delay dependent h filtering for singular markovian jump systems with general uncomplete transition probabilities this paper is devoted to the investigation of the delay dependent h filtering problem for a kind of singular markovian jump time delay systems with general unknown transition probabilities in this model the transition rates of the jumping process are assumed to be partly available that is some elements have been exactly known some ones have been merely known with lower and upper bounds others may have no information to use using the lyapunov functional theory a stochastically stable filter is designed to guarantee both the mean square exponential admissibility and a prescribed level of h performance for the singular markovian jump time delay systems with general unknown transition probabilities a sufficient condition is derived for the existence of such a desired filter in terms of linear matrix inequalities lmis a numerical example is provided to demonstrate the effectiveness of the proposed theory

optimal experimental designs in the flow rate of particles this article focuses on analyzing the process of jam formation during the discharge by gravity of granular material stored in a two dimensional silo the aim of the article is two fold first optimal experimental designs are computed in which four approaches are considered d optimality a combination of d optimality and a cost gain function bayesian d optimality and sequential designing these results reveal that the efficiency of the design used by the experimenters can be improved dramatically a sensitivity analysis with respect to the most important parameter is also performed second estimation of the unknown parameters is done using least squares that is assuming normality and also via maximum likelihood assuming the exponential distribution simulations for the designs considered in this article show that the variance the mean squared error and the bias of the estimators using maximum likelihood are in most cases lower than those using least squares supplementary materials for this arti

a foundation on semigroups of operators defined on the set of triangular fuzzy numbers and its application to fuzzy fractional evolution equations abstract in this article we study the strongly continuous semigroups of fuzzy valued operators defined on the space of triangular fuzzy numbers new notions of fuzzy infinitesimal generators and fuzzy resolvent operators of fuzzy semigroups are established in the sense of the generalized hukuhara difference a hille yosida like theorem in the framework of fuzzy metric space is investigated we demonstrate the efficiency of theoretical results by studying the existence of mild solutions of fuzzy nonlinear fractional evolution equations

the use of a canonical form in the construction of locally optimal designs for non linear problems optimal experimental designs for non linear problems depend on the values of the underlying undknown parameters in the model for various reasons there is interest in providing explicit formulae for the optimal designs as a function of the unknown parameters this paper shows that for a certain class of generalized linear models the problem can be reduced to a canonical form this simplifies the underlying problem and designs are constructed for several contexts with a single variable using geometric and other arguments

computation of minimum volume covering ellipsoids we present a practical algorithm for computing the minimum volume n dimensional ellipsoid that must contain m given points a1 am n this convex constrained problem arises in a variety of applied computational settings particularly in data mining and robust statistics its structure makes it particularly amenable to solution by interior point methods and it has been the subject of much theoretical complexity analysis here we focus on computation we present a combined interior point and active set method for solving this problem our computational results demonstrate that our method solves very large problem instances m 30 000 and n 30 to a high degree of accuracy in under 30 seconds on a personal computer

fractional calculus for interval valued functions abstract we use a generalization of the hukuhara difference for closed intervals on the real line to develop a theory of the fractional calculus for interval valued functions the properties of riemann liouville fractional integral riemann liouville fractional derivative and caputo fractional derivative for interval valued functions are investigated several examples are presented to illustrate the concepts and results

nonlinear iteration semigroups of fuzzy cauchy problems in this paper we introduce an iteration semigroup of a nonlinear fuzzy valued function we show that the iterates converge and the limit function called the fuzzy exponential function is a solution to an autonomous fuzzy cauchy problem

stochastic stability of jump linear systems in this note some testable conditions for mean square i e second moment stability for discrete time jump linear systems with time homogenous and time inhomogenous finite state markov chain form processes are presented

almost sure instability of the random harmonic oscillator the problem of almost sure stability of the random harmonic oscillator with a jump process coefficient is studied it is shown that the sample paths are almost surely unstable and an asymptotic series expansion in the powers of the noise strength for the asymptotic exponential growth rate is obtained

optimal design for additive partially nonlinear models we develop optimal design theory for additive partially nonlinear regression models showing that bayesian and standardized maximin d optimal designs can be found as the products of the corresponding optimal designs in one dimension a sufficient condition under which analogous results hold for ds optimality is derived to accommodate situations in which only a subset of the model parameters is of interest to facilitate prediction of the response at unobserved locations we prove similar results for q optimality in the class of all product designs the usefulness of this approach is demonstrated through an application from the automotive industry where optimal designs for least squares regression splines are determined and compared with designs commonly used in practice

