an analysis and design method for a class of nonlinear systems with nested saturations abstractthis paper is concerned with the analysis and design of a class of nonlinear systems subject to nested saturations the proposed controller incorporates both an extended state observer eso which is utilised to estimate the nonlinear dynamics of the plant as well as a set of observer based feedbacks we first present analysis results for systems with nonlinear esos and show that local stabilisation can be achieved in a region including the origin then in the case that the eso is in linear form leso the conditions for determining the estimate of the domain of attraction of the resulting closed loop system are formulated as a convex optimisation problem a linear matrix inequality based algorithm is then established to design the feedback gains and the leso gain an illustrative example is given to show the effectiveness of the proposed approach

finite time observers application to secure communication in this paper control theory is used to formalize finite time chaos synchronization as a nonlinear finite time observer design issue this paper introduces a finite time observer for nonlinear systems that can be put into a linear canonical form up to an output injection the finite time convergence relies on the homogeneity properties of nonlinear systems the observer is then applied to the problem of secure data transmission based on the finite time chaos synchronization and the two channel transmission method

design of observers for linear systems with unknown inputs with a straightforward treatment a design of reduced order observers is presented for linear systems with unknown inputs the observers are derived with a physical meaning some explanations are given within the framework of descriptor system observer design principles the conditions for the existence of the observers are presented some illustrative examples are included

stabilisation of a thermo elastic system under nonuniformly bounded disturbances in the boundary input abstractwe consider the exponential stabilisation for a thermo elastic system of type ii with nonuniformly bounded external disturbances in the boundary control we begin with finding feedback controls for the system without disturbances by lyapunov function approach then based on the resulting feedback control we give new dynamic feedback control laws that make the system exponentially stable by tracking disturbances exponentially through a time varying high gain observer we apply the linear operator semi group theory to prove the well posedness of the resulting closed system finally we prove that the solution of the closed loop system can approach zero polynomially or exponentially by the lyapunov function approach

the active disturbance rejection control to stabilization for multi dimensional wave equation with boundary control matched disturbance in this paper we consider boundary stabilization for a multi dimensional wave equation with boundary control matched disturbance that depends on both time and spatial variables the active disturbance rejection control adrc approach is adopted in investigation an extended state observer is designed to estimate the disturbance based on an infinite number of ordinary differential equations obtained from the original multi dimensional system by infinitely many test functions the disturbance is canceled in the feedback loop together with a collocated stabilizing controller all subsystems in the closed loop are shown to be asymptotically stable in particular the time varying high gain is first time applied to a system described by the partial differential equation for complete disturbance rejection purpose and the peaking value reduction caused by the constant high gain in literature the overall picture of the adrc in dealing with the disturbance for multi dimensional partial differential equation is presented through this system the numerical experiments are carried out to illustrate the convergence and effect of peaking value reduction

stabilisation of an anti stable joint string with boundary disturbance in this paper we consider the boundary stabilisation for a one dimensional joint anti stable string equation with input disturbance entering the control end a backstepping transformation is used

state and unknown input observers for nonlinear systems with bounded exogenous inputs a systematic design methodology for state observers for a large class of nonlinear systems with bounded exogenous inputs disturbance inputs and sensor noise is proposed the nonlinearities under consideration are characterized by an incremental quadratic constraint parameterized by a set of multiplier matrices linear matrix inequalities are developed to construct observer gains which ensure that a performance output based on the state estimation error satisfies a prescribed degree of accuracy furthermore conditions guaranteeing estimation of the unknown inputs to arbitrary degrees of accuracy are provided the proposed scheme is illustrated with a numerical example which does not satisfy the so called matching conditions

stability analysis of the anti stable heat equation with uncertain disturbance on the boundary abstract in this paper we study the stability of the anti stable 1 d heat equation with uncertain disturbance on the boundary we first estimate the disturbance in terms of the output then we design some control strategy to stabilize the anti stable system

homogeneous lyapunov function for homogeneous continuous vector field the goal of this article is to provide a construction of a homogeneous lyapunov function p associated with a system of differential equations j f x x r n 1 under the hypotheses 1 f c r n vanishes at x 0 and is homogeneous 2 the zero solution of this system is locally asymptotically stable moreover the lyapunov function v x tends to infinity with 1 x i and belongs to c r 0 r n cp with p e as large as wanted as application to the theory of homogeneous systems we present two well known results of robustness in a slightly extended form and with simpler proofs

active disturbance rejection control based on weighed moving average state observer abstract in this work we are concerned with the boundary stabilization of a one dimensional anti stable wave equation corrupted by a boundary disturbance we firstly propose by weighed moving average technique a state observer to make an estimation of the disturbance secondly we design a control by the active disturbance rejection strategy to stabilize the system

