions either with or without zeros in the right half plane the approach is based on the use of a weighted seminorm on the algebra of operators to measure sensitivity and on the concept of an approximate inverse approximate invertibility of the plant is shown to be a necessary and sufficient condition for sensitivity reduction an indicator of approximate invertibility called a measure of singularity is introduced the measure of singularity of a linear time invariant plant is shown to be determined by the location of its right half plane zeros in the absence of plant uncertainty the sensitivity to output disturbances can be reduced to an optimal value approaching the singularity measure in particular if there are no right half plane zeros sensitivity can be made arbitrarily small the feedback schemes used in the optimization of sensitivity resemble the lead lag networks of classical control design some of their properties and methods of constructing them in special cases are presented

global l p estimates for degenerate ornstein uhlenbeck operators we consider a class of degenerate ornstein uhlenbeck operators in mathbb r n of the kind mathcal a equiv sum i j 1 p 0 a ij partial x i x j 2 sum i j 1 n b ij x i partial x j where aij bij are constant matrices aij is symmetric positive definite on mathbb r p 0 p0 n and bij is such that mathcal a is hypoelliptic for this class of operators we prove global lp estimates 1 p of the kind left vert partial x i x j 2 u right vert l p left mathbb r n right leq c left left vert mathcal a u right vert l p left mathbb r n right left vert u right vert l p left mathbb r n right right rm for i j 1 2 ldots p 0 and corresponding weak type 1 1 estimates this result seems to be the first case of global estimates in lebesgue lp spaces for complete hormander s operators sum x i 2 x 0 proved in absence of a structure of homogeneous group we obtain the previous estimates as a byproduct of the following one which is of interest in its own left vert partial x i x j 2 u right vert l p left s right leq c left vert lu right vert l p left s right for any u in c 0 infty left s right where s is the strip mathbb r n times left 1 1 right and l is the kolmogorov fokker planck operator mathcal a partial t to get this estimate we use in a crucial way the left invariance of l with respect to a lie group structure in mathbb r n 1 and some results on singular integrals on nonhomogeneous spaces recently proved in bramanti revista matematica iberoamericana 2009 in press

stabilization of networked control systems with sparse observer controller networks in this technical note we provide a set of stability conditions for linear time invariant networked control systems with arbitrary topology using a lyapunov direct approach we then use these stability conditions to provide a novel low complexity algorithm for the design of a sparse observer based control network we employ distributed observers by employing the output of other nodes to improve the stability of each observer dynamics to avoid unbounded growth of controller and observer gains we impose bounds on their norms the effects of relaxation of these bounds is discussed when trying to find the complete decentralization conditions

dynamics of a non local delayed reaction diffusion equation without quasi monotonicity this paper is concerned with the dynamics of a non local delayed reaction diffusion equation without quasi monotonicity on an infinite n dimensional domain which can be derived from the growth of a stage structured single species population we first prove that solutions of the cauchy type problem are positively preserving and bounded if the initial value is non negative and bounded then by establishing a comparison theorem and a series of comparison arguments we prove the global attractivity of the positive equilibrium when there exist no positive equilibria we prove that the zero equilibrium is globally attractive in particular these results are still valid for the non local delayed reaction diffusion equation on a bounded domain with the neumann boundary condition finally we establish the existence of new entire solutions by using the travelling wave solutions of two auxiliary equations and the global attractivity of the positive equilibrium

stabilization of bilinear sparse matrix control systems using periodic inputs abstract in this brief paper using results from the theory of averaging of bilinear systems we provide a graph theoretic characterization for the existence of periodic control inputs that stabilize a sparse matrix system to the origin in particular we introduce a class of extensions to the directed graph corresponding to a given sparse matrix system which when contains a stable sparse matrix system implies that the original system is stabilizable using periodic inputs when this condition holds we provide a systematic procedure for designing such controllers our technical approach combines ideas from the theory of bilinear control systems and averaging theory with graph theoretic results