h sub infinity control and quadratic stabilization of systems with parameter uncertainty via output feedback the article concerns linear systems which are subject to both time varying norm bounded parameter uncertainty and exogenous disturbance it addresses the robust h sub infinity control problem of designing a linear dynamic output feedback controller such that the closed loop system is quadratically stable and achieves a prescribed level of disturbance attenuation for all admissible parameter uncertainties it is shown that such a problem is equivalent to a scaled h sub infinity control problem

generalized differentiability of fuzzy valued functions in the present paper using novel generalizations of the hukuhara difference for fuzzy sets we introduce and study new generalized differentiability concepts for fuzzy valued functions several properties of the new concepts are investigated and they are compared to similar fuzzy differentiabilities finding connections between them characterization and relatively simple expressions are provided for the new derivatives

on the solution of fuzzy fractional optimal control problems with the caputo derivative abstract this paper presents an extension to fractional optimal control problems with ambiguity as the ambiguity is modeled with fuzzy method we encounter with a fuzzy fractional optimal control problem the objective in fuzzy fractional optimal control problem is to determine the best possible fuzzy control which satisfies the related fuzzy fractional dynamic systems and minimizes the fuzzy performance index here the fractional derivative is described in the caputo sense to find the solution first we state some definitions and prove some required theorems then we employ the obtained result to determine the necessary conditions furthermore we show that the obtained necessary optimality conditions become sufficient by considering some extra assumptions finally some examples are presented for more illustration of the subject

nonlinear experiments optimal design and inference based on likelihood abstract nonlinear experiments involve response and regressors that are connected through a nonlinear regression type structure examples of nonlinear models include standard nonlinear regression logistic regression probit regression poisson regression gamma regression inverse gaussian regression and so on the fisher information associated with a nonlinear experiment is typically a complex nonlinear function of the unknown parameter of interest as a result we face an awkward situation designing an efficient experiment will require knowledge of the parameter but the purpose of the experiment is to generate data to yield parameter estimates our principal objective here is to investigate proper designing of nonlinear experiments that will let us construct efficient estimates of parameters we focus our attention on a very general nonlinear setup that includes many models commonly encountered in practice the experiments considered have two fundamental stages a static design in the initial stage

generalizations of the differentiability of fuzzy number valued functions with applications to fuzzy differential equations the usual concept of differentiability of fuzzy number valued functions has the following shortcoming if c is a fuzzy number and g a b r is an usual real valued function differentiable on x 0 a b with g x 0 0 then f x c g x is not differentiable on x 0 in this paper we introduce and study generalized concepts of differentiability of any order n n which solves this shortcoming newton leibnitz type formula is obtained and existence of the solutions of fuzzy differential equations involving generalized differentiability is studied also some concrete applications to partial and ordinary fuzzy differential equations with fuzzy input data of the form c g x are given

control of markovian jump discrete time systems with norm bounded uncertainty and unknown delay this paper studies the problem of control for discrete time delay linear systems with markovian jump parameters the system under consideration is subjected to both time varying norm bounded parameter uncertainty and unknown time delay in the state and markovian jump parameters in all system matrices we address the problem of robust state feedback control in which both robust stochastic stability and a prescribed h sub spl infin performance are required to be achieved irrespective of the uncertainty and time delay it is shown that the above problem can be solved if a set of coupled linear matrix inequalities has a solution

stochastic stability properties of jump linear systems jump linear systems are defined as a family of linear systems with randomly jumping parameters usually governed by a markov jump process and are used to model systems subject to failures or changes in structure the authors study stochastic stability properties in jump linear systems and the relationship among various moment and sample path stability properties it is shown that all second moment stability properties are equivalent and are sufficient for almost sure sample path stability and a testable necessary and sufficient condition for second moment stability is derived the lyapunov exponent method for the study of almost sure sample stability is discussed and a theorem which characterizes the lyapunov exponents of jump linear systems is presented finally for one dimensional jump linear system it is proved that the region for delta moment stability is monotonically converging to the region for almost sure stability at delta down arrow 0 sup

brief paper stability and stabilization of markovian jump linear systems with partly unknown transition probabilities in this paper the stability and stabilization problems of a class of continuous time and discrete time markovian jump linear system mjls with partly unknown transition probabilities are investigated the system under consideration is more general which covers the systems with completely known and completely unknown transition probabilities as two special cases the latter is hereby the switched linear systems under arbitrary switching moreover in contrast with the uncertain transition probabilities studied recently the concept of partly unknown transition probabilities proposed in this paper does not require any knowledge of the unknown elements the sufficient conditions for stochastic stability and stabilization of the underlying systems are derived via lmis formulation and the relation between the stability criteria currently obtained for the usual mjls and switched linear systems under arbitrary switching are exposed by the proposed class of hybrid systems two numerical examples are given to show the validity and potential of the developed results

