further results on output feedback stabilization for a class of stochastic nonlinear systems for a class of stochastic nonlinear systems in which the drift and diffusion vector fields depend on the unmeasurable states besides the measurable output the research purpose of this technical note is to find the maximum value interval of observer gain for the desired control performance for this interval the designed output feedback controller ensures that the equilibrium at the origin is globally asymptotically stable in probability and the inverse optimal stabilization in probability is achieved

lasalle type theorems for stochastic differential delay equations the main aim of this paper is to establish the lasalle type asymptotic convergence theorems for the solutions of stochastic differential delay equations these stochastic versions are then applied to establish sufficient criteria for the stochastically asymptotic stability of the delay equations several examples are also given for illustration

a homogeneous domination approach to state feedback of stochastic high order feedforward nonlinear systems this paper investigates stochastic high order feedforward nonlinear systems for the first time by introducing the homogeneous domination approach and solving several troublesome obstacles in the design and analysis procedure a state feedback controller is constructed to render the closed loop system globally asymptotically stable in probability

global stabilization of stochastic high order feedforward nonlinear systems with time varying delay in this paper we consider the problem of global stabilization for a class of stochastic high order feedforward nonlinear systems with time varying delay by introducing the homogeneous domination design method and constructing the appropriate lyapunov krasovskii functional a state feedback controller is constructed to drive the closed loop system to be globally asymptotically stable in probability

adaptive output feedback control for a class of uncertain stochastic non linear systems with time delays in this paper we investigate the adaptive output feedback stabilisation for a class of stochastic non linear systems with time varying time delays first we give some sufficient conditions to ensure the existence and uniqueness of the solution process for stochastic non linear systems with time delays and introduce a new stability notion and the related criterion then for a class of stochastic non linear systems with time varying time delays uncertain parameters in both drift and diffusion terms and general constant virtual control coefficients we present a systematic design procedure for a memoryless adaptive output feedback control law by using the backstepping method it is shown that under the control law based on a memoryless observer the closed loop equilibrium of interest is globally stable in probability and moreover the solution process can be regulated to the origin almost surely

stability criteria of random nonlinear systems and their applications stochastic differential equations sdes are widely adopted to describe systems with stochastic disturbances while they are not necessarily the best models in some specific situations this paper considers the nonlinear systems described by random differential equations rdes the notions and the corresponding criteria of noise to state stability asymptotic gain and asymptotic stability are proposed in the m th moment or in probability several estimation methods of stochastic processes are presented to explain the reasonability of the assumptions used in theorems as applications of stability criteria some examples about stabilization regulation and tracking are considered respectively a theoretical framework on stability of rdes is finally constructed which is distinguished from the existing framework of sdes

robust backstepping control for a class of time delayed systems in this note the problem of robust output feedback control for a class of nonlinear time delayed systems is considered the systems considered are in strict feedback form state observer is first designed then based on the observed states the controller is designed via backstepping method both the designed observer and controller are independent of the time delays based on lyapunov stability theory we prove that the constructed controller can render the closed loop system asymptotically stable simulation results further verify the effectiveness of the proposed approach

exponential multistability of memristive cohen grossberg neural networks with stochastic parameter perturbations abstract due to instability being induced easily by parameter disturbances of network systems this paper investigates the multistability of memristive cohen grossberg neural networks mcgnns under stochastic parameter perturbations it is demonstrated that stable equilibrium points of mcgnns can be flexibly located in the odd sequence or even sequence regions some sufficient conditions are derived to ensure the exponential multistability of mcgnns under parameter perturbations it is found that there exist at least w 2 l or w 1 l exponentially stable equilibrium points in the odd sequence or the even sequence regions in the paper two numerical examples are given to verify the correctness and effectiveness of the obtained results

delay dependent exponential stability of stochastic systems with time varying delay nonlinearity and markovian switching the problem of delay dependent stability in the mean square sense for stochastic systems with time varying delays markovian switching and nonlinearities is investigated both the slowly time varying delays and fast time varying delays are considered based on a linear matrix inequality approach delay dependent stability criteria are derived by introducing some relaxation matrices which can be chosen properly to lead to a less conservative result numerical examples are given to illustrate the effectiveness of the method and significant improvement of the estimate of stability limit over some existing results in the literature

