decomposition of garside groups and self similar l algebras abstract picantin s iterated crossed product representation of garside monoids is extended and reproved for a wide class of not necessarily noetherian partially ordered groups with a right invariant lattice structure it is shown that the tree like structure of such an iterated crossed product is equivalent to a partial cycle set closely related to a class of set theoretic solutions of the quantum yang baxter equation the decomposition of finite square free solutions is related to the crossed product representation of the corresponding structure group

on lmi conditions to design observers for lipschitz nonlinear systems this paper addresses the problem of observer design for lipschitz nonlinear systems via lmi the goal of this note is to clarify some recent results and to propose a new design methodology this is based on the reformulation of the lipschitz property using some mathematical tools this reformulation is a relevant and useful lipschitz condition which leads to less restrictive lmi conditions to show the superiority of this latter two numerical examples are presented

partial state observers for nonlinear systems this note deals with the design of reduced order observers for a class of nonlinear systems the order reduction of the observer is achieved by only estimating a required partial set of the state vector necessary and sufficient conditions are derived for the existence of reduced order observers an observer design procedure based on linear matrix inequalities is given a numerical example is given to illustrate the design method

robust fault estimation using relative information in linear multi agent networks in this technical note a robust fault estimation method based on sliding mode observers is proposed for a collection of agents undertaking a shared task and exchanging only relative information over a communication network since the system of systems formed by the agents is not observable with respect to relative sensing information by appropriate transformations and scalings of the inputs and outputs of the actual system a meaningful observable subsystem is created for this new subsystem after modal decomposition based on the associated laplacian decoupled sliding mode observers depending only on the individual node level dynamics of the network can be created exploiting an existing design philosophy these collectively form a centralized fault estimation scheme for the original system

linearization by output injection and nonlinear observers abstract observers can easily be constructed for those nonlinear systems which can be transformed into a linear system by change of state variables and output injection necessary and sufficient conditions for the existence of such a transformation are given

persistence of excitation in linear systems abstract this paper develops output reachability characterizations of linear finite dimensional multivariate systems so as to translate excitation properties of system inputs to excitation properties of system outputs states or associated regression vectors such properties are of fundamental concern for convergence of algorithms involving on line identification adaptive state estimation prediction and control persistence of excitation guarantees convergence without a priori stability assumptions and ensures robustness properties

state feedback and output feedback control of a class of nonlinear systems with delayed measurements this paper is concerned with the problem of state feedback and output feedback control of a class of nonlinear systems with delayed measurements this class of nonlinear systems is made up of continuous time linear systems with nonlinear perturbations the nonlinearity is assumed to satisfy a global lipschitz condition and the time delay is assumed to be time varying and have no restriction on its derivative on the basis of the lyapunov krasovskii approach sufficient conditions for the existence of the state feedback controller and the output feedback controller are derived in terms of linear matrix inequalities methods of calculating the controller gain matrices are also presented two numerical examples are given to illustrate the effectiveness of the proposed methods c 2006 elsevier ltd all rights reserved

observer design for unknown input nonlinear descriptor systems via convex optimization this paper treats the design problem of full order observers for nonlinear descriptor systems with unknown input ui depending on the available knowledge on the ui dynamics two cases are considered first a ui proportional observer uipo is proposed when the spectral domain of the ui is unknown second a pio is proposed when the spectral domain of the ui is in the low frequency range sufficient conditions for the existence and stability of such observers are given and proved based on the linear matrix inequality lmi approach an algorithm is presented to compute the observer gain matrix that achieves the asymptotic stability objective an example is included to illustrate the method

self tuning control with a filter and a neural compensator for a class of nonlinear systems considering the mismatching of model process order in this brief a self tuning proportional integral derivative pid like controller is proposed by combining a pole assignment self tuning pid controller with a filter and a neural compensator to design the pid controller a reduced order model is introduced whose linear parameters are identified by a normalized projection algorithm with a deadzone the higher order nonlinearity is estimated by a high order neural network the gains of the pid controller are obtained by pole assignment which together with other parameters are tuned on line the bounded input bounded output stability condition and convergence condition of the closed loop system are presented simulations are conducted on the continuous stirred tank reactors system the results show the effectiveness of the proposed method

