necessary and sufficient small gain conditions for integral input to state stable systems a lyapunov perspective this paper is concerned with conditions for the stability of interconnected nonlinear systems consisting of integral input to state stable iiss systems with external inputs the treatment of iiss and input to state stable iss systems is unified both necessary conditions and sufficient conditions are investigated using a lyapunov formulation in the presence of model uncertainty this paper proves that for the stability of the interconnected system at least one subsystem is necessarily iss which is a stronger stability property in the set of iiss the necessity of a small gain type property is also demonstrated this paper proposes a common form of smooth lyapunov functions which can establish the iiss and the iss of the interconnection comprising iiss and iss subsystems whenever the small gain type condition is satisfied the result covers situations more general than the earlier study and removes technical conditions assumed in the previous literature global asymptotic stability is discussed as a special case

robust finite time h control of singular stochastic systems via static output feedback abstract this paper addresses the problem of robust finite time stabilization of singular stochastic systems via static output feedback firstly sufficient conditions of singular stochastic finite time boundedness on static output feedback are obtained for the family of singular stochastic systems with parametric uncertainties and time varying norm bounded disturbance then the results are extended to singular stochastic h finite time boundedness for the class of singular stochastic systems designed algorithm for static output feedback controller is provided to guarantee that the underlying closed loop singular stochastic system is singular stochastic h finite time boundedness in terms of strict linear matrix equalities with a fixed parameter finally an illustrative example is presented to show the validity of the developed methodology

adaptive cost dynamic time warping distance in time series analysis for classification dynamic time warping dtw distance is commonly used in measuring similarity between time series for classification in order to obtain the minimum cumulative distance however dtw distance may map multiple points on one time series to one point on another and this makes time series over stretched and compressed resulting in missing important feature information thus influence the classification accuracy in this paper we propose a method called adaptive cost dynamic time warping distance ac dtw which adjusts the number of points on one time series mapped to the points on another ac dtw records the trajectories of all points and then adaptively allocates the cost rate to each point by calculating cost function at the next step the results of the experiments implemented on 17 ucr datasets by using nearest neighbor classifier demonstrate that ac dtw prevails in criterion of higher accuracy rate in comparison with some existing methods adaptive cost is introduced to dynamic time warping for better classification cost function is proposed for dynamic time warping experiments on ucr datasets prove that ac dtw perform better than other methods

two dimensional dissipative control and filtering for roesser model this paper investigates the problems of two dimensional 2 d dissipative control and filtering for a linear discrete time roesser model first a novel sufficient condition is proposed such that the discrete time roesser system is asymptotically stable and 2 d q s r hbox alpha dissipative special cases such as 2 d passivity performance and 2 d h infty performance and feedback interconnected systems are also discussed based on this condition new 2 d q s r hbox alpha dissipative state feedback and output feedback control problems are defined and solved for a discrete time roesser model the design problems of 2 d q s r hbox alpha dissipative filters of observer form and general form are also considered using a linear matrix inequality lmi approach two examples are given to illustrate the effectiveness and potential of the proposed design techniques

theory of stochastic dissipative systems by introducing the escape time a new definition of the dissipativity is introduced under some assumptions that are very reasonable for most physical models based on this definition criteria on the existence and the stability of the solution are presented which can be seen as the extension of lyapunov method to the non smooth case the dissipativity is applied to cascaded nonlinear stochastic systems and interconnected systems to display the superiority of the new framework which shows that there is no need to calculate the first exit time and the escape time

modeling and adaptive tracking for a class of stochastic lagrangian control systems this paper focuses on the problem of modeling and adaptive tracking for a class of stochastic lagrangian control systems with unknown parameters by reasonably introducing random noise a method to construct stochastic lagrangian control systems is given under some milder assumptions an adaptive tracking controller is designed such that the mean square of the tracking error converges to an arbitrarily small neighborhood of zero by tuning design parameters the reasonability of assumptions and the efficiency of the controller are demonstrated by a mechanics model in random vibration environment

stability of stochastic nonlinear systems with state dependent switching in this paper the problem of stability on stochastic systems with state dependent switching is investigated to analyze properties of the switched system by means of ito s formula and dynkin s formula it is critical to show switching instants being stopping times when the given active region set can be replaced by its interior the local solution of the switched system is constructed by defining a series of stopping times as switching instants and the criteria on global existence and stability of solution are presented by lyapunov approach for the case where the active region set can not be replaced by its interior the switched systems do not necessarily have solutions thereby quasi solution to the underlying problem is constructed and the boundedness criterion is proposed the significance of this paper is that all the results presented depend on some easily verified assumptions that are as elegant as those in the deterministic case and the proofs themselves provide design procedures for switching controls

