prediction based stabilization of linear systems subject to input dependent input delay of integral type in this paper it is proved that a predictor based feedback controller can effectively yield asymptotic convergence for a class of linear systems subject to input dependent input delay this class is characterized by the delay being implicitly related to past values of the input via an integral model this situation is representative of systems where transport phenomena take place as is frequent in the process industry the sufficient conditions obtained for asymptotic stabilization bring a local result and require the magnitude of the feedback gain to be consistent with the initial conditions scale arguments of proof for this novel result include general halanay inequalities for delay differential equations and build on recent advances of backstepping techniques for uncertain or varying delay systems

determination of weights of interacting criteria from a reference set abstract in this paper we present a model allowing to determine the weights related to interacting criteria this is done on the basis of the knowledge of a partial ranking over a reference set of alternatives prototypes a partial ranking over the set of criteria and a partial ranking over the set of interactions between pairs of criteria

global stabilization of a class of nonlinear reaction diffusion partial differential equations by boundary feedback this paper provides global exponential stabilization results by means of boundary feedback control for one dimensional nonlinear unstable reaction diffusion partial differential equations pdes wi

some quantities represented by the choquet integral this paper shows that the choquet integral can represent some useful quantities such as supremum infimum essential supremum essential infimum mean median quantile 100 percentile and l estimators including trimmed mean

on equivalence classes of fuzzy connectives the case of fuzzy integrals an equivalence relation between connectives or operators in the framework of multiple criteria decision making is introduced two operators are said to be equivalent if they lead to the same ranking of alternatives some general results to find equivalence classes of operators are given through the concept of level surfaces in a second part these results are applied to the case of discrete fuzzy integrals which are considered here as n place operators first some general results on the situation of fuzzy integrals among fuzzy operators are given and then the equivalence classes of fuzzy integrals

assessing non additive utility for multicriteria decision aid abstract in the framework of multi attribute utility theory maut several methods have been proposed to build a decision maker s dm utility function representing his her preferences among such methods the uta method infers an additive utility function from a set of exemplary decisions using linear programming however the uta method does not guarantee to find a utility function which is coherent with the available information this drawback is due to the underlying utility model of uta viz the additive one which does not allow to include additional information such as an interaction among criteria in this paper we present a methodology for building a non additive utility function in the framework of the so called fuzzy integrals which permits to model preference structures with interaction between criteria like in the uta method we aim at searching a utility function representing the dm s preferences but unlike uta the functional form is a specific fuzzy integral choquet integral as a result we obtain weights which can be interpreted as the importance of coalitions of criteria exploiting the potential interaction between criteria as already proposed by other authors however within the same framework we obtain also the marginal utility functions relative to each one of the considered criteria that are evaluated on a common scale as a consequence of the implemented methodology finally we illustrate our approach with an example

generalizations of owa operators owa operators can be seen as symmetrized weighted arithmetic means as choquet integrals with respect to symmetric measures or as comonotone additive functionals following these three different looks on owas we discuss several already known generalizations of owa operators including gowa iowa oma operators as well as we propose new types of such generalizations

completion and continuation of nonlinear traffic time series a probabilistic approach when dealing with nonlinear time series of car traffic on highways one of the outstanding problems to be solved is completion and continuation of data in space and time to this end the underlying process is decomposed into stochastic and deterministic components the former is approximated by gaussian white noise while the latter refers apart from always existing trends to the space and time dependent jam propagation process jams are modelled in terms of dynamical bayesian networks with radial basis functions involved the models developed are used to tackle travel time estimation and prediction results are obtained for one of the most crowded traffic areas of europe namely the ring like highway around cologne