further results on output feedback regulation of stochastic nonlinear systems with siiss inverse dynamics this article further discusses the problem of output feedback regulation for more general stochastic nonlinear systems with stochastic integral input to state stable inverse dynamics and focuses on solving the important and unsolved problem proposed in yu and xie yu x and xie x j 2010 output feedback regulation of stochastic nonlinear systems with stochastic iiss inverse dynamics ieee transactions on automatic control 55 304 320 how to weaken the conditions on nonlinearities in drift and diffusion vector fields under the weaker conditions how to make full use of the known information of stochastic nonlinear systems to design an adaptive output feedback controller such that all the closed loop signals are almost surely bounded and the output is driven to zero almost surely

stability of the solution of backward heat equation on a weak compactum the paper investigates the stability of the cauchy problem for the backward heat equation under the a priori assumption that the solution is bounded a special metrization of the weak topology in the space l 2 and the standard fourier series technique are applied to obtain stability bounds for the solution of the cauchy problem on the class of absolutely bounded functions

finite time output feedback control for a class of stochastic low order nonlinear systems abstractthis paper discusses the problem of finite time stabilisation for a class of stochastic low order nonlinear systems via output feedback by generalising the adding a power integrator technique constructing an implementable reduced order observer and using the stochastic finite time stability criterion a finite time output feedback controller is presented to guarantee that the closed loop system is finite time stable in probability a simulation example is provided to verify the effectiveness of the proposed design method

state feedback control of high order stochastic nonlinear systems with siiss inverse dynamics this technical note considers a class of high order stochastic nonlinear systems with stochastic integral input to state stability siiss inverse dynamics and drift and diffusion terms depending upon the stochastic inverse dynamics and all the states a new design and analysis approach to the problem of state feedback global regulation is developed to guarantee that all the signals of the closed loop system are bounded almost surely and the states can be regulated to zero almost surely

noise to state stability for a class of random systems with state dependent switching this note is intended to investigate noise to state stability for random nonlinear systems with state dependent switching under some mild and easily verified conditions the existence of global solution to random switched systems can be proved based on a reasonable requirement for the random disturbance the criteria on noise to state stability of random switched systems are presented by the aid of single lyapunov function technique the reasonability of the obtained results is illustrated by using a mechanical model in random vibration environment

output feedback stabilization for a class of stochastic time delay nonlinear systems this note focuses on a class of stochastic time delay nonlinear systems the problem we address is to design a controller such that the closed loop system is exponentially stable it is shown that the stabilization via output feedback can be solved by a lyapunov based recursive design method

non smooth lyapunov function based global stabilization for quantum filters this paper addresses the global stabilization problem for a class of quantum filters via non smooth lyapunov functions due to the intrinsic symmetric topology of filter state space the smooth controls synthesized via the classical lyapunov stochastic stability theory fail to obtain the global stabilizability because of the existence of the so called antipodal eigenstates as such for the first time we introduce a non smooth lyapunov like theory for generic stochastic nonlinear systems which includes a continuous lyapunov like theorem and a discontinuous lyapunov like theorem for stability in probability applying the non smooth lyapunov like theory switching control and continuous control in saturation form are constructed for the quantum filters with consideration of the sliding motion of filter state the non smooth property enables these controls to deal with the symmetric topology of filter state space and to solve the problem of global stabilization for quantum filters the eigenstate transferring is obtained as a special result distinguishing these non smooth lyapunov based controls from classical control approaches for quantum filters the effectiveness of the non smooth lyapunov based controls is illustrated through the control design for the spin 1 2 systems simulation results are presented and discussed to show the effectiveness of the controls

adaptive fuzzy tracking control for stochastic nonlinear systems with unknown time varying delays an adaptive fuzzy controller is presented for a class of stochastic nonlinear systems an quadratic function is constructed to give the condition of the stability of systems the scheme guarantees the stability of closed loop system in the mean square sense the drawback of the quartic moment approach is overcome and the method is simplified this paper addresses the problem of adaptive tracking control for a class of stochastic strict feedback nonlinear time varying delays systems using fuzzy logic systems fls in this paper quadratic functions are used as lyapunov functions to analyze the stability of systems other than the fourth moment approach proposed by h deng and m krstic and the hyperbolic tangent functions are introduced to deal with the hessian terms this approach overcomes the drawback of the traditional quadratic moment approach and reduce the complexity of design procedure and controller based on the backstepping technique the appropriate lyapunov krasovskii functionals and the fls the adaptive fuzzy controller is well designed the proposed adaptive fuzzy controller guarantees that all the signals in the closed loop system are bounded in probability and the tracking error can converge to a small residual set around the origin in the mean square sense

