h_ infty fuzzy control for a class of nonlinear coupled ode pde systems with input constraint this paper deals with the problem of h infty fuzzy control design with an input constraint for a class of coupled systems which consist of an n dimensional nonlinear subsystem of ordinary differential equations odes and a scalar linear parabolic subsystem of partial differential equation pde connected in feedback initially the nonlinear coupled system is represented by a takagi sugeno t s fuzzy coupled ode pde model then based on the fuzzy model and parallel distributed compensation scheme a fuzzy state feedback control design is developed via lyapunov s direct method such that the resulting closed loop fuzzy coupled system is exponentially stable and a prescribed h infty performance of disturbance attenuation is satisfied the existing condition of the proposed h infty fuzzy controllers is given in terms of linear matrix inequalities lmis moreover in order to make the attenuation level as small as possible while the input constraint is respected to avoid the high magnitude a suboptimal h infty constrained fuzzy control problem is also addressed which is formulated as an lmi optimization problem finally the proposed method is applied to the control of a hypersonic rocket car to illustrate its effectiveness

state and output feedback boundary control for a coupled pde ode system abstract this note is devoted to stabilizing a coupled pde ode system with interaction at the interface first a state feedback boundary controller is designed and the system is transformed into an exponentially stable pde ode cascade with an invertible integral transformation where pde backstepping is employed moreover the solution to the resulting closed loop system is derived explicitly second an observer is proposed which is proved to exhibit good performance in estimating the original coupled system and then an output feedback boundary controller is obtained for both the state and output feedback boundary controllers exponential stability analyses in the sense of the corresponding norms for the resulting closed loop systems are provided the boundary controller and observer for a scalar coupled pde ode system as well as the solutions to the closed loop systems are given explicitly

a class of path valued markov processes and its applications to superprocesses let s be a continuous markov process satisfying certain regularity assumptions we introduce a path valued strong markov process associated with s which is closely related to the so called superprocess with spatial motion s in particular a subseth of the state space of s intersects the range of the superprocess if and only if the set of paths that hith is not polar for the path valued process the latter property can be investigated using the tools of the potential theory of symmetric markov processes a set is not polar if and only if it supports a measure of finite energy the same approach can be applied to study sets that are polar for the graph of the superprocess in the special case when s is a diffusion process we recover certain results recently obtained by dynkin

new stability conditions based on piecewise fuzzy lyapunov functions and tensor product transformations improvements of recent stability conditions for continuous time takagi sugeno t s fuzzy systems are proposed the key idea is to bring together the so called local transformations of membership functions and new piecewise fuzzy lyapunov functions by relying on these special local transformations the associated linear matrix inequalities that are used to prove the system s stability can be relaxed without increasing the number of conditions in addition to enhance the usefulness of the proposed methodology one can choose between two different sets of conditions characterized by independence or dependence on known bounds of the membership functions time derivatives a standard example is presented to illustrate that the proposed method is able to provide substantial improvements in some cases

h _ infty fuzzy observer based control for a class of nonlinear distributed parameter systems with control constraints an hinfin fuzzy observer based control design is proposed for a class of nonlinear parabolic partial differential equation pde systems with control constraints for which the eigenspectrum of the spatial differential operator can be partitioned into a finite dimensional slow one and an infinite dimensional stable fast complement in the proposed control scheme galerkin s method is initially applied to the pde system to derive a nonlinear ordinary differential equation ode system that accurately describes the dynamics of the dominant slow modes of the pde system the resulting nonlinear ode system is subsequently represented by the takagi sugeno t s fuzzy model then based on the t s fuzzy model a fuzzy observer based controller is developed to stabilize the nonlinear pde system and achieve an optimized hinfin disturbance attenuation performance for the finite dimensional slow system while control constraints are respected the outcome of the hinfin fuzzy observer based control problem is formulated as a bilinear matrix inequality bmi optimization problem a local optimization algorithm that treats the bmi as a double linear matrix inequality is presented to solve this bmi optimization problem finally the proposed design method is applied to the control of the temperature profile of a catalytic rod to illustrate its effectiveness

exact packing measure of the range of psi super brownian motions we consider super processes whose spatial motion is the d dimensional brownian motion and whose branching mechanism psi is critical or subcritical such processes are called psi super brownian motions if d 2 varvec gamma varvec gamma 1 where varvec gamma in 1 2 is the lower index of psi at infty then the total range of the psi super brownian motion has an exact packing measure whose gauge function is g r log log 1 r varphi 1 1 r log log 1 r 2 where varphi psi prime circ psi 1 more precisely we show that the occupation measure of the psi super brownian motion is the g packing measure restricted to its total range up to a deterministic multiplicative constant only depending on d and psi this generalizes the main result of duquesne ann probab 37 6 2431 2458 2009 that treats the quadratic branching case for a wide class of psi the constant 2 varvec gamma varvec gamma 1 is shown to be equal to the packing dimension of the total range