sequential experimental designs for generalized linear models we consider the problem of experimental design when the response is modeled by a generalized linear model glm and the experimental plan can be determined sequentially most previous research on this problem has been limited either to one factor binary response experiments or to augmenting the design when there are already sufficient data to compute parameter estimates we suggest a new procedure for the sequential choice of observations that offers five important advantages 1 it can be applied to multifactor experiments and is not limited to the one factor setting 2 it can be used with any glm not just binary responses 3 both fully sequential and group sequential settings are treated 4 it enables efficient design from the outset of the experiment and 5 the experimenter is not constrained to specify a single model and can use the prior to reflect uncertainty as to the link function and the form of the linear predictor our procedure is based on a d optimality criterion and on a bayesian

on fuzzy solutions for heat equation based on generalized hukuhara differentiability abstract in this paper a fuzzy heat equation with fuzzy initial values is considered the concept of generalized hukuhara differentiation is interpreted thoroughly in the univariate and multivariate cases and also several properties for generalized hukuhara differentiability are obtained on the topics such as switching point the univariate and multivariate fuzzy chain rules fuzzy mean value theorem among others the objective of this paper is to prove the uniqueness of a solution for a fuzzy heat equation and show that a fuzzy heat equation can be modeled as two systems of fuzzy differential equations by considering the type of differentiability of solutions finally some examples show the behavior of the solutions obtained

stochastic stability analysis for continuous time fault tolerant control systems active fault tolerant control systems are feedback control systems that reconfigure the control law in real time based on the response from an automatic failure detection and identification fdi scheme the dynamic behaviour of such systems is characterized by stochastic differential equations because of the random nature of the failure events and the fdi decisions the stability analysis of these systems is addressed in this paper using stochastic lyapunov functions and supermartingale theorems both exponential stability in the mean square and almost sure asymptotic stability in probability are addressed in particular for linear systems where the coefficients of the closed loop system dynamics are functions of two random processes with markovian transition characteristics one representing the random failures and the other representing the fdi decision behaviour necessary and sufficient conditions for exponential stability in the mean square are developed

new approach for studying nonlocal problems related to differential systems and partial differential equations in generalized fuzzy metric spaces abstract this study considers the solvability of nonlocal problems for fuzzy differential systems under gh differentiability using some linear transforms we convert partial differential equations into fuzzy integral systems before some similar results are obtained for fuzzy wave equations with nonlocal conditions as a consequence we give some further estimates of the convergence rates of approximation schemes to exact solutions the main tool used in our proofs is based on perov s fixed point principle which is applied to vector valued integral operators these operators appear as the sum of two integral operators where one is fredholm type and the other is of a volterra type that depends on the restriction of the domain the novel feature of this study is that we combine the matrix convergent to zero technique with calculations of fuzzy valued functions in generalized fuzzy metric spaces some examples are presented to demonstrate our theoretical results

stabilization of jump linear gaussian systems without mode observations systems such as those subject to abrupt changes including failure or those with uncertain dynamic model or more than one possible model can be naturally modelled as jump linear jl systems because of their applications in fields such as tracking fault tolerant control manufacturing process and robots jl systems have drawn extensive attention the optimal control and stabilization problem for jl systems when the mode system model is not assumed to be directly and perfectly observed a realistic assumption in many applications is nonlinear and prohibitive both analytically and computationally because of the dual effect the main contribution of this work is the sufficient condition for stabilization for a class of adaptive controllers when the mode is not directly observed we first present the optimal controller under an assumption of a certain type of mode availability using this optimal feedback gain we derive a condition that ensures the stabilizing property for a class of adaptive cont

brief constrained quadratic state feedback control of discrete time markovian jump linear systems in this paper we consider the quadratic optimal control problem of a discrete time markovian jump linear system subject to constraints on the state and control variables it is desired to find a state feedback controller which may also depend on the jump variable that minimizes a quadratic cost and satisfies some upper bounds on the norms of some random variables related to the state and control variables of the system the transition probability of the markov chain and initial condition of the system may belong to appropriate convex sets we obtain an approximation for the optimal solution of this problem in terms of linear matrices inequalities so that convex programming can be used for numerical calculations examples are presented to illustrate the usefulness of the developed results

