combined filtering and parameter estimation approximations and robustness abstract the filtering problem for a non linear discrete time model is considered that includes as a special case the problem of combined filtering and parameter estimation for linear models the filter derived in the paper is shown to be robust in a specific sense with respect to small variations in the a priori distributions in the model

nearly optimal state feedback controls for stochastic systems with wideband noise disturbances much of optimal stochastic control theory is concerned with diffusion models such models are often only idealizations or limits in an appropriate sense of the actual physical process which might be driven by a wide bandwidth not white process or be a discrete parameter system with correlated driving noises optimal or nearly optimal controls derived for the diffusion models would not normally be useful or even of much interest if they were not also nearly optimal for the physical system which the diffusion approximates under quite broad conditions the nearly optimal control for the physical process do have this robustness property even when compared to controls which can depend on all the past driving noise we treat the problem over a finite time interval as well as the average cost per unit time problem weak convergence methods provide the appropriate analytical tools

energy based event triggered state estimation for hidden markov models abstract in this work a problem of energy based event triggered remote state estimation for systems described by discrete finite state hidden markov models is investigated we consider energy harvesting sensors which absorb power from the environment or other resources and convert it to electrical power the event triggering condition etc considered depends on the sensor energy level which evolves according to a markov process the reference measure approach is used to obtain the optimal estimates of the state based on event triggered measurement information available at the remote estimator by introducing a reference probability measure and a map from the real world measure to the reference measure we derive the recursive expression of the unnormalized state conditional distribution under the reference measure which depends on the estimate of the energy level next we propose a second level of reference probability measure under which the state measurement energy level and event trigger are mutually independent so that the recursive form of unnormalized estimate of the energy level under this reference measure can be obtained with the help of the two reference measures the state estimate in the real world probability measure can be derived the effectiveness of the proposed method is illustrated with simulation results for a linear gaussian system quantized and parameterized into a hidden markov model

on the interplay of singular perturbations and wide band stochastic fluctuations a class of nonlinear singularly perturbed systems driven by wide band noise is considered the asymptotic behavior of the slow variables is studied when the fast variables are sufficiently fast represented by mu to 0 and the wide band noise is sufficiently wide represented by varepsilon to 0 a reduced order markov model which represents the behavior of the slow variables is derived it is shown that the slow variables converge weakly to the solution of this reduced order model as varepsilon and mu tend to zero the coefficients of this reduced order model depend in general on the speeds of varepsilon and mu as they approach zero the implication of such dependence on the engineering practice of neglecting parasitic elements is discussed special cases where the model is independent of the speeds of varepsilon and mu are explored

stability of markovian jump generalized neural networks with interval time varying delays this paper examines the problem of asymptotic stability for markovian jump generalized neural networks with interval time varying delays markovian jump parameters are modeled as a continuous time and finite state markov chain by constructing a suitable lyapunov krasovskii functional lkf and using the linear matrix inequality lmi formulation new delay dependent stability conditions are established to ascertain the mean square asymptotic stability result of the equilibrium point the reciprocally convex combination technique jensen s inequality and the wirtinger based double integral inequality are used to handle single and double integral terms in the time derivative of the lkf the developed results are represented by the lmi the effectiveness and advantages of the new design method are explained using five numerical examples

stability analysis for neural networks with time varying interval delay this letter is concerned with the stability analysis of neural networks nns with time varying interval delay the relationship between the time varying delay and its lower and upper bounds is taken into account when estimating the upper bound of the derivative of lyapunov functional as a result some improved delay interval dependent stability criteria for nns with time varying interval delay are proposed numerical examples are given to demonstrate the effectiveness and the merits of the proposed method

sampled data state estimation for markovian jumping fuzzy cellular neural networks with mode dependent probabilistic time varying delays in this paper the problem of state estimation for markovian jumping fuzzy cellular neural networks fcnns using sampled data with mode dependent probabilistic time varying delays is investigated by developing a delay decomposition approach the information of the delayed states can be taken into full consideration by introducing a stochastic variable with a bernoulli distribution the information of probability distribution of the time varying delay is considered and transformed into one with deterministic time varying delay the main purpose of this paper is to estimate the neuron states through available output measurements such that the dynamics of the estimation error is globally asymptotically stable in the mean square based on the lyapunov krasovskii functional including triple integral terms and decomposed integral intervals delay distribution dependent stability criteria are obtained in terms of linear matrix inequalities lmis finally two numerical examples are given to illustrate the effectiveness of the proposed theoretical results