stability and performance for saturated systems via quadratic and nonquadratic lyapunov functions in this paper we develop a systematic lyapunov approach to the regional stability and performance analysis of saturated systems in a general feedback configuration the only assumptions we make about the system are well posedness of the algebraic loop and local stability problems to be considered include the estimation of the domain of attraction the reachable set under a class of bounded energy disturbances and the nonlinear l2 gain the regional analysis is established through an effective treatment of the algebraic loop and the saturation deadzone function this treatment yields two forms of differential inclusions a polytopic differential inclusion pdi and a norm bounded differential inclusion ndi that contain the original system adjustable parameters are incorporated into the differential inclusions to reflect the regional property the main idea behind the regional analysis is to ensure that the state remain inside the level set of a certain lyapunov function where the pdi or the ndi is valid with quadratic lyapunov functions conditions for stability and performances are derived as linear matrix inequalities lmis to obtain less conservative conditions we use a pair of conjugate non quadratic lyapunov functions the convex hull quadratic function and the max quadratic function these functions yield bilinear matrix inequalities bmis as conditions for stability and guaranteed performance level the bmi conditions cover the corresponding lmi conditions as special cases hence the bmi results are guaranteed to be as good as the lmi results in most examples the bmi results are significantly better than the lmi results

lower tail probability estimates for subordinators and nondecreasing random walks f xn ex 00 oo and a is the infimum of the support of the distribution of x1 for a xn lk we obtain the asymptotic behavior of log p sn nxn as n oo under the additional assumption of stochastic compactness a stronger result is obtained which gives the asymptotic behavior of p sn nxn itself analogues of these results are given for subordinators when t o oo or t o 0

compensating actuator and sensor dynamics governed by diffusion pdes for possibly unstable ode systems with actuator delay predictor based infinite dimensional feedback can compensate for actuator delay of arbitrary length and achieve stabilization we extend this concept to another class of pde ode cascades where the infinite dimensional part of the plant is of diffusive rather than convective type we derive predictor like feedback laws and observers with explicit gain kernels the gain kernels involve second order matrix exponentials of the system matrix of the ode plant which is the result of the second order in space character of the actuator sensor dynamics the construction of the kernel functions is performed using the continuum version of the backstepping method robustness to small perturbations in the diffusion coefficient is proved

brief analysis and control of parabolic pde systems with input constraints this paper develops a general framework for the analysis and control of parabolic partial differential equations pde systems with input constraints initially galerkin s method is used for the derivation of ordinary differential equation ode system that capture the dominant dynamics of the pde system this ode systems are then used as the basis for the synthesis via lyapunov techniques of stabilizing bounded nonlinear state and output feedback control laws that provide an explicit characterization of the sets of admissible initial conditions and admissible control actuator locations that can be used to guarantee closed loop stability in the presence of constraints precise conditions that guarantee stability of the constrained closed loop parabolic pde system are provided in terms of the separation between the fast and slow eigenmodes of the spatial differential operator the theoretical results are used to stabilize an unstable steady state of a diffusion reaction process using constrained control action

last exit decompositions and regularity at the boundary of transition probabilities the purpose of this paper is to give a probabilistic approach to studying the regularity at the boundary of the transition probabilities of certain hypoelliptic diffusions with boundary conditions the main tools are last exit decompositions of brownian motion the malliavin calculus the theory of excursions and the calculus of variations on brownian excursions

the uniform random tree in a brownian excursion to any brownian excursione with duration e and anyt 1 t p 0 e we associate a branching tree withp branches denoted byt p e t 1 t p which is closely related to the structure of the minima ofe our main theorem states that ife is chosen according to the ito measure and t 1 t p according to lebesgue measure on 0 e p the treet p e t 1 t p is distributed according to the uniform measure on the set of trees withp branches the proof of this result yields additional information about the subexcursions ofe corresponding to the different branches of the tree thus generalizing a well known representation theorem of bismut if we replace the ito measure by the law of the normalized excursion a simple conditioning argument leads to another remarkable result originally proved by aldous with a very different method

super brownian motion path properties and hitting probabilities sample path properties of super brownian motion including a one sided modulus of continuity and exact hausdorff measure function of the range and closed support are obtained analytic estimates for the probability of hitting balls lead to upper bounds on the hausdorff measure of the set of k multiple points and a sufficient condition for a set to be polar