quantum measurement based feedback control a nonsmooth time delay control approach this paper addresses the problem of measurement based feedback control for quantum systems in which the time to compute the filter based control input is taken into account by considering the input delay it starts with a new lyapunov lasalle like theorem for delay dependent stochastic stability of a class of time delay stochastic nonlinear systems nonsmooth time delay control is then constructed to compensate for the control computation time which is known but arbitrarily long while globally stabilizing the quantum filters almost surely the nonsmooth property enables the control to deal with the symmetric topology of filter state space the effectiveness of the proposed control is illustrated through the global stabilization of the spin 1 2 systems simulation results are presented and discussed to show the effectiveness of the proposed control

brief paper inverse optimal stabilization for stochastic nonlinear systems whose linearizations are not stabilizable after considering the stabilization of a class of high order stochastic nonlinear systems which are neither necessarily feedback linearizable nor affine in the control input in this brief paper we further address the problem of state feedback inverse optimal stabilization in probability i e our redesigned stabilizing backstepping controller is also optimal with respect to meaningful cost functionals

decentralised adaptive output feedback stabilisation for stochastic time delay systems via lasalle yoshizawa type theorem abstractthis paper deals with the decentralised output feedback stabilisation problem for a class of large scale stochastic time delay nonlinear systems a general theorem is firstly given to guarantee the global existence and uniqueness of the solution for stochastic time delay systems in addition a stochastic version of the well known lasalle yoshizawa theorem with time varying delay is initially proposed for the controller design and stability analysis then for a class of large scale stochastic systems with time varying delays totally decentralised adaptive delay dependent controllers are designed by using k filter and backstepping approach via lasalle yoshizawa type theorem and constructing a general lyapunov function it is shown that all signals in the closed loop system are bounded almost surely and the solution is almost surely asymptotically stable finally a simulation example is given to illustrate the effectiveness of the results of this paper

robust h spl infin control for uncertain stochastic systems with state delay this note deals with the problems of robust stochastic stabilization and robust h control for uncertain stochastic systems with a time varying delay in the state the parameter uncertainties are assumed to be time varying norm bounded appearing in both the state and input matrices the purpose of the robust stochastic stabilization problem is the design of a memoryless state feedback controller such that the closed loop system is mean square asymptotically stable for all admissible uncertainties in the robust h control problem in addition to the mean square asymptotic stability requirement a prescribed h performance is required to be achieved in terms of a linear matrix inequality sufficient conditions for the solvability of these problems are proposed respectively the expressions of desired state feedback controllers are given an example illustrating the proposed approach is provided

output feedback control using small gain conditions for stochastic nonlinear systems with siiss inverse dynamics this article further discusses output feedback control for stochastic nonlinear systems with stochastic integral input to state stability siiss inverse dynamics based on the stochastic lasalle theorem and small gain type conditions on siiss an output feedback controller using the backstepping method is constructively designed to guarantee that all the closed loop signals are bounded almost surely and the stochastic closed loop system is globally asymptotically stable in probability

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

further results on output feedback stabilization for stochastic high order nonlinear systems with time varying delay this article further discusses the output feedback stabilization problem for stochastic high order nonlinear systems with time varying delay under the weaker conditions on nonlinearities in drift and diffusion vector fields by using the idea of homogeneous domination approach skillfully choosing an appropriate lyapunov krasoviskii functional and successfully solving several troublesome obstacles in the design and analysis procedure an output feedback controller is constructed to render the closed loop system globally asymptotically stable in probability

finite time stabilization of stochastic nonlinear systems in strict feedback form in this paper we investigate the problem of almost surely finite time stabilization of a class of stochastic nonlinear systems based on the recently proposed almost surely finite time stability theorem in yin khoo man and yu 2011 we prove that almost surely global finite time stability of stochastic nonlinear systems in strict feedback form can be guaranteed by a continuous control law a systematic design algorithm is developed for the construction of the controller simulation results are given to illustrate the theoretical analysis

technical communique stabilization of a class of uncertain large scale stochastic systems with time delays this paper focuses on a class of large scale interconnected bilinear stochastic systems with time delays and time varying parameter uncertainties the problem we address is to design a robust decentralized controller such that the closed loop interconnected stochastic system is globally asymptotically stable in probability for all admissible uncertainties and time delays first robust stability analysis is given in terms of a set of linear matrix inequalities lmis then it is shown that the robust decentralized stabilization can be solved by an lmi based design method

