brief paper reach set computation and control synthesis for discrete time dynamical systems with disturbances the paper is devoted to the formulation of the reachability problem for discrete time dynamical systems with disturbances the concept of maxmin and minmax forward and backward reach sets is addressed invariance of the backward reach set is discussed the emphasis of the paper is on discrete time linear systems for which the ellipsoidal computational method is described the synthesis of maxmin and minmax closed loop control for steering the system to a given target set using ellipsoidal backward reach set approximations is explained the ellipsoidal method covered in the paper is implemented in the ellipsoidal toolbox for matlab a popular collection of ellipsoidal calculus routines freely available online

operations on l fuzzy topological spaces abstract the aim of the paper is mainly to introduce and study operations on l fuzzy topological spaces the algebraic properties of some of these operations are discussed most of the concepts of compactness continuity lindelof spaces and separation axioms are considered

fµ strongly semiopen sets fµ strong semicontinuity and fµ strongly semiretracts throughout the literature if x d is an f ts and y x the induced f topological subspace y d y is defined so that d y n g y n d macho stadler and de prada vicente fuzzy sets and systems 58 1993 365 introduced a new concept of f topological subspaces which coincides with the usual definition in the case that m g y also they introduced the concepts of f m open sets and f m continuity in this paper using the previous concepts we introduce weaker forms of f m open sets and f m continuity the notion of an f retract was introduced by rodabough j math anal appl 79 1981 273 here we introduce the notion of a f m retract and weaker forms of it the basic properties of these notions are given many results are obtained

ellipsoidal parameter or state estimation under model uncertainty ellipsoidal outer bounding of the set of all feasible state vectors under model uncertainty is a natural extension of state estimation for deterministic models with unknown but bounded state perturbations and measurement noise the technique described in this paper applies to linear discrete time dynamic systems it can also be applied to weakly non linear systems if non linearity is replaced by uncertainty many difficulties arise because of the non convexity of feasible sets combined quadratic constraints on model uncertainty and additive disturbances are considered in order to simplify the analysis analytical optimal or suboptimal solutions of the basic problems involved in parameter or state estimation are presented which are counterparts in this context of uncertain models to classical approximations of the sum and intersection of ellipsoids the results obtained for combined quadratic constraints are extended to other types of model uncertainty

brief paper state estimation in the presence of bounded disturbances this contribution proposes a robust recursive algorithm for the state estimation of linear models with unknown but bounded disturbances corrupting both the state and measurement vectors a novel approach based on state bounding techniques is presented the proposed algorithm can be decomposed into two steps time updating and observation updating that uses a switching estimation kalman like gain matrix particular emphasis will be given to the design of a weighting factor that ensures the stability of the estimation error

on various weak fuzzy pairwise retracts the notion of a fuzzy retract was introduced by rodabaugh j math anal appl 79 1981 273 and this notion was extended to the fuzzy bitopological setting j fuzzy math 9 1 2001 207 in this paper we define the notions of fuzzy pairwise semiretracts fuzzy pairwise preretracts fuzzy pairwise strongly semiretracts fuzzy pairwise less strongly semiretracts and fuzzy pairwise semi preretracts we establish some properties of these concepts moreover the relations between these new concepts are discussed

sequential approximation of feasible parameter sets for identification with set membership uncertainty in this paper the problem of approximating the feasible parameter set for identification of a system in a set membership setting is considered the system model is linear in the unknown parameters a recursive procedure providing an approximation of the parameter set of interest through parallelotopes is presented and an efficient algorithm is proposed its computational complexity is similar to that of the commonly used ellipsoidal approximation schemes numerical results are also reported on some simulation experiments conducted to assess the performance of the proposed algorithm

making and evaluating point forecasts typically point forecasting methods are compared and assessed by means of an error measure or scoring function with the absolute error and the squared error being key examples the individual scores are averaged over forecast cases to result in a summary measure of the predictive performance such as the mean absolute error or the mean squared error i demonstrate that this common practice can lead to grossly misguided inferences unless the scoring function and the forecasting task are carefully matched effective point forecasting requires that the scoring function be specified ex ante or that the forecaster receives a directive in the form of a statistical functional such as the mean or a quantile of the predictive distribution if the scoring function is specified ex ante the forecaster can issue the optimal point forecast namely the bayes rule if the forecaster receives a directive in the form of a functional it is critical that the scoring function be consistent for it in the sense that t

