an improved chattering free vsc scheme for uncertain dynamical systems a control strategy proposed by the authors in previous works to reduce the effect of chattering led to the solution of a differential inequality involving the first and second derivatives of the control signal and a parameter for a first order observer the analysis was carried out assuming this parameter to be constant in the present paper this assumption is removed thus allowing the solution of the differential inequality to be a function of a piecewise continuous first derivative of the control signal without need for assuming a priori knowledge of bounds to the plant trajectories

robust observer design under measurement noise with gain adaptation and saturated estimates abstract we use incremental homogeneity gain adaptation and incremental observability for proving new results on robust observer design for systems with noisy measurement and bounded trajectories a state observer is designed by dominating the incrementally homogeneous nonlinearities of the observation error system with its linear approximation while gain adaptation and incremental observability guarantee an asymptotic upper bound for the estimation error depending on the limsup of the norm of the measurement noise a characteristic and innovative feature of this observer is the mixed low high gain structure in combination with saturated state estimates and dynamically tuned gains and saturation levels the gain adaptation is implemented as the output of a stable filter using the squared norm of the measured output estimation error and the mismatch between each estimate and its saturated value

finite time trajectory tracking control in a task space of robotic manipulators this work addresses the problem of the accurate task space control subject to finite time convergence dynamic equations of a rigid robotic manipulator are assumed to be uncertain moreover globally unbounded disturbances are allowed to act on the manipulator when tracking the trajectory by the end effector based on suitably defined task space non singular terminal sliding vector variable and the lyapunov stability theory we derive a class of absolutely continuous jacobian transpose robust controllers which seem to be effective in counteracting uncertain dynamics unbounded disturbances and possible kinematic and or algorithmic singularities met on the end effector trajectory the numerical simulations carried out for a robotic manipulator of a scara type consisting of two revolute kinematic pairs and operating in a two dimensional task space illustrate performance of the proposed controllers

the group of isometries of a banach space and duality we construct an example of a real banach space whose group of surjective isometries has no uniformly continuous one parameter semigroups but the group of surjective isometries of its dual contains infinitely many of them other examples concerning numerical index hermitian operators and dissipative operators are also shown

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

proper discretization of homogeneous differentiators homogeneous sliding mode based differentiators hd are known to provide for the high accuracy robust estimation of derivatives in the presence of sampling noises and discrete measurements provided that the differentiator dynamics evolve in continuous time the popular one step euler discrete time implementation is proved to cause differentiation accuracy deterioration if the differentiation order exceeds 1 a novel discrete time realization of the hd is proposed which preserves the ultimate accuracy of the continuous time hd also with discrete measurements

robust exact differentiation via sliding mode technique abstract the main problem in differentiator design is to combine differentiation exactness with robustness in respect to possible measurement errors and input noises the proposed differentiator provides for proportionality of the maximal differentiation error to the square root of the maximal deviation of the measured input signal from the base signal such an order of the differentiation error is shown to be the best possible one when the only information known on the base signal is an upper bound for lipschitz s constant of the derivative

control of mobile manipulators in a task space this note addresses the problem of position control of mobile manipulators operating in the task space with state constraints a relatively simple class of task space regulators consisting of a generalized transpose jacobian controller with a nonlinear quasi velocity term an integral term including a function of manipulator coordinates and the task error plus the gradient of a kinematic criterion function is proposed the lyapunov stability theory is used to derive the control scheme through the use of the gradient of the criterion function an optimal solution to the mobile manipulator task is ensured the performance of the proposed control strategy is illustrated through computer simulations for a mobile manipulator operating in a three dimensional task space

reduced order observers for the sliding mode control of mechanical systems with elastic joints in this article the control of mechanical systems with elastic joints is addressed this kind of system is characterised by a high relative degree the mechanical control input must be designed to be continuous different reduced order observers are introduced and conditions are found to guarantee the exponential convergence of the observation errors the error stability is ensured provided a certain matrix inequality has a solution the proposed second order sliding mode point to point controller based on the observed state is proven to stabilise the mechanical system with elastic joints about the desired reference position

an algebraic riccati equation approach to h optimization abstract this paper considers the general so called four block h optimal control problem with the assumption that system states are available for feedback it is shown that infimization of the h norm of the closed loop transfer function over all linear constant i e nondynamic stabilizing state feedback laws can be completely characterized via an algebraic riccati equation it is further shown that the optimal norm is not improved by allowing feedback to be dynamic thus the general state feedback h optimal control problem can be solved by iteratively solving one are and the controller can be chosen to be static gain