outlier resistant filtering and smoothing abstract we consider a stationary gaussian information process transmitted through an additive noise channel we assume that the noise and information processes are mutually independent and we model the noise process as nominally gaussian with additive outliers for the above system model we first develop a theory for outlier resistant filtering and smoothing operations we then design specific such nonlinear operations and we study their performance the performance criteria are the asymptotic mean squared error at the gaussian nominal model the breakdown point and the influence function we find that the proposed operations combine excellent performance at the nominal model with strong resistance to outliers

nonlinear filters for linear models a robust approach we consider the altering problem for linear models where the driving noises may be quite general nonwhite and non gaussian and where the observation noise may only be known to belong to a finite family of possible disturbances using diffusion approximation methods we show that a certain nonlinear filter minimizes the asymptotic filter variance this nonlinear filter is obtained by choosing at each moment on the basis of the observations one of a finite number of kalman type filters driven by a suitable nonlinear transformation of the innovations as a byproduct we obtain also the asymptotic identification of the a priori unknown observation noise disturbance by yielding an asymptotically efficient filter in face of an unknown observation noise our approach may also be viewed as a robust approach to filtering for linear models

some remarks on the riccati equation arising in an optimal control problem with state and control dependent noise this paper solves a quadratic optimal control for a linear stochastic evolution equation with unbounded coefficients it is assumed that the stochastic noise depends both on the state and on the control the dynamic programming approach is used and attention is focused on the riccati equation in 5 and 6 some attractivity and maximality properties of the solutions of the algebraic riccati equation are proved and it is shown that in some special cases there exists a maximal solution

some results on the controllability of forward stochastic heat equations with control on the drift abstract in this paper we establish the null approximate controllability for forward stochastic heat equations with control on the drift the null controllability is obtained by a time iteration method and an observability estimate on partial sums of eigenfunctions for elliptic operators as a consequence of the null controllability we obtain the observability estimate for backward stochastic heat equations which leads to a unique continuation property for backward stochastic heat equations and hence the desired approximate controllability for forward stochastic heat equations it deserves to point out that one needs to introduce a little stronger assumption on the controller for the approximate controllability of forward stochastic heat equations than that for the null controllability this is a new phenomenon arising in the study of the controllability problem for stochastic heat equations

a game theoretic approach to robust filtering a game theoretic approach to the filtering or smoothing problem is presented a family of stationary information carrying processes and generalized models for the noise channel and the filter is considered sufficient conditions for the existence of saddle point type solutions are stated in addition the solution for a special case of noise channel a family of information carrying processes and a nonlinear filter are found

wirtinger based integral inequality application to time delay systems in the last decade the jensen inequality has been intensively used in the context of time delay or sampled data systems since it is an appropriate tool to derive tractable stability conditions expressed in terms of linear matrix inequalities lmis however it is also well known that this inequality introduces an undesirable conservatism in the stability conditions and looking at the literature reducing this gap is a relevant issue and always an open problem in this paper we propose an alternative inequality based on the fourier theory more precisely on the wirtinger inequalities it is shown that this resulting inequality encompasses the jensen one and also leads to tractable lmi conditions in order to illustrate the potential gain of employing this new inequality with respect to the jensen one two applications on time delay and sampled data stability analysis are provided

delay slope dependent stability results of recurrent neural networks by using the fact that the neuron activation functions are sector bounded and nondecreasing this brief presents a new method named the delay slope dependent method for stability analysis of a class of recurrent neural networks with time varying delays this method includes more information on the slope of neuron activation functions and fewer matrix variables in the constructed lyapunov krasovskii functional then some improved delay dependent stability criteria with less computational burden and conservatism are obtained numerical examples are given to illustrate the effectiveness and the benefits of the proposed method

impulsive control for existence uniqueness and global stability of periodic solutions of recurrent neural networks with discrete and continuously distributed delays in this paper a class of recurrent neural networks with discrete and continuously distributed delays is considered sufficient conditions for the existence uniqueness and global exponential stability of a periodic solution are obtained by using contraction mapping theorem and stability theory on impulsive functional differential equations the proposed method which differs from the existing results in the literature shows that network models may admit a periodic solution which is globally exponentially stable via proper impulsive control strategies even if it is originally unstable or divergent two numerical examples and their computer simulations are offered to show the effectiveness of our new results