forty years of hutton fuzzy unit interval this note is a very short history of a specific fuzzy topological space the hutton s fuzzy unit interval 0 1 l which occupies one of the central positions in fuzzy topology on that occasion the superiority of l valued topology over 0 1 valued topology is being discussed we then show how the hutton s concept evolved after obvious identifications we can today say that 0 1 l is the tensor product 0 1 l of the lattices 0 1 and l an account of the consequences of this new view point is hoped to appear thereafter

on the value of information in system identification bounded noise case assuming instantaneous bounds on the noise system parameter identification is formulated as membership set estimation problem sequential algorithms are constructed to estimate the membership sets of the parameters which are consistent with the measurements and the noise constraints the important new feature of the proposed algorithms is their ability to ignore redundant data the efficient data extraction property of the new algorithms is achieved with small computational effort and with improved performance when compared to the least square algorithm the convergence properties and the notion of identifiability in the set theoretic context are also studied

a theory of fuzzy uniformities with applications to the fuzzy real lines abstract for each completely distributive lattice l with order reversing involution the fuzzy real line r l is uniformizable by a uniformity which both generates the canonical fuzzy topology and induces a pseudometric generating the canonical topology if l is also a chain the usual addition and multiplication defined on r r 0 1 extend jointly fuzzy continuously to and on r l three fundamental questions in fuzzy sets until now are question a if l 1 l 2 is r l 1 uniformly isomorphic to r l 2 in some sense question b for each chain l is jointly uniformly continuous in a sense which guarantees its joint continuity on r l question c is r l a complete pseudometric space in some sense we construct categories qu and u using the quasi uniformities of b hutton which enable us to answer these questions in the affirmative these results enhance the canonical standing of the fuzzy real lines and so give additional justification for answering in the affirmative question d does fuzzy topology have deep specific canonical examples

ellipsoidal techniques for reachability analysis of discrete time linear systems this paper describes the computation of reach sets for discrete time linear control systems with time varying coefficients and ellipsoidal bounds on the controls and initial conditions the algorithms construct external and internal ellipsoidal approximations that touch the reach set boundary from outside and from inside recurrence relations describe the time evolution of these approximations an essential part of the paper deals with singular discrete time linear systems

computing reachable states for nonlinear biological models in this paper we describe reachability computation for continuous and hybrid systems and its potential contribution to the process of building and debugging biological models we summarize the state of the art for linear systems and then develop a novel algorithm for computing reachable states for nonlinear systems we report experimental results obtained using a prototype implementation applied to several biological models we believe these results constitute a promising contribution to the analysis of complex models of biological systems

set membership filtering with incomplete observations abstract this study addresses the set membership estimation problem for a class of discrete time varying systems with incomplete observations a set membership filter is developed and a recursive algorithm is proposed to calculate the state estimate ellipsoid which contains the true value to solve the problem that the conventional set membership filter cannot guarantee the stability when applied to discrete time varying systems with incomplete observations a quantitative analysis method about incomplete observations is developed and a tight bound of the estimation error is found based on interval analysis and some bounded noise assumptions in terms of bounded assumptions the relationship between the bound of estimated error and the data dropout rate is obtained if the data dropout rate is less than a maximal value the set membership filter is asymptotically stable the proposed filter is applied to a two state example to demonstrate the effectiveness of theoretical results

ellipsoidal bounds for uncertain linear equations and dynamical systems abstract in this paper we discuss semidefinite relaxation techniques for computing minimal size ellipsoids that bound the solution set of a system of uncertain linear equations the proposed technique is based on the combination of a quadratic embedding of the uncertainty and the s procedure this formulation leads to convex optimization problems that can be essentially solved in o n3 n being the size of unknown vector by means of suitable interior point barrier methods as well as to closed form results in some particular cases we further show that the uncertain linear equations paradigm can be directly applied to various state bounding problems for dynamical systems subject to set valued noise and model uncertainty

dynamic topologies and their applications to crisp topologies fuzzifications of crisp topologies and fuzzy topologies on the crisp real line abstract we introduce and develop topologies whose members are dynamic sets a la zeleny this development spawns the notions of phase and co phase spaces fuzzy dual dynamic dual and co fuzzy dual with the following results being obtained result a the notion of fuzzy dual provides a unifying framework for the diverse fuzzification schemes of hutton gantner steinlage warren klein and lowen result b the dynamic duals of the fuzzy real lines are both homeostatic and coheterostatic result c the fuzzy real lines re interpreted as fuzzy duals of r with the usual euclidean topology t induce on r via the notion of co fuzzy dual a class of canonical stratified fuzzy topologies co r l e g if l is a demorgan algebra and lc 1 then the compactness of a r is equivalent to the ordinary compactness of a w r t t and if l is a hutton algebra r l co r l is metrizable in the sense of hutton and erceg with erceg metric d l such that d l p r 1 p s 1 r s where pr is the crisp point or impulse with support r i e d l extends the euclidean metric on r

