finite horizon ℋ 2 ℋ control for a class of nonlinear markovian jump systems with probabilistic sensor failures this article is concerned with the mixed 2 control problem over a finite horizon for a class of nonlinear markovian jump systems with both stochastic nonlinearities and probabilistic sensor failures the stochastic nonlinearities described by statistical means could cover several types of well studied nonlinearities and the failure probability for each sensor is governed by an individual random variable satisfying a certain probability distribution over a given interval the purpose of the addressed problem is to design state feedback controllers such that the closed loop system achieves the expected 2 performance requirement with a guaranteed disturbance attenuation level the solvability of the addressed control problem is expressed as the feasibility of certain coupled matrix equations the controller gain at each time instant k can be obtained by solving the corresponding set of matrix equations a numerical example is given to illustrate the effectiveness and applicability of the proposed al

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

numerical method for non linear wave and diffusion equations by the variational iteration method this paper applies he s variational iteration to the wave equations in an infinite one dimensional medium and some non linear diffusion equations a suitable choice of an initial solution can lead to the needed exact solution by a few iterations copyright 2007 john wiley sons ltd

generic spectral results for cmv matrices with dynamically defined verblunsky coefficients abstract we consider cmv matrices with dynamically defined verblunsky coefficients these coefficients are obtained by continuous sampling along the orbits of an ergodic transformation we investigate whether certain spectral phenomena are generic in the sense that for a fixed base transformation the set of continuous sampling functions for which the spectral phenomenon occurs is residual among the phenomena we discuss are the absence of absolutely continuous spectrum and the vanishing of the lebesgue measure of the spectrum

variational iteration method for autonomous ordinary differential systems in this paper a new iteration technique is proposed to solve autonomous ordinary differential systems in this method general lagrange multipliers are introduced to construct correction functionals for the systems the multipliers in the functionals can be identified by the variational theory the initial approximations can be freely chosen with possible unknown constants which can be determined by imposing the boundary initial conditions some examples are given the results reveal that the method is very effective and convenient

adaptive fault tolerant stabilization for nonlinear systems with markovian jumping actuator failures and stochastic noises in this paper we consider the fault tolerant stabilization problem for a class of nonlinear systems with uncertain parameters uncertainties caused by markovian jumping actuator failures and stochastic noises are also taken into consideration different from most existing results the number of actuator failures may be infinite and stochastic functions related to multi markovian variables have been introduced to denote the failure scaling factors for the actuators which is practical but challenging three main difficulties arise first is how to establish fundamentals for systems involving multi markovian variables and stochastic noises including the joint transition probability the infinitesimal generator the existence and uniqueness of the solution and so on second is how to handle the extra transition rate related terms appearing in the infinitesimal generator of the lyapunov function last is how to cope with the involved higher order hessian term in the ito stochastic differentiation by proposing a new adaptive fault tolerant control scheme the boundedness in probability of all the closed loop signals has been ensured an example of altitude fault tolerant control for a generic hypersonic air vehicle is presented to show the effectiveness of the proposed scheme

numerical simulation of equal width wave equation by means of the variational iteration method the solution of the equal width wave equation is numerically obtained and compared with that obtained by the adomian decomposition method numerical results show that the variational iteration method can readily be implemented with excellent accuracy to nonlinear equations

a difference equation arising from the trigonometric moment problem having random reflection coefficients an operator theoretic approach abstract operators associated with polynomials orthogonal on the unit circle and their doubly infinite analogs are considered we assume that the elements in the operators are obtained from a stationary stochastic process and we investigate the properties of the spectrum of these operators lyapunov exponents are introduced and we examine their relationship with the absolutely continuous components of the spectrum of the above operators

application of galerkin s method to equal width wave equation the non linear equal width equation is solved by galerkin s method using linear finite elements a linear recurrence relationship for the numerical solution of the resulting system of ordinary differential equations is found employing the crank nicolson approach including a product approximation the three invariants of the motion are calculated to determine the conservation properties of the system l 2 and l error norms are used to measure differences between the exact and numerical solutions the simulations of solitary wave motion are used to determine the properties of the algorithm finally the development of an undular bore is studied

