almost sure well posedness of the cubic nonlinear schrodinger equation below l 2 mathbb t we consider the cauchy problem for the one dimensional periodic cubic non linear schrodinger equation nls with initial data below l 2 in particular we exhibit nonlinear smoothing when the initial data are randomized then we prove local well posedness of nls almost surely for the initial data in the support of the canonical gaussian measures on h s t for each s 1 and global well posedness for each s 1 12

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

exponential stabilization of nonholonomic chained systems this paper presents a feedback control scheme for the stabilization of two input driftless chained nonholonomic systems also called chained form these systems are controllable but not asymptotically stabilizable by a smooth static state feedback control law in addition exponential stability cannot be obtained with a smooth time varying feedback control law here global asymptotical stability with exponential convergence is achieved about any desired configuration by using a nonsmooth time varying feedback control law the control law depends in addition to the state and time on a function which is constant except at predefined instants of time where the function is recomputed as a nonsmooth function of the state the inputs are differentiable with respect to time and tend exponentially toward zero for use in the analysis a lemma on the exponential convergence of a stable time varying nonlinear system perturbed by an exponentially decaying signal is presented simulation results are also shown

invariance of white noise for kdv on the line we consider the korteweg de vries equation with white noise initial data posed on the whole real line and prove the almost sure existence of solutions moreover we show that the solutions obey the group property and follow a white noise law at all times past or future as an offshoot of our methods we also obtain a new proof of the existence of solutions and the invariance of white noise measure in the torus setting

variable structure exponential stabilization of chained systems based on the extended nonholonomic integrator abstract in this paper a new variable structure control strategy for exponentially stabilizing chained systems is presented based on the extended nonholonomic integrator model the discontinuous coordinate transformation and the reaching law method in variable structure control design the proposed approach converts the stabilization problem of an n dimensional chained system into the pole assignment problem of an n 3 dimensional linear time invariant system and consequently simplifies the stabilization controller design of nonholonomic chained systems

preconditioning for pde constrained optimization with total variation regularization abstract the efficient solution of pde constrained optimization problems is of great significance in many scientific and engineering applications the key point of achieving this goal is to solve the linear systems arising from such problems more efficiently by preconditioning in this paper we consider preconditioning the linear systems arising from pde constrained optimization problems with total variation tv regularization based on the block structure of the coefficient matrix or its row and column transformed forms we propose three kinds of new preconditioners by approximating the schur complements in different ways we analyze the eigenvalue properties of the preconditioned coefficient matrices and provide the eigenvalue bounds independent of mesh size we also show the relations of eigenvalue bounds corresponding to different preconditioners numerical results illustrate the efficiency of the proposed preconditioners by comparison with other existing methods

periodic nonlinear schrodinger equation and invariant measures in this paper we continue some investigations on the periodic nlseiu u iu xx u u p 2 p 6 started in lrs we prove that the equation is globally wellposed for a set of data of full normalized gibbs measrue e beta h phi hd phi x h phi tfrac 1 2 int left phi right 2 tfrac 1 p int left phi right p after suitablel 2 truncation the set and the measure are invariant under the flow the proof of a similar result for the kdv and modified kdv equations is outlined the main ingredients used are some estimates from b1 on periodic nls and kdv type equations

brief exponential stabilization of nonholonomic dynamic systems by smooth time varying control a general dynamic model is proposed for describing a large class of nonholonomic systems including extended chained systems extended power systems underactuated surface vessel systems etc by introducing an assistant state variable and a time varying state transformation based on the concept of minimal dilation degree this class of nonholonomic systems is transformed into linear time varying control systems and the asymptotic exponential stability is thus achieved by using a smooth time varying feedback control law the existence and uniqueness of the minimal dilation degree for the discussed systems are also proved under certain conditions

global finite time stabilisation for a class of stochastic high order time varying nonlinear systems abstractin this paper the problem of global finite time stabilisation by state feedback is investigated for a class of stochastic high order nonlinear systems with time varying nonlinearities based on the generalised stochastic lyapunov theorem on finite time stability and by skillfully using the method of adding a power integrator a continuous state feedback controller is successfully constructed to guarantee that the closed loop system is globally finite time stable in probability finally several simulation examples are provided to illustrate the effectiveness of the proposed method