event triggered generalized dissipativity filtering for neural networks with time varying delays this paper is concerned with event triggered generalized dissipativity filtering for a neural network nn with a time varying delay the signal transmission from the nn to its filter is completed through a communication channel it is assumed that the network measurement of the nn is sampled periodically an event triggered communication scheme is introduced to design a suitable filter such that precious communication resources can be saved significantly while certain filtering performance can be ensured on the one hand the event triggered communication scheme is devised to select only those sampled signals violating a certain threshold to be transmitted which directly leads to saving of precious communication resources on the other hand the filtering error system is modeled as a time delay system closely dependent on the parameters of the event triggered scheme based on this model a suitable filter is designed such that certain filtering performance can be ensured provided that a set of linear matrix inequalities are satisfied furthermore since a generalized dissipativity performance index is introduced several kinds of event triggered filtering issues such as h infty filtering passive filtering mixed h infty and passive filtering q s r dissipative filtering and mathcal l 2 mathcal l infty filtering are solved in a unified framework finally two examples are given to illustrate the effectiveness of the proposed method

further results on exponential stability for impulsive switched nonlinear time delay systems with delayed impulse effects this paper is concerned with the problem of exponential stability for a class of impulsive switched nonlinear time delay systems with delayed impulse effects by using the multiple lyapunov krasovskii functionals technique some exponential stability criteria are obtained respectively for two kinds of impulsive signals destabilizing impulsive signal and stabilizing impulsive signal the derived results not only characterise the effects of delayed impulse time delay and switching on nonlinear systems but also remove some restriction conditions furthermore a more precise bound of system state is given compared with existing results on related problems the obtained results are less conservative three examples are provided to illustrate the effectiveness and the generality of the proposed results

event triggered state estimation for discrete time multidelayed neural networks with stochastic parameters and incomplete measurements in this paper the event triggered state estimation problem is investigated for a class of discrete time multidelayed neural networks with stochastic parameters and incomplete measurements in order to cater for more realistic transmission process of the neural signals we make the first attempt to introduce a set of stochastic variables to characterize the random fluctuations of system parameters in the addressed neural network model the delays among the interconnections are allowed to be different which are more general than those in the existing literature the incomplete information under consideration includes randomly occurring sensor saturations and quantizations for the purpose of energy saving an event triggered state estimator is constructed and a sufficient condition is given under which the estimation error dynamics is exponentially ultimately bounded in the mean square it is worth noting that the ultimate boundedness of the error dynamics is explicitly estimated the characterization of the desired estimator gain is designed in terms of the solution to a certain matrix inequality finally a numerical simulation example is presented to illustrate the effectiveness of the proposed event triggered state estimation scheme

reciprocally convex approach to stability of systems with time varying delays whereas the upper bound lemma for matrix cross product introduced by park 1999 and modified by moon park kwon and lee 2001 plays a key role in guiding various delay dependent criteria for delayed systems the jensen inequality has become an alternative as a way of reducing the number of decision variables it directly relaxes the integral term of quadratic quantities into the quadratic term of the integral quantities resulting in a linear combination of positive functions weighted by the inverses of convex parameters this paper suggests the lower bound lemma for such a combination which achieves performance behavior identical to approaches based on the integral inequality lemma but with much less decision variables comparable to those based on the jensen inequality lemma

survey paper a partial history of the early development of continuous time nonlinear stochastic systems theory this article is a survey of the early development of selected areas in nonlinear continuous time stochastic control key developments in optimal control and the dynamic programming principle existence of optimal controls under complete and partial observations nonlinear filtering stochastic stability the stochastic maximum principle and ergodic control are discussed issues concerning wide bandwidth noise for stability modeling filtering and ergodic control are dealt with the focus is on the earlier work but many important topics are omitted for lack of space

state estimation for markovian jump linear systems with bounded disturbances in this paper we investigate the state estimation problem for a class of markovian jump linear systems mjlss in the presence of bounded polyhedral disturbances a set membership estimation algorithm is first proposed to find the smallest consistent set of all possible states which is shown to be expressed by a union of multiple polytopes the posterior probabilities of the system jumping modes are then estimated by introducing the lebesgue measure based on which the optimal point estimate is further provided moreover a similarity relationship for polytopes is defined and an approximate method is presented to calculate the minkowski sum of polytopes which can help reduce the computational complexity of the overall estimation algorithm

qualitative robustness in time series abstract we consider robust operations in time series we present a definition and subsequent qualitative analysis of robustness we also present meaningful definitions of performance criteria such as the breakdown point and the sensitivity of robust operations we present some specific classes of robust operations and we discuss and analyze their properties finally we fully analyze a particular class of robust predictors and interpolators for a linearly contaminated class of stationary stochastic processes