stochastic adaptive backstepping controller design by introducing dynamic signal and changing supply function a more general class of stochastic non linear systems with unmodelled dynamics and uncertain non linear functions are considered in this paper with the concept of isps being extended to stochastic case by combining changing supply function technique with backstepping design technique an adaptive output feedback controller is proposed it is shown that all the solutions of the closed loop system are uniformly bounded in probability and the output can be regulated to an arbitrarily small neighbourhood of the origin in probability a simulation example demonstrates the control scheme

stochastic nonlinear stabilization i a backstepping design while the current robust nonlinear control toolbox includes a number of methods for systems affine in deterministic bounded disturbances the problem when the disturbance is unbounded stochastic noise has hardly been considered we present a control design which achieves global asymptotic lyapunov stability in probability for a class of strict feedback nonlinear continuous time systems driven by white noise in a companion paper we develop inverse optimal control laws for general stochastic systems affine in the noise input and for strict feedback systems a reader of this paper needs no prior familiarity with techniques of stochastic control

adaptive backstepping controller design using stochastic small gain theorem a more general class of stochastic nonlinear systems with unmodeled dynamics and uncertain nonlinear functions are considered in this paper with the concept of input to state practical stability isps and nonlinear small gain theorem being extended to stochastic case by combining stochastic small gain theorem with backstepping design technique an adaptive output feedback controller is proposed it is shown that the closed loop system is practically stable in probability a simulation example demonstrates the control scheme

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

how to avoid spurious cluster validation a methodological investigation on simulated and fmri data abstract this paper presents an evaluation of a common approach that has been considered as a promising option for exploratory fmri data analyses the approach includes two stages creating from the data a sequence of partitions with increasing number of subsets clustering and selecting the one partition in this sequence that exhibits the clearest indications of an existing structure cluster validation in order to achieve that the selected partition is actually the best characterization of the data structure previous studies were directed to find the most appropriate validity function s in our analysis protocol we first optimize the sequence of partitions according to the given objective function our study showed that an insufficient optimization of the partition for one or more numbers of clusters can easily yield a spurious validation result which in turn may lead the analyst to a misleading interpretation of the fmri experiment however a sufficient optimization for each included number of clusters provided the basis for a reliable adequate characterization of the data furthermore it enabled an adequate evaluation of the validity functions these findings were obtained independently for three clustering algorithms representing the hard and fuzzy clustering variant and three up to date cluster validity functions the findings were derived from analyses of gaussian clusters simulated data sets that mimic typical fmri response signals and real fmri data based on our results we propose a number of options of how to configure improved clustering tools

stability of stochastic systems with uncertain time delays abstract for linear delay systems with bilinear noise sufficient conditions are given for the global asymptotic stochastic stability independent of the length of the delay s for linear stochastic noise terms sufficient conditions for the existence of an invariant distribution for all values of the delay are given it is shown that the gaussian distribution is the unique invariant distribution the covariance and correlation matrix function of the resulting stationary process are completely characterized by a lyapunov type equation all these sufficient conditions are obtained in the form of the existence of some positive definite matrices satisfying certain riccati type equations

time varying state feedback stabilisation of stochastic feedforward nonlinear systems with unknown growth rate abstractwe consider the time varying state feedback stabilisation problem for a class of stochastic feedforward nonlinear systems with unknown growth rate in this paper a new lasalle type theorem for stochastic time varying systems is firstly established by using the generalized weakly positive definite function as an application to deal with serious uncertainties in the unknown growth rate a time varying approach rather than an adaptive one is adopted to design the scheme of a state feedback controller for stochastic feedforward systems based on the established lasalle type theorem it is shown that all signals of the resulting closed loop system converge to zero almost surely illustrative examples are given to verify the theoretical findings

adaptive approximation based regulation control for a class of uncertain nonlinear systems without feedback linearizability in this paper for a general class of uncertain nonlinear cascade systems including unknown dynamics which are not feedback linearizable and cannot be solved by existing approaches an innovative adaptive approximation based regulation control aarc scheme is developed within the framework of adding a power integrator api by deriving adaptive laws for output weights and prediction error compensation pertaining to single hidden layer feedforward network slfn from the lyapunov synthesis a series of slfn based approximators are explicitly constructed to exactly dominate completely unknown dynamics by the virtue of significant advancements on the api technique an adaptive api methodology is eventually established in combination with slfn based adaptive approximators and it contributes to a recursive mechanism for the aarc scheme as a consequence the output regulation error can asymptotically converge to the origin and all other signals of the closed loop system are uniformly ultimately bounded simulation studies and comprehensive comparisons with backstepping and api based approaches demonstrate that the proposed aarc scheme achieves remarkable performance and superiority in dealing with unknown dynamics