entire solutions of a monostable age structured population model in a 2d lattice strip abstract this paper is concerned with the entire solutions for a monostable age structured population model in a 2d lattice strip i e solutions defined in the whole space and for all time t r in the quasi monotone case we first establish the existence and asymptotic behavior of solutions of the equation without j z variable combining traveling wave fronts with different speeds and a solution without j variable the existence and qualitative features of entire solutions are then proved in the non quasi monotone case we introduce two auxiliary quasi monotone equations and establish a comparison argument for the three systems some new entire solutions are then constructed by using the comparison argument the traveling wave fronts and a solution without j variable of the auxiliary equations

optimal symmetric h sub 2 controllers for systems with collocated sensors and actuators this note addresses the problem of designing the optimal symmetric h 2 controller for a plant with collocated sensors and actuators but with possibly asymmetric disturbance injection and performance specification for such a control problem the generalized plant has a symmetric block representing the transfer matrix from the control input to the measured output a complete solution to the optimal h 2 control problem with the symmetric structural constraint is given in terms of the optimal solution to a standard h 2 model matching problem without the constraint

entire solutions for nonlocal dispersal equations with spatio temporal delay monostable case abstract this paper deals with entire solutions for a general nonlocal dispersal monostable equation with spatio temporal delay i e solutions that are defined in the whole space and for all time t r we first derive a particular model for a single species and show how such systems arise from population biology then we construct some new types of entire solutions other than traveling wave solutions and equilibrium solutions of the equation under consideration with quasi monotone and non quasi monotone nonlinearities various qualitative properties of the entire solutions are also investigated in particular the relationship between the entire solutions and the traveling wave fronts which they originated is considered our main arguments are based on the comparison principle the method of super and sub solutions and the construction of auxiliary control systems

on the viscosity solutions of a stochastic differential utility problem we prove existence uniqueness and gradient estimates of stochastic differential utility as a solution of the cauchy problem for the following equation in r 3 xxu u yu tu f u where f is lipschitz continuous we also characterize the solution in the vanishing viscosity sense r 2002 elsevier science usa all rights reserved

pointwise local estimates and gaussian upper bounds for a class of uniformly subelliptic ultraparabolic operators abstract we consider a class of second order ultraparabolic differential equations in the form t u i j 1 m x i a i j x j u x 0 u where a a i j is a bounded symmetric and uniformly positive matrix with measurable coefficients under the assumption that the operator i 1 m x i 2 x 0 t is hypoelliptic and the vector fields x 1 x m and x 0 t are invariant with respect to a suitable homogeneous lie group we adapt the moser s iterative methods to the non euclidean geometry of the lie groups and we prove an l loc bound of the solution u in terms of its l loc p norm we then use a technique going back to aronson to prove a pointwise upper bound of the fundamental solution of the operator i j 1 m x i a i j x j x 0 t the bound is given in terms of the value function of an optimal control problem related to the vector fields x 1 x m and x 0 t finally by using the upper bound the existence of a fundamental solution is then established for smooth coefficients a i j

harnack inequality for a class of kolmogorov fokker planck equations in non divergence form we prove invariant harnack inequalities for certain classes of non divergence form equations of kolmogorov type the operators we consider exhibit invariance properties with respect to a homogeneous lie group structure the coefficient matrix is assumed either to satisfy a cordes landis condition on the eigenvalues or to admit a uniform modulus of continuity

from global finite time linear computations to local edge based interaction rules a network of locally interacting agents can be thought of as performing a distributed computation but not all computations can be faithfully distributed this technical note investigates which global linear transformations can be computed in finite time using local rules with time varying weights i e rules which rely solely on information from adjacent nodes in a network the main result states that a linear transformation is computable in finite time using local rules if and only if the transformation has positive determinant an optimal control problem is solved for finding the local interaction rules and simulations are performed to elucidate how optimal solutions can be obtained