two new l fuzzy topologies on r l in this paper two new topologies 1 2 on r l are constructed using i we produced two l fuzzy topologies i on r l other than the l fuzzy topology t introduced by hutton we have proved that 1 is finer than 2 and 2 is finer than t 2 is the coarsest among the induced l fuzzy topologies which are finer than t we have shown that lr l i the induced space of r l i possesses many good properties such as stronger separation suitability etc we proved that closed interval a b l 2 a b l is closed connected and n compact the addition and multiplication defined on r l by rodabaugh are still jointly continuous

probability guaranteed h finite horizon filtering for a class of nonlinear time varying systems with sensor saturations in this paper the probability guaranteed h finite horizon filtering problem is investigated for a class of nonlinear time varying systems with uncertain parameters and sensor saturations the system matrices are functions of mutually independent stochastic variables that obey uniform distributions over known finite ranges attention is focused on the construction of a time varying filter such that the prescribed h performance requirement can be guaranteed with probability constraint by using the difference linear matrix inequalities dlmis approach sufficient conditions are established to guarantee the desired performance of the designed finite horizon filter the time varying filter gains can be obtained in terms of the feasible solutions of a set of dlmis that can be recursively solved by using the semi definite programming method a computational algorithm is specifically developed for the addressed probability guaranteed h finite horizon filtering problem finally a simulation example is given to illustrate the effectiveness of the proposed filtering scheme 2012 elsevier b v all rights reserved

computational techniques for reachability analysis of max plus linear systems this work discusses a computational approach to reachability analysis of max plus linear mpl systems a class of discrete event systems widely used in synchronization and scheduling applications given a set of initial states we characterize and compute its reach tube namely the collection of set of reachable states regarded step wise as reach sets by an alternative characterization of the mpl dynamics we show that the exact computation of the reach sets can be performed quickly and compactly by manipulations of difference bound matrices and further derive worst case bounds on the complexity of these operations the approach is also extended to backward reachability analysis the concepts and results are elucidated by a running example and we further illustrate the performance of the approach by a numerical benchmark the technique comfortably handles twenty dimensional mpl systems i e with twenty continuous state variables and as such it outperforms the state of the art alternative approaches in the literature

generalized lowen functors according to their value ranges l topological spaces form different categories clearly the investigation on their relationships is certainly important and necessary lowen was one of the first authors who had studied the relation between the category of i topological spaces and that of topological spaces he introduced two well known functors and i later these functors namely lowen functors were extended by different authors for various kinds of lattices studying the relation between l top and top in this paper we introduce two functors f and if between l1 top and l2 top for each scott continuous mapping f l2 l1 where l1 and l2 are arbitrary two completely distributive lattices some topological properties related to these functors are revealed e g for li topological space xi i i 1 2 both f x1 1 and if x2 2 are lowen spaces in the case that f is the identity mapping on a linearly ordered complete lattice for l topological space x f is the finest lowen topology on x contained in and if is the coarsest lowen topology on x containing etc

errata complete fuzzy topological hyperfields and fuzzy multiplication in the fuzzy real lines abstract we construct a fuzzy multiplication for the case l a chain in the l fuzzy real line r l which is jointly fuzzy continuous and which is the unique piecewise consistent extension of ordinary multiplication to r l distributing over the fuzzy addition constructed by the author in 47 we also specify the fuzzy integers and give an extensive analysis of fuzzy contractions and expansions these results the constructions of this paper and the results of 47 are used to prove r l and the stratified r c l are nontopologically isomorphic complete fuzzy topological hyperfields if l is a chain with l 3 we can now completely answer for l a chain the following question of 27 in the affirmative can a set of fuzzy numbers its fuzzy topology and its fuzzy addition and multiplication be defined such that these operations are jointly fuzzy continuous extensions of the usual addition and multiplication of r and can we specify the fuzzy integers these results in combination with recent papers of several authors would seem to answer in the affirmative the following philosophical question cf 34 does fuzzy topology have deep specific canonical examples

