disturbance observer based control for semi markovian jump systems with generally uncertain transition rate and saturation nonlinearity abstract this paper deals with the problem of disturbance observer based control dobc for semi markovian jump systems s mjss with generally uncertain transition rate tr and saturation nonlinearity unlike the existing theories the proposed method considers the external disturbance and saturation nonlinearity in s mjss with more general tr first of all to study this dobc problem the sufficient condition for stochastic stability of the system is derived by the use of lyapunov krasovskii functional then the design methods of the anti disturbance controller and the disturbance observer are proposed based on the given stability condition of the closed loop system furthermore the maximum domain of attraction is estimated by solving an optimization iterative algorithm finally two numerical examples are given to prove the correctness of the proposed results

analyticity of periodic traveling free surface water waves with vorticity we prove that the prole of a periodic traveling wave propagating at the surface of water above a at bed in a ow with a real analytic vorticity must be real analytic provided the wave speed exceeds the horizontal uid velocity throughout the ow the real analyticity of each streamline be

global output feedback stabilisation of a class of stochastic systems with unknown growth rate this paper is concerned with the global output feedback stabilisation problem for a class of stochastic systems with unknown growth rate the output of the system under consideration contains unkno

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 existence and blow up phenomena for the weakly dissipative novikov equation in this paper we consider the global existence and blow up for the weakly dissipative novikov equation we firstly establish the local well posedness for the weakly dissipative novikov equation by kato s theorem then we present some blow up results finally we present the global existence of strong solutions to the weakly dissipative equation c 2011 elsevier ltd all rights reserved

adding one power integrator a tool for global stabilization of high order lower triangular systems a new feedback design tool called adding a power integrator is introduced and used to solve the problem of global robust stabilization for a significant class of uncertain nonlinear systems that are of a lower triangular form but neither necessarily feedback linearizable fully or partially nor affine in the control input and therefore cannot be dealt with via conventional approaches sufficient conditions are presented under which a globally stabilizing smooth state feedback control law can be explicitly constructed using repeatedly the adding one power integrator technique this novel design technique permits removal of the feedback linearizability and linearity of the control input which have been two common assumptions so far in the literature of nonlinear control

global weak solutions to the novikov equation abstract the existence of global weak solutions to the cauchy problem for the novikov equation is established in the space c 0 r l 0 h 1 r without the sign condition on the initial value the limit of viscous approximations for the equation is used to establish the existence of the global weak solution the key elements in our analysis include a new one sided super bound and a new higher norm estimate on the first order derivatives of the solution

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

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

blow up blow up rate and decay of the solution of the weakly dissipative camassa holm equation in this paper we mainly study several problems on the weakly dissipative periodic camassa holm equation at first the local well posedness of the equation is obtained by kato s theorem a necessary and sufficient condition of the blow up of the solution and some criteria guaranteeing the blow up of the solution are established then the blow up rate of the solution is discussed moreover we prove that the equation has global solutions and these global solutions decay to zero as time goes to infinite provided the potentials associated to their initial date are of one sign

on the weakly dissipative camassa holm degasperis procesi and novikov equations abstract we show that the weakly dissipative camassa holm degasperis procesi hunter saxton and novikov equations can be reduced to their non dissipative versions by means of an exponentially time dependent scaling hence up to a simple change of variables the non dissipative and dissipative versions of these equations are equivalent similar results hold also for the equations in the so called b family of equations as well as for the two component and versions of the above equations

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

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

further results on global adaptive stabilisation for a class of uncertain stochastic nonlinear systems this paper considers the global adaptive stabilisation for a class of uncertain stochastic nonlinear systems comparing with the existing relevant literature the systems under investigation allow more serious unknowns uncertainties more importantly by remarkably reducing the dimension of dynamic compensator for system unknowns from n to 2 and considerably diminishing the overparametrisation in the existing literature this paper proposes an improved design scheme for adaptive state feedback controllers it is turned out that with the designed controller in loop all the closed loop system states are globally bounded and the original system states converge to the origin both in the sense of probability one a simulation example is also given to demonstrate the effectiveness of the theoretical results