dynamic time warping under limited warping path length dynamic time warping dtw is probably the most popular distance measure for time series data because it captures flexible similarities under time distortions however dtw has long been suffering from the pathological alignment problem and most existing solutions which essentially impose rigid constraints on the warping path are likely to miss the correct alignments a crucial observation on pathological alignment is that it always leads to an abnormally large number of links between two sequences based on this new observation we propose a novel variant of dtw called ldtw which limits the total number of links during the optimization process of dtw ldtw not only oppresses the pathological alignment effectively but also allows more flexibilities when measuring similarities it is a softer constraint because we still let the optimization process of dtw decide how many links to allocate to each data point and where to put these links in this paper we introduce the motivation and algorithm of ldtw and we conduct a nearest neighbor classification experiment on ucr time series archive to show its performance

brief paper backstepping controller design for a class of stochastic nonlinear systems with markovian switching a more general class of stochastic nonlinear systems with irreducible homogenous markovian switching are considered in this paper as preliminaries the stability criteria and the existence theorem of strong solutions are first presented by using the inequality of mathematic expectation of a lyapunov function the state feedback controller is designed by regarding markovian switching as constant such that the closed loop system has a unique solution and the equilibrium is asymptotically stable in probability in the large the output feedback controller is designed based on a quadratic plus quartic form lyapunov function such that the closed loop system has a unique solution with the equilibrium being asymptotically stable in probability in the large in the unbiased case and has a unique bounded in probability solution in the biased case

a universal differential equation of degree 6 abstract l a rubel s universal differential equation 1981 bull ams4 345 349 corresponds to an algebraic polynomial in four variables of degree seven a simpler universal differential equation is found where the attached polynomial is homogeneous of degree six we investigate complex valued c solutions of this differential equation whose imaginary parts approximate arbitrary continuous functions on r

dissipativity theory for nonlinear stochastic dynamical systems in this paper we develop stochastic dissipativity theory for nonlinear dynamical systems using basic input output and state properties specifically a stochastic version of dissipativity using both an input output as well as a state dissipation inequality in expectation for controlled markov diffusion processes is presented the results are then used to derive extended kalman yakubovich popov conditions for characterizing necessary and sufficient conditions for stochastic dissipativity of stochastic dynamical systems using two times continuously differentiable storage functions in addition feedback interconnection stability in probability results for stochastic dynamical systems are developed thereby providing a generalization of the small gain and positivity theorems to stochastic systems

paradigms and puzzles in the theory of dynamical systems a self contained exposition is given of an approach to mathematical models in particular to the theory of dynamical systems the basic ingredients form a triptych with the behavior of a system in the center and behavioral equations with latent variables as side panels the author discusses a variety of representation and parametrization problems in particular questions related to input output and state models the proposed concept of a dynamical system leads to a new view of the notions of controllability and observability and of the interconnection of systems in particular to what constitutes a feedback control law the final issue addressed is that of system identification it is argued that exact system identification leads to the question of computing the most powerful unfalsified model

on a universal differential equation for the analytic terms of c superpositions on the real line it is proved that every continuous function on the real line can be approximated uniformly in the sense of a specific norm by superpositions of analytic functions which are solutions of a single universal differential equation every superposition is some function belonging to c r this improves a former result of the author from which the superpositions are known to be continuous

output feedback regulation of stochastic nonlinear systems with stochastic iiss inverse dynamics this paper develops a unifying framework for output feedback regulation of stochastic nonlinear systems with more general stochastic inverse dynamics the contributions of this work are characterized by the following novel features 1 motivated by the concept of integral input to state stability iiss in deterministic systems and stochastic input to state stability siss using lyapunov function in stochastic systems a concept of stochastic integral input to state stability siiss using lyapunov function is first introduced two important properties of siiss are obtained i siiss is strictly weaker than siss using lyapunov function ii siiss is stronger than the minimum phase property however only under the minimum phase assumption there is no dynamic output feedback control law for global stabilization in probability 2 almost sure boundedness a reasonable and stronger concept than boundedness in probability is introduced the purpose of introducing the concept is to prove the boundedness and convergence of some signals in the closed loop control system 3 some important mathematical tools which play an essential role in the boundedness and convergence analysis of the closed loop system are established 4 a unifying framework is proposed to design a dynamic output feedback control law which drives the states to the origin almost surely while maintaining all the closed loop signals bounded almost surely