technical communique stabilization of a class of nonlinear systems by adaptive output feedback in recent years several results have been proposed on global stabilization of a class of nonlinear systems that are dominated by a triangular system satisfying the linear growth condition however in these works at least the linear growth bound is assumed to be known in designing stabilizing controllers in our work we propose an adaptive output feedback control scheme in which the high gain parameter is tuned on line thus a priori knowledge on the linear growth bound of system nonlinearities is not required in our scheme

finite time and fixed time observer design implicit lyapunov function approach abstract this work deals with the problem of finite time and fixed time observation of linear multiple input multiple output mimo control systems the proposed nonlinear dynamic observers guarantee convergence of the observer states to the original system state in a finite and in a fixed defined a priori time algorithms for the observers parameters tuning are also provided and a robustness analysis against input disturbances and measurement noises is carried out the theoretical results are illustrated by numerical examples that consider both noisy and noise free measurements and a comparison with a high gain observer is included

high gain observers in the state and estimation of robots having elastic joints the paper deals with the state and parameter estimation of robots having elastic joints the estimation of the unknown parameters of the robot is reduced to the estimation of its state variables by a state space immersion the luenberger observer is used in the state estimation of the extended robot model the use of high gains is studied in the cancellation of nonlinearities in order to simplify the observer design the high gain induces a time scale separation between the robot model and the observer and therefore the singular perturbation theory can be used in the stability analysis of the estimate error dynamics in particular it is shown that the error dynamics reaches the stable equilibrium in a very fast transient ensuring that the slow dynamics of the observer is just that of the given robot

exact differentiation of signals with unbounded higher derivatives arbitrary order homogeneous differentiators based on high order sliding modes are generalized to ensure exact robust kth order differentiation of signals with a given functional bound of the k 1 th derivative the asymptotic accuracies in the presence of noises and discrete sampling are estimated the results are applicable for the global observation of system states with unbounded dynamics computer simulation demonstrates the applicability of the modified differentiators

brief paper modified transpose jacobian control of robotic systems the simplicity of transpose jacobian tj control is a significant characteristic of this algorithm for controlling robotic manipulators nevertheless a poor performance may result in tracking of fast trajectories since it is not dynamics based use of high gains can deteriorate performance seriously in the presence of feedback measurement noise another drawback is that there is no prescribed method of selecting its control gains in this paper based on feedback linearization approach a modified tj mtj algorithm is presented which employs stored data of the control command in the previous time step as a learning tool to yield improved performance the gains of this new algorithm can be selected systematically and do not need to be large hence the noise rejection characteristics of the algorithm are improved based on lyapunov s theorems it is shown that both the standard and the mtj algorithms are asymptotically stable analysis of the required computational effort reveals the efficiency of the proposed mtj law compared to the model based algorithms simulation results are presented which compare tracking performance of the mtj algorithm to that of the tj and model based algorithms in various tasks results of these simulations show that performance of the new mtj algorithm is comparable to that of computed torque algorithms without requiring a priori knowledge of plant dynamics and with reduced computational burden therefore the proposed algorithm is well suited to most industrial applications where simple efficient algorithms are more appropriate than complicated theoretical ones with massive computational burden

brief paper an adaptive high gain observer for nonlinear systems in this paper the authors provide a solution to the noise sensitivity of high gain observers the resulting nonlinear observer possesses simultaneously 1 extended kalman filter s good noise filtering properties and 2 the reactivity of the high gain extended kalman filter with respect to large perturbations the authors introduce innovation as the quantity that drives the gain adaptation they prove a general convergence result propose guidelines to practical implementation and show simulation results for an example

an adaptive regulator of robotic manipulators in the task space this note addresses the problem of position control of robotic manipulators both nonredundant and redundant in the task space a computationally simple class of task space regulators consisting of a transpose adaptive jacobian controller plus an adaptive term estimating generalized gravity forces is proposed the lyapunov stability theory is used to derive the control scheme the conditions on controller gains ensuring asymptotic stability are obtained herein in a form of simple inequalities including some information extracted from both robot kinematic and dynamic equations the performance of the proposed control strategy is illustrated through computer simulations for a direct drive arm of a scara type redundant manipulator with the three revolute kinematic pairs operating in a two dimensional task space