on the blow up rate and the blow up set of breaking waves for a shallow water equation we consider the problem of the development of singularities for classical solutions to a new periodic shallow water equation blow up can occur only in the form of wave breaking i e the solution remains bounded but its slope becomes unbounded in finite time a quite detailed description of the wave breaking phenomenon is given there is at least a point in general depending on time where the slope becomes infinite exactly at breaking time the precise blow up rate is established and for a large class of initial data we also determine the blow up set

integrable peakon equations with cubic nonlinearity we present a new integrable partial differential equation found by vladimir novikov like the camassa holm and degasperis procesi equations this new equation admits peaked soliton peakon solutions but it has nonlinear terms that are cubic rather than quadratic we give a matrix lax pair for v novikov s equation and show how it is related by a reciprocal transformation to a negative flow in the sawada kotera hierarchy infinitely many conserved quantities are found as well as a bi hamiltonian structure the latter is used to obtain the hamiltonian form of the finite dimensional system for the interaction of n peakons and the two body dynamics n 2 is explicitly integrated finally all of this is compared with some analogous results for another cubic peakon equation derived by zhijun qiao

global fixed time stabilization for switched stochastic nonlinear systems under rational switching powers abstract this note studies global fixed time stabilization for switched stochastic nonlinear systems under rational switching powers with the aid of stochastic fixed time stability theorem a new control approach is presented to ensure that the system state globally reaches zero almost surely in fixed time independent of initial conditions the developed scheme is used to controller design of the liquid level system

a homogeneous domination approach to state feedback of stochastic high order nonlinear systems with time varying delay the homogeneous domination approach is introduced to solve the state feedback stabilization problem for stochastic high order nonlinear systems with time varying delay under the weaker conditions on the drift and diffusion terms by using 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

a combined homogeneous domination and sign function approach to output feedback stabilization of stochastic high order nonlinear systems for a class of stochastic high order nonlinear systems by introducing the combined homogeneous domination and sign function design approach this technical note solves the problem of output feedback control under the weaker high order and nonlinear growth conditions

nonlinear asymptotic impedance model for a helmholtz resonator liner the usual nonlinear corrections for a helmholtz resonator type impedance do not seem to be based on a systematic asymptotic solution of the pertaining equations we aim to present a systematic derivation of a solution of the nonlinear helmholtz resonator equation in order to obtain analytically expressions for impedances close to resonance while including nonlinear effects the amplitude regime considered is such that when we stay away from the resonance condition the nonlinear terms are relatively small and the solution obtained is of the linear equation formed after neglecting the nonlinear terms close to the resonance frequency the nonlinear terms can no longer be neglected and algebraic equations are obtained that describe the corresponding nonlinear impedance sample results are presented including a few comparisons with measurements available in the literature the validity of the model is understood in the near resonance and nonresonance regimes

on the optimal control problem for the novikov equation with strong viscosity abstract in this paper we consider an optimal control problem for the novikov equation with strong viscosity using the faedo galerkin method we derive the existence of a unique weak solution to this equation applying lions theory we obtain the existence of an optimal solution to the control problem for this equation we also deduce the first order necessary optimality condition moreover we establish two second order sufficient optimality conditions which require coercivity of the augmented lagrangian functional on the whole space or on a suitable subspace

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

robust output feedback stabilization of uncertain nonlinear systems with uncontrollable and unobservable linearization this paper investigates the problem of robust output feedback stabilization for a family of uncertain nonlinear systems with uncontrollable unobservable linearization to achieve global robust stabilization via smooth output feedback we introduce a rescaling transformation with an appropriate dilation which turns out to be very effective in dealing with uncertainty of the system using this rescaling technique combined with the nonseparation principle based design method we develop a robust output feedback control scheme for uncertain nonlinear systems in the p normal form under a homogeneous growth condition the construction of smooth state feedback controllers and homogeneous observers uses only the knowledge of the bounding homogeneous system rather than the uncertain system itself the robust output feedback design approach is then extended to a class of uncertain cascade systems beyond a strict triangular structure examples are provided to illustrate the results of the paper