output tracking of high order stochastic nonlinear systems with application to benchmark mechanical system this note considers output tracking of high order stochastic nonlinear systems without imposing any restriction on the high order and the drift and diffusion terms by using the backstepping design technique a smooth state feedback controller is given to guarantee that the solution process is bounded in probability and the error signal between the output and the reference signal can be regulated into a small neighborhood of the origin in probability a practical example of stochastic benchmark mechanical system and simulation are provided to demonstrate the effectiveness of the control scheme

brief paper feedback stabilization for high order feedforward nonlinear time delay systems this paper investigates the problem of global strong stabilization by state feedback for a family of high order feedforward nonlinear time delay systems the uncertain nonlinearities are assumed to satisfy a polynomial growth assumption with an input or delayed input dependent rate with the help of the appropriate lyapunov krasovskii functionals and a rescaling transformation with a gain to be tuned online by a dynamic equation we propose a dynamic low gain state feedback control scheme a simulation example is given to demonstrate the effectiveness of the proposed design procedure

identification of the initial condition in backward problem with nonlinear diffusion and reaction abstract in this paper we study the backward in time problem for nonlinear parabolic equations associated with nonlinear diffusion coefficient the problem is ill posed in the sense of hadamard under an a priori assumption on the exact solution in gevrey space we propose a new regularization method for stabilising the ill posed problem our results extend some earlier works on backward problems for nonlinear parabolic equations

brief canonical forms for stochastic nonlinear systems necessary and sufficient conditions for the existence of diffeomorphisms that transform stochastic nonlinear systems to three canonical forms are derived based on the so called invariance under transformation rule

output feedback control of a class of high order stochastic nonlinear systems this article investigates the problem of output feedback stabilisation for a class of high order stochastic non linear systems in which the diffusion terms depend on unmeasurable states besides the output by introducing a new rescaling transformation adopting an effective observer and choosing the appropriate lyapunov function an output feedback controller is constructed to ensure that the equilibrium at the origin of the closed loop system is globally asymptotically stable in probability the output can be regulated to the origin almost surely and the problem of inverse optimal stabilisation in probability is solved the efficiency of the output feedback controller is demonstrated by several simulation examples

brief paper finite time stability and instability of stochastic nonlinear systems this paper presents a new definition of finite time stability for stochastic nonlinear systems this definition involves stability in probability and finite time attractiveness in probability an important lyapunov theorem on finite time stability for stochastic nonlinear systems is established a theorem extending the stochastic lyapunov theorem is also proved moreover an example and a lemma are presented to illustrate the scope of extension a useful inequality extended from bihari s inequality is derived which plays an important role in showing the lyapunov theorem finally a lyapunov theorem on finite time instability is proved which states that almost surely globally asymptotical stability is not equivalent to finite time stability for some stochastic systems two simulation examples are given to illustrate the theoretical analysis

on input to state stability of stochastic retarded systems with markovian switching this note develops a razumikhin type theorem on pth moment input to state stability of hybrid stochastic retarded systems also known as stochastic retarded systems with markovian switching which is an improvement of an existing result an application to hybrid stochastic delay systems verifies the effectiveness of the improved result

an efficient vector quantizer providing globally optimal solutions this paper presents a new approach in vector quantization that is designed for clustering or source coding it incorporates both the capability of fast convergence from a monotonically descending algorithm and provides a globally optimal solution by a random optimization technique thus it benefits from properties of deterministic and stochastic search comprehensive experiments demonstrate that the new algorithm actually assimilated the advantages of the both components it may be therefore regarded as an accelerated global optimization method whose convergence is theoretically proved according to the complexity of the quantization problem the convergence rate is shown numerically to approach that of a coordinate descent algorithm which is an iterative updating of a single codevector at a time generalized lloyd algorithm gla i e k means the new method is investigated and compared with gla and a globally operating stochastic relaxation technique the comparison was made with respect to quality reliability and efficiency and applied to four categories of data an easy to grasp example patterns derived from the eeg gauss markov and image sources