brief paper dynamic sliding mode control design using attracting ellipsoid method a methodology for the design of sliding mode controllers for linear systems subjected to matched and unmatched perturbations is proposed it is considered that the control signal is applied through a first order low pass filter the technique is based on the existence of an attracting invariant ellipsoid such that the convergence to a quasi minimal region of the origin using the suboptimal control signal is guaranteed the design procedure is given in terms of the solution of a set of matrix inequalities a benchmark example illustrating the design is given

approximate high gain observers for non lipschitz observability forms a methodology for the design of continuous practical high gain observers for non linear observable systems is presented only two conditions are required injectivity of the observability map of order n and uniform continuity of its inverse using this map the system is transformed to observability normal form which could have a non lipschitz continuous right hand side and eventually multiplicity of solutions a so called e approximate high gain observer is designed for this form constituting the dynamic part of the observer a uniformly continuous extension of the inverse of the transformation is used as the algebraic part convergence of the error to a neighbourhood of the origin is guaranteed

extremals of the supereigenvector cone in max algebra a combinatorial description abstract we give a combinatorial description of extremal generators of the supereigenvector cone x a x x in max algebra

geometric characterization of tripotents in real and complex jb triples abstract we establish a geometric characterization of tripotents in real and complex jb triples as a consequence we obtain an alternative proof of kaup s banach stone theorem for jb triples

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

discrete differentiators based on sliding modes abstract sliding mode based differentiation of the input f t yields exact estimations of the derivatives f f n provided an upper bound l t of f n 1 t is available in real time in practice it involves discrete sampling and numerical integration of the internal variables between the measurements accuracy asymptotics of different discretization schemes are calculated for discrete noisy sampling whereas sampling and integration steps are independently variable or constant proposed discrete differentiators restore the optimal accuracy asymptotics of their continuous time counterparts event triggered sampling is considered extensive numeric experiments are presented and analyzed

a polynomial algorithm for solving system of inequalities in max plus algebra abstract this paper deals with the system of inequalities a x x in which a is a square matrix x is a column vector and is a max plus composition it provides two algorithms which can be used to find a finite proper supereigenvectors of a corresponding to the eigenvalue 0 in a case of irreducible matrix a with the maximum cycle mean a 0 and a finite solution of the system in a case of reducible matrix a respectively in a polynomial number of steps

on multi input chattering free second order sliding mode control a solution to the problem of eliminating the chattering effect which is always associated with practical implementations of variable structure control is presented with reference to a class of uncertain multi input nonlinear systems the solution procedure relies on the application of an original control approach capable of enforcing a second order sliding mode i e a sliding regime on a surface s x t 0 in the system state space with s spl dot x t identically equal to zero a regime enforced by a control signal depending on s x t but directly acting only on s spl uml x t such an approach in its original formulation only applies to single input nonlinear systems with particular types of uncertainties in the present paper its validity is extended to multi input nonlinear systems characterized by uncertainties of more general nature covering a wide class of real processes

an observer based controller for nonlinear systems a gain scheduling approach abstract this paper presents an observer based controller for discrete time nonlinear systems whose control inputs are subject to a set of equality and or inequality constraints firstly a regularized least square estimator is developed to estimate the states of the nonlinear system then the estimated states are used to generate a feedback control law using the jacobean linearization in conjunction with gain scheduling the stability of the closed loop control system is rigorously investigated applications of the proposed observer based control scheme to two numerical examples are presented then the developed controller is used to control a synchronous machine which is subject to constraints on the control the simulation results show the effectiveness of the proposed observer based control scheme

multiple time scale decomposition in cheap control problems singular control a linear quadratic regulator problem where a small parameter 2multiplies the control cost is considered as mu rightarrow 0 it exhibits a dynamic behavior with multiple time scales whereas for mu 0 it is a singular control problem at first a multiparameter singularly perturbed model of the given problem is constructed by transferring the singularity that exists in the performance index to the dynamic equations then the problem is decomposed into several subproblems of minimal order each pertaining to only one time scale the method developed permits under a single framework the characterization of asymptotic behavior of optimal closed loop poles state and control trajectories performance index and optimal transfer function as mu rightarrow 0 moreover the asymptotic solution brings into focus 1 the nature of singular control and its connection to transmission zeros and 2 the presence of various types of impulses and other higher order distributions in both state and control the approach unifies and extends significantly several ideas previously somewhat disjoint

