hjb equations in infinite dimensions with locally lipschitz hamiltonian and unbounded terminal condition we study hamilton jacobi bellman equations in an infinite dimensional hilbert space with lipschitz coefficients where the hamiltonian has superquadratic growth with respect to the derivative of the value function and the final condition is not bounded this allows to study stochastic optimal control problems for suitable controlled state equations with unbounded control processes the results are applied to a controlled wave equation

h control for descriptor systems a matrix inequalities approach abstract this paper considers the h control problem for descriptor systems that possibly have impulsive modes and or j axis zeros first we propose matrix inequalities that give a generalized stability condition and an h norm condition for descriptor systems using these matrix inequalities we show that the solvability of a set of matrix inequalities is necessary and sufficient to the existence of a proper controller that satisfies a prescribed h norm condition as well as stabilizing the closed loop system and eliminating all impulsive modes these inequalities are equivalent to certain linear matrix inequalities to which we can get solutions whenever they exist using efficient polynomial time algorithms

brief paper actuator fault robust estimation and fault tolerant control for a class of nonlinear descriptor systems for lipschitz nonlinear descriptor systems with bounded input disturbances by solving a lyapunov equation a robust state space observer is proposed to simultaneously estimate descriptor system states actuator faults their finite times derivatives and attenuate input disturbances in any desired accuracy the considered faults can be unbounded provided that their qth derivatives are bounded the present fault estimation approaches can handle a large class of faults by using the estimates of descriptor states and faults and the linear matrix inequality lmi technique a fault tolerant control scheme is worked out the nonlinear fault tolerant control system can be made solvable causal asymptotically stable and attenuate input uncertainties in terms of the prescribed performance index only original coefficient matrices are used in the proposed state space observers and fault tolerant controllers therefore the present design approaches are preferable in applications finally a numerical example is given to illustrate the design procedure and simulations demonstrate the efficiency of the proposed design

fault estimation for a class of nonlinear systems based on intermediate estimator this technical note investigates the problem of fault estimation for a class of nonlinear systems with lipschitzian nonlinearities in most of the existing fault estimation approaches the observer matching condition should be satisfied however this condition is hard to meet for many systems to overcome this restriction a new fault estimation method is proposed where an intermediate variable is introduced and a specially designed intermediate estimator is proposed to estimate the state and the faults simultaneously by exploiting the properties of fault distribution matrix it is proved that the states of the error system are uniformly ultimately bounded simulation examples verify the effectiveness of the proposed method

observer design and detection for nonlinear descriptor systems a nonlinear observer is considered for a class of continuous nonlinear descriptor systems subject to unknown inputs and faults this class is partly characterized by globally lipschitz nonlinearities and a member system may be singular and possibly non causal the observer structure chosen makes it useful for both state estimation for feedback controls and residual generation for fault detection results on the existence of solutions are given and some useful bounds are derived which are important in the observer design which is based on a transformed system and on the solution of a riccati equation the existence convergence properties and robustness of the observer are investigated by the use of a quadratic lyapunov function conditions are given for a bound to hold on the norm of the transfer function relating the residual error to the disturbance linear case a design algorithm is given and applied to the estimation of the states of a flexible joint robot

constructing integral lattices with prescribed minimum ii methods for computing integral laminated lattices with prescribed minimum are developed laminating is a process of stacking layers of an n 1 dimensional lattice as densely as possible to obtain an n dimensional lattice our side conditions are all scalar products of lattice vectors are rational integers and all lattices are generated by vectors of prescribed minimum square length et for m 3 all such lattices are determined

state noise estimator for descriptor systems with application to sensor fault diagnosis for descriptor systems with measurement output noises input disturbances may exist at the same time a new descriptor estimator technique is developed the necessary and sufficient condition for the existence of the present estimator is derived and a systematic design approach is addressed the effect of uncertainties is decoupled completely and the asymptotic estimates of the descriptor system state and the output noise are obtained simultaneously furthermore a normal state disturbance estimator is also given for a class of nonlinear descriptor systems with both output noises and input uncertainties a nonlinear descriptor estimator is derived by using the proposed design approach together with the linear matrix inequality technique the existence and convergence of the nonlinear descriptor estimator is proven the asymptotic estimates of the descriptor nonlinear system state and the output noise are obtained at the same time the present estimators are applied to the sensor fault diagnosis and hence the sensor fault can be estimated asymptotically finally two numerical examples are included to illustrate the proposed design procedures and applications