compensation of wave actuator dynamics for nonlinear systems the problem of stabilization of pde ode cascades has been solved in the linear case for several pde classes whereas in the nonlinear case the problem has been solved only for the transport delay pde namely for compensation of an arbitrary delay at the input of a nonlinear plant motivated by a specific engineering application in off shore drilling we solve the problem of stabilization of the cascade of a wave pde with a general nonlinear ode due to the presence of nonlinearities of arbitrary growth and the time reversibility of the wave pde and due to the possibility of using arguments based on lyapunov functionals or explicit solutions several stability analysis approaches are possible we present stability results in the h 2 times h 1 and c 1 times c 0 norms for general nonlinear odes as well as in the h 1 times l 2 norm for linear odes we specialize our general design for wave pde ode cascades to the case of a wave pde whose uncontrolled end does not drive an ode but is instead governed by a nonlinear robin boundary condition a nonlinear spring as in the friction law in drilling this is the first global stabilization result for wave equations that incorporate non collocated destabilizing nonlinearities of superlinear growth we present two numerical examples one with a nonlinear ode and one with a nonlinear spring at the uncontrolled boundary of the wave pde

predicting time series using a neural network as a method of distinguishing chaos from noise a neural network approach is presented for making short term predictions on time series the neural network does better at short term predictions of a chaotic signal than does an optimum autoregressive model also the neural network is clearly capable of distinguishing between chaos and additive noise

brief paper lyapunov tools for predictor feedbacks for delay systems inverse optimality and robustness to delay mismatch we consider lti finite dimensional completely controllable but possibly open loop unstable plants with arbitrarily long actuator delay and the corresponding predictor based feedback for delay compensation we study the problem of inverse optimal re design of the predictor based feedback law we obtain a simple modification of the basic predictor based controller which employs a low pass filter and has been proposed previously by mondie and michiels for achieving robustness to discretization of the integral term in the predictor feedback law the key element in our work is the employment of an infinite dimensional backstepping transformation and the resulting lyapunov function for the infinite dimensional systems consisting of the state of the ode plant and the delay state the lyapunov function allows us to quantify the lyapunov stability properties under the modified feedback the inverse optimality of the feedback and its disturbance attenuation properties for the basic predictor feedback the availability of the lyapunov function also allows us to prove robustness to small delay mismatch in both positive and negative directions

nonlinear component analysis as a kernel eigenvalue problem a new method for performing a nonlinear form of principal component analysis is proposed by the use of integral operator kernel functions one can efficiently compute principal components in high dimensional feature spaces related to input space by some nonlinear map for instance the space of all possible five pixel products in 16 16 images we give the derivation of the method and present experimental results on polynomial feature extraction for pattern recognition

time series prediction by feedforward neural networks is it difficult the difficulties that a neural network faces when trying to learn from a quasiperiodic time series are studied analytically using a teacher student scenario where the random input is divided into two macroscopic regions with different variances 1 and 1 2 1 t he generalization error is found to decrease

the application of fuzzy integrals in multicriteria decision making abstract this paper presents a synthesis on the application of fuzzy integrals as an innovative tool for criteria aggregation in decision problems the main point is that fuzzy integrals are able to model interaction between criteria in a flexible way the methodology has been elaborated mainly in japan and has been applied there successfully in various fields such as design reliability evaluation of goods etc it seems however that this technique is still very little known in europe it is one of the aims of this review to disseminate this emerging technology in many industrial fields

improved time series prediction with a new method for selection of model parameters a new method for model selection in prediction of time series is proposed apart from the conventional criterion of minimizing rms error the method also minimizes the error on the distribution of singularities evaluated through the local holder estimates and its probability density spectrum predictions of two simulated and one real time series have been done using kernel principal component regression kpcr and model parameters of kpcr have been selected employing the proposed as well as the conventional method results obtained demonstrate that the proposed method takes into account the sharp changes in a time series and improves the generalization capability of the kpcr model for better prediction of the unseen test data

relaxation and phase space singularities in time series of human magnetoencephalograms as indicator of photosensitive epilepsy to analyze the crucial role of fluctuation and relaxation effects for the function of the human brain we studied some statistical quantifiers that support the information characteristics of neuromagnetic brain responses magnetoencephalogram meg the signals to a flickering stimulus of different color combinations have been obtained from a group of control subjects which is then contrasted with those of a patient suffering photosensitive epilepsy pse we found that the existence of the specific stratification of the phase clouds and the concomitant relaxation singularities of the corresponding nonequilibrium dynamics of the chaotic behavior of the signals in separate areas in a patient provide likely indicators for the zones which are responsible for the appearance of pse