a remark on the problem of semiglobal nonlinear output regulation this paper shows how the method for semiglobal stabilization by output feedback based on high gain observer and saturation and the method for structurally stable regulation based on system immersion can be effectively coupled in order to solve problems of robust output regulation in the presence of parameter uncertainties ranging over compact sets

high gain observers in the presence of measurement noise a switched gain approach this paper considers output feedback control using high gain observers in the presence of measurement noise for a class of nonlinear systems we study stability in the presence of measurement noise and illustrate the tradeoff when selecting the observer gain between state reconstruction speed and robustness to model uncertainty on the one hand versus amplification of noise on the other based on this tradeoff we propose a high gain observer that switches between two gain values this scheme is able to quickly recover the system states during large estimation error and reduce the effect of measurement noise in a neighborhood of the origin of the estimation error we argue boundedness and ultimate boundedness of the closed loop system under switched gain output feedback

multirate sampled data output feedback control with application to smart material actuated systems we consider multirate sampled data output feedback control of a class of nonlinear systems using high gain observers where the measurement sampling rate is made faster than the control update rate we show that in the presence of bounded disturbances given a sampled data state feedback controller that achieves stabilization with respect to a closed set the multirate output feedback controller recovers stabilization of the same set provided the measurement sampling rate is sufficiently fast as an application we consider the control of smart material actuated systems this scheme combines a discrete time high gain observer with a hysteresis inversion controller where the hysteresis is modeled using a preisach operator experimental results for the control of a shape memory alloy actuated rotary joint are provided

on tropical supereigenvectors abstract the task of finding tropical eigenvectors and subeigenvectors that is non trivial solutions to a x x and a x x in the max plus algebra has been studied by many authors since the 1960s in contrast the task of finding supereigenvectors that is solutions to a x x has attracted attention only recently we present a number of properties of supereigenvectors focusing on a complete characterization of the values of associated with supereigenvectors and in particular finite supereigenvectors the proof of the main statement is constructive and enables us to find a non trivial subspace of finite supereigenvectors we also present an overview of key related results on eigenvectors and subeigenvectors

separate weak continuity of the triple product in dual real jb triples we prove that if e is a real jb triple having a predual e then e is the unique predual of e and the triple product on e is separately sigma e e continuous

a nonlinear high gain observer for systems with measurement noise in a feedback control framework we address the problem of state estimation for a class of nonlinear systems with measurement noise in the context of feedback control it is well known that high gain observers are robust against model uncertainty and disturbances but sensitive to measurement noise when implemented in a feedback loop this work presents the benefits of a nonlinear gain structure in the innovation process of the high gain observer in order to overcome the tradeoff between fast state reconstruction and measurement noise attenuation the goal is to generate a larger observer gain during the transient response than in the steady state response thus by reducing the observer gain after achieving satisfactory state estimates the effect of noise on the steady state performance is reduced moreover the nonlinear gain observer presented in this paper is shown to surpass the system performance achieved when using comparable linear gain observers the proof argues boundedness and ultimate boundedness of the closed loop system under the proposed output feedback

energy based approach to sliding composite adaptive control for rigid robots with finite error convergence time in this paper a terminal sliding mode adaptive control scheme for robotic manipulators designed following an energybased approach is presented the control comprises two basic terms a composite adaptive term which implements a feedback law for compensating the modelled dynamics and a non linear sliding mode term for overcoming the unmodelled dynamics and perturbations the resulting closed loop system is proved to be stable and it is also shown that the trajectory tracking error converges to zero in finite time moreover an upper bound of this error convergence time is calculated finally the design is evaluated by means of simulations

cheap and singular controls for linear quadratic regulators a general not necessarily square and not necessarily invertible linear system with quadratic cost function where a small parameter 2multiplies the control cost is considered due to the cheapness of control a strong control action in the form of high gain feedback forces the given system to have slow and fast transients of a hierarchy of time scales coupled with high and low amplitude interactions by appropriate amplitude and time scaling of variables these interactions are normalized and the problem is decomposed into several nonsingular subproblems of minimal order each pertaining to only one time scale complete results characterizing the limiting behavior of the optimal performance index eigenvalues trajectory and control variables as mu rightarrow 0 are given all the different ways by which nonuniqueness can occur into singular control are discussed more importantly the method developed here allows the design of a high gain feedback system in terms of the design of several lower order subproblems thus it gives a strong impetus for practical implementation of the theory developed