reachability analysis using dissipation inequalities for uncertain nonlinear systems abstract we propose a method to outer bound forward reachable sets on finite horizons for uncertain nonlinear systems with polynomial dynamics this method makes use of time dependent polynomial storage functions that satisfy appropriate dissipation inequalities that account for time varying uncertain parameters l 2 disturbances and perturbations characterized by integral quadratic constraints iqcs with both hard and soft factorizations the use of iqcs in forward reachability analysis allows for various types of uncertainty including unmodeled dynamics the generalized s procedure and sum of squares techniques are used to derive algorithms with the goal of finding the tightest outer bound with a desired shape both pedagogical and practically motivated examples are presented including a 7 state f 18 aircraft model

suitability in fuzzy topological spaces abstract an l fuzzy topological space is said to be suitable if it possesses a nontrivial crisp closed subset basic properties of and sufficient conditions for suitable spaces are derived characterizations of the suitable subspaces of the fuzzy unit interval the fuzzy open unit interval and the fuzzy real line are obtained suitability is l fuzzy productive nondegenerate 1 hausdorff spaces are suitable the fuzzy unit interval the fuzzy open unit interval and the fuzzy real line are not suitable and no suitable subspace of the fuzzy unit interval the fuzzy open unit interval or the fuzzy real line is a fuzzy retract of the fuzzy unit interval the fuzzy open unit interval or the fuzzy real line respectively without restrictions there cannot be a fuzzy extension theorem

kalman filtering with intermittent observations motivated by navigation and tracking applications within sensor networks we consider the problem of performing kalman filtering with intermittent observations when data travel along unreliable communication channels in a large wireless multihop sensor network the effect of communication delays and loss of information in the control loop cannot be neglected we address this problem starting from the discrete kalman filtering formulation and modeling the arrival of the observation as a random process we study the statistical convergence properties of the estimation error covariance showing the existence of a critical value for the arrival rate of the observations beyond which a transition to an unbounded state error covariance occurs we also give upper and lower bounds on this expected state error covariance

brief paper set membership filtering for systems with sensor saturation this paper addresses the set membership filtering problem for a class of discrete time varying systems with sensor saturation in the presence of unknown but bounded process and measurement noises a sufficient condition for the existence of set membership filter is derived a convex optimisation method is proposed to determine a state estimation ellipsoid that is a set of states compatible with sensor saturation and unknown but bounded process and measurement noises a recursive algorithm is developed for computing the ellipsoid that guarantees to contain the true state by solving a time varying linear matrix inequality simulation results are provided to demonstrate the effectiveness of the proposed method

ic l cotopological spaces the aim of this paper is to define and study ic l cotopological spaces a generalization of martin s weakly induced i topological spaces particularly weiss s induced spaces and lowen s topologically generated spaces under a moderate restriction to l we prove that icltop c the category of ic l cotopological spaces and continuous mappings is an isomorphism closed full proper subcategory of ltop c the category of l cotopological spaces and continuous mappings which is simultaneously bireflective and bicoreflective in ltop c and that an l cotopological space x d is an ic space if and only if its induced i l cotopological space x w l o p d is an ic space

the extended kalman filter as an exponential observer for nonlinear systems we analyze the behavior of the extended kalman filter as a state estimator for nonlinear deterministic systems using the direct method of lyapunov we prove that under certain conditions the extended kalman filter is an exponential observer i e the dynamics of the estimation error is exponentially stable furthermore we discuss a generalization of the kalman filter with exponential data weighting to nonlinear systems

brief paper recursive state bounding by parallelotopes in this paper the problem of recursively estimating the state uncertainty set of a discrete time linear dynamical system is addressed a novel approach based on minimum volume bounding parallelotopes is introduced and an algorithm of polynomial complexity is derived simulation results and performance comparisons with ellipsoidal recursive state bounding algorithms are also given

a note on stratified l real line and unit l interval we show that the stratified l real line and the stratified unit l interval have no non trivial crisp open sets simple characterizations for boolean valued stratified l interval and l line are also given

robust filtering for discrete time systems with bounded noise and parametric uncertainty this note presents a new approach to finite horizon guaranteed state prediction for discrete time systems affected by bounded noise and unknown but bounded parameter uncertainty our framework handles possibly nonlinear dependence of the state space matrices on the uncertain parameters the main result is that a minimal confidence ellipsoid for the state consistent with the measured output and the uncertainty description may be recursively computed in polynomial time using interior point methods for convex optimization with n states l uncertain parameters appearing linearly in the state space matrices with rank one matrix coefficients the worst case complexity grows as o l n l sup 3 5 with unstructured uncertainty in all system matrices the worst case complexity reduces to o n sup 3 5