stabilization on zero error manifolds and the nonlinear servomechanism problem the extended linearization methodology is applied to the nonlinear servomechanism problem for the case of time varying exogenous signals this yields a novel approach to establishing exponential manifold known as the zero error manifold advantages of the approach are that the underlying theory is relatively simple and that a requirement of small derivatives for the exogenous signals is used rather than a requirement that the exogenous signals remain small thus certain cases of unbounded exogenous signals can be treated a transmission zero condition for existence of the requisite zero error manifold is given

filtering and smoothing in an h sup infinity setting the problems of filtering and smoothing are considered for linear systems in an h sup infinity setting i e the plant and measurement noises have bounded energies are in l sub 2 but are otherwise arbitrary two distinct situations for the initial condition of the system are considered the initial condition is assumed known in one case while in the other the initial condition is not known but the initial condition the plant and measurement noise are in some weighted ball of r sup n xl sub 2 finite horizon and infinite horizon cases are considered necessary and sufficient conditions are presented for the existence of estimators both filters and smoothers that achieve a prescribed performance bound and algorithms that result in performance within the bounds are developed in case of smoothers the optimal smoother is also presented the approach uses basic quadratic optimization theory in a time domain setting as a consequence of which both linear time varying and time invariant systems can be considered with equal ease in the smoothing problem for linear time varying systems one considers only the finite horizon case

dual euclidean artin groups and the failure of the lattice property abstract the irreducible euclidean coxeter groups that naturally act geometrically on euclidean space are classified by the well known extended dynkin diagrams and these diagrams also encode the modified presentations that define the irreducible euclidean artin groups these artin groups have remained mysterious with some exceptions until very recently craig squier clarified the structure of the three examples with three generators more than twenty years ago and francois digne more recently proved that two of the infinite families can be understood by constructing a dual presentation for each of these groups and showing that it forms an infinite type garside structure in this article i establish that none of the remaining dual presentations for irreducible euclidean artin groups correspond to garside structures because their factorization posets fail to be lattices these are the first known examples of artin groups where all of their dual presentations fail to form garside structures nevertheless the results presented here about the cause of this failure form the foundation for a subsequent article in which the structure of euclidean artin groups is finally clarified

design of state observers from a drift observability property in this paper the problem of state observation with exponential error decay for nonlinear systems affine in the input is considered and an observer is proposed for such an observer the drift observability property of the system i e observability for zero input together with an assumption on the input amplitude or on the observation relative degree are sufficient conditions for exponential convergence of the observation error the existence of an exponential observer is correlated to the existence of a solution for an h sub spl infin riccati like inequality global and semiglobal convergence results are presented

global exponential regulation of discrete time linear systems with unknown neutrally stable exosystems discrete time linear stabilizable and detectable systems with known parameters are considered the regulation problem is addressed when the reference output and or the disturbances contain sinusoidal terms generated by a linear exosystem with unknown parameters only an upper bound on the number of unknown sinusoids is supposed to be known a constructive algorithm is proposed to drive the regulation error exponentially to zero on the basis of its measurement only under the same necessary and sufficient conditions which are required when the exosystem is known the control strategy includes an online detector for the number of excited frequencies and exponentially converging global estimates of the exosystem unknown parameters an illustrative example containing a variable number of frequencies is worked out and simulated

brief paper global nonlinear output regulation convergence based controller design in this paper we present output feedback controllers solving the global output regulation problem for a class of nonlinear systems the proposed controllers are based on the notion of convergent systems the presented solution extends well established results on the linear output regulation problem and the local nonlinear output regulation problem to the global case for lur e systems which are not necessarily in the output feedback form the proposed controllers can be found by solving the regulator equations and certain linear matrix inequalities for systems in the output feedback form with uncertain parameters and uncertain nonlinearities we provide a robust regulator that does not rely on the minimum phaseness assumption on the system which is crucial in the previous regulator designs for output feedback systems the results are illustrated by examples

on observers for nonlinear differential algebraic systems we extend a recent approach to observer design for linear differential algebraic systems to systems with lipschitz nonlinearities the observer design further extends the standard luenberger type observer design we show that the design parameters for the observer can be obtained by the solution of a riccati type inequality the solutions of the latter can in turn be obtained by solving a set of linear matrix inequalities lmis and bilinear matrix inequalities bmis which provides a computational procedure a feature of the presented observer design is the possibility of reformulation as an ordinary differential equation