robustness of nonlinear predictor feedback laws to time and state dependent delay perturbations much recent progress has been achieved for stabilization of linear and nonlinear systems with input delays that are long and dependent on either time or the plant state provided the dependence is known in this paper we consider the delay variations as unknown and study robustness of nominal constant delay predictor feedbacks under delay variations that depend on time and the state we show that when the delay perturbation and its rate have sufficiently small magnitude the local asymptotic stability of the closed loop system under the nominal predictor based design is preserved for the special case of linear systems and under only time varying delay perturbations we prove robustness of global exponential stability of the predictor feedback when the delay perturbation and its rate are small in any one of four different metrics we present two examples one that is concerned with the control of a dc motor through a network and one of a teleoperation like system

wavelet transform based multifractal formalism in outlier detection and localisation for financial time series we present a method of detecting and localising outliers in financial time series and other stochastic processes the method checks the internal consistency of the scaling behaviour of the process within the paradigm of the multifractal spectrum deviation from the expected spectrum is interpreted as the potential presence of outliers the detection part of the method is then supplemented by the localisation analysis part using the local scaling properties of the time series localised outliers can then be removed one by one with the possibility of dynamic verification of spectral properties both the multifractal spectrum formalism and the local scaling properties of the time series are implemented on the wavelet transform modulus maxima tree

compensating a string pde in the actuation or sensing path of an unstable ode how to control an unstable linear system with a long pure delay in the actuator path this question was resolved using predictor or finite spectrum assignment designs in the 1970s here we address a more challenging question how to control an unstable linear system with a wave partial differential equation pde in the actuation path physically one can think of this problem as having to stabilize a system to whose input one has access through a string the challenges of overcoming string wave dynamics in the actuation path include their infinite dimension finite propagation speed of the control signal and the fact that all of their infinitely many eigenvalues are on the imaginary axis in this technical note we provide an explicit feedback law that compensates the wave pde dynamics at the input of an linear time invariant ordinary differential equation and stabilizes the overall system in addition we prove robustness of the feedback to the error in a priori knowledge of the propagation speed in the wave pde finally we consider a dual problem where the wave pde is in the sensing path and design an exponentially convergent observer

multifractal formalism for fractal signals the structure function approach versus the wavelet transform modulus maxima method several attempts have been made recently to generalize the multifractal formalism originally introduced for singular measures to fractal signals we report on a systematic comparison between the structure function approach pioneered by parisi and frisch in 2 proceedings of the international school on turbulence and predictability in geophysical fluid dynamics and climate dynamics edited by m ghil r benzi and g parisi north holland amsterdam 1985 p 84 to account for the multifractal nature of fully developed turbulent signals and an alternative method we have developed within the framework of the wavelet transform analysis we comment on the intrinsic limitations of the structure function approach this technique has fundamental drawbacks and does not provide a full characterization of the singularities of a signal in many cases we demonstrate that our method based on the wavelet transform modulus maxima representation works in most situations and is likely to be the ground of a unified multifractal description of self affine distributions our theoretical considerations are both illustrated on pedagogical examples and supported by numerical simulations

k order additive discrete fuzzy measures and their representation abstract in order to face with the complexity of discrete fuzzy measures we propose the concept of k orderadditive fuzzy measure including usual additive measures and fuzzy measures every discrete fuzzy measure is a k order additive fuzzy measure for a unique k a related topic of the paper is to introduce an alternative representation of fuzzy measures called the interaction representation which sets and extends in a common framework the shapley value and the interaction index proposed by murofushi and soneda

an axiomatic approach of the discrete sugeno integral as a tool to aggregate interacting criteria in a qualitative framework we present a model allowing us to aggregate decision criteria when the available information is of a qualitative nature the use of the sugeno integral as an aggregation function is justified by an axiomatic approach it is also shown that the mutual preferential independence of criteria reduces the sugeno integral to a dictatorial aggregation

linear systems with delayed controls a reduction linear systems with delayed control action are transformed into systems without delays under an absolute continuity condition the new system is an ordinary differential control equation in the general case the new system is a measure differential control system it is shown how the controllability stabilization and various optimization problems can be analyzed via the reduced systems