g fuzzy topologies on algebraic structures abstract considering complete boolean algebras as sets of truth values the structure of a fuzzy topological group fuzzy topological ring etc is specified the probabilistic completion of ordinary topological algebraic structures shows the applicability of these concepts to the theory of stochastic processes e g a new definition of the stochastic integral is presented in section 5

stabilization for sampled data systems under noisy sampling interval in engineering practice the sampling interval for a sampled data system often fluctuates around a nominal ideal value based on certain probability distributions that can be specified a priori through statistical tests in this paper a fundamental stabilization problem is investigated for a class of sampled data systems under noisy sampling interval the stochastic sampled data control system under consideration is first converted into a discrete time system whose system matrix is represented as an equivalent yet tractable form via the matrix exponential computation then by introducing a vandermonde matrix the mathematical expectation of the quadratic form of the system matrix is computed by recurring to the kronecker product operation the sampled data stabilization controller is designed such that the closed loop system is stochastically stable in the presence of noisy sampling interval subsequently a special case is considered where the sampling interval obeys the continuous uniform distribution and the corresponding stabilization controller is designed finally a numerical simulation example is provided to demonstrate the effectiveness of the proposed design approach

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

set membership filtering for discrete time systems with nonlinear equality constraints in this technical note the problem of set membership filtering is considered for discrete time systems with nonlinear equality constraint between their state variables the nonlinear equality constraint is first linearized and transformed into a state linear equality constraint with two uncertain quantities related to linearizing truncation error and base point error s procedure method is then applied to merge all inequalities into one inequality and the solution to the unconstrained set membership filtering problem is provided the set membership filter with state constraint is finally derived from projecting the unconstrained set membership filter onto the constrained surface by using finsler s lemma a time varying linear matrix inequality optimization based approach is proposed to design the set membership filter with nonlinear equality constraint a recursive algorithm is developed for computing the state estimate ellipsoid that guarantees to contain the true state an illustrative example is provided to demonstrate the effectiveness of the proposed set membership filtering with nonlinear equality constraint

higher order elicitability and osband s principle a statistical functional such as the mean or the median is called elicitable if there is a scoring function or loss function such that the correct forecast of the functional is the unique minimizer of the expected score such scoring functions are called strictly consistent for the functional the elicitability of a functional opens the possibility to compare competing forecasts and to rank them in terms of their realized scores in this paper we explore the notion of elicitability for multi dimensional functionals and give both necessary and sufficient conditions for strictly consistent scoring functions we cover the case of functionals with elicitable components but we also show that one dimensional functionals that are not elicitable can be a component of a higher order elicitable functional in the case of the variance this is a known result however an important result of this paper is that spectral risk measures with a spectral measure with finite support are jointly elicitable if one adds the correct quantiles a direct consequence of applied interest is that the pair value at risk expected shortfall is jointly elicitable under mild conditions that are usually fulfilled in risk management applications

brief guaranteed state estimation by zonotopes this paper presents a new approach to guaranteed state estimation for non linear discrete time systems with a bounded description of noise and parameters the main result is an algorithm to compute a set that contains the states consistent with the measured output and the given noise and parameters this set is represented by a zonotope the size of the zonotope is minimized each sample time by an analytic expression or by solving a convex optimization problem interval arithmetic is used to calculate a guaranteed trajectory of the process state two examples have been provided to clarify the algorithm

kalman filtering for general discrete time linear systems recursive state estimation problems for explicit and implicit time invariant linear systems both for systems with and without unknown inputs can be formulated as a single problem usually referred to as descriptor kalman filtering solutions to this problem have been proposed in the literature however these solutions either neglect possible contributions of future dynamics to the current estimate or make unnecessary assumptions on the structure of the system in this paper the authors propose a solution to this problem which leads to a constructive method lifting these unnecessary assumptions this method uses a generalization of the shuffle algorithm

a comprehensive method for reachability analysis of uncertain nonlinear hybrid systems reachability analysis of nonlinear uncertain hybrid systems i e continuous discrete dynamical systems whose continuous dynamics guard sets and reset functions are defined by nonlinear functions can be decomposed in three algorithmic steps computing the reachable set when the system is in a given operation mode computing the discrete transitions i e detecting and localizing when and where the continuous flowpipe intersects the guard sets and aggregating the multiple trajectories that result from an uncertain transition once the whole flow pipe has transitioned so that the algorithm can resume this paper proposes a comprehensive method that provides a nicely integrated solution to the hybrid reachability problem at the core of the method is the concept of mspb i e geometrical object obtained as the minkowski sum of a parallelotope and an axes aligned box mspb are a way to control the over approximation of the taylor s interval integration method as they happen to be a specific type of zonotope they articulate perfectly with the zonotope bounding method that we propose to enclose in an optimal way the set of flowpipe trajectories generated by the transition process the method is evaluated both theoretically by analyzing its complexity and empirically by applying it to well chosen hybrid nonlinear examples