output feedback stabilization for one dimensional wave equation subject to boundary disturbance we consider boundary output feedback stabilization for a one dimensional anti stable wave equation subject to general control matched disturbance the active disturbance rejection control adrc approach is adopted in investigation using the output of the system we first design a variable structure unknown input type state observer which is shown to be exponentially convergent the disturbance is estimated in real time through an extended state observer for an ode reduced from the pde observer the disturbance is then canceled in the feedback loop by its approximated value the stability of the resulting closed loop system is proven simulation results are presented to validate the theoretical conclusions and to exhibit the peaking value reduction by time varying gain instead of constant high gain

disturbance decoupling using constrained sylvester equations presents numerically efficient algorithms for the problem of disturbance decoupling with arbitrary pole placement using state feedback with or without disturbance measurement the problem is studied under conditions of generic solvability the main tool for the development of the proposed algorithm is the notion of constrained sylvester equations these equations follow naturally from the already existing geometric conditions for the same problem in the literature

active disturbance rejection control approach to output feedback stabilization of a class of uncertain nonlinear systems subject to stochastic disturbance the active disturbance rejection control adrc is now considered as a powerful control strategy in dealing with large uncertainty covering unknown dynamics external disturbance and unknown part in coefficient of the control however all theoretical works up to present are limited to deterministic uncertainty in this technical note we generalize the adrc to uncertain nonlinear systems subject to external bounded stochastic disturbance described by an uncertain stochastic differential equation driven by white noise we first design an extended state observer eso that is used to estimate both state and total disturbance which includes the internal uncertain nonlinear part and the external uncertain stochastic disturbance it is shown that the resulting closed loop system is practically stable in the mean square topology the numerical experiments are carried out to illustrate effectiveness of the proposed approach

eigenvalues of discrete linear second order periodic and antiperiodic eigenvalue problems with sign changing weight abstract by virtue of the eigenvalues of discrete linear second order neumann eigenvalue problems we study the eigenvalues of discrete linear second order periodic and antiperiodic eigenvalue problems with sign changing weight we find that these two problems have t real eigenvalues including the multiplicity respectively furthermore the numbers of positive eigenvalues are equal to the numbers of positive elements in the weight function and the numbers of negative eigenvalues are equal to the numbers of negative elements in the weight function furthermore these eigenvalues including the eigenvalues of neumann problem satisfy the order relation

the active disturbance rejection control approach to stabilisation of coupled heat and ode system subject to boundary control matched disturbance we consider stabilisation for a linear ordinary differential equation system with input dynamics governed by a heat equation subject to boundary control matched disturbance the active disturbance rejection control approach is applied to estimate in real time the disturbance with both constant high gain and time varying high gain the disturbance is cancelled in the feedback loop the closed loop systems with constant high gain and time varying high gain are shown respectively to be practically stable and asymptotically stable

state observation of nonlinear uncertain dynamical systems this note proposes new types of observers for nonlinear dynamical systems subjected to bounded nonlinearities or uncertainties the design of these observers utilizes techniques related to variable structure systems theory a measure for the rate at which the estimates converge to the actual states is derived

on convergence of tracking differentiator the tracking differentiator was first proposed by han in 1989 and the proof of convergence was presented the first time in han and wang han j q and wang w 1994 nonlinear tracking differentiator journal of systems science and mathematical science 14 177 183 in chinese unfortunately the proof there is incomplete this problem has been open for over two decades in this article we give a rigorous proof under some additional conditions an application for online estimation of the unknown frequencies for the finite sum of the sinusoidal signals is presented the numerical simulations illustrate the effectiveness of the estimation for both linear and nonlinear tracking differentiators

active disturbance rejection control for rejecting boundary disturbance from multidimensional kirchhoff plate via boundary control in this paper an algorithm is developed to reject time and spatially varying boundary disturbances from a multidimensional kirchhoff plate via boundary control the disturbance and control input are assumed to be matched the active disturbance rejection control approach is adopted for developing the algorithm a state feedback scheme is designed to estimate the disturbance based on an infinite number of ordinary differential equations obtained from the original multidimensional system using infinitely many time dependent test functions the proposed control law cancels the disturbance using its estimated value all subsystems in the closed loop are shown to be asymptotically stable simulation results are presented to validate the theoretical conclusions and to exhibit the reduction in the peaking phenomenon due to the use of time varying gains instead of constant high gains

the active disturbance rejection and sliding mode control approach to the stabilization of the euler bernoulli beam equation with boundary input disturbance in this paper we are concerned with the boundary feedback stabilization of a one dimensional euler bernoulli beam equation with the external disturbance flowing to the control end the active disturbance rejection control adrc and sliding mode control smc are adopted in investigation by the adrc approach the disturbance is estimated through an extended state observer and canceled online by the approximated one in the closed loop it is shown that the external disturbance can be attenuated in the sense that the resulting closed loop system under the extended state feedback tends to any arbitrary given vicinity of zero as the time goes to infinity in the second part we use the smc to reject the disturbance by removing the condition in adrc that the derivative of the disturbance is supposed to be bounded the existence and uniqueness of the solution for the closed loop via smc are proved and the monotonicity of the reaching condition is presented without the differentiation of the sliding mode function for which it may not always exist for the weak solution of the closed loop system the numerical simulations validate the effectiveness of both methods