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

a review of the decomposition method in applied mathematics abstract the decomposition method can be an effective procedure for analytical solution of a wide class of dynamical systems without linearization or weak nonlinearity assumptions closure approximations perturbation theory or restrictive assumptions on stochasticitiy

novel neural control for a class of uncertain pure feedback systems this paper is concerned with the problem of adaptive neural tracking control for a class of uncertain pure feedback nonlinear systems using the implicit function theorem and backstepping technique a practical robust adaptive neural control scheme is proposed to guarantee that the tracking error converges to an adjusted neighborhood of the origin by choosing appropriate design parameters in contrast to conventional lyapunov based design techniques an alternative lyapunov function is constructed for the development of control law and learning algorithms differing from the existing results in the literature the control scheme does not need to compute the derivatives of virtual control signals at each step in backstepping design procedures furthermore the scheme requires the desired trajectory and its first derivative rather than its first n derivatives in addition the useful property of the basis function of the radial basis function which will be used in control design is explored simulation results illustrate the effectiveness of the proposed techniques

decomposition method for solving fractional riccati differential equations in this article we implement a relatively new analytical technique the adomian decomposition method for solving fractional riccati differential equations the fractional derivatives are described in the caputo sense in this scheme the solution takes the form of a convergent series with easily computable components the diagonal pade approximants are effectively used in the analysis to capture the essential behavior of the solution the corresponding solutions of the integer order equations are found to follow as special cases of those of fractional order equations some numerical examples are presented to illustrate the efficiency and reliability of the method

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

adaptive output feedback control for nonlinear time delay systems by fuzzy approximation approach in this paper the problem of adaptive fuzzy tracking control via output feedback for a class of uncertain single input single output siso strict feedback nonlinear systems with unknown time delay functions is investigated dynamic surface control technique is used to avoid the problem of explosion of complexity which is caused by repeated differentiation of certain nonlinear functions in the backstepping design process in addition the fuzzy logic systems are utilized to approximate the unknown and desired control input signals directly instead of the unknown nonlinear functions the designed controller can guarantee all the signals in the closed loop system to be semiglobally uniformly ultimately bounded and the tracking error to converge to a small neighborhood of the origin simulations results are provided to demonstrate the effectiveness of the proposed methods

adaptive control based barrier lyapunov functions for a class of stochastic nonlinear systems with full state constraints abstract an adaptive control scheme is developed in the paper for nonlinear stochastic systems with unknown parameters all the states in the systems are required to be constrained in a bounded compact set i e the full state constraints are considered in the systems it is for the first time to control nonlinear stochastic systems with the full state constraints in contrast to deterministic systems the stochastic systems with the full state constraints are more difficult to be stabilized and the design procedures are more complicated by constructing barrier lyapunov functions blf in symmetric and asymmetric forms it can be ensured that all the states of the stochastic systems are not to transgress their constraint bounds thus the proposed scheme not only solves the stability problem of stochastic systems but also overcomes the effect of the full state constraints on the control performance finally it is proved that all the signals in the closed loop system are semi global uniformly ultimately bounded sguub in probability the system output is driven to follow the reference signals and all the states are ensured to remain in the predefined compact sets the validity of the proposed scheme is verified by a simulation example

dynamics modeling and tracking control of robot manipulators in random vibration environment in this technical brief the problem of modeling and tracking control for the manipulator with multi revolute joints in random vibration environment is considered by analyzing the effect of environment to the mass points and introducing an equivalent stochastic noise process a stochastic hamiltonian dynamic model is constructed to describe the motion of the manipulator based on the constructed model a state feedback backstepping controller in vector form is designed such that the unique solution of the closed loop system is bounded in probability and the mean square of the tracking error converges to an arbitrarily small neighborhood of zero

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

variational iteration method new development and applications variational iteration method has been favourably applied to various kinds of nonlinear problems the main property of the method is in its flexibility and ability to solve nonlinear equations accurately and conveniently in this paper recent trends and developments in the use of the method are reviewed major applications to nonlinear wave equation nonlinear fractional differential equations nonlinear oscillations and nonlinear problems arising in various engineering applications are surveyed the confluence of modern mathematics and symbol computation has posed a challenge to developing technologies capable of handling strongly nonlinear equations which cannot be successfully dealt with by classical methods variational iteration method is uniquely qualified to address this challenge the flexibility and adaptation provided by the method have made the method a strong candidate for approximate analytical solutions this paper outlines the basic conceptual framework of variational iteration technique with application to nonlinear problems both achievements and limitations are discussed with direct reference to approximate solutions for nonlinear equations a new iteration formulation is suggested to overcome the shortcoming a very useful formulation for determining approximately the period of a nonlinear oscillator is suggested examples are given to illustrate the solution procedure