on arithmetic properties of the solutions of a universal differential equation at algebraic points in 1981 l a rubel found an explicit algebraic differential equation ade of order four such that every real continuous function on the real line can be uniformly approximated by the c solutions of this ade it is shown that an ade of order five exists where the c solutions additionally satisfy some algebraic properties in the sense of c l siegel s results from the analytical theory of numbers for instance all the solutions and their derivatives are transcendental at algebraic points and large sets of these numbers are linearly independent over the field of real algebraic numbers

small gain theorems for large scale systems and construction of iss lyapunov functions we consider interconnections of n nonlinear subsystems in the input to state stability iss framework for each subsystem an iss lyapunov function is given that treats the other subsystems as independent inputs a gain matrix is used to encode the mutual dependencies of the systems in the network under a small gain assumption on the monotone operator induced by the gain matrix a locally lipschitz continuous iss lyapunov function is obtained constructively for the entire network by appropriately scaling the individual lyapunov functions for the subsystems the results are obtained in a general formulation of iss the cases of summation maximization and separation with respect to external gains are obtained as corollaries

on extended dissipativity of discrete time neural networks with time delay in this brief the problem of extended dissipativity analysis for discrete time neural networks with time varying delay is investigated the definition of extended dissipativity of discrete time neural networks is proposed which unifies several performance measures such as the h infty performance passivity l 2 l infty performance and dissipativity by introducing a triple summable term in lyapunov function the reciprocally convex approach is utilized to bound the forward difference of the triple summable term and then the extended dissipativity criterion for discrete time neural networks with time varying delay is established the derived condition guarantees not only the extended dissipativity but also the stability of the neural networks two numerical examples are given to demonstrate the reduced conservatism and effectiveness of the obtained results

time is money dynamic model based time series data mining for correlation analysis of commodity sales abstract the correlation analysis of commodity sales is very important in cross marketing a means of undertaking dynamic model based time series data mining was proposed to analyze the sales correlations among different commodities a dynamic model comprises some distance models in different observation windows for a time series database that is transformed from a commodities transaction database there are sales correlations in two time series at different times and this may produce valuable rules and knowledge for those who wish to practice cross marketing and earn greater profits it means that observation time points denoting the time at which the sales correlation occurs constitute important information the dynamic model that leverages the techniques inherent in time series data mining can uncover the kinds of commodities that have similar sales trends and how those sales trends change within a particular time period which indicates that the right commodities can be commended to the right customers at the right time moreover some of the time periods used to pinpoint similar sales patterns can be used to retrieve much more valuable information which can in turn be used to increase the sales of the correlated commodities and improve market share and profits analysis results of retail commodities datasets indicate that the proposed method takes into consideration the time factor and can uncover interesting sales patterns by which to improve cross marketing quality moreover the algorithm can be regarded as an intelligent component of the recommendation and marketing systems so that human computer interaction system can make intelligent decision

state feedback h_ infty control for a class of nonlinear stochastic systems this paper discusses the h infty control problem for a class of nonlinear stochastic systems with both state and disturbance dependent noise by means of hamilton jacobi equations both infinite and finite horizon nonlinear stochastic h infty control designs are developed some results on nonlinear h infty control of deterministic systems are generalized to a stochastic setting we introduce some useful concepts such as zero state observability and zero state detectability which together with the stochastic lasalle invariance principle yield some valuable consequences in infinite horizon nonlinear stochastic h infty control

a passive system approach to feedback stabilization of nonlinear control stochastic systems the purpose of this paper is to provide sufficient conditions for asymptotic stabilization in probability of nonlinear control stochastic differential systems by means of smooth state feedback laws in particular we prove that as in the case of stochastic differential systems affine in the control one can compute stabilizing feedback laws provided the unforced stochastic differential system is lyapunov stable in probability and some rank conditions are fulfilled some well known stabilization results for stochastic differential systems affine in the control proved in the literature are extended to nonaffine nonlinear control stochastic differential systems

robust stability and controllability of stochastic differential delay equations with markovian switching in this paper we investigate the almost surely asymptotic stability for the nonlinear stochastic differential delay equations with markovian switching some sufficient criteria on the controllability and robust stability are also established for linear stochastic differential delay equations with markovian switching