a nonlinear extended state observer based on fractional power functions abstract in this paper we investigate a nonlinear extended state observer eso constructed from piece wise smooth functions consisted of linear and fractional power functions this structure of eso was first proposed in the 1990 s and has been widely used in active disturbance rejection control for engineering controls its convergence however has remained an open problem up to this day the main objective of this paper is to provide a convergence theory with explicit error estimation the performances of this type eso are studied by numerical simulation and compared with linear eso the numerical results show that the eso proposed in this paper enjoys the advantages of smaller peaking value and better measurement noise tolerance

on the convergence of an extended state observer for nonlinear systems with uncertainty abstract the extended state observer first proposed by jingqing han in j q han a class of extended state observers for uncertain systems control decis 10 1 1995 85 88 in chinese is the key link toward the active disturbance rejection control that is taking off as a technology after numerous successful applications in engineering unfortunately there is no rigorous proof of convergence to date in this paper we attempt to tackle this long unsolved extraordinary problem the main idea is to transform the error equation of objective system with its extended state observer into a asymptotical stable system with a small disturbance for which the effect of total disturbance error is eliminated by the high gain

output feedback stabilization of nonlinear mimo systems having uncertain high frequency gain matrix abstract the purpose of this paper is to provide a method for semi global asymptotic stabilization of a nonlinear minimum phase mimo system under a mild hypothesis of the so called high frequency gain matrix this result is based on a non trivial extension to the mimo setting of the approach based on the use of extended observers as a byproduct a dynamic output feedback control is obtained that asymptotically stabilizes the equilibrium of the closed loop system in spite of uncertainties in the high frequency gain matrix

state and input estimation for a class of uncertain systems we consider here the problem of state and input estimation for a class of uncertain systems which consist of a nominally linear part and an uncertain nonlinear time varying part which can be regarded as a state dependent time varying input we obtain a lyapunov type characterization of the assumptions commonly found in the literature on this problem using this characterization we obtain estimators which using only a measured output can asymptotically estimate to any desired accuracy the system state and the input

active disturbance rejection control for uncertain nonaffine in control nonlinear systems in this technical note the active disturbance rejection control adrc is generalized to uncertain nonaffine in control nonlinear systems the proposed controller incorporates both an extended state observer eso as well as a dynamic inversion the eso is designed to estimate system state and total uncertainty which includes the uncertain internal dynamics and the external disturbance and is nonaffine in control based on the output of the eso the dynamic inversion is used to deal with the nonaffine in control problem the proposed control has a multi time scale structure in which the eso is the fastest time scale the dynamic inversion is the second and the considered nonlinear system is the slowest the practical convergence of the resulting closed loop system is obtained an example is presented to illustrate the efficiency of the proposed method

full order observers for linear systems with unknown inputs this note presents a simple method to design a full order observer for linear systems with unknown inputs the necessary and sufficient conditions for the existence of the observer are given

comparative study of non linear state observation techniques abstract this paper contains a comparative study of four techniques for observing the slates of non linear systems the first technique examined is inspired by bestle and zeitz and icrener and respondek in this method a non linear transformation is found that brings the system into a canonical form from where observer design is facilitated the second technique is attributable to thau in this method the error between the system s true state and the output of the observer is shown to be asymptotically convergent to zero provided that an additional assumption is valid the third technique is due to baumann and rugh in this method extended or pseudolinearization of the error differential equation about a family of equilibrium points results in an observer design such that the eigenvalues of the linearized error equation are locally invariant finally techniques from variable structure systems are utilized to design an observer that yields an exponentially decaying error like thau s observer but unl

discrete time implementation of high gain observers for numerical differentiation high gain observers have been used in non linear control to estimate derivatives of the output in this paper we study discrete time implementation of high gain observers and their use as numerical differentiators in noise free as well as noisy measurements we show that discretization using the bilinear transformation method gives better results than other discretization methods we also show that many of the available numerical differentiators are special cases of the bilinear discrete time equivalents of full order or reduced order high gain observers

output feedback stabilization of an unstable wave equation with general corrupted boundary observation we consider boundary output feedback stabilization for an unstable wave equation with boundary observation subject to a general disturbance we adopt for the first time the active disturbance rejection control approach to stabilization for a system described by the partial differential equation with corrupted output feedback by the approach the disturbance is first estimated by a relatively independent estimator it is then canceled in the feedback loop as a result the control law can be designed almost as that for the system without disturbance we show that with a time varying gain properly designed the observer driven by the disturbance estimator is convergent and that all subsystems in the closed loop are asymptotically stable in the energy state space we also provide numerical simulations which demonstrate the convergence results and underline the effect of the time varying gain estimator on peaking value reduction