variational iteration method for solving burger s and coupled burger s equations by means of variational iteration method the solutions of burger s equation and coupled burger s equations are exactly obtained comparison with the adomian decomposition method is made showing that the former is more effective than the later in this paper he s variational iteration method is introduced to overcome the difficulty arising in calculating adomian polynomials

finite time stabilization of switched stochastic nonlinear systems with mixed odd and even powers this paper investigates the finite time stabilization of a class of switched stochastic nonlinear systems in p normal form where the power orders of the system are dependent upon the switching signal and the system structure is in non triangular form compared with the existing results some power orders of the system are allowed to be even under suitable assumptions a state feedback control law with state dependent switching is designed by using the convex combination method and the adding a power integrator technique it is shown that the resulting closed loop system is finite time stable in probability simulation results of a continuously stirred tank reactor cstr system are provided to show the effectiveness and applicability of the proposed method

numerical steady state and hopf bifurcation analysis on the diffusive nicholson s blowflies equation1research partially supported by natural sciences and engineering research council of canada 1 for the dirichlet boundary value problem of the diffusive nicholson s blowflies equation it was shown in ref 17 that in a certain range of the parameter space there is a unique positive steady state solution in this paper we propose a scheme to compute this steady state numerically in addition we describe an iterative procedure to locate the critical values of the delay where a hopf bifurcation of time periodic solutions takes place near the steady state some numerical simulations of both schemes are given

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

numerical solution of a biological population model using he s variational iteration method this paper presents numerical solution of a degenerate parabolic equation arising in the spatial diffusion of biological populations the variational iteration method and adomian decomposition method are used for solving this equation and then numerical results are compared with each other showing that the variational iteration method leads to more accurate results furthermore variational iteration method overcomes the difficulty arising in calculating the adomian s polynomials which is an important advantage over the adomian decomposition method

stochastic stabilization of singular systems with markovian switchings this paper studies the stochastic stabilization problem for a class of singular markovian jump system the aim is to determine whether or not there is a stochastic feedback controller stabilizing a given singular markovian jump system smjs a new kind of stochastic controller only in the diffusion part is proposed such that the closed loop system has a unique solution and is almost surely exponentially admissible new sufficient condition for the existence of such a controller is given as linear matrix inequalities lmis based on this more extensions to transition probability matrix tpm with elements partially unknown and system states partially observable are developed a numerical example is used to demonstrate the effectiveness of the proposed methods

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

collocation method using quartic b spline for the equal width ew equation the equal width ew equation is solved numerically by giving a new algorithm based on collocation method using quartic b splines at the mid knots points as element shape also we use the fourth runge kutta method for solving the system of first order ordinary differential equations instead of finite difference method our test problems including the migration and interaction of solitary waves are used to validate the algorithm which is found to be accurate and efficient the three invariants of the motion are evaluated to determine the conservation properties of the algorithm the temporal evaluation of a maxwellian initial pulse is then studied

variational iteration method for solving the epidemic model and the prey and predator problem in this article two problems are considered the first one is the problem of the spread of a non fatal disease in a population which is assumed to have constant size over the period of the epidemic and the other one is the problem of prey and predator the variational iteration method is employed to compute an approximation to the solutions of the systems of nonlinear ordinary differential equations governing on these problems the results are compared with the results obtained by adomian decomposition and power series methods some plots are presented to show the reliability and simplicity of the method

solitary waves induced by the boundary forced ew equation the development of a train of ew solitary waves induced by boundary forcing is studied using a petrov galerkin finite element scheme with shape functions taken as quadratic b spline functions a linear recurrence relationship for the numerical scheme is obtained via a crank nicholson approach involving a product approximation results are compared with those for the rlw and kdv equations

global stabilisation for a class of switched high order stochastic nonlinear systems abstractthis paper is devoted to the problem of global stabili sation for a class of switched high order stochastic nonlinear systems under arbitrary switchings by extending the adding a power integrator technique and choosing an appropriate common lyapunov function a common state feedback controller is explicitly constructed to render the closed loop system globally asymptotically stable in probability the effectiveness of the proposed approach is demonstrated by a simulation example