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

qualitative analysis for the new shallow water model with cubic nonlinearity abstract considered in this paper is the new shallow water model with cubic nonlinearity which admits the single peaked solitons and multi peakon solutions and includes both the modified camassa holm equation also called fokas olver rosenau qiao equation and the novikov equation as two special cases the main investigation is the cauchy problem of the new shallow water model with qualitative properties of its solutions we first establish the local well posedness for the cauchy problem of the new shallow water model and then derive a precise blow up scenario and the blow up mechanisms for solutions with certain initial profiles moreover with analytic initial data we show that its solutions are analytic in both variables globally in space and locally in time finally we investigate the persistence properties of the solution to the cauchy problem of the new shallow water model

global stabilization of stochastic nonlinear systems via c 1 and c infty controllers the problem of designing c 1 or c infty controllers for a class of stochastic nonlinear systems snss in lower triangular form is studied in this note by using the well known backstepping method the concept of homogeneity with monotone degrees hwmd and the sign function approach we construct a c 1 state feedback controller recursively meanwhile by employing a polynomial lyapunov function with sign functions we prove that the solution to snss is globally asymptotically stable in probability furthermore based on the concept of hwmd it shows that c 1 controllers for a class of three dimensional snss can be modified to c infty controllers under certain conditions finally two simulation examples are given to demonstrate the effectiveness of the proposed controllers

blow up phenomenon for the integrable novikov equation abstract in this paper we investigate a new integrable equation derived recently by v s novikov generalizations of the camassa holm equation j phys a 42 34 2009 342002 14 pp analogous to the camassa holm equation and the degasperis procesi equation this new equation possesses the blow up phenomenon under the special structure of this equation we establish sufficient conditions on the initial data to guarantee the formulation of singularities in finite time a global existence result is also found

a unified time varying feedback approach and its applications in adaptive stabilization of high order uncertain nonlinear systems we are concerned with two key problems of adaptive control design one is to find the feasible conditions and the valid boundary of the time varying feedback scheme another one lies in the improved generalization of the homogeneous idea in the global adaptive stabilization of high order uncertain nonlinear systems the distinguished feature of the system to be investigated is the serious coexistence between unknown time varying parameters and unknown time varying control coefficients design procedures of the continuous controller are provided based on the sign function technique and the delicate search of the time varying function and a lyapunov function finally the control of uncertain single link robotic manipulator demonstrates the application of design scheme

cooperative control of multiple stochastic high order nonlinear systems abstract distributed cooperative control of multiple stochastic high order nonlinear systems has not been addressed in literature this paper presents an approach to design of distributed cooperative controllers for multiple stochastic high order nonlinear systems under directed leader followers type network topology via the so called distributed integrator backstepping method by using the algebraic graph theory and stochastic analysis method it is shown that the output tracking errors between the followers and the leader can be tuned arbitrarily small while all the states of the closed loop system remain bounded in probability finally the effectiveness of the proposed control approach is illustrated on a stochastic underactuated mechanical system

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

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

on a non linear differential equation modelling helmholtz resonator response abstract the non linear differential equation y dot y sgn y e y y sin t proposed by hersh and walker 1 as a model for helmholtz resonator response to a sound wave in the presence of grazing mean flow is studied by matched asymptotic expansion for e 1 the waveform contains a smooth outer part and a boundary layer of rapid change approximations to two terms are found in each region and approximate value for all fourier coefficients also found and compared very favourably with numerical curve fits for the first coefficients given in reference 1 the asymptotic approximations are found to be highly accurate over the whole waveform when compared with numerical solutions

higher regularity of global attractors of a weakly dissipative fractional korteweg de vries equation in this paper we study the long time behavior of solutions to a weakly dissipative fractional korteweg de vries kdv equation on the real line r the main difficulty lies in that the dissipative term is a nonlocal operator we overcome this difficulty by the commutator estimates and product estimates associated with fractional laplacian the asymptotical compactness of solution semigroup is proved by the tail estimates finally we conclude the existence of h2 r h5 r global attractor of the weakly dissipative fractional kdv equation