optimal motion planning for nonholonomic systems using genetic algorithm with wavelet approximation an optimal motion planning scheme using genetic algorithm with wavelet approximation is proposed for nonholonomic systems the motion planning of nonholonomic systems can be formulated as an optimal control of a driftfree system a cost function is introduced to incorporate the control energy and the final state errors the control inputs are determined to minimize the cost functional by using the method of wavelet the infinite dimensional optimal control problem is truncated to a finite dimensional one based on the wavelet bases the genetic algorithm is employed to solve a feasible trajectory satisfying nonholonomic constraints the proposed scheme is applied to a free floating robot consisting of two one link arms connected to a main base via revolute joints the numerical results demonstrate that the genetic algorithm with the wavelet approximation is an effective approach to steer a nonholonomic system from its initial state to its final state 2006 published by elsevier inc

homogeneous observers iterative design and global stabilization of high order nonlinear systems by smooth output feedback we study the problem of global stabilization by smooth output feedback for a class of n dimensional homogeneous systems whose jacobian linearization is neither controllable nor observable a new output feedback control scheme is proposed for the explicit design of both homogeneous observers and controllers while the smooth state feedback control law is constructed based on the tool of adding a power integrator the observer design is new and carried out by developing a machinery which makes it possible to assign the observer gains one by one in an iterative manner such design philosophy is fundamentally different from that of the traditional luenberger observer in which the observer gain is determined by observability in the case of linear systems our design method provides not only a new insight but also an alternative solution to the output feedback stabilization problem for a class of high order nonhomogeneous systems we further show how the proposed design method with an appropriate modification can still achieve global output feedback stabilization examples and simulations are given to demonstrate the main features and effectiveness of the proposed output feedback control schemes

robust reliable stabilization of stochastic switched nonlinear systems under asynchronous switching this paper is concerned with the problem of robust reliable control for a class of uncertain stochastic switched nonlinear systems under asynchronous switching where the switching instants of the controller experience delays with respect to those of the system a design scheme for the reliable controller is proposed to guarantee almost surely exponential stability for stochastic switched systems with actuator failures and the dwell time approach is utilized for the stability analysis then the approach is extended to take into account stochastic switched system with lipschitz nonlinearities and structured uncertainties finally a numerical example is employed to verify the proposed method

adaptive output feedback stabilization for nonholonomic systems with strong nonlinear drifts abstract this paper investigates the design of an output feedback adaptive stabilization controller for a nonholonomic chained system with strong nonlinear drifts including modeled nonlinear dynamics unmodeled dynamics and dynamics modeled with unknown parameters also the virtual control directions of the system are unknown the purpose is to design a nonlinear output feedback switching controller such that the closed loop system is globally asymptotically stable a novel observer and estimator are introduced for states and parameter estimates respectively a constructive procedure of design for an output feedback adaptive controller is given by using the integrator backstepping approach and based on the proposed observer and parameter estimator an example is given to show the effectiveness of the proposed scheme

least squares solutions of the matrix equation axb cyd e with the least norm for symmetric arrowhead matrices in this paper the least squares solution of the matrix equation axb cyd e for symmetric arrowhead matrices with the least norm is discussed by using moore penrose inverse and the kronecker product the general expression of the solution to this problem is derived a corresponding numerical algorithm and an example are also given

kdv preserves white noise it is shown that white noise is an invariant measure for the korteweg devries equation on mathbb t this is a consequence of recent results of kappeler and topalov establishing the well posedness of the equation on appropriate negative sobolev spaces together with a result of cambronero and mckean that white noise is the image under the miura transform ricatti map of the weighted gibbs measure for the modified kdv equation proven to be invariant for that equation by bourgain

the empirical mode decomposition and the hilbert spectrum for nonlinear and non stationary time series analysis a new method for analysing nonlinear and non stationary data has been developed the key part of the method is the empirical mode decomposition method with which any complicated data set can be dec

preconditioning toeplitz plus diagonal linear systems using the sherman morrison woodbury formula in order to solve the toeplitz plus diagonal linear systems arising from image restorations efficiently we propose a sparse approximate inverse preconditioner based on the sherman morrison woodbury formula the preconditioner can be constructed through an incomplete factorization combined with some dropping strategies when the preconditioner is applied to the conjugate gradient method for solving the toeplitz plus diagonal linear systems numerical results show that our preconditioning method is more effective than other existing ones

nonholonomic motion planning steering using sinusoids methods for steering systems with nonholonomic c onstraints between arbitrary configurations are investigated suboptimal trajectories are derived for systems that are not in canonical form systems in which it takes more than one level of bracketing to achieve controllability are considered the trajectories use sinusoids at integrally related frequencies to achieve motion at a given bracketing level a class of systems that can be steered using sinusoids claimed systems is defined conditions under which a class of two input systems can be converted into this form are given