stochastic nonlinear stabilization ii inverse optimality after considering the stabilization of a specific class of stochastic nonlinear systems in a companion paper in this second part we address the classical question of when is a stabilizing in probability controller optimal and show that for every system with a stochastic control lyapunov function it is possible to construct a controller which is optimal with respect to a meaningful cost functional then we return to the problem from part i and design an optimal backstepping controller whose cost functional includes penalty on control effort and which has an infinite gain margin

stability analysis of random nonlinear systems with time varying delay and its application this paper studies a class of random nonlinear systems with time varying delay in which the r order moment of the random disturbance is finite firstly some general conditions are proposed to guarantee the existence and uniqueness of the global solution to random nonlinear time delay systems secondly some criteria on noise to state stability in the moment sense and in probability sense are given by lyapunov method respectively finally an adaptive output feedback regulation controller is constructed for a class of random nonlinear time delay systems and the effectiveness of the proposed recursive procedure is demonstrated by a simulation example

robust stability of uncertain stochastic differential delay equations in this paper we first discuss the robust stability of uncertain linear stochastic differential delay equations we then extend the theory to cope with the robust stability of uncertain semi linear stochastic differential delay equations we shall also give several examples to illustrate our theory

a note on the lasalle type theorems for stochastic differential delay equations the main aim of this note is to improve some results obtained in the author s earlier paper 1999 j math anal appl 236 350 369 from the improved result follow some useful criteria on the stochastic asymptotic stability and boundedness

delay adaptive feedback for linear feedforward systems abstract predictor techniques are an indispensable part of the control design toolbox for plants with input and state delays of significant size yet they suffer from sensitivity to the design values explicit feedback laws were recently introduced by jankovic for a class of feedforward linear systems with simultaneous state and input delays for the case where the delays are of unknown length using the certainty equivalence principle we design a lyapunov based adaptive controller which achieves global stability and regulation for arbitrary initial estimates for the delays we consider a two block sub class of linear feedforward systems a generalization to the n block case involves a recursive application of the same techniques

practical output feedback risk sensitive control for stochastic nonlinear systems with stable zero dynamics this paper addresses the design problem of practical or satisfaction output feedback controls for stochastic strict feedback nonlinear systems in observer canonical form with stable zero dynamics under long term average tracking risk sensitive cost criteria the cost function adopted here is of the quadratic integral type usually encountered in practice rather than the quartic integral one used to avoid difficulty in control design and performance analysis of the closed loop system a sequence of coordinate diffeomorphisms is introduced to separate the zero dynamics from the entire system so that the transformed system has an appropriate form suitable for integrator backstepping design for any given risk sensitivity parameter and desired cost value by using the integrator backstepping methodology an output feedback control is constructively designed such that a the closed loop system is bounded in probability and b the long term average risk sensitive cost is upper bounded by the desired value in addition this paper does not require the uniform boundedness of the gain functions of the system noise furthermore an example is given to show the effectiveness of the theory

brief paper small gain control method for stochastic nonlinear systems with stochastic iiss inverse dynamics this paper investigates the small gain type conditions on stochastic iiss siiss systems and makes full use of these conditions in the design and analysis of the controller the contributions are as follows 1 a new proof of the stochastic lasalle theorem is provided 2 the small gain type conditions on siiss are developed and their relationship is discussed 3 based on the stochastic lasalle theorem and siiss small gain type conditions the adaptive controllers are designed to guarantee that all of the closed loop signals are bounded almost surely and the stochastic closed loop systems are globally asymptotically stable in probability

on a backward heat problem with time dependent coefficient regularization and error estimates in this paper we consider a homogeneous backward heat conduction problem which appears in some applied subjects this problem is ill posed in the sense that the solution if it exists does not depend continuously on the final data a new regularization method is applied to formulate regularized solutions which are stably convergent to the exact ones with holder estimates a numerical example shows that the computational effect of the method is all satisfactory