improved delay dependent stabilization for a class of networked control systems with nonlinear perturbations and two delay components abstract this paper focuses on the problem of delay dependent state feedback control for a class of networked control systems ncss with nonlinear perturbations and two delay components based on the dynamic delay interval ddi method and the wirtinger integral inequality some improved delay dependent stability analysis are obtained furthermore the results are extended to the conditions of ncss with one time delay and the corresponding stability analysis results and state feedback controller are obtained finally some numerical examples and simulations are given to show the effectiveness of the proposed methods

non linear observer design by transformation into a generalized observer canonical form an observer design method for a certain class of non linear single output systems is introduced the characteristic feature of this method consists of the fact that it does not require any linearization in the way that the given non linear system is approximated by a linear one the present paper deals with the derivation of a transformation of the considered non linear system into a generalized observer canonical form gocf which enables a systematic observer design similar to the linear one based on the well known linear observer canonical form to assign conditions for its existence the transformation into the gocf is carried out in two steps via a generalized observability canonical form gobcf in contrast to previous forms used for linear systems the two non linear canonical forms presented here also depend on the time derivatives of the input variables this means that the resulting observer has to be supplied not only with the input and output variables of the given system but also with deri

a stabilization algorithm for a class of uncertain linear systems abstract this paper presents an algorithm for the stabilization of a class of uncertain linear systems the uncertain systems under consideration are described by state equations which depend on time varying unknown but bounded uncertain parameters the construction of the stabilizing controller involves solving a certain algebraic riccati equation furthermore the solution to this riccati equation defines a quadratic lyapunov function which is used to establish the stability of the closed loop system this leads to a notion of quadratic stabilizability it is shown that the stabilization procedure will succeed if and only if the given uncertain linear system is quadratically stabilizable the paper also deals with a notion of overbounding for uncertain linear systems this procedure enables the stabilization algorithm to be applied to a larger class of uncertain linear systems also included in the paper are results which indicate the degree of conservativeness introduced by this overbounding process

artin groups of euclidean type this article resolves several long standing conjectures about artin groups of euclidean type specifically we prove that every irreducible euclidean artin group is a torsion free centerless group with a decidable word problem and a finite dimensional classifying space we do this by showing that each of these groups is isomorphic to a subgroup of a group with an infinite type garside structure the garside groups involved are introduced here for the first time they are constructed by applying semi standard procedures to crystallographic groups that contain euclidean coxeter groups but which need not be generated by the reflections they contain

on uniform observation of nonuniformly observable systems abstract in 4 7 9 12 classes of nonlinear systems are considered for which observers can be designed although observability of nonlinear systems is known to be dependent on the input the proposed observers have the property that the estimation error decays to zero irrespective of the input in the first part of this paper it is shown that this phenomenon follows from a common property of these systems for all of them the unobservable states with respect to some input are in some sense stable in the linear case these systems are called detectable and for this reason a reduced order observer can be designed in the second part is given a more general class of nonlinear systems for which such an observer can be designed

non resonance conditions for uniform observability in the problem of nonlinear output regulation abstract this paper deals with the design of an internal model based semiglobal output feedback regulator for possibly non minimum phase nonlinear systems taking advantage of the design tool proposed in isidori ieee trans automat control 45 10 2000 we show how the problem of output regulation can be reformulated into an output feedback stabilization problem of a suitably defined extended auxiliary system the output feedback stabilization of the extended auxiliary system is addressed in the second part of the paper where an observer based stabilizer is proposed the existence of the latter is characterized in terms of necessary and sufficient conditions which can be interpreted as nonlinear non resonance conditions between the modes of the exosystem and the zero dynamics of the controlled plant