output tracking control for generalised high order nonlinear system with serious uncertainties abstractthis paper focuses on the problem of output tracking control for a class of generalised high order uncertain nonlinear systems serious uncertainties are composed of unknown high order terms unknown nonlinear functions and the signal to be tracked the new feedback scheme guarantees that the tracking error belongs to a prescribed small neighbourhood of the origin in finite time design procedures are presented by combining improved adding a power integrator method with the recursive construction as an application the control methodology is used in the tracking control of the mass spring mechanical system

on the cauchy problem for the modified novikov equation with peakon solutions abstract a new nonlinear dispersive partial differential equation with cubic nonlinearity which includes the famous novikov equation as special case is investigated we first establish the local well posedness in a range of the besov spaces b p r s p r 1 s max 3 2 1 1 p but s 2 1 p which generalize the sobolev spaces h s well posedness in h s with s 3 2 is also established by applying kato s semigroup theory then we give the precise blow up scenario moreover with analytic initial data we show that its solutions are analytic in both variables globally in space and locally in time finally we prove that peakon solutions to the equation are global weak solutions

the cauchy problem for a generalized camassa holm equation abstract in this paper we are concerned with the cauchy problem of the generalized camassa holm equation using a galerkin type approximation scheme it is shown that this equation is well posed in sobolev spaces h s s 3 2 for both the periodic and the nonperiodic case in the sense of hadamard that is the data to solution map is continuous furthermore it is proved that this dependence is sharp by showing that the solution map is not uniformly continuous the nonuniform dependence is proved using the method of approximate solutions and well posedness estimates moreover it is shown that the solution map for the generalized camassa holm equation is holder continuous in h r topology finally with analytic initial data we show that its solutions are analytic in both variables globally in space and locally in time

helmholtz resonator impedance model part 1 nonlinear behavior a one dimensional preliminary design impedance prediction model is derived for helmholtz resonators constructed with circular orie ces the model addresses only the effects of resonator geometry and incident sound pressure amplitude the effects of grazing e ow are not included an experimental program was conducted to calibrate unknown empirical parameters derived in the model the model was shown to predict reasonably accurately impedance data published in the open literature for resonators constructed with single and multiple orie ces over a wide range of sound pressure amplitudes and frequencies the model provides a rapid means of calculating resonator impedance as a function of resonator geometry incident sound pressure amplitude and frequency

global state feedback stabilisation of nonlinear systems with high order and low order nonlinearities this paper studies the state feedback control problem for a class of nonlinear systems with high order and low order nonlinearities the introduction of the sign function together with the method of adding a power integrator and lyapunov stability theorem makes the closed loop system globally asymptotically stable exploiting the idea of how to deal with growth nonlinearities with both high order and low order being relaxed to some intervals is the focus of this work

exponential state estimation for stochastically disturbed discrete time memristive neural networks multiobjective approach the state estimation of the discrete time memristive model is studied in this article by applying the stochastic analysis technique sufficient formulas are established to ensure the exponentially mean square stability of the error model moreover the derived control gain matrix can be calculated via the linear matrix inequality lmi it should be mentioned that by extending the derived conclusion to a multiobjective optimization problem the maximum bound of the active function and the minimum bound of the disturbance attenuation are derived the corresponding simulation figures are provided in the end

the cauchy problem for the integrable novikov equation in this paper we consider the cauchy problem for the integrable novikov equation by using the littlewood paley decomposition and nonhomogeneous besov spaces we prove that the cauchy problem for the integrable novikov equation is locally well posed in the besov space b p r s with 1 max 1 1 p 3 2 in particular when u 0 is an element of b p r s boolean and h l with 1 max 1 1 p 3 2 for all t is an element of 0 t we have that vertical bar vertical bar u t vertical bar vertical bar h l vertical bar vertical bar u 0 vertical bar vertical bar h l we also prove that the local well posedness of the cauchy problem for the novikov equation fails in b 2 3 2 infinity c 2012 elsevier inc all rights reserved

well posedness and persistence properties for the novikov equation abstract recently novikov found a new integrable equation we call it the novikov equation in this paper which has nonlinear terms that are cubic rather than quadratic and admits peaked soliton solutions peakons firstly we prove that the cauchy problem for the novikov equation is locally well posed in the besov spaces b 2 r s which generalize the sobolev spaces h s with the critical index s 3 2 then well posedness in h s with s 3 2 is also established by applying kato s semigroup theory finally we present two results on the persistence properties of the strong solution for the novikov equation

finite time output feedback stabilization of high order uncertain nonlinear systems this paper studies the problem of finite time output feedback stabilization for a class of high order nonlinear systems with the unknown output function and control coefficients under the