holder exponent spectra for human gait abstract the stride interval time series in normal human gait is not strictly constant but fluctuates from step to step in a complex manner more precisely it has been shown that the control process for human gait is a fractal random phenomenon that is one with a long term memory herein we study the holder exponent spectra for the slow normal and fast gaits of 10 young healthy men in both free and metronomically triggered conditions and establish that the stride interval time series is more complex than a monofractal phenomenon a slightly multifractal and non stationary time series under the three different gait conditions emerges

control of transport pde nonlinear ode cascades with state dependent propagation speed in this paper we deal with the control of a transport partial differential equation nonlinear ordinary differential equation pde nonlinear ode cascade system in which the transport coefficient depends on the ode state we develop a pde based predictor feedback boundary control law which compensates the transport dynamics of the actuator and guarantees global asymptotic stability of the closed loop system the stability proof is based on an infinite dimensional backstepping transformation and a lyapunov like argument the relation of the pde ode cascade with a state dependent propagation speed to an ode system with a state dependent input delay which is defined implicitly via an integral of past values of the ode state is also highlighted and the corresponding equivalent predictor feedback design is presented together with an alternative proof of global asymptotic stability of the closed loop system based on the construction of a lyapunov functional the practical relevance of our control framework is illustrated in an example that is concerned with the control of a metal rolling process

novel survival functions based on conditional aggregation operators abstract in this paper we define a novel survival function motivated by real life problems which generalizes the super level measure introduced by do and thiele 2015 this concept is based on conditional aggregation operators extending the definition of aggregation operators introduced by calvo et al 2002 for all bounded measurable functions and not only for finite sequences some basic properties and several examples of conditional aggregation operators are presented using the novel survival function the choquet stieltjes functional is introduced and the conditions are indicated under which this functional can be called an integral the new functional generalizes several known integrals including the choquet stieltjes integral as well as choquet integral with respect to level dependent capacity introduced by greco et al 2011

control and state estimation of the one phase stefan problem via backstepping design this paper develops a control and estimation design for the one phase stefan problem the stefan problem represents a liquid solid phase transition as time evolution of a temperature profile in a liquid solid material and its moving interface this physical process is mathematically formulated as a diffusion partial differential equation pde evolving on a time varying spatial domain described by an ordinary differential equation ode the state dependency of the moving interface makes the coupled pde ode system a nonlinear and challenging problem we propose a full state feedback control law an observer design and the associated output feedback control law of both neumann and dirichlet boundary actuations via the backstepping method also the state feedback control law is provided when a robin boundary input is considered the designed observer allows the estimation of the temperature profile based on the available measurements of liquid phase length and the heat flux at the interface the associated output feedback controller ensures the global exponential stability of the estimation errors the mathcal h 1 norm of the distributed temperature and the moving interface at the desired setpoint under some explicitly given restrictions on the setpoint and observer gain

k maxitive aggregation functions abstract inspired by the idea of k maxitive measures we introduce and study k maxitive aggregation functions in particular 1 maxitive aggregation functions are shown to be just maxitive aggregation functions i e maxima of distorted inputs we introduce among others a representation of symmetric k maxitive aggregation functions moreover we show that for any k maxitive capacity and the smallest universal integral based on an arbitrary fixed semicopula including the sugeno and shilkret integrals the resulting aggregation function is k maxitive

stabilization by means of approximate predictors for systems with delayed input sufficient conditions for global stabilization of nonlinear systems with delayed input by means of approximate predictors are presented an approximate predictor is a mapping which approximates the exact values of the stabilizing input for the corresponding system with no delay a systematic procedure for the construction of approximate predictors is provided for globally lipschitz systems the resulting stabilizing feedback can be implemented by means of a dynamic distributed delay feedback law illustrative examples show the efficiency of the proposed control strategy

the choquet integral with respect to a level dependent capacity we present a generalization of choquet integral in which the capacity depends also on the value of the aggregated variables we show that as particular cases of our generalization of choquet integral there are the sugeno integral the sipos integral and the cumulative prospect theory functional we also show that many concepts such as mobius transform importance index interaction index k order capacities and owa operators introduced in the research about choquet integral can be generalized in the considered context