nonlinear observers for lipschitz continuous systems with inputs this paper considers the state observation problem for nonlinear dynamical systems the proposed framework is a direct generalization of a method introduced in a recent paper for autonomous system its characteristic feature is that the dynamic part of the observer is linear and as a consequence that convergence takes place globally in the observer coordinates the observer is completed by a static nonlinearity which maps the observer state in the original state space an associated observation mapping is introduced and is interpreted in terms of an orthonormal expansion of the input and the output with respect to a certain basis in a suitable hilbert space it is shown that by choosing the observer dimension properly an observer with arbitrary small asymptotic observation error is obtained provided that some compactness properties for the subset to be observed and the set of input signals hold under a stronger condition the finite complexity property an exact observer is achieved finally an integral formula representation for the observer nonlinearity is given

global and exact hosm differentiator with dynamic gains for output feedback sliding mode control in this paper we introduce a global differentiator based on higher order sliding modes hosm and dynamic gains to solve the problem of trajectory tracking via output feedback for a class of uncertain nonlinear plants with arbitrary relative degree and disturbances norm observers for the unmeasured state are employed to dominate the disturbances as well as to adapt the gains of the proposed differentiator since the nonlinearities may be state dependent and time varying uniform global stability and robust exact tracking are guaranteed employing the proposed hosm based exact differentiator the obtained results are not restricted to first order sliding mode control feedback but applies for second order sliding mode algorithms twisting super twisting and variable gain super twisting as well as quasi continuous hosm finite time controllers simulations with an aircraft pitch control application illustrate the claimed properties even in the presence of measurement noise

globally convergent differentiators with variable gains a new robust exact sliding mode sm based differentiator is proposed which provides for the fast global finite time convergence of its outputs to the first n exact derivatives of its input f t t

approximately norm unital products on c algebras and a non associative gelfand naimark theorem abstract we describe the non associative products on a c algebra a which convert the banach space of a into a banach algebra having an approximate unit bounded by 1 and determine among them those which are associative as a consequence if such a product p satisfies p a b p b a and p a a a 2 for all a b a and some conjugate linear vector space involution on a then p is associative the proof of the above result involves also a new gelfand naimark type theorem asserting that non associative c algebras defined verbatim as in the associative case but removing associativity are alternative if and only if they have an approximate unit bounded by 1

homogeneity approach to high order sliding mode design it is shown that a general uncertain single input single output regulation problem is solvable only by means of discontinuous control laws giving rise to the so called high order sliding modes the homogeneity properties of the corresponding controllers yield a number of practically important features in particular finite time convergence is proved and asymptotic accuracy is calculated in a very general way in the presence of input noises discrete measurements and switching delays a robust homogeneous differentiator is included in the control structure thus yielding robust output feedback controllers with finite time convergence it is demonstrated that homogeneity features significantly simplify the design and investigation of a new family of high order sliding mode controllers finally simulation results are presented

weakly open sets in the unit ball of the projective tensor product of banach spaces abstract a banach space is said to have the diameter two property if every non empty relatively weakly open subset of its unit ball has diameter two we prove that the projective tensor product of two banach spaces whose centralizer is infinite dimensional has the diameter two property the same statement also holds for x y if the centralizer of x is infinite dimensional and the unit sphere of y contains an element of numerical index one we provide examples of classical banach spaces satisfying the assumptions of the results if k is any infinite compact hausdorff topological space then c k y has the diameter two property for any nonzero banach space y we also provide a result on the diameter two property for the injective tensor product

singularly perturbed analysis of chattering in relay control systems for sliding mode control systems with fast actuators sufficient conditions for the exponential decreasing of the amplitude of chattering and unlimited growth of frequency are found the connection between the stability of actuators and the stability of the plant on the one hand and the stability of the sliding mode system as the whole on the other hand is investigated the algorithm for correction of sliding mode equations is suggested for taking into account the presence of fast actuators