controllability stabilizability and continuous time markovian jump linear quadratic control consideration is given to the control of continuous time linear systems that possess randomly jumping parameters which can be described by finite state markov processes the relationship between appropriately defined controllability stabilizability properties and the solution of the infinite time jump linear quadratic jlq optimal control problems is also examined although the solution of the continuous time markov jlq problem with finite or infinite time horizons is known only sufficient conditions for the existence of finite cost constant stabilizing controls for the infinite time problem appear in the literature in this paper necessary and sufficient conditions are established these conditions are based on new definitions of controllability observability stabilizability and detectability that are appropriate for continuous time markovian jump linear systems these definitions play the same role for the jlq problem as the deterministic properties do for the linear quadratic regulator lqr problem

performance of the maximum likelihood constant frequency estimator for frequency tracking the performance of maximum likelihood ml estimators for an important frequency estimation problem is considered when the signal model assumptions are not valid the motivation for this problem is to understand the robustness of the hidden markov model maximum likelihood hmm ml tandem frequency estimator where the signal is divided into time blocks and the frequency in each time block is estimated using the ml approach under the assumption that the signal has a constant frequency in each time block in order to analyze the sensitivity of ml estimators to the model assumptions the mean frequency of a discrete complex tone that has a time varying ramp frequency is estimated under the incorrect assumption that it has a constant frequency in particular the behavior of the threshold region with respect to different chirp rates is analyzed and a simple rule is given the mean squared error above the threshold region is shown to be constant even at very high snr levels these results are supported by simulations

statistical modeling and analysis for robust synthesis of nanostructures we systematically investigate the best process conditions that ensure synthesis of different types of one dimensional cadmium selenide nanostructures with high yield and reproducibility through a designed experiment and rigorous statistical analysis of experimental data models linking the probabilities of obtaining specific morphologies to the process variables are developed a new iterative algorithm for fitting a multinomial generalized linear model is proposed and used the optimum process conditions which maximize the preceding probabilities and make the synthesis process robust i e less sensitive to variations in process variables around set values are derived from the fitted models using monte carlo simulations cadmium selenide has been found to exhibit one dimensional morphologies of nanowires nanobelts and nanosaws often with the three morphologies being intimately intermingled within the as deposited material a slight change in growth condition can result in a totally different morpho

a d optimal design for estimation of parameters of an exponential linear growth curve of nanostructures we consider the problem of determining an optimal experimental design for estimation of parameters of a class of complex curves characterizing nanowire growth that is partially exponential and partially linear locally d optimal designs for some of the models belonging to this class are obtained by using a geometric approach further a bayesian sequential algorithm is proposed for obtaining d optimal designs for models with a closed form solution and for obtaining efficient designs in situations where theoretical results cannot be obtained the advantages of the proposed algorithm over traditional approaches adopted in recently reported nanoexperiments are demonstrated using monte carlo simulations the computer code implementing the sequential algorithm is available as supplementary materials

a survey on fuzzy fractional differential and optimal control nonlocal evolution equations abstract we survey some representative results on fuzzy fractional differential equations controllability approximate controllability optimal control and optimal feedback control for several different kinds of fractional evolution equations optimality and relaxation of multiple control problems described by nonlinear fractional differential equations with nonlocal control conditions in banach spaces are considered

the solvability of fuzzy fractional partial differential equations under caputo gh differentiability the foundation of the concepts of fuzzy fractional integral and caputo gh partial for fuzzy valued multivariable functions is defined as a result fuzzy fractional partial differential equations are considered and the appropriateness of local boundary value problems for hyperbolic equations is proved we present two new results on the existence of two kinds of gh weak solutions of these problems the first result is based on the banach fixed point theorem with the lipschitz condition of functions on the right hand side of equations the second result is based on the nonlinear alternative of the schauder type for fuzzy valued continuous functions without the lipschitz condition moreover we indicate the boundedness and continuous dependence of solutions on the initial data of the problems our models are embedded in the sense of caputo gh differentiability some examples are presented to illustrate the results

h control for discrete time markov jump systems with uncertain transition probabilities in this technical note the h control problem for a class of discrete time markov jump systems mjss with uncertain transition probabilities tps is investigated the uncertain information of transition probabilities is quantized by gaussian transition probability density function pdf in light of the proposed descriptions the mjss with gaussian pdf of tps cover the systems with precisely known and partially known tps as two special cases sufficient conditions for the existence of h controller of the underlying systems are derived in term of linear matrix inequalities a numerical example is presented to illustrate the effectiveness and potential of the developed theoretical results