approximate controllability of semilinear deterministic and stochastic evolution equations in abstract spaces various sufficient conditions for approximate controllability of linear evolution systems in abstract spaces have been obtained but approximate controllability of semilinear control systems usually requires some complicated and limited assumptions in this paper we show the approximate controllability of the abstract semilinear deterministic and stochastic control systems under the natural assumption that the associated linear control system is approximately controllable the results are obtained using new properties of symmetric operators which are proved in this paper compact semigroups the schauder fixed point theorem and or the contraction mapping principle

null controllability of an infinite dimensional sde with state and control dependent noise abstract we consider a controlled stochastic linear differential equation with state and control dependent noise in a hilbert space h we investigate the relation between the null controllability of the equation and the existence of the solution of singular riccati operator equations moreover for a fixed interval of time the null controllability is characterized in terms of the dual state examples of stochastic pdes are also considered

optimal and approximately optimal control policies for queues in heavy traffic the approximately optimal control problem for tandem queueing or production networks with local feedback allowed under heavy traffic is treated the buffers scaled with traffic are finite the controls allow various inputs connecting links and the processors to be shut down or opened to manage the system the service and arrival rates as well as the routing probabilities can also be controlled and the system statistics can depend on the system state scaled buffer occupancies the associated costs involve holding costs costs for shutting off turning on the links or processors and the opportunity cost for lost production it is shown that the scaled controlled system converges weakly in an appropriate sense to a controlled limit reflected diffusion in the resealed time the actions of the controllers lead to multiple simultaneous impulses in the limit problem thus a nonstandard limit control problem is obtained and the usual methods of weak convergence for systems under heavy traffi

filtering and control for wide bandwidth noise driven systems much of modern stochastic control theory uses ideal white noise driven models ito equations if the observed data are corrupted by noise then the noise is usually assumed to be white gaussian typically if the underlying models are linear one uses a kalman bucy filter to get an estimate of the state and then bases the control on this estimate in practice the noises are rarely white and the reference signals and the systems are only approximations in some sense to a diffusion nevertheless owing to lack of viable alternatives one still uses the kalman bucy filter etc then the estimates are not optimal and indeed might be quite far from being optimal the same is true for the corresponding control examples are given to illustrate this the sense in which the estimates and or control is useful needs to be examined in order to justify the use of the commonly used procedure the issue is much deeper than mere robustness in the usual sense since basic questions of interpretation of the results are involved this paper deals with these questions for the filtering problem where the signal is a near gauss markov process and the observation noise wide band it is shown that the usual method is nearly optimal with respect to a class of alternative data processors this alternative class is rather natural and includes the data processors which one would normally want to use it is unlikely that the class can be enlarged very much in general the asymptotic in time and bandwidth problem is treated as is the much harder conditional gaussian case and a case where the observations are nonlinear the basic techniques are those of weak convergence theory similar results are obtained for the combined filtering and control problem where it is shown that good controls for the ideal model are also good for the actual physical model with respect to a natural case of alternative controls the control problem over a finite interval as well as the average cost per unit time problem are considered

sliding block encoders that are rho bar continuous functions of their input corresp sliding block encoders operating within a statistically contaminated source environment are considered stationary analog sources are studied using the rho bar distance as the measure of contamination sufficient constructive conditions are developed for the design of sliding block encoders that guarantee rho bar stability of their output when operating within a statistically contaminated source environment the relationship of this stability to the robustness of the encoding scheme is discussed where robustness is a local stability property applied on the output entropy and the average distortion

robust recursive estimation in the presence of heavy tailed observation noise a first order approximation is derived for the conditional prior distribution of the state of a discrete time stochastic linear dynamic system in the presence of contaminated normal observation noise this distribution is then used to derive a first order approximation of the conditional mean minimum variance estimator if the observation noise distribution can be represented as a member of the e contaminated normal neighborhood then the conditional prior is also to first order an analogous perturbation from a normal distribution whose first two moments are given by the kalman filter moreover the perturbation is itself of a special form combining distributions whose parameters are given by banks of parallel kalman filters and optimal smoothers

on the filtering of noise contaminated signals observed via hard limiters the problem of signal estimation from a measurement of its noise crossings is considered following a nonlinear filtering approach that is different from the classical davenport method by focusing on a specific noise model and applying recent results on the excursions of a brownian motion an exact representation of the optimal filter is derived various extensions of the results are considered