isometries of real hilbert c modules abstract let t v w be a surjective real linear isometry between full real hilbert c modules over real c algebras a and b respectively we show that the following conditions are equivalent a t is a 2 isometry b t is a complete isometry c t preserves ternary products d t preserves inner products e t is a module map when a and b are commutative we give a full description of the structure of t

on the sliding mode control of nonlinear systems abstract implications of fliess s differential algebraic approach for the study of systems dynamics are explored in the context of sliding regimes of nonlinear systems this viewpoint directly leads to the possibilities of dynamically generated sliding mode controllers characterizing sliding motions which are generically devoid of undesirable input chattering a definite connection between controllability and the possibility of creation of higher order sliding regimes is also established using differential algebra

geometric unitaries in jb algebras abstract in this note we study geometric unitaries of jb algebras in particular self adjoint parts of c algebras by using order theoretical arguments we show that the geometric unitaries of a jb algebra are precisely the central algebraic unitaries or central symmetries

banach space characterizations of unitaries a survey abstract we survey banach space characterizations of unitary elements of c algebras jb triples and jb algebras in the case of the existence of a pre dual appropriate specializations of these characterizations are also reviewed

robust adaptive motion force tracking control design for uncertain constrained robot manipulators in the presence of uncertain constraint and robot model an adaptive controller with robust motion force tracking performance for constrained robot manipulators is proposed first robust motion and force tracking is considered where a performance criterion containing disturbance and estimated parameter attenuations is presented then the proposed controller utilizes an adaptive scheme and an auxiliary control law to deal with the uncertain environmental constraint disturbances and robotic modeling uncertainties after solving a simple linear matrix inequality for gain conditions the effect from disturbance and estimated parameter errors to motion force errors is attenuated to an arbitrary prescribed level moreover if the disturbance and estimated parameter errors are square integrable then an asymptotic motion tracking is achieved while the force error is as small as the inversion of control gain finally numerical simulation results for a constrained planar robot illustrate the expected performance

a new varying gain exponent based differentiator observer an efficient balance between linear and sliding mode algorithms it is well known that the supertwisting algorithm is robust to matched perturbation but is sensitive to measurement noise contrary to this the classical linear algorithm is less sensitive to measurement noise but less robust to perturbation to combine both the good accuracy of the supertwisting algorithm with respect to perturbation and the good performance of the linear algorithm with respect to measurement noise this article proposes a new differentiator observer with a varying exponent gain alpha whose variation depends on the magnitude of measurement noise high frequency signal when the magnitude of measurement noise increases respectively decreases alpha tends to 1 respectively tends to 0 5 and the proposed differentiator observer behaves as a linear algorithm respectively as a supertwisting algorithm thus by one parameter alpha the differentiator observer can take care of high frequency noise and matched perturbations a complete stability analysis of the proposed differentiator observer is provided to highlight the applicability of the proposed methodology the dedicated differentiator observer is respectively validated on the electropneumatic actuator and electric machine test benches these experimental results are compared to those of linear and supertwisting algorithms

an exact handling of the gradient for overcoming persistent problems in nonlinear observer design via convex optimization techniques abstract this paper proposes a comprehensive solution to persistent problems faced by nonlinear observer design via convex optimization techniques namely the construction of an exact error model and the handling of unmeasurable premises instead of using the differential mean value theorem it is shown that the error system is always exactly amenable via algebraic rearrangements to an explicit matrix polynomial form of the gradient where the error signal appears factorized at the rightmost side thus allowing lyapunov based derivation of conditions in the form of linear matrix inequalities or sum of squares an effective exploitation of the nonlinear characteristics of the observer while naturally decoupling available and non available signals is achieved via exact takagi sugeno tensor product models or polynomial rewriting of the error system not the plant generalizations such as h disturbance rejection or decay rate are straightforward in contrast with recent approaches the output is not required to be linear nor the systems involved to be affine in control illustrative examples are provided that overcome recent approaches on the subject

nonlinear approximate observers for feedback control a class of approximate nonlinear observers is presented and when used to implement stabilizing state feedback control laws shown to yield asymptotically stable output feedback regulation

error bounds in differentiation of noisy signals by high gain observers the error in estimating the derivative s of a noisy signal by using a high gain observer is studied and quantified the error is bounded in terms of the infinity norms of the noise and a derivative of the signal the error bound is independent of the frequency or derivatives of the noise guidelines are presented for the observer gain design when it is used for on line differentiation analytical and simulation results are presented