covariant image representation with applications to classification problems in medical imaging images are often considered as functions defined on the image domains and as functions their intensity values are usually considered to be invariant under the image domain transforms this functional viewpoint is both influential and prevalent and it provides the justification for comparing images using functional mathbf l p lp norms however with the advent of more advanced sensing technologies and data processing methods the definition and the variety of images has been broadened considerably and the long cherished functional paradigm for images is becoming inadequate and insufficient in this paper we introduce the formal notion of covariant images and study two types of covariant images that are important in medical image analysis symmetric positive definite tensor fields and gaussian mixture fields images whose sample values covary i e jointly vary with image domain transforms rather than being invariant to them we propose a novel similarity measure between a pair of covariant images considered as embedded shapes manifolds in the ambient space a cartesian product of the image and its sample value domains the similarity measure is based on matching the two embedded low dimensional shapes and both the extrinsic geometry of the ambient space and the intrinsic geometry of the shapes are incorporated in computing the similarity measure using this similarity as an affinity measure in a supervised learning framework we demonstrate its effectiveness on two challenging classification problems classification of brain mr images based on patients age and alzheimer s disease status and seizure detection from high angular resolution diffusion magnetic resonance scans of rat brains

probabilistic and fractal aspects of levy trees we investigate the random continuous trees called levy trees which are obtained as scaling limits of discrete galton watson trees we give a mathematically precise definition of these random trees as random variables taking values in the set of equivalence classes of compact rooted trees which is equipped with the gromov hausdorff distance to construct levy trees we make use of the coding by the height process which was studied in detail in previous work we then investigate various probabilistic properties of levy trees in particular we establish a branching property analogous to the well known property for galton watson trees conditionally given the tree below level a the subtrees originating from that level are distributed as the atoms of a poisson point measure whose intensity involves a local time measure supported on the vertices at distance a from the root we study regularity properties of local times in the space variable and prove that the support of local time is the full level set except for certain exceptional values of a corresponding to local extinctions we also compute several fractal dimensions of levy trees including hausdorff and packing dimensions in terms of lower and upper indices for the branching mechanism function which characterizes the distribution of the tree we finally discuss some applications to super brownian motion with a general branching mechanism

robust h fuzzy control for uncertain nonlinear markovian jump systems with time varying delay this paper investigates the problem of robust h fuzzy control for a class of uncertain nonlinear markovian jump systems with time varying delay the class of systems under consideration is described by the takagi sugeno fuzzy model the goal of the paper is to design a mode dependent fuzzy state feedback controller such that the closed loop system is stochastically stable with a prescribed h performance of disturbance attenuation for all admissible parameter uncertainties in order to obtain a less conservative control design a new stochastic lyapunov krasovskii functional is first constructed by decomposing the delay interval into multiple equidistant subintervals then by employing this functional a delay decomposition approach to the design of robust h fuzzy controllers is developed in terms of linear matrix inequalities finally two examples are given to illustrate the merit and usability of the proposed design method

the packing measure of the range of super brownian motion we prove that the total range of super brownian motion with quadratic branching mechanism has an exact packing measure with respect to the gauge function g r r 4 log log1 r 3 in super critical dimensions d geq 5 more precisely we prove that the total occupation measure of super brownian motion is equal to the g packing measure restricted to its range up to a deterministic multiplicative constant that only depends on space dimension d

switching type h filter design for t s fuzzy systems with unknown or partially unknown membership functions this paper is concerned with the h filter design problem for takagi sugeno t s fuzzy systems with unknown or partially unknown membership functions if the membership functions are allowed to be unknown or partially unknown then a fuzzy system may describe a wide class of nonlinear systems however in this case the filter design of fuzzy systems which is based on parallel distributed compensator strategy is infeasible to tackle this difficulty a switching mechanism which depends on the lower and upper bounds of the unknown membership functions is introduced to construct the h filter with varying gains some examples given in the simulation section show that the proposed method can achieve a better disturbance attenuation performance than a simple fixed gain filter design approach

the continuum random tree iii let mathscr r k k geq 1 be random trees with k leaves satisfying a consistency condition removing a random leaf from mathscr r k gives mathscr r k 1 then under an extra condition this family determines a random continuum tree mathscr l which it is convenient to represent as a random subset of l 1 this leads to an abstract notion of convergence in distribution as n rightarrow infty of rescaled random trees mathscr j n on n vertices to a limit continuum random tree mathscr l the notion is based upon the assumption that for fixed k the subtrees of mathscr j n determined by k randomly chosen vertices converge to mathscr r k as our main example under mild conditions on the offspring distribution the family tree of a galton watson branching process conditioned on total population size equal to n can be rescaled to converge to a limit continuum random tree which can be constructed from brownian excursion