finite time state estimation for recurrent delayed neural networks with component based event triggering protocol this paper deals with the event based finite time state estimation problem for a class of discrete time stochastic neural networks with mixed discrete and distributed time delays in order to mitigate the burden of data communication a general component based event triggered transmission mechanism is proposed to determine whether the measurement output should be released to the estimator at certain time point according to a specific triggering condition a new concept of finite time boundedness in the mean square is put forward to quantify the estimation performance by introducing a settling like time function the objective of the addressed problem is to construct an event based state estimator to estimate the neuron states such that in the presence of both mixed time delays and external noise disturbances the dynamics of the estimation error is finite time bounded in the mean square with a prescribed error upper bound sufficient conditions are established via stochastic analysis techniques to guarantee the desired estimation performance by solving an optimization problem with some inequality constraints the explicit expression of the estimator gain matrix is characterized to minimize the settling like time finally a numerical simulation example is exploited to demonstrate the effectiveness of the proposed estimator design scheme

approximate and approximate null controllability of a class of piecewise linear markov switch systems abstract we propose an explicit easily computable algebraic criterion for approximate null controllability of a class of general piecewise linear switch systems with multiplicative noise this gives an answer to the general problem left open in goreac and martinez 2015 the proof relies on recent results in confortola et al 2015 allowing to reduce the dual stochastic backward system to a family of ordinary differential equations second we prove by examples that the notion of approximate controllability is strictly stronger than approximate null controllability a sufficient criterion for this stronger notion is also provided the results are illustrated on a model derived from repressed bacterium operon given in krishna et al 2005 and reduced in crudu et al 2009

controllability of linear impulsive stochastic systems in hilbert spaces this paper is concerned with the controllability of linear impulsive stochastic systems lisss in hilbert spaces for this class of systems the concepts of null controllability and approximate null controllability are introduced to overcome the difficulties related we construct the adjoint systems and the quasi backward stochastic systems of lisss necessary and sufficient conditions for the null controllability and the approximate null controllability are developed by utilizing our introduced quasi backward stochastic systems furthermore an equivalence is established between the null controllability of lisss and some initial state of quasi backward stochastic systems

state estimation on positive markovian jump systems with time varying delay and uncertain transition probabilities investigate the positive discrete time mjs with disturbance input time varying delay and uncertain transition probabilities together for the first time where the transition probability matrix is described by a polytope set provide a necessary and sufficient condition of stochastic stability with regard to the resulting error dynamic system present the exact computation of l gain index for the resulting stochastically stable error dynamic systems firstly and derive a necessary and sufficient condition of the l gain performance correspondingly provide a sufficient condition on the existence of a desired observer to solve the state estimation problem such that the error dynamic system is stochastically stable with a prescribed l gain performance all the proposed conditions are expressed in linear programming forms which can be solved effectively by using some existing softwares and the observer gain matrices can be directly obtained by an effective algorithm this paper is concerned with the state estimation problem based on an l observer for a class of positive discrete time markovian jump systems mjss the system under consideration consists of time varying delay and uncertain transition probabilities where the transition probability matrix is described by a polytope set necessary and sufficient conditions are presented in linear programming lp form for the resulting error dynamic system to be stochastically stable and stochastically stable with an l gain performance respectively furthermore an l observer design scheme is presented to solve the state estimation problem such that the resulting error dynamic system is stochastically stable and achieves a prescribed l gain performance all the proposed conditions are solvable in terms of lp with additional parameters finally some examples are given to demonstrate the validity of the developed technique

impulsive differential equations this paper deals with the periodic solutions problem for impulsive differential equations by using lyapunov s second method and the contraction mapping principle some conditions ensuring the existence and global attractiveness of unique periodic solutions are derived which are given from impulsive control and impulsive perturbation points of view as an application the existence and global attractiveness of unique periodic solutions for hopfield neural networks are discussed finally two numerical examples are provided to demonstrate the effectiveness of the proposed results

null controllability with vanishing energy linear null controllable systems for which an arbitrary initial state can be transferred to the origin with arbitrarily small energy are characterized theorems are stated in terms of an associated algebraic riccati equation and in terms of the spectrum of the linear part of the system the results so obtained allow us to determine ornstein uhlenbeck operators for which the liouville theorem about bounded harmonic functions holds

event triggered state estimation for markovian jumping impulsive neural networks with interval time varying delays abstractthis paper investigates the event triggered state estimation problem of markovian jumping impulsive neural networks with interval time varying delays the purpose is to design a state estimator to estimate system states through available output measurements in the neural networks there are a set of modes which are determined by markov chain a markovian jumping time delay impulsive neural networks model is employed to describe the event triggered scheme and the network related behaviour such as transmission delay data package dropout and disorder the proposed event triggered scheme is used to determine whether the sampled state information should be transmitted the discrete delays are assumed to be time varying and belong to a given interval which means that the lower and upper bounds of interval time varying delays are available first we design a state observer to estimate the neuron states second based on a novel lyapunov krasovskii functional lkf with triple integral terms and us