functional unknown input reconstruction of descriptor systems the problem of finding conditions for the reconstruction of a linear combination of the vector of unknown inputs is tackled appropriate definitions are given in order to address formally the analysis thus necessary and sufficient conditions are obtained for two cases when the reconstruction may be achieved in finite time and when it is possible to do it asymptotically the results are applied for the fault detection with the respective deduction of analogous conditions

finite horizon h_ infty filtering with missing measurements and quantization effects in this paper a new h filtering approach is developed for a class of discrete time varying systems subject to missing measurements and quantization effects the missing measurements are modeled via a diagonal matrix consisting of a series of mutually independent random variables satisfying certain probabilistic distributions on the interval 0 1 the measured output is quantized by a logarithmic quantizer attention is focused on the design of a stochastic h filter such that the h estimation performance is guaranteed over a given finite horizon in the simultaneous presence of probabilistic missing measurements quantization effects as well as external non gaussian disturbances a necessary and sufficient condition is first established for the existence of the desired time varying filters in virtue of the solvability of certain coupled recursive riccati difference equations rdes owing to its recursive nature the proposed rde approach is shown to be suitable for online application without the need of increasing the problem size the simulation experiment is carried out for the mobile robot localization problem with non gaussian disturbances missing measurements and quantization effects the effectiveness of the proposed method is demonstrated in the numerical example

robust fault diagnosis for non linear difference algebraic systems a new robust fault diagnosis method based on linear matrix inequality lmi for non linear difference algebraic systems das with uncertainties is proposed based on the known nominal model of das it firstly constructs an auxiliary system consisting of a difference equation and an algebraic equation then converts the problem of fault identification into the problem of parameter estimation and finally realizes fault identification using an lmi method this method can not only detect isolate and identify faults for das but also give the upper bounds of fault identification error simulation indicates that it can give satisfactory diagnostic results for both abrupt and incipient faults

quadratic bsdes with convex generators and unbounded terminal conditions in briand and hu probab theory relat fields 136 4 604 618 2006 the authors proved an existence result for bsdes with quadratic generators with respect to the variable z and with unbounded terminal conditions however no uniqueness result was stated in that work the main goal of this paper is to fill this gap in order to obtain a comparison theorem for this kind of bsdes we assume that the generator is convex with respect to the variable z under this assumption of convexity we are also able to prove a stability result in the spirit of the a priori estimates stated in karoui et al math finance 7 1 1 71 1997 with these tools in hands we can derive the nonlinear feynman kac formula in this context

user s guide to viscosity solutions of second order partial differential equations the notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems existence theorems and theorems about continuous dependence may now be proved by very efficient and striking arguments the range of important applications of these results is enormous this article is a self contained exposition of the basic theory of viscosity solutions

fault estimation and tolerant control for fuzzy stochastic systems this paper deals with the problem of fault estimation and fault tolerant control for takagi sugeno t s fuzzy stochastic systems with sensor failures where the system under consideration contains ito type stochastic disturbances a new robust observer technique is presented to obtain the estimates of the system states and the sensor faults simultaneously and a fuzzy fault tolerant control scheme is developed to guarantee the closed loop system to be exponentially stable in mean square sufficient conditions are obtained for the existence of admissible controllers and it is shown that the reachability of the sliding mode dynamics can be guaranteed under the proposed control techniques finally a numerical example is provided to illustrate the effectiveness and applicability of the theoretic results obtained

adapted solution of a backward stochastic differential equation abstract let wt t 0 1 be a standard k dimensional weiner process defined on a probability space f p and let ft denote its natural filtration given a f1 measurable d dimensional random vector x we look for an adapted pair of processes x t y t t 0 1 with values in rd and rd k respectively which solves an equation of the form x t t 1 f s x s y s ds t 1 g s x s y s dw s x a linearized version of that equation appears in stochastic control theory as the equation satisfied by the adjoint process we also generalize our results to the following equation x t t 1 f s x s y s ds t 1 g s x s y s dw s x under rather restrictive assumptions on g