a mollification method for ill posed problems a mollification method for a class of ill posed problems is suggested the idea of the method is very simple and natural if the data are given inexactly then we try to find a sequence of mollification operators which map the improper data into well posedness classes of the problem mollify the improper data within these mollified data our problem becomes well posed and when these facts are in hand we try to obtain error estimates and optimal or quasi optimal mollification parameters the method is working not only for problems in hilbert spaces but also for problems in banach spaces applications of the method to concrete problems like numerical differentiation parabolic equations backwards in time the cauchy problem for the laplace equation one and multidimensional non characteristic cauchy problems for parabolic equations in infinite or finite domains give us very sharp stability estimates of h older continuous type in these cases the method is optimal in the sense that it gives the same order of h older continuous dependence on the data as for the regularized problems furthermore the method may be implemented numerically using fast fourier transforms for the first time a uniform stability estimate of h older continuous type of the solution of the heat equation backwards in time in the space l p bbb r for all p in 1 infty could be established by our mollification method a new simple sharp pointwise estimate of h older type for the weak solution of a non characteristic cauchy problem for parabolic equations in a finite domain is established

a stability estimate on the regularized solution of the backward heat equation inverse problems where one looks for causes for observed or desired effects are usually ill posed i e their solution is not unique or unstable with respect to data perturbations we derive a stability estimate for the regularized solution of the backward heat equation which is needed for stable solution of this ill posed problem for this purpose we construct a regularizer for a certain minimization problem and in conclusion the stability of this minimization procedure

finite time state feedback stabilisation of stochastic high order nonlinear feedforward systems abstractthis paper studies the finite time state feedback stabilisation of stochastic high order nonlinear feedforward systems based on the stochastic lyapunov theorem on finite time stability by using the homogeneous domination method the adding one power integrator and sign function method constructing a c2 lyapunov function and verifying the existence and uniqueness of solution a continuous state feedback controller is designed to guarantee the closed loop system finite time stable in probability

analysis and synthesis of markov jump linear systems with time varying delays and partially known transition probabilities in this note the stability analysis and stabilization problems for a class of discrete time markov jump linear systems with partially known transition probabilities and time varying delays are investigated the time delay is considered to be time varying and has a lower and upper bounds the transition probabilities of the mode jumps are considered to be partially known which relax the traditional assumption in markov jump systems that all of them must be completely known a priori following the recent study on the class of systems a monotonicity is further observed in concern of the conservatism of obtaining the maximal delay range due to the unknown elements in the transition probability matrix sufficient conditions for stochastic stability of the underlying systems are derived via the linear matrix inequality lmi formulation and the design of the stabilizing controller is further given a numerical example is used to illustrate the developed theory

convergence of the lloyd algorithm for computing centroidal voronoi tessellations centroidal voronoi tessellations cvts are voronoi tessellations of a bounded geometric domain such that the generating points of the tessellations are also the centroids mass centers of the corresponding voronoi regions with respect to a given density function centroidal voronoi tessellations may also be defined in more abstract and more general settings due to the natural optimization properties enjoyed by cvts they have many applications in diverse fields the lloyd algorithm is one of the most popular iterative schemes for computing the cvts but its theoretical analysis is far from complete in this paper some new analytical results on the local and global convergence of the lloyd algorithm are presented these results are derived through careful utilization of the optimization properties shared by cvts numerical experiments are also provided to substantiate the theoretical analysis

a novel alleviating fuzzy control algorithm for a class of nonlinear stochastic systems in pure feedback form abstract in this paper a novel alleviating computation adaptive fuzzy control scheme is presented for a class of uncertain stochastic nonlinear pure feedback systems different from the existing results that are based on traditional back stepping schemes as well as approximation technique of fuzzy logic systems flss for stochastic nonlinear systems this new approach assumes that the norm of optimal approximation parameter vector of flss is bounded by unknown parameter at each design step of this new approach fewer bounded adaptive parameters need to be adjusted thus this new approach can alleviate the online computation burden and improve the robust control performance meanwhile combining lyapunov theorem analysis it is proven that all the signals in the closed loop system are uniformly ultimately bounded uub and the tracking error can converge to a small neighborhood of zero the good performance of this approach is well demonstrated in a simulation example

global finite time stabilisation for a class of stochastic nonlinear systems by output feedback in this paper the problem of global finite time stabilisation by output feedback is considered for a class of stochastic nonlinear systems first based on homogeneous systems theory and the adding a power integrator technique a homogeneous reduced order observer and control law are constructed in a recursive manner for the nominal system then the homogeneous domination approach is used to deal with the nonlinearities in drift and diffusion terms it is shown that the proposed output feedback control law can guarantee that the closed loop system is global finite time stable in probability finally simulation examples are carried out to demonstrate the effectiveness of the proposed control scheme

state feedback stabilization for stochastic feedforward nonlinear systems with time varying delay this paper investigates a class of stochastic feedforward nonlinear systems with time varying delay by introducing the homogeneous domination approach to stochastic systems a state feedback controller is constructed to render the closed loop system globally asymptotically stable in probability

regularization for ill posed cauchy problems associated with generators of analytic semigroups this paper is concerned with the ill posed cauchy problem associated with a densely defined linear operator a in a banach space our main result is that if a is the generator of an analytic semigroup then there exists a family of regularizing operators for such an ill posed cauchy problem by using the quasi reversibility method fractional powers and semigroups of linear operators the applications to ill posed partial differential equations are also given