asymptotic stability of empirical processes and related functionals abstract let e be a space of observables in a sequence of trials n and define m n to be the empirical distributions of the outcomes we discuss the almost sure convergence of the sequence m n in terms of the weak topology of measures when the sequence n is assumed to be stationary in this respect the limit variable is naturally described as a certain canonical conditional distribution then given some functional defined on a space of laws the consistency of the estimators m n is investigated moreover a result on the asymptotic stability of the distribution of m n w r t certain transformations of the data is given

state bounding with ellipsoidal set description of the uncertainty the paper presents recursive algorithms for state bounding using ellipsoidal sets to describe the state uncertainties and to bound the process and observation noises the algorithms optimize each stage of updating according to the minimum volume and minimum trace criteria simulations compare the performance of the bounding algorithms with that of a kalman filter and investigate the influence of noise distribution within the bounds

h_ infty state estimation for complex networks with uncertain inner coupling and incomplete measurements in this paper the h state estimation problem is investigated for a class of complex networks with uncertain coupling strength and incomplete measurements with the aid of the interval matrix approach we make the first attempt to characterize the uncertainties entering into the inner coupling matrix the incomplete measurements under consideration include sensor saturations quantization and missing measurements all of which are assumed to occur randomly by introducing a stochastic kronecker delta function these incomplete measurements are described in a unified way and a novel measurement model is proposed to account for these phenomena occurring with individual probability with the measurement model a set of h state estimators is designed such that for all admissible incomplete measurements as well as the uncertain coupling strength the estimation error dynamics is exponentially mean square stable and the h performance requirement is satisfied the characterization of the desired estimator gains is derived in terms of the solution to a convex optimization problem that can be easily solved using the semidefinite program method finally a numerical simulation example is provided to demonstrate the effectiveness and applicability of the proposed design approach

complexity reduction through a schur based decomposition for reachability analysis of linear time invariant systems this article presents a method for complexity reduction in reachability analysis and safety preserving controller synthesis via schur based decomposition the decomposition results in either decoupled or weakly coupled lower dimensional subsystems reachable sets computed independently for each subsystem are back projected and intersected to yield an overapproximation of the actual reachable set moreover applying this technique to a class of unstable lti systems we show that when certain eigenvalue and state constraint conditions are satisfied further reduction of complexity is possible evaluating our method for a variety of examples we demonstrate that significant reduction in the computational costs can be achieved this technique has considerable potential utility for use in conjunction with computationally intensive reachability tools

stable interval observers in bbc for linear systems with time varying input bounds this technical note deals with the design of stable interval observers and estimators for continuous time linear dynamic systems under uncertain initial states and uncertain inputs enclosed within time varying zonotopic bounds no monotony assumption such as cooperativity is required in the vector field the interval observer stability directly derives from the stability of the observer state matrix where any poles real or complex single or multiple are handled in the same way

zonotopes and kalman observers state bounding observation based on zonotopes is the subject of this paper dealing with zonotopes is motivated by set operations resulting in simple matrix calculations with regard to the often huge number of facets and vertices of the equivalent polytopes discrete time ltv lpv systems with state and measurement uncertainties are considered based on a new zonotope size criterion called f w radius and by merging optimal and robust observer gain designs a zonotopic kalman filter zkf is proposed with a proof of robust convergence the notion of covariation is introduced and results in an explicit bridge between the zonotopic set membership and the stochastic paradigms for kalman filtering no intersection is used and the influence of the reduction operator limiting to a tunable maximum the size of the matrices involved in the zonotopic set computations is fully taken into account in the lmi based robust stability analysis a numerical example illustrates the effectiveness of the proposed zkf

separation axioms and the fuzzy real lines we show that for each lattice l which is completely distributive and equipped with an order reversing involution the canonical topology of the fuzzy real line l is uniformizable in the sense of hutton furthermore this uniformity induces a pseudometric which induces the canonical topology consequently l satisfies the higher order separation axioms of hutton and sarkar more generally we answer most of the open questions concerning l and its subspaces with respect to each of the separation axiom schemes of hutton and sarkar answer some of these same questions for the stratified fuzzy real line c l and its subspaces and analyze c l and its subspaces with respect to the separation axioms of rodabaugh