adaptive stabilization of stochastic nonholonomic systems with nonlinear parameterization this paper investigates the problem of adaptive stabilization by state feedback for a class of stochastic nonholonomic systems in chained form with nonlinear parameterization a parameter separation technique is introduced to transform the nonlinear parameterized nonholonomic system into a linear like parameterized one then using input state scaling and backstepping techniques an adaptive state feedback controller is obtained based on switching strategy to eliminate the phenomenon of uncontrollability global asymptotic regulation in probability of the closed loop system states are guaranteed finally a simulation example is provided to illustrate the effectiveness of the proposed method

on the computation of inverses and determinants of a kind of special matrices abstract in this paper the inverse and determinant of a special kind of centrosymmetric matrices are investigated based on the partition property of a matrix with centrosymmetric structure and algorithms for the inverse and determinant proposed in chen and yu 2011 a computation algorithm for the inverse and determinant of a centrosymmetric matrix is finally developed

a switching algorithm for global exponential stabilization of uncertain chained systems this note deals with chained form systems with strongly nonlinear unmodeled dynamics and external disturbances the objective is to design a robust nonlinear state feedback law such that the closed loop system is globally kexponentially stable we propose a novel switching control strategy involving the use of input state scaling and integrator backstepping the new features of our controllers include the ability to achieve lyapunov stability exponential convergence and robustness to a set of uncertain drift terms

control of high order nonholonomic systems in power chained form using discontinuous feedback addresses the problems of almost asymptotic stabilization and global asymptotic regulation gar for a class of high order nonholonomic systems in power chained form this particular class of nonlinear systems is an extension of a nonholonomic system in chained form that has received considerable attention in the past few years the nonholonomic system considered in this paper is not necessarily affine in the control variables and therefore cannot be handled by existing methods sufficient conditions are presented under which a discontinuous state feedback control law or a switching controller can be recursively constructed using the so called adding a power integrator technique of c qian et al 2001 we also illustrate how the results can be extend to multi input systems in power chained form simulation examples are provided to demonstrate the effectiveness of the proposed controllers

on lagrangian dynamics and its control formulations this paper exploits the equivalence between constrained dynamics problems and a class of tracking control problems an alternative derivation of the modern formulation of parczewski and blajer j appl math 56 1989 676 684 is presented including some new analysis on the almost singular case followed by a critique of the classical lagrangian formulation in addition a new formulation which allows the constraints to be satisfied approximately is presented a general closed loop control law which depends on a user specified threshold of constraint errors e is proposed transforming the default dae problem into a stiff ode initial value problem which can be routinely solved on computers it is shown that certain explosively unstable open loop systems may be stabilized by the use of closed loop control using a small but finite e an example is worked out using both the open loop and the closed loop control formulations

adaptive global stabilization of nonholonomic systems with strong nonlinear drifts a new input to state scaling scheme is first introduced to transform a class of nonholonomic systems in a chained form with strong nonlinear drifts and unknown constant parameters into a strict feedback form the backstepping technique is then applied to design a global adaptive stabilization controller a switching strategy based on the control input magnitude rather than the time is derived to get around the phenomenon of uncontrollability simulation examples validate the effectiveness of the proposed controller

output feedback adaptive stabilization control design for non holonomic systems with strong non linear drifts this paper investigates the problem of output feedback adaptive stabilization control design for non holonomic chained systems with strong non linear drifts including modelled non linear dynamics unmodelled dynamics and those modelled but with unknown parameters an observer and an estimator are introduced for state and parameter estimates respectively by using the integrator backstepping approach and based on the observer and parameter estimator a constructive design procedure for output feedback adaptive stabilization control is given it is shown that under some conditions the control design ensures the closed loop system is globally asymptotically stable when there is no non linear drift in the first subsystem and semiglobally asymptotically stable otherwise an example is given to show the effectiveness of the theory

invariant measures and long time behaviour for the benjamin ono equation iii we complete the program developed in our previous works aiming to construct an infinite sequence of invariant measures of gaussian type associated with the conservation laws of the benjamin ono equation

global inverse optimal stabilization of stochastic nonholonomic systems abstract optimality has not been addressed in existing works on control of stochastic nonholonomic systems this paper presents a design of optimal controllers with respect to a meaningful cost function to globally asymptotically stabilize in probability nonholonomic systems affine in stochastic disturbances the design is based on the lyapunov direct method the backstepping technique and the inverse optimal control design a class of lyapunov functions which are not required to be as nonlinearly strong as quadratic or quartic is proposed for the control design thus these lyapunov functions can be applied to design of controllers for underactuated stochastic mechanical systems which are usually required lyapunov functions of a nonlinearly weak form the proposed control design is illustrated on a kinematic cart of which wheel velocities are perturbed by stochastic noise