peaking free variable structure control of uncertain linear systems based on a high gain observer an output feedback model reference variable structure controller based on a high gain observer hgo is proposed and analyzed for single input single output siso linear plants with relative degree greater than one the control law is generated using the hgo signals only to drive the sign function of the variable structure control component while the sign function gain also called modulation as well as the other components of the control signal are generated using signals from state variable filters which do not require high gain and are free of peaking this scheme achieves global exponential stability with respect to a small residual set and does not generate peaking in the control signal

technical communique on lmi conditions to design observer based controllers for linear systems with parameter uncertainties this paper deals with the problem of observer based stabilization for linear systems with parameter inequality a new design methodology is proposed thanks to a judicious use of the famous young relation this latter leads to a less restrictive synthesis condition expressed in term of linear matrix inequality lmi than those available in the literature numerical comparisons are provided in order to show the validity and superiority of the proposed method

finite time control of robotic manipulators this work offers the solution at the control feed back level of the accurate trajectory tracking subject to finite time convergence dynamic equations of a rigid robotic manipulator are assumed to be uncertain moreover globally unbounded disturbances are allowed to act on the manipulator when tracking the trajectory based on the suitably defined non singular terminal sliding vector variable and the lyapunov stability theory we propose a class of absolutely continuous robust controllers which seem to be effective in counteracting both uncertain dynamics and unbounded disturbances the numerical simulation results carried out for a robotic manipulator consisting of two revolute kinematic pairs operating in a two dimensional joint space illustrate performance of the proposed controllers

on multiplicatively closed subsets of normed algebras abstract it is well known that if s is a bounded and multiplicatively closed subset of an associative normed algebra a then there exists an equivalent algebra norm on a such that s 1 for every s s although associativity is not an essential requirement in this result it is easy to find examples of nonassociative normed algebras a where such a result fails actually it can fail even if the subset s is reduced to a nonzero idempotent we prove that it remain true in the nonassociative setting whenever the subset s is assumed to be contained in the nucleus of a in the particular case that the subset s reduces to a nonzero nuclear idempotent p we show that the equivalent algebra norm above can be chosen so that p becomes a strongly exposed point of the closed unit ball of a we study those possibly nonassociative normed algebras a satisfying the norm one boundedness property in short nbp which means that as happened in the associative case for every bounded and multiplicatively closed subset s of a there exists an equivalent algebra norm on a such that s 1 for every s s we show that absolute valued algebras jb algebras and nilpotent normed algebras fulfil the nbp we also show that if an anti commutative complete normed algebraic algebra a satisfies the nbp then there exists n n such that l a n 0 for every a a where l a denotes the operator of left multiplication by a it follows from a celebrated theorem of e i zel manov on the so called engel lie algebras that a complete normed algebraic lie algebra satisfies the nbp if and only if it is nilpotent

certainty equivalence feedback design with polynomial type feedbacks which guarantee iss the purpose of this note is to establish a certainty equivalence feedback design for inverse optimally controlled affine systems in particular it is shown that a class of polynomial type state feedbacks in conjunction with a globally asymptotically convergent observer leads to a globally asymptotically stable closed loop a key step in the proposed certainty equivalence feedback design procedure is the identification of a new class of polynomial type inverse optimal feedbacks which guarantees input to state stability iss with respect to measurement errors as a consequence the proposed certainty equivalence feedback design has the important feature that the state feedback is allowed to contain polynomial nonlinearities of arbitrarily high degree in the unmeasured states this feature is illustrated on an example

nonassociative unitary banach algebras abstract we generalize the theory of associative unitary normed algebras to the setting of noncommutative jordan algebras special attention is devoted to the case of alternative algebras

c algebras that arei rings a ring r is said to be an i ring if and only if for every non nilpotent element a in r there exists b g r b 0 such that bab s b equivalently r has this property if and only if each non nil right ideal contains w x an idempotent i rings apparently first occurred in a paper of kothe 14 who was then searching for a non commutative substitute of the finiteness condition for rings which today usually is contained in the expression w x noetherian it was later observed by kaplansky 13 that an i ring either contains an infinite number of mutually orthogonal idempotents or satis fies the descending chain condition modulo its radical in his paper kothe shows among other things that each minimal non nil right ideal of an arbitrary ring contains an idempotent and that i rings contain what today is occasionally called a kothe radical i e a unique maximal bilateral ideal which contains all left and right nil ideals of the ring in question i rings appear next in the literature as a weak form of von neumann s w x regular rings 11 13 and have then systematically been investigated by w x w levitzki 17 18 for an investigation of i rings with involution see 15 x 16 the structure of regular rings within the category of banach algebras is w x fairly well understood all of them are finite dimensional 12 the situa