discrete time markovian jump linear quadratic optimal control this paper is concerned with the optimal control of discrete time linear systems that possess randomly jumping parameters described by finite state markov processes for problems having quadratic costs and perfect observations the optimal control laws and expected costs to go can be precomputed from a set of coupled riccati like matrix difference equations necessary and sufficient conditions are derived for the existence of optimal constant control laws which stabilize the controlled system as the time horizon becomes infinite with finite optimal expected cost

robust stabilization of uncertain linear systems quadratic stabilizability and h sup infinity control theory the problem of robustly stabilizing a linear uncertain system is considered with emphasis on the interplay between the time domain results on the quadratic stabilization of uncertain systems and the frequency domain results on h sup infinity optimization a complete solution to a certain quadratic stabilization problem in which uncertainty enters both the state and the input matrices of the system is given relations between these robust stabilization problems and h sup infinity control theory are explored it is also shown that in a number of cases if a robust stabilization problem can be solved via lyapunov methods then it can be also be solved via h sup infinity control theory based methods

transition probability bounds for the stochastic stability robustness of continuous and discrete time markovian jump linear systems this paper considers the robustness of stochastic stability of markovian jump linear systems in continuous and discrete time with respect to their transition rates and probabilities respectively the continuous time discrete time system is described via a continuous valued state vector and a discrete valued mode which varies according to a markov process chain by using stochastic lyapunov function approach and kronecker product transformation techniques sufficient conditions are obtained for the robust stochastic stability of the underlying systems which are in terms of upper bounds on the perturbed transition rates and probabilities analytical expressions are derived for scalar systems which are straightforward to use numerical examples are presented to show the potential of the proposed techniques

random fuzzy fractional integral equations theoretical foundations abstract this paper presents mathematical foundations for studies of random fuzzy fractional integral equations which involve a fuzzy integral of fractional order we consider two different kinds of such equations their solutions have different geometrical properties the equations of the first kind possess solutions with trajectories of nondecreasing diameter of their consecutive values on the other hand the solutions to equations of the second kind have trajectories with nonincreasing diameter of their consecutive values firstly the existence and uniqueness of solutions is investigated this is showed by using a method of successive approximations an estimation of error of n th approximation is given also a boundedness of the solution is indicated to show well posedness of the considered theory we prove that solutions depend continuously on the data of the equations some concrete examples of random fuzzy fractional integral equations are solved explicitly

output feedback for a class of linear systems with stochastic jump parameters a class of linear systems subject to sudden jumps in parameter values is studied for a quadratic performance index the optimal controller has already been proposed it consists of a full state feedback that requires the synthesis of an observer for the plant state and mode to avoid this difficulty the present note develops new results that lead to the selection of the best feedback control law depending only on measurable outputs necessary optimality conditions are derived and two computationnal algorithms proposed an example is included

on a partially observable lqg problem for systems with markovian jumping parameters in this paper a variant of the lqg problem for systems with markovian jumping parameters is studied it is assumed that the system is partially observable in the sense that we do not have access to the jumping parameter via nonlinear filtering the problem is recast as one with complete information it is then shown that a certain averaged control is an optimal policy vis a vis a modified quadratic cost apart from its intrinsic theoretical interest this result has an important bearing on a number of different analyses related with the original quadratic cost

stabilization of continuous time jump linear systems we investigate almost sure and moment stabilization of continuous time jump linear systems with a finite state markov jump form process we first clarify the concepts of spl delta moment stabilizability exponential spl delta moment stabilizability and stochastic spl delta moment stabilizability we then present results on the relationships among these concepts coupled riccati equations that provide necessary and sufficient conditions for mean square stabilization are given in detail and an algorithm for solving the coupled riccati equations is proposed moreover we show that individual mode controllability implies almost sure stabilizability which is not true for other types of stabilizability finally we present some testable sufficient conditions for spl delta moment stabilizability and almost sure stabilizability

stabilisation of mode dependent singular markovian jump systems with generally uncertain transition rates this paper is devoted to investigating the stability and stabilisation problems for continuous time mode dependent singular markovian jump systems smjss with generally uncertain transition rates gutrs first we establish a sufficient condition in terms of a set of coupled linear matrix inequalities lmis to ensure the systems to be regular impulse free and stochastically stable then we design a mode dependent state feedback controller to guarantee the closed loop systems stochastically admissible by applying the lmi technique finally a numerical example is presented to illustrate the effectiveness and efficiency of the proposed method