riccati map on l02 t and its applications abstract this paper is concerned with the spectral properties of the schrodinger operator l q def d 2 d x 2 q with periodic potential q from the sobolev space h 1 t we obtain asymptotic formulas and a priori estimates for the periodic and dirichlet eigenvalues which generalize known results for the case of potentials q l 2 t the key idea is to reduce the problem to a known one the spectrum of the impedance operator via a nonlinear analytic isomorphism between l 0 2 t and the sobolev space h 0 1 t

discontinuous control of nonholonomic systems the problem of asymptotic convergence for a class of nonholonomic control systems via discontinuous control is addressed and solved from a new point of view it is shown that control laws which ensures asymptotic exponential convergence of the closed loop system can be easily designed if the system is described in proper coordinates in such coordinates the system is discontinuous hence the problem of local asymptotic stabilization for a class of discontinuous nonholonomic control systems is dealt with and a general procedure to transform a continuous system into a discontinuous one is presented moreover a general strategy to design discontinuous control laws yielding asymptotic convergence for a class of nonholonomic control systems is proposed the enclosed simulation results show the effectiveness of the method

robust stability and stabilization of a class of nonlinear discrete time stochastic systems an lmi approach abstract a problem of robust state feedback stability and stabilization of nonlinear discrete time stochastic processes is considered the linear rate vector of a discrete time system is perturbed by a nonlinear function that satisfies a quadratic constraint our objective is to show how linear constant feedback laws can be formulated to stabilize this type of nonlinear discrete time systems and at the same time maximize the bounds on this nonlinear perturbing function which the system can tolerate without becoming unstable the state dependent diffusion is modeled by a normal sequence of identically independently distributed random variables the new formulation provides a suitable setting for robust stabilization of nonlinear discrete time systems where the underlying deterministic systems satisfy the generalized matching conditions our method which is based on linear matrix inequalities lmis is distinctive from the existing robust control and absolute stability techniques examples are given to demonstrate the obtained results

adaptive control of nonlinearly parameterized systems the smooth feedback case studies global adaptive control of nonlinearly parameterized systems with uncontrollable linearization using a parameter separation technique and the tool of adding a power integrator we develop a feedback domination design approach for the explicit construction of a smooth adaptive controller that solves the problem of global state regulation in contrast to the existing results in the literature a key feature of our adaptive regulator is its minimum order property namely no matter how big the number of unknown parameters is the order of the dynamic compensator is identical to one and is therefore minimal as a consequence global state regulation of feedback linearizable systems with nonlinear parameterization is achieved by one dimensional adaptive controllers without imposing any extra e g convex concave conditions on the unknown parameters

improved schur complement preconditioners for block toeplitz systems with small size blocks in this paper we employ the preconditioned conjugate gradient method with the improved schur complement preconditioners for hermitian positive definite block toeplitz systems with small size blocks schur complement preconditioners have been proved to be an effective method for such block toeplitz systems ching et al 2007 the modification is based on taylor expansion approximation we prove that the matrices preconditioned by improved schur preconditioners have more clustered spectra compared to that of the schur complement preconditioners hence preconditioned conjugate gradient type methods will converge faster numerical examples are given to demonstrate the efficiency of the proposed method

control and stabilization of nonholonomic dynamic systems a class of inherently nonlinear control problems has been identified the nonlinear features arising directly from physical assumptions about constraints on the motion of a mechanical system models are presented for mechanical systems with nonholonomic constraints represented both by differential algebraic equations and by reduced state equations control issues for this class of systems are studied and a number of fundamental results are derived although a single equilibrium solution cannot be asymptotically stabilized using continuous state feedback a general procedure for constructing a piecewise analytic state feedback which achieves the desired result is suggested

some studies on nonpolynomial interpolation and error analysis abstract in this paper we propose nonpolynomial and hermite nonpolynomial interpolation with multiple parameters and present method to determine optimal value of parameters which generate minimum error in approximation the generalized error analysis results for nonpolynomial and hermite nonpolynomial interpolations are derived we establish theoretical relationship among nonpolynomial polynomial interpolation and the fourier series and propose solution to runge s phenomenon through nonpolynomial interpolation the hermite nonpolynomial cubic spline nonpolynomial cubic spline interpolation methods and their error analysis are presented numerical simulations are carried out for the analysis of error in cubic spline interpolations proposed method is applied to the analysis of various time series to show comparison in errors between polynomial and nonpolynomial spline interpolations and to empirical mode decomposition emd to illustrate practical usefulness of the results