spreading and predictable sampling in exchangeable sequences and processes abstract rydll nardzewski 1957 proved that an infinite sequence of random variables is exchangeable if every subsequence has the same distribution this document discusses some restatements and extensions of this result in terms of martingales and stopping times in the other direction it is shown that the distribution of a finite or infinite exchangeable sequence is invariant under sampling by means of a s distinct but not necessarily ordered predictable stopping times both types of result generalize to exchangeable processes in continuous time author

a new method of reachable set estimation for time delay systems with polytopic uncertainties we address the reachable set bounding problem of linear systems subject to both time varying delay and polytopic uncertainties a novel criterion is established to give a more accurate description of the set which bounds the states starting from the origin by inputs with peak values by combining the maximal lyapunov functional and the reciprocally convex approach we obtain a tighter reachable set estimation with lower computational complexity the corresponding reachable set condition for the common lyapunov functional can be obtained naturally as a special case of the above result finally two examples illustrate the advantages of our proposed method

l fuzzy normal spaces and tietze extension theorem abstract in this paper we prove a characterization theorem for normal l fuzzy topological spaces l is an infinitely distributive lattice with an order reversing involution in the particular case l 0 1 this theorem reduces to a known result of kat tov fund math 38 1951 85 91 and tong duke math j 19 1952 289 292 as an important application we obtain a fuzzy version of tietze extension theorem this yields an affirmative answer to a question raised in a series of papers by rodabaugh fuzzy sets and systems 11 1983 163 183

the universal glivenko cantelli property let mathcal f be a separable uniformly bounded family of measurable functions on a standard measurable space x mathcal x and let n mathcal f varepsilon mu be the smallest number of varepsilon brackets in l1 needed to cover mathcal f the following are equivalent 1 mathcal f is a universal glivenko cantelli class 2 n mathcal f varepsilon mu 0 and every probability measure 3 mathcal f is totally bounded in l1 for every probability measure 4 mathcal f does not contain a boolean independent sequence it follows that universal glivenko cantelli classes are uniformity classes for general sequences of almost surely convergent random measures

probability guaranteed set membership filtering for systems with incomplete measurements in this note the probability guaranteed set membership filtering problem is investigated for a class of time varying systems with incomplete measurements the uniform distribution over known finite ranges is assumed for mutually independent stochastic variables existing in the functions of system matrices the process noise and measurement noise are unknown bounded and confined to a specified ellipsoidal set respectively which is handled by transformation to the inequality constraints the purpose is to design a set membership filter for all the admissible unknown but bounded noises known deterministic input and incomplete measurements such that the ellipsoidal set including all possible states can be determined by a convex optimization approach with probability constraint a recursive linear matrix inequality rlmi approach is proposed to address the probability guaranteed set membership filtering problem finally a simulation example demonstrates the effectiveness of the proposed filtering scheme

on stochastic linear systems with zonotopic support sets abstract this paper analyzes stochastic linear discrete time processes whose process noise sequence consists of independent and uniformly distributed random variables on given zonotopes we propose a cumulant based approach for approximating both the transient and limit distributions of the associated state sequence the method relies on a novel class of k symmetric lyapunov equations which are used to construct explicit expressions for the cumulants the state distribution is recovered via a generalized gram charlier expansion with respect to products of a multivariate variant of wigner s semicircle distribution using chebyshev polynomials of the second kind this expansion converges uniformly under surprisingly mild conditions to the exact state distribution of the system a robust feedback control synthesis problem is used to illustrate the proposed approach

a short note on constrained linear control systems with multiplicative ellipsoidal uncertainty this technical note revisits the classical robust control question of how to design linear control laws for uncertain linear dynamic systems we formulate this robust control design problem from a modern optimal control perspective which allows us to take into account control and state constraints that have to be satisfied by the closed loop system for all possible uncertainty scenarios the contribution of this technical note is the derivation of a conservative but computationally tractable robust control design problem formulation for the case that multiplicative uncertainties are present in the linear dynamic systems which render the robust control problem non convex in general here our approximation technique relies on propagating ellipsoidal bounds on the reachable states of the closed loop system the methods developed in this technical note can also be used as a building block for tube based model predictive control schemes where robustly designed linear control laws can help to reduce the conservatism of open loop predictions we illustrate the proposed techniques with a numerical case study