observer design for discrete time descriptor systems an lmi approach abstract in this paper the observer design problem for discrete time descriptor systems is considered for the discrete time linear descriptor systems the necessary and sufficient conditions for the existence and convergence of the proposed observer are given and proved and a systemic design approach is presented via the linear matrix inequalities formulation furthermore an extension to a class of nonlinear descriptor systems with lipschitz constraints is investigated simulation examples are given to illustrate the estimation performance of the proposed method

fault detection for t s fuzzy systems with partly unmeasurable premise variables abstract this paper studies the fault detection problem for t s fuzzy systems with partly unmeasurable premise variables by using measurable premise variables and estimations of unmeasurable premise variables of fuzzy models as the premise variables of observers a novel fuzzy fault detection observer scheme is constructed and the corresponding design condition is proposed via a set theoretic description different from the conventional fault detection observer schemes where all premise variables of the observer are the estimations of the premise variables in the fuzzy systems the proposed method can take full advantage of the partly measurable premise variables for achieving a better fault detection performance a numerical example is given to illustrate the effectiveness of the proposed method

convergent fault estimation for linear systems with faults and disturbances the problem of convergent fault estimation for a class of linear systems with faults and disturbances is addressed for the first time in this technical note a differential equation based convergence theorem of mean sequence of estimates is proposed which provides an iterative mean estimation technique that has not been fully reported yet in the literature based on the technique a convergent fault estimation strategy for the linear system in consideration is designed and the convergence of mean sequence of fault estimates is proved theoretically an iterative algorithm is given subsequently to compute the fault estimates numerical simulation results demonstrate the effectiveness and merits of the proposed method

finite horizon estimation of randomly occurring faults for a class of nonlinear time varying systems this paper is concerned with the finite horizon estimation problem of randomly occurring faults for a class of nonlinear systems whose parameters are all time varying the faults are assumed to occur in a random way governed by two sets of bernoulli distributed white sequences the stochastic nonlinearities entering the system are described by statistical means that can cover several classes of well studied nonlinearities the aim of the problem is to estimate the random faults over a finite horizon such that the influence from the exogenous disturbances onto the estimation errors is attenuated at the given level quantified by an h norm in the mean square sense by using the completing squares method and stochastic analysis techniques necessary and sufficient conditions are established for the existence of the desired finite horizon h fault estimator whose parameters are then obtained by solving coupled backward recursive riccati difference equations rdes a simulation example is utilized to illustrate the effectiveness of the proposed fault estimation method

fuzzy model based fault tolerant design for nonlinear stochastic systems against simultaneous sensor and actuator faults this paper addresses the problem of fault estimation and fault tolerant control for a class of takagi sugeno t s fuzzy ito stochastic systems subject to simultaneously sensor and actuator faults the main difficulty in this study is that sensor faults actuator faults and stochastic noise that are governed by brownian motion are taken into simultaneous consideration in a unified framework and traditional fault tolerant approaches are not effective to solve this research issue a new descriptor fuzzy sliding mode observer approach is presented in this paper to obtain the simultaneous estimates of system state sensor fault and actuator fault vectors based on the state estimates an observer based fault tolerant control ftc scheme is developed to stabilize the resulting closed loop system finally a simulation example is provided to show the effectiveness of the proposed fault tolerant approach

technical communique a note on the existence of a solution and stability for lipschitz discrete time descriptor systems this paper addresses the existence and uniqueness of a solution and stability for lipschitz discrete time descriptor systems by means of the fixed point principle a criterion is presented via a matrix inequality and the criterion guarantees the existence and uniqueness of a solution in addition a sufficient condition is also presented to ensure that the solution exists for any compatible initial condition and the system is globally exponentially stable simultaneously it is shown that the criterion presented in this paper is easy to verify and independent of the choices of decomposition matrices for the given system finally the approach is illustrated by a numerical example

controllability and elimination of impulsive modes in descriptor systems as a refined notion impulsive mode controllability is suggested for the general class of linear continuous descriptor systems this notion reveals rich properties of the general descriptor systems in terms of admissibility of initial conditions admissibility of feedback control and impulsive mode elimination the condition for impulsive mode controllability is derived and proved to be necessary and sufficient for the existence of admissible feedback controls eliminating impulsive modes under impulsive mode controllability admissible feedback controls are constructed for eliminating impulsive modes on the basis of numerically reliable decompositions of the system s coefficient matrices