variational iteration method for solving nonlinear boundary value problems abstract in this paper he s variational iteration method is implemented to give approximate and analytical solutions for a class of boundary value problems the variational iteration method which produces the solutions in terms of convergent series requiring no linearization or small perturbation numerical examples are given and comparisons are made with the adomian decomposition method the fact that this method solves nonlinear equations without using adomian polynomials can be considered as an advantage of this method over adomian decomposition method

variational approach to solitary wave solution of the generalized zakharov equation he s semi inverse method is applied to search for the solitary wave solution of the generalized zakharov equation gze the solution process reveals that the method is easy and straightforward

rotation number associated with difference equations satisfied by polynomials orthogonal on the unit circle abstract the techniques of topological dynamics and differential dynamical systems are used to study polynomials orthogonal with respect to a measure supported on the unit circle it is assumed that the reflection coefficients associated with these polynomials form a stationary stochastic ergodic process in particular the techniques mentioned above are used to prove a gap labelling result

counterexamples to the kotani last conjecture for continuum schrodinger operators via character automorphic hardy spaces abstract the kotani last conjecture states that every ergodic operator in one space dimension with non empty absolutely continuous spectrum must have almost periodic coefficients this statement makes sense in a variety of settings for example discrete schrodinger operators jacobi matrices cmv matrices and continuum schrodinger operators in the main body of this paper we show how to construct counterexamples to the kotani last conjecture for continuum schrodinger operators by adapting the approach developed by volberg and yuditskii to construct counterexamples to the kotani last conjecture for jacobi matrices this approach relates the reflectionless operators associated with the prescribed spectrum to a family of character automorphic hardy spaces and then relates the shift action on the space of operators to the resulting action on the associated characters the key to our approach is an explicit correspondence between the space of continuum reflectionless schrodinger operators associated with a given set and the space of reflectionless jacobi matrices associated with a derived set once this correspondence is established we can rely to a large extent on the previous work of volberg and yuditskii to produce the resulting action on the space of characters we analyze this action and identify situations where we can observe absolute continuity without almost periodicity in the appendix we show how to implement this strategy and obtain analogous results for extended cmv matrices

on designing of sliding mode control for stochastic jump systems in this note we consider the problems of stochastic stability and sliding mode control for a class of linear continuous time systems with stochastic jumps in which the jumping parameters are modeled as a continuous time discrete state homogeneous markov process with right continuous trajectories taking values in a finite set by using linear matrix inequalities lmis approach sufficient conditions are proposed to guarantee the stochastic stability of the underlying system then a reaching motion controller is designed such that the resulting closed loop system can be driven onto the desired sliding surface in a limited time it has been shown that the sliding mode control problem for the markovian jump systems is solvable if a set of coupled lmis have solutions a numerical example is given to show the potential of the proposed techniques

stabilization of continuous time randomly switched systems via the lmi approach this paper is concerned on the stabilization problem of continuous time switched systems with random switching signal where the dwell time in each subsystem consists of a fixed part and random part new sufficient conditions for stabilizing controllers including mode independent case are provided in terms of lmis which could be solved directly moreover the obtained results are extended to a more general case that the corresponding operation mode of a controller experiences a disordering phenomenon without designing a controller depending on new operation modes noms a kind of controller only depending on the original operation modes ooms is proposed and satisfies a minimum variance approximation whose solvable conditions are also with lmi forms finally numerical examples are used to demonstrate the effectiveness of the proposed methods

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

a least squares finite element scheme for the ew equation abstract the equal width ew equation is solved by a least squares technique using linear space time finite elements in simulations of the migration of a single solitary wave this algorithm is shown to have good accuracy and conservation the development of solitary waves from an arbitrary initial condition within an ew environment is examined

output tracking of stochastic high order nonlinear systems with markovian switching this technical note poses and solves the output tracking problem for a class of stochastic high order nonlinear systems with stationary markovian switching by introducing a ii operator and using dynkin formula for markovian switching systems a switching controller is constructed to ensure that the closed loop system has a unique solution and is bounded in probability also the tracking error converges to an arbitrarily small neighborhood of zero the efficiency of the tracking controller is demonstrated by a simulation example