the generators of the solution space for a system of inequalities the generators of the solution space for a system of inequalities a x x are considered in this paper where a is a square matrix over r r x is a column vector and is a max plus composition this paper presents some properties of solutions to the system of inequalities and proposes an algorithm to find a set of generators for the solution space of the system of inequalities with a r n n

finite time stability and settling time estimation of nonlinear impulsive systems abstract this paper studies the problem of finite time stability fts for nonlinear impulsive systems based on impulsive control theory several lyapunov based fts theorems involving stabilizing impulses and destabilizing impulses are established respectively our proposed results provide sufficient conditions for estimating the settling time with respect to suitable classes of impulse time sequences it is shown that the settling time of nonlinear impulsive systems depends not only on the initial state but also on the impulse effect as compared with the case without using stabilizing impulses a smaller bound of setting time can be derived when a fts system is subject to stabilizing impulses conversely a larger bound of settling time can be derived when the fts system is subject to destabilizing impulses as compared with the case without using destabilizing impulses as a special case we extend the ideas to nonlinear impulsive delay systems and derive some delay independent fts results examples and their simulations are given to demonstrate the applicability of the proposed results

observer based dynamic surface control for a class of nonlinear systems an lmi approach this note presents a new analysis method to design an observer based dynamic surface controller odsc for a class of nonlinear systems while the separation principle from linear system theory does not generally hold for nonlinear systems a separation principle for the odsc systems will be shown for a class of nonlinear systems thus enabling the independent design of the observer and dsc furthermore a convex optimization problem to test quadratic stability of odsc will be formulated later

second order sliding mode observer for mechanical systems the super twisting second order sliding mode algorithm is modified in order to design a velocity observer for uncertain mechanical systems the finite time convergence of the observer is proved thus the observer can be designed independently of the controller a discrete version of the observer is considered and the corresponding accuracy is estimated

peaking free output feedback adaptive neural control under a nonseparation principle high gain observers have been extensively applied to construct output feedback adaptive neural control anc for a class of feedback linearizable uncertain nonlinear systems under a nonlinear separation principle yet due to static gain and linear properties high gain observers are usually subject to peaking responses and noise sensitivity existing adaptive neural network nn observers cannot effectively relax the limitations of high gain observers this paper presents an output feedback indirect anc strategy under a nonseparation principle where a hybrid estimation scheme that integrates an adaptive nn observer with state variable filters is proposed to estimate plant states by applying a single lyapunov function candidate to the entire system it is proved that the closed loop system achieves practical asymptotic stability under a relatively low observer gain dominated by controller parameters our approach can completely avoid peaking responses without control saturation while keeping favourable noise rejection ability simulation results have shown effectiveness and superiority of this approach

recognizing weakly stable matrices a max plus matrix a is called weakly stable if the sequence orbit x a otimes x a 2 otimes x ldots does not reach an eigenvector of a for any x unless x is an eigenvector this is in contrast to previously studied strongly stable robust matrices for which the orbit reaches an eigenvector with any nontrivial starting vector max plus matrices are used to describe multiprocessor interactive systems for which reachability of a steady regime is equivalent to reachability of an eigenvector by a matrix orbit we prove that an irreducible matrix is weakly stable if and only if its critical graph is a hamiltonian cycle in the associated graph we extend this condition to reducible matrices these criteria can be checked in polynomial time

separation results for the stabilization of nonlinear systems using different high gain observer designs high gain observers have been used in the design of output feedback controllers due to their ability to robustly estimate the unmeasured states while asymptotically attenuating disturbances the available techniques for the design of high gain observers can be classified into three groups pole placement algorithms riccati equation based algorithms and lyapunov equation based algorithms in 1 we presented separation results for globally bounded stabilizing state feedback controllers when the high gain observer is designed using pole placement so as to create a closed loop system with two time scale structure in this paper we show that the separation results of 1 hold for the other observer designs