the cauchy problem for ut δu u q with q a positive real number the nonlinear partial differential equation in the title of the paper arises in the study of the growth of surfaces in that context it is known as the generalized deterministic kpz equation the paper is concerned with the initial value problem for the equation under the assumption that the initial data function is bounded and continuous results on the existence uniqueness and regularity of solutions are obtained

l p solutions of multidimensional bsdes with weak monotonicity and general growth generators abstract in this paper we first establish the existence and uniqueness of l p p 1 solutions for multidimensional backward stochastic differential equations bsdes under a weak monotonicity condition together with a general growth condition in y for the generator g then we overview several conditions related closely to the weak monotonicity condition and compare them in an effective way finally we put forward and prove a stability theorem and a comparison theorem of l p p 1 solutions for this kind of bsdes

descriptor recursive estimation for multiple sensors with different delay rates in this article the problem of recursive estimation is studied for a class of descriptor systems measured by multiple sensors with different delay rates the delay phenomenon occurs in a random way and the delay rate for each sensor is characterised by an individual binary switching sequence obeying a conditional probability distribution the original descriptor system is transformed into two non descriptor stochastic subsystems with autocorrelated and cross correlated noises by using the singular value decomposition and the state augmentation applying an innovation analysis approach and the orthogonal projection theorem recursive estimators including filter predictor and smoother are first derived for each subsystem and the process noise then based on the newly obtained recursive state estimators and process noise estimators the recursive filter predictor and smoother are obtained for the original descriptor system measured by multiple sensors with different delay rates a numerical simulation ex

h h fault detection filter design for discrete time takagi sugeno fuzzy system abstract in this note a robust fault detection observer is designed for a t s takagi sugeno fuzzy model with sensor faults and unknown bounded disturbances the method applies the technique of descriptor systems by considering sensor faults as an auxiliary state variable the idea is to formulate the robust fault detection observer design as an h h problem based on nonquadratic lyapunov functions a solution of the considered problem is then given via a linear matrix inequality lmi formulation an example is proposed to illustrate the design conditions

backward sdes with superquadratic growth in this paper we discuss the solvability of backward stochastic differential equations bsdes with superquadratic generators we first prove that given a superquadratic generator there exists a bounded terminal value such that the associated bsde does not admit any bounded solution on the other hand we prove that if the superquadratic bsde admits a bounded solution then there exist infinitely many bounded solutions for this bsde finally we prove the existence of a solution for markovian bsdes where the terminal value is a bounded continuous function of a forward stochastic differential equation

bsde with quadratic growth and unbounded terminal value in this paper we study the existence of solution to bsde with quadratic growth and unbounded terminal value the main idea consists in using a localization procedure together with a priori bounds

filtering and fault estimation of descriptor switched systems in this paper the problems of state and fault estimation are addressed for a class of switched descriptor systems subject to lipschitz nonlinearities and unknown inputs ui the ui appear both on the dynamic and on the measurement equations two problems are addressed by l 2 gain minimization with the use of switched lyapunov functions and formulated by lmi first a functional observer for switched lipschitz nonlinear descriptor system is proposed for robust state estimation second fault estimation is performed by filtering the output estimation error as usually done in the residual generation framework moreover frequency weighting functions can be used to shape the response to the fault and thus improve the estimation

backward stochastic differential equations and partial differential equations with quadratic growth we provide existence comparison and stability results for one dimensional backward stochastic differential equations bsdes when the coefficient or generator f t y z is continuous and has a quadratic growth in z and the terminal condition is bounded we also give in this framework the links between the solutions of bsdes set on a diffusion and viscosity or sobolev solutions of the corresponding semilinear partial differential equations

second order backward stochastic differential equations and fully nonlinear parabolic pdes for a d dimensional diffusion of the form dxt xt dt xt dwt and continuous functions f and g we study the existence and uniqueness of adapted processes y z and a solving the second order backward stochastic differential equation 2bsde dyt f t xt yt zt t dt z dxt t 0 t dzt at dt t dxt