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

quasi invariant gaussian measures for the cubic fourth order nonlinear schrodinger equation we consider the cubic fourth order nonlinear schrodinger equation on the circle in particular we prove that the mean zero gaussian measures on sobolev spaces h s mathbb t s frac 3 4 are quasi invariant under the flow

an improved empirical mode decomposition method based on the cubic trigonometric b spline interpolation algorithm abstract empirical mode decomposition emd is a new method presented recently for analyzing nonlinear and non stationary signals its basic idea is to decompose the signal into a series of complete orthogonal intrinsic mode functions imfs based on the local characteristics of the signal in time domain the key step of emd is to use the cubic spline interpolation to connect the maximum and minimum values of the signals into upper and lower envelopes respectively and then calculate the mean values of upper and lower envelopes based on the cubic trigonometric b spline interpolation algorithm a new improved method for emd is proposed named ctb emd in this paper in this method the interpolation curve is more flexible because of the adjustability of shape of the cubic trigonometric b splines curve thus the overshoot and undershoot problems in the cubic spline interpolation curve can be avoided and then the decomposition of the signal is more accurate and effect through numerical experiments we compare the effect of this method with other methods on decomposing simulation signals and real signals experimental results show that this method can decompose signals more effectively and accurately

exponential stabilization of driftless nonlinear control systems using homogeneous feedback this paper focuses on the problem of exponential stabilization of controllable driftless systems using time varying homogeneous feedback the analysis is performed with respect to a homogeneous norm in a nonstandard dilation that is compatible with the algebraic structure of the control lie algebra it can be shown that any continuous time varying controller that achieves exponential stability relative to the euclidean norm is necessarily non lipschitz despite these restrictions we provide a set of constructive sufficient conditions for extending smooth asymptotic stabilizers to homogeneous exponential stabilizers the modified feedbacks are everywhere continuous smooth away from the origin and can be extended to a large class of systems with torque inputs the feedback laws are applied to an experimental mobile robot and show significant improvement in convergence rate over smooth stabilizers

stability of linear stochastic systems via lyapunov exponents and applications to power systems this paper studies linear systems under sustained random perturbations the stochastic perturbation model is given by a bounded markov diffusion process as it appears e g in the description of load or generation uncertainties of power systems for such systems the lyapunov exponents describe necessary and sufficient conditions for almost sure asymptotic stability the paper presents several numerical methods for the computation of lyapunov exponents and applies this methodology to linear oscillators in dimension 2 and 3 and to a one machine infinite bus electric power system

adaptive repetitive control for a class of nonlinearly parametrized systems in this note lyapunov based adaptive repetitive control is presented for a class of nonlinearly parametrized systems through the use of an integral lyapunov function the controller singularity problem is elegantly solved as it avoids the nonlinear parametrization from entering into the adaptive control and repetitive control global stability of the adaptive system and asymptotic convergence of the tracking error are established and tracking error bounds are provided to quantify the control performance both partially and fully saturated learning laws are analyzed in detail and compared analytically

a bilinear estimate with applications to the kdv equation u x 0 u0 x where u0 h r our principal aim here is to lower the best index s for which one has local well posedness in h r i e existence uniqueness persistence and continuous dependence on the data for a finite time interval whose size depends on u0 hs equation in 1 1 was derived by korteweg and de vries 21 as a model for long wave propagating in a channel a large amount of work has been devoted to the existence problem for the ivp 1 1 for instance see 9 10 the inverse scattering method applies to this problem and under appropriate decay assumptions on the data several existence results have been established see 5 6 14 28 33 another approach inherited from hyperbolic problems relies on the energy estimates and in particular shows that 1 1 is locally well posed in h r for s 3 2 see 2 3 12 29 30 31 using these results and conservation laws global in time well posedness in h r s 2 was established see 3 12 30 also global in time weak solutions in the energy space h r were constructed in 34 in 13 and 22 a local smoothing effect for solutions of 1 1 was discovered this combined with the conservation laws was used in 13 and 22 to construct global in time weak solutions with data in h r and even in l r in 16 we introduced oscillatory integral techniques to establish local well posedness of 1 1 in h r s 3 4 and hence global in time well posedness in h r s 1 in 16 we showed how to obtain the above mentioned result by picard iteration in an appropriate function space in 4 j bourgain introduced new function spaces adapted to the linear operator t 3 x for which there are good bilinear estimates for the nonlinear term x u 2 using these spaces bourgain was able to establish local well posedness of 1 1 in h r l r and hence by a conservation