h infinity set membership observer design for discrete time lpv systems this paper presents a new set membership observer design method for discrete time linear parameter varying systems the real process is assumed to be perturbed by unknown but bounded disturbances

event triggered consensus control for discrete time stochastic multi agent systems this paper is concerned with the event triggered consensus control problem for a class of discrete time stochastic multi agent systems with state dependent noises a novel definition of consensus in probability is proposed to better describe the dynamics of the consensus process of the addressed stochastic multi agent systems the measurement output available for the controller is not only from the individual agent but also from its neighboring ones according to the given topology an event triggered mechanism is adopted with hope to reduce the communication burden where the control input on each agent is updated only when a certain triggering condition is violated the purpose of the problem under consideration is to design both the output feedback controller and the threshold of the triggering condition such that the closed loop system achieves the desired consensus in probability first of all a theoretical framework is established for analyzing the so called input to state stability in probability issip for general discrete time nonlinear stochastic systems within such a theoretical framework some sufficient conditions on event triggered control protocol are derived under which the consensus in probability is reached furthermore both the controller parameter and the triggering threshold are obtained in terms of the solution to certain matrix inequalities involving the topology information and the desired consensus probability finally a simulation example is utilized to illustrate the usefulness of the proposed control protocol

asymptotically convergent modified recursive least squares with data dependent updating and forgetting factor for systems with bounded noise continual updating of estimates required by most recursive estimation schemes often involves redundant usage of information and may result in system instabilities in the presence of bounded output disturbances an algorithm which eliminates these difficulties is investigated based on a set theoretic assumption the algorithm yields modified least squares estimates with a forgetting factor it updates the estimates selectively depending on whether the observed data contain sufficient information the information evaluation required at each step involves very simple computations in addition the parameter estimates are shown to converge asymptotically at an exponential rate to a region around the true parameter

probability guaranteed robust h performance analysis and state feedback design abstract this paper addresses the common engineering practice of specifying a required probability of attaining some performance level the problem setup is that of a robust h performance analysis state feedback synthesis of an affinely parameter dependent linear system except that the parameter hyper rectangle box is allowed to shrink representing a probability less than one in order to accommodate a polytopic performance goal that is better than the one attainable for the original parameter box a new version of the bounded real lemma brl which assigns a different lyapunov function to each of the vertices of the uncertainty polytope and includes a scalar free parameter seems to reduce the overdesign associated with the polytopic problem to the bare minimum the shrinking of the parameter box leads to bi linear matrix inequalities blmis since the final vertices are also unknown these blmis are solved iteratively three steps have sufficed both in the analysis and in the state feedback design examples a uniform distribution is assumed for all the system parameters following the uniformity principle the probability requirement is expressed by a set of linear matrix inequalities lmis that is derived by extending an existing second order cone method these lmis are concurrently solved with the blmis of the brl the features of the proposed method are demonstrated via two examples

reachability analysis of linear dynamic systems with constant arbitrary and lipschitz continuous inputs abstract this paper sets forth a method for reachability analysis of linear dynamic systems in continuous time that can be used to compute time domain bounds of states and outputs with floating point precision the focus is on the particular initial conditions and inputs that cause state or output trajectories to attain their extreme values in time inputs can be constant arbitrary or lipschitz continuous waveforms uncertainties in initial conditions and inputs are modeled using zonotopes the calculations exploit the definition of zonotopes and the modal information of the linear system dynamics

fuzzy addition in the l fuzzy real line abstract under the hypothesis l is a chain we construct a binary operation on the l fuzzy real line r l which reduces to the usual addition on r if is restricted to the embedded image of r in r l which yields a partially ordered abelian cancellation semigroup with identity and which is jointly fuzzy continuous on r l we show is unique i e it is the only extension of addition to r l which is consistent we study the relationship between and other fuzzy continuous extensions of the usual addition we also show that fuzzy translation is a weak fuzzy homeomorphism and under certain conditions a fuzzy homeomorphism

a categorical accommodation of various notions of fuzzy topology different definitions of fuzzy topology have been stated and developed in the literature but have not been satisfactorily related to each other and to ordinary topology to remedy this a new fuzzy topological category fuzz is defined it is a significant generalization of previous definitions it is the simplest setting yet constructed into which ordinary topology and these previous definitions may be placed by identifying each with a different subcategory of fuzz it therefore allows us to conveniently analyze the relative merits of previous definitions give coherence to known results and indicate appropriate directions for future development and it generates and may be viewed as both including and included in categories of fuzzy topological spaces which exhibit higher order fuzziness