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

finite time stabilisation of a class of stochastic nonlinear systems with dead zone input this paper addresses the problem of finite time stabilisation by state feedback for a class of stochastic nonlinear systems in strict feedback form remarkably the system under consideration posse

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

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

generalizations of the camassa holm equation we classify generalized camassa holm type equations which possess infinite hierarchies of higher symmetries we show that the obtained equations can be treated as negative flows of integrable quasi linear scalar evolution equations of orders 2 3 and 5 we present the corresponding lax representations or linearization transformations for these equations some of the obtained equations seem to be new

the trajectories of particles in stokes waves analyzing a free boundary problem for harmonic functions we show that there are no closed particle paths in an irrotational inviscid traveling wave propagating at the surface of water over a flat bed within a period each particle experiences a backward forward motion with a slight forward drift

a direct algorithm of one dimensional optimal system for the group invariant solutions a direct and systematic algorithm is proposed to find one dimensional optimal system for the group invariant solutions which is attributed to the classification of its corresponding one dimensional lie algebra since the method is based on different values of all the invariants the process itself can both guarantee the comprehensiveness and demonstrate the inequivalence of the optimal system with no further proof to leave the algorithm clear we illustrate each stage with a couple of well known examples the korteweg de vries equation and the heat equation finally we apply our method to the novikov equation and use the found optimal system to investigate the corresponding invariant solutions

global stabilisation for a class of more general high order time delay nonlinear systems by output feedback this paper addresses the problem of global stabilisation by output feedback for a class of high order time delay nonlinear systems with more general uncertainties which cover both high order and low order nonlinearities by introducing sign function and necessarily modifying the homogeneous domination approach an output feedback controller is successfully constructed to guarantee the global asymptotic stability of the resulting closed loop system due to the versatility of the homogeneous domination approach and homogeneous properties the proposed method is also utilised to the control design of upper triangular systems

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

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

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 continuous feedback approach to global strong stabilization of nonlinear systems we present a continuous feedback approach to the problem of global strong stabilization for genuinely nonlinear systems that may not be stabilized even locally by any smooth feedback we describe conditions under which it is possible to prove while no smooth controllers exist the existence of continuous state feedback control laws that achieve global strong stability gss in the sense of kurzweil 1956 the proof is constructive and carried out by developing a machinery which combines the theory of homogeneous systems with the idea of adding a power integrator for the explicit construction of globally stabilizing continuous controllers we then illustrate by means of examples how this machinery can be used to overcome the topological obstruction caused by smooth feedback and hence resulting in new solutions to a variety of open control problems including global stabilization of an underactuated unstable two degree of freedom mechanical system

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

practical asymptotic stability of stochastic systems driven by levy processes and its application to control of tora systems two lyapunov type theorems are developed to investigate global practical asymptotic stability in probability for sdes driven by non vanishing levy processes which can be either affine or non a

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

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

global existence and blow up phenomena for the weakly dissipative camassa holm equation abstract this paper is concerned with global existence and blow up phenomena for the weakly dissipative camassa holm equation a new global existence result and a new blow up result for strong solutions to the equation with certain profiles are presented the obtained results improve considerable the previous results

further results on adaptive state feedback stabilization for stochastic high order nonlinear systems this paper aims to relax the results in xie and tian 2009 from the following two aspects completely removing the power order restriction and largely relaxing the growth conditions of nonlinear functions by using the backstepping design method and homogeneous domination technique this paper investigates the problem of adaptive state feedback stabilization for a class of stochastic high order nonlinear systems with nonlinear parameterization the closed loop system can be proved to be globally stable in probability and the states can be regulated to the origin almost surely the efficiency of the adaptive state feedback controller is demonstrated by a simulation example