adaptive state observer for lipschitz nonlinear systems abstract the problem of adaptive observer synthesis for lipschitz nonlinear systems is addressed in the case of known parameters the convergence property of state observer is first discussed based on a generalized lipschitz condition the sufficient conditions to ensure the stability of observer error dynamics are presented in terms of some lmis in the case of system dynamics with some unknown parameters the proposed conditions along with an equality constraint are then employed to guarantee the convergence property of an adaptive state observer moreover an adaptive observer form is derived which can be utilized in designing the reduced order state observer the simulation results are finally given to exhibit the effectiveness of proposed synthesis approaches in dealing with the practical systems

on distributed pinning observers for a network of dynamical systems in this technical note a distributed observer structure is proposed to estimate the states of a large scale network of semi linear systems interconnected by a positive time varying coupling strength the distributed observer comprises distinct sub observers which require only local node level information and exchange their local state estimates with their neighboring observers the key idea here is to use a minimum number or at least relatively few measurements from the network being monitored to reduce the sensor requirements the problem is formulated as a two stage lmi optimization problem

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

brief paper circle criterion approach to discrete time nonlinear observer design this paper addresses the design of discrete time nonlinear observers through the circle criterion the new design method is mainly devoted to either globally lipschitz systems or bounded state systems whose nonlinearities can be decomposed into a linear combination of positive slope nonlinearities the observer design is not restricted to systems with positive slope nonlinearities but it encompasses systems with non positive slope nonlinearities too stability conditions of the observation error are given in terms of numerically tractable linear matrix inequalities illustrative examples are presented in order to highlight the main features and advantages of the new proposed technique over some classical designs

novel lmi conditions for observer based stabilization of lipschitzian nonlinear systems and uncertain linear systems in discrete time in this paper it is shown that the observer based control of uncertain discrete time linear systems is conditioned by the solvability of three linear matrix inequalities that must hold simultaneously the developed theory is then extended to lipschitz discrete time nonlinear systems we show that the observer based control problem which is originally a non convex issue can be decomposed into two separate convex problems formulated as a set of numerically tractable linear matrix inequalities conditions the new proposed linear matrix inequalities are neither iterative nor subject to any equality constraint illustrative examples are given to indicate the novelty and effectiveness of the proposed design

a dissipativity based approach to output regulation of non minimum phase systems abstract the present paper presents a new contribution to the design of output regulators for a class of nonlinear systems characterized by a possibly unstable zero dynamics it is shown that the problem in question can be reduced to a stabilization problem with a supplementary gain constraint for a suitably defined reduced auxiliary plant

on robustness of lurie systems with multiple non linearities abstract the robustness of absolute stability of lurie systems with multiple non linearities with respect to model variations is considered two approaches for robustness analysis are developed one is based on the popov frequency domain criterion and the other on the algebraic criterion for the absolute stability it is shown that there exist finite perturbations in the system model which admit certain norm bounds so that the stability of the system is not affected computationally the method is very feasible it involves a very simple numerical algorithm two illustrative examples are worked out the theory is applied to characterize the robustness properties of a steam boiler example of a yugoslav thermal power plant

h sub spl infin observer design for lipschitz nonlinear systems the problem of observer design for lipschitz nonlinear systems is considered a new dynamic framework which is a generalization of previously used lipschitz observers is introduced and the generalized sufficient condition that ensures asymptotic convergence of the state estimates is presented the equivalence between this condition and an h sub spl infin optimal control problem which satisfies the standard regularity assumptions in h sub spl infin optimization theory is shown and a parameterization of all possible observers is also presented a design procedure which is less restrictive than the existing design approaches is proposed and a simulation example is given to illustrate the observer design

observers for systems with nonlinearities satisfying incremental quadratic constraints we consider the problem of designing observers to asymptotically estimate the state of a system whose nonlinear time varying terms satisfy an incremental quadratic inequality that is parameterized by a set of multiplier matrices observer design is reduced to solving linear matrix inequalities for the observer gain matrices the proposed observers guarantee exponential convergence of the state estimation error to zero in addition to considering a larger class of nonlinearities than previously considered this paper unifies earlier related results in the literature the results are illustrated by application to several examples

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

reinforcement learning state estimator in this study we propose a novel use of reinforcement learning for estimating hidden variables and parameters of nonlinear dynamical systems a critical issue in hidden state estimation is that we cannot directly observe estimation errors however by defining errors of observable variables as a delayed penalty we can apply a reinforcement learning frame work to state estimation problems specifically