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

a fractional variational iteration method for solving fractional nonlinear differential equations recently fractional differential equations have been investigated by employing the famous variational iteration method however all the previous works avoid the fractional order term and only handle it as a restricted variation a fractional variational iteration method was first proposed in g c wu e w m lee fractional variational iteration method and its application phys lett a 374 2010 2506 2509 and gave a generalized lagrange multiplier in this paper two fractional differential equations are approximately solved with the fractional variational iteration method

equality of the spectral and dynamical definitions of reflection for full line jacobi matrices schrodinger operators and cmv matrices we show that being reflectionless in the sense of the well known property of m functions is equivalent to a lack of reflection in the dynamics in the sense that any state that goes entirely to x as t goes entirely to x as t this allows us to settle a conjecture of deift and simon from 1983 regarding ergodic jacobi matrices

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

adaptive tracking for stochastic nonlinear systems with markovian switching the problem of the adaptive tracking for a class of stochastic nonlinear systems with stationary markovian switching is considered in this note an ito formula is proposed for stochastic integral equations with an integral about martingale measure an adaptive backstepping controller is designed such that the closed loop system has a unique solution that is globally bounded in probability and l4 norm of the tracking error converges to an arbitrarily small neighborhood of zero a simulation example demonstrates the efficiency of the proposed scheme

adaptive backstepping controller design for stochastic jump systems in this technical note we improve the results in a paper by shi et al in which problems of stochastic stability and sliding mode control for a class of linear continuous time systems with stochastic jumps were considered however the system considered is switching stochastically between different subsystems the dynamics of the jump system can not stay on each sliding surface of subsystems forever therefore it is difficult to determine whether the closed loop system is stochastically stable in this technical note the backstepping techniques are adopted to overcome the problem in a paper by shi et al the resulting closed loop system is bounded in probability it has been shown that the adaptive control problem for the markovian jump systems is solvable if a set of coupled linear matrix inequalities lmis have solutions a numerical example is given to show the potential of the proposed techniques

analogs of the m function in the theory of orthogonal polynomials on the unit circle we show that the multitude of applications of the weyl titchmarsh m function leads to a multitude of different functions in the theory of orthogonal polynomials on the unit circle that serve as analogs of the m function

technical communique global stabilization of switched stochastic nonlinear systems in strict feedback form under arbitrary switchings this paper is concerned with the problem of global stabilization in probability for a class of switched stochastic nonlinear systems under arbitrary switchings the subsystems are assumed to be in strict feedback form and driven by white noise by introducing a common lyapunov function the common state feedback controller independent of switching signals is constructed based on the backstepping approach it is proved that the zero solution of the closed loop system is fourth moment globally exponentially stable two examples are given to show the effectiveness of the proposed method

state feedback stabilization for stochastic high order nonlinear systems with markovian switching abstract this paper aims to investigate the problem of state feedback stabilization for stochastic high order nonlinear systems with markovian switching by using the generalized ito formula and dynkin formula for markovian switching systems a state feedback controller is constructed to ensure that the closed loop system has a unique solution and the solution of the closed loop systems is almost surely asymptotically stable finally the effectiveness of the controller is demonstrated by a simulation example

exponential stability for discrete time infinite markov jump systems this technical note addresses a class of discrete time stochastic systems with infinite markov jump parameter first of all spectral criterion and lyapunov type criteria are presented for the exponential stability of considered systems further under the condition of strong detectability a barbashin krasovskii stability theorem is shown in terms of a generalized lyapunov equation with a positive semi definite term as an application of the proposed lyapunov stability criterion a sufficient condition of ell 2 input state stability is derived for the infinite markov jump systems disturbed by finite energy random disturbance

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

algebro geometric solutions of the baxter szegő difference equation we derive theta function representations of algebro geometric solutions of a discrete system governed by a transfer matrix associated with an extension of the trigonometric moment problem studied by szeg and baxter we also derive a new hierarchy of coupled nonlinear difference equations satisfied by these algebro geometric solutions

technical communique infinite horizon h2 h control for stochastic systems with markovian jumps this paper studies robust h 2 h control problem for systems subjected to multiplicative noise and markovian parameter jumps a necessary sufficient condition for the existence of h 2 h control is presented by means of two coupled algebraic riccati equations respectively finally a suboptimal h 2 h controller design algorithm is also obtained by solving a convex optimization problem

a new algorithm for calculating adomian polynomials for nonlinear operators in this paper a reliable technique for calculating adomian polynomials for nonlinear operators will be developed the new algorithm offers a promising approach for calculating adomian polynomials for all forms of nonlinearity the algorithm will be illustrated by studying suitable forms of nonlinearity a nonlinear evolution model will be investigated