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

minimization by random search techniques we give two general convergence proofs for random search algorithms we review the literature and show how our results extend those available for specific variants of the conceptual algorithm studied here we then exploit the convergence results to examine convergence rates and to actually design implementable methods finally we report on some computational experience

output feedback stabilization of stochastic high order nonlinear systems under weaker conditions under the weaker conditions on the power order and the nonlinear functions this paper investigates the output feedback stabilization problem for a class of stochastic high order nonlinear systems based on the backstepping design method and homogeneous domination technique the closed loop system can be proved to be globally asymptotically stable in probability

a multiple model mrac scheme for multivariable systems with matching uncertainties this paper develops a multivariable multiple model adaptive control scheme for adaptive state feedback state tracking control of systems whose plant model matching conditions are uncertain and parameters are unknown to deal with the uncertainty of plant model matching conditions needed for adaptive control multiple reference model systems are employed to generate multiple parameter estimation and feedback control signals from which a most suitable control input is selected by a control switching mechanism designed using multiple estimation errors such a new multiple model control design is based on an expanded control system parametrization which has the capacity to cover system structural uncertainties stability analysis and simulation results ensure and verify the desired adaptive control system stability and tracking performance

noise to state stability of random switched systems and its applications noise to state stability of random switched systems is investigated in this technical note by the aid of fubini s formula the criteria on noise to state stability in the moment of random switched systems are established under a reasonable assumption of second order processes as applications the control problems of spring pendulum in random environment are researched in addition nonlinear filtering is considered to ensure noise to state stability of filter error switched systems

decentralized adaptive output feedback stabilization for large scale stochastic nonlinear systems in this paper the problem of decentralized adaptive output feedback stabilization is investigated for large scale stochastic nonlinear systems with three types of uncertainties including parametric uncertainties nonlinear uncertain interactions and stochastic inverse dynamics under the assumption that the inverse dynamics of the subsystems are stochastic input to state stable an adaptive output feedback controller is constructively designed by the backstepping method it is shown that under some general conditions the closed loop system trajectories are bounded in probability and the outputs can be regulated into a small neighborhood of the origin in probability in addition the equilibrium of interest is globally stable in probability and the outputs can be regulated to the origin almost surely when the drift and diffusion vector fields vanish at the origin the contributions of the work are characterized by the following novel features 1 even for centralized single input single output systems this paper presents a first result in stochastic nonlinear adaptive output feedback asymptotic stabilization 2 the methodology previously developed for deterministic large scale systems is generalized to stochastic ones at the same time novel small gain conditions for small signals are identified in the setting of stochastic systems design 3 both drift and diffusion vector fields are allowed to be dependent not only on the measurable outputs but some unmeasurable states 4 parameter update laws are used to counteract the parametric uncertainty existing in both drift and diffusion vector fields which may appear nonlinearly 5 the concept of stochastic input to state stability and the method of changing supply functions are adapted for the first time to deal with stochastic and nonlinear inverse dynamics in the context of decentralized control

finite time stabilization of high order stochastic nonlinear systems in strict feedback form this paper deals with the problem of finite time stabilization for a class of high order stochastic nonlinear systems in strict feedback form by using ito s formula mathematical induction and backstepping design method a novel state feedback controller is constructed to guarantee that the closed loop high order nonlinear system has a unique solution and the solution of the closed loop high order nonlinear system is finite time stable a systematic design algorithm is developed for the construction of the backstepping controller finally the effectiveness of the state feedback controller is illustrated by two examples

centroidal voronoi tessellations applications and algorithms a centroidal voronoi tessellation is a voronoi tessellation whose generating points are the centroids centers of mass of the corresponding voronoi regions we give some applications of such tessellations to problems in image compression quadrature finite difference methods distribution of resources cellular biology statistics and the territorial behavior of animals we discuss methods for computing these tessellations provide some analyses concerning both the tessellations and the methods for their determination and finally present the results of some numerical experiments