on a linear transcendence measure for the solutions of a universal differential equation at algebraic points in this paper the author continues his work on arithmetic properties of the solutions of a universal differential equation at algebraic points every real continuous function on the real line can be uniformly approximated by c solutions of a universal differential equation an algebraic universal differential equation of order five and degree 11 is explicitly given such that every finite set of nonvanishing derivatives y k1 y kr 1 k1 kr at an algebraic point is linearly independent over the field of algebraic numbers a linear transcendence measure for these values is effectively computed

dissipativity based sliding mode control of switched stochastic systems this technical brief is concerned with dissipativity analysis and dissipativity based sliding mode control smc of continuous time switched stochastic systems firstly a sufficient condition is proposed to guarantee the mean square exponential stability and strict dissipativity for the switched stochastic system then an integral type sliding surface function is designed for establishing a sliding mode dynamics which can be formulated by a switched stochastic system with an external disturbance uncertainty dissipativity analysis and synthesis are both investigated for the sliding mode dynamics and consequently sufficient conditions are derived which pave the way for solving the dissipativity analysis and control problems moreover a smc law is synthesized to drive the system trajectories onto the predefined sliding surface in a finite time finally the efficiency of the theoretical findings is demonstrated by an illustrative example

universal formulae and universal differential equations etude des solutions des equations differentielles algebriques en relation avec l approximation uniforme des fonctions

dissipativity based small gain theorems for stochastic network systems in this paper some small gain theorems are proposed for stochastic network systems which describe large scale systems with interconnections uncertainties and random disturbances by the aid of conditional dissipativity and showing times of stochastic interval small gain conditions proposed for the deterministic case are extended to the stochastic case when some design parameters are tunable in practice we invaginate a simpler method to verify small gain condition by selecting one subsystem as a monitor compared with the existing results the existence and uniqueness of solution and ultimate uniform boundedness of input are removed from requirements of input to state stability and small gain theorems

output feedback stabilization using small gain method and reduced order observer for stochastic nonlinear systems this technical note further investigates more general stochastic nonlinear systems with stochastic integral input to state stability siiss inverse dynamics and focuses on solving the following problems 1 a class of counterexamples which are different from that in are reconstructed to discuss the relationship between two small gain type conditions on siiss and 2 under the weaker conditions on nonlinearities based on a reduced order observer small gain type condition on siiss and stochastic lasalle theorem an output feedback controller is constructed to guarantee the global asymptotical stability in probability of the closed loop stochastic system

exponentially incremental dissipativity for nonlinear stochastic switched systems in this paper we investigate the exponentially incremental dissipativity for nonlinear stochastic switched systems by using the designed state dependent switching law and multiple lyapunov functio

feedback stabilizability of non linear stochastic systems with state dependent noise this paper deals with non linear stochastic systems with state dependent noise based on the solution of the stochastic algebraic riccati equation sufficient conditions are derived which assure the existence of state feedback control laws such that the closed loop system is locally and globally stable in probability

a geometric analysis of time series leading to information encoding and a new entropy measure abstract a time series is uniquely represented by its geometric shape which also carries information a time series can be modeled as the trajectory of a particle moving in a force field with one degree of freedom the force acting on the particle shapes the trajectory of its motion which is made up of elementary shapes of infinitesimal neighborhoods of points in the trajectory it has been proved that an infinitesimal neighborhood of a point in a continuous time series can have at least 29 different shapes or configurations so information can be encoded in it in at least 29 different ways a 3 point neighborhood the smallest in a discrete time series can have precisely 13 different shapes or configurations in other words a discrete time series can be expressed as a string of 13 symbols across diverse real as well as simulated data sets it has been observed that 6 of them occur more frequently and the remaining 7 occur less frequently based on frequency distribution of 13 configurations or 13 different ways of information encoding a novel entropy measure called semantic entropy e has been defined following notion of power in newtonian mechanics of the moving particle whose trajectory is the time series a notion of information power p has been introduced for time series e p turned out to be an important indicator of synchronous behavior of time series as observed in epileptic eeg signals

a geometric approach to h control of nonlinear markovian jump systems this paper first discusses the h control problem for a class of general nonlinear markovian jump systems from the viewpoint of geometric control theory following with the updating of the markovian jump mode the appropriate diffeomorphism can be adopted to transform the system into special structures which establishes the basis for the geometric control of nonlinear markovian jump systems through discussing the strongly minimum phase property or the strongly dissipativity of the zero output dynamics the h control can be designed directly without solving the traditional coupled hamilton jacobi inequalities a numerical example is presented to illustrate the effectiveness of our results