solitary wave solutions of the improved kdv equation by vim the variational iteration method vim is applied to solve numerically the improved korteweg de vries equation ikdv a correction function is constructed with a general lagrange multiplier that can be identified optimally via the variational theory this technique provides a sequence of functions with easily computable components that converge rapidly to the exact solution of the ikdv equation propagation of single interaction of two and three solitary waves and also birth of solitons have been discussed three invariants of motion have been evaluated to determine the conservation properties of the problem this procedure is promising for solving other nonlinear equations

a reliable modification of adomian decomposition method in this paper we propose a powerful modification of adomian decomposition method that will accelerate the rapid convergence of the series solution the validity of the modified technique is verified through illustrative examples in all cases of differential and integral equations we obtained excellent performance from the modified algorithm the modification could lead to a promising approach for many applications in applied sciences

approximate analytical solution for seepage flow with fractional derivatives in porous media abstract in this paper a new and more exact model for seepage flow in porous media with fractional derivatives has been proposed which has modified the well known darcy law and overcome the continuity assumption of seepage flow a new kind of analytical method of nonlinear problem called the variational iteration method is described and used to give approximate solutions of the problem the results show that the proposed iteration method requiring no linearization or small perturbation is very effective and convenient

backstepping controller design for nonlinear stochastic systems under a risk sensitive cost criterion this paper develops a methodology for recursive construction of optimal and near optimal controllers for strict feedback stochastic nonlinear systems under a risk sensitive cost function criterion the design procedure follows the integrator backstepping methodology and the controllers obtained guarantee any desired achievable level of long term average cost for a given risk sensitivity parameter theta furthermore they lead to closed loop system trajectories that are bounded in probability and in some cases asymptotically stable in the large these results also generalize to nonlinear systems with strongly stabilizable zero dynamics a numerical example included in the paper illustrates the analytical results

application of he s methods to nonlinear chemistry problems in this paper he s variational iteration method vim and homotopy perturbation method hpm are implemented for solving analytically two systems of ordinary differential equations that often appear in chemical applications in both methods the initial approximations can be freely chosen with possible unknown constants which can be determined by imposing the boundary and initial conditions the solution procedure is of utter simplicity and the obtained solution is of high accuracy

decentralized adaptive output feedback controller design for stochastic nonlinear interconnected systems in this paper the controller design for a class of stochastic interconnected systems with both parametric uncertainties and unknown nonlinear interactions is presented the diffusion terms considered are dependent on the outputs of local subsystems and allowed to be unbounded first by employing decentralized state observers totally decentralized adaptive tracking controllers with suitable parameter adaptive laws are designed to ensure the boundedness in probability of all the signals in the closed loop system it is shown that the tracking errors converge to small residual sets around the origin then for systems with relaxed diffusion vector fields a decentralized adaptive stabilizing scheme is proposed to ensure the boundedness in probability of all signals in the closed loop system

reduced order observer based control design for nonlinear stochastic systems in this paper we investigate the stabilization control design problem of nonlinear stochastic siso systems in strict feedback form by introducing a novel reduced order observer an output feedback based control is constructively designed which renders the closed loop system asymptotically stable in the large when the nonlinearities and stochastic disturbance equal zero at the equilibrium point of the open loop system and bounded in probability otherwise besides the obtained controller preserves the equilibrium point of the open loop nonlinear system

inverse problem for polynomials orthogonal on the unit circle polynomials orthogonal on the unit circle with random recurrence coefficients and finite band spectrum are investigated it is shown that the coefficients are in fact quasi periodic the measures associated with these quasi periodic coefficients are exhibited and necessary and sufficient conditions relating quasi periodicity and spectral measures of this type are given analogs for polynomials orthogonal on subsets of the real line are also presented

adaptive tracking control for a class of stochastic switched systems the problem of adaptive tracking is considered for a class of stochastic switched systems in this paper as preliminaries the criterion of global asymptotical practical stability in probability i

approximate solution of nonlinear differential equations with convolution product nonlinearities in this paper a new iteration method is proposed to solve nonlinear problems special attention is paid to nonlinear differential equations with convolution product nonlinearities the results reveal the approximations obtained by the proposed method are uniformly valid for both small and large parameters in nonlinear problems furthermore the first order of approximations are more accurate than perturbation solutions at high order of approximation