error adaptive modeling of streaming time series data using radial basis functions abstract we propose an error adaptive method for constructing time series models for novelty detection using radial basis functions the optimization problem is implemented in an incremental or online manner and permits the balancing of the quality of the data fit and the sparsity of the model in the objective function of a linear program the resulting algorithm is applied to several examples of streaming time series data novel data points are identified using an infeasibility criterion while feasible data points are not used for training and may be discarded in practice only a small fraction of observed streaming data points are actually required to update the model the sparsity promoting term in the objective function serves to determine the location and number of rbfs required to fit the data balancing sparsity with the accuracy of the model allows the user to adjust model complexity it appears that the ability to adapt the error bound in the optimization problem may help to prevent over fitting we illustrate the approach with several examples and show that the fitting procedure is robust to additive gaussian noise with non stationary variance we compare the proposed algorithm with several other methods in the literature including both online and batch algorithms

stochastic input to state stability of switched stochastic nonlinear systems in this paper global asymptotic stability in probability gasip and stochastic input to state stability siss for nonswitched stochastic nonlinear nssnl systems and switched stochastic nonlinear ssnl systems are investigated for the study of gasip the definition which we considered is not the usual notion of asymptotic stability in probability stability in probability plus attractivity in probability it can depict the properties of the system quantitatively correspondingly based on this definition some sufficient conditions are provided for nssnl systems and ssnl systems furthermore the definition of siss is introduced and corresponding criteria are provided for nssnl systems and ssnl systems in the proof of the above results to overcome the difficulties coming with the appearance of switching and the stochastic property at the same time we generalize the past comparison principle and fully use the properties of the functions which we constructed in terms of the average dwell time of the switching laws a sufficient siss condition is obtained for ssnl systems finally some examples are provided to demonstrate the applicability of our results

stabilization of stochastic nonlinear systems driven by noise of unknown covariance this paper poses and solves a new problem of stochastic nonlinear disturbance attenuation where the task is to make the system solution bounded by a monotone function of the supremum of the covariance of the noise this is a natural stochastic counterpart of the problem of input to state stabilization in the sense of sontag 1989 our development starts with a set of new global stochastic lyapunov theorems for an exemplary class of stochastic strict feedback systems with vanishing nonlinearities where the equilibrium is preserved in the presence of noise we develop an adaptive stabilization scheme based on tuning functions that requires no a priori knowledge of a bound on the covariance next we introduce a control lyapunov function formula for stochastic disturbance attenuation finally we address optimality and solve a differential game problem with the control and the noise covariance as opposing players for strict feedback systems the resulting isaacs equation has a closed form solution

h spl infin output feedback controller design for linear systems with time varying delayed state this paper considers the h spl infin controller design problem for linear systems with time varying delays in states the authors obtain sufficient conditions for the existence of h spl infin controllers in terms of three linear matrix inequalities lmis these sufficient conditions are dependent on the maximum value of the time derivative of time varying delay furthermore they briefly explain how to construct such controllers from the positive definite solutions of their lmis and give an example

stochastic barbalat s lemma and its applications in the deterministic case a significant improvement on stability analysis of nonlinear systems is caused by introducing barbalat s lemma into control area after lyapunov s second method and lasalle s theorem were established this note considers the extension of barbalat s lemma to the stochastic case to this end the uniform continuity and the absolute integrability are firstly described in stochastic forms it is nevertheless a small generalization upon the existing references since our result can be used to adapted processes which are not necessarily ito diffusions when it is applied to ito diffusion processes many classical results on stochastic stability are covered as special cases

optimal control of switching diffusions with application to flexible manufacturing systems a controlled switching diffusion model is developed to study the hierarchical control of flexible manufacturing systems the existence of a homogeneous markov nonrandomized optimal policy is established by a convex analytic method using the existence of such a policy the existence of a unique solution in a certain class to the associated hamilton jacobi bellman equations is established and the optimal policy is characterized as a minimizing selector of an appropriate hamiltonian

stability of nonlinear feedback systems a new small gain theorem for the feedback interconnection of general nonlinear systems the classical small gain condition is sufficient but not necessary for robust stability we introduce a weaker notion of gain which yields a small gain condition that is both necessary and sufficient for robust stability we also discuss conditions under which the two notions coincide and we further provide results for dissipation performance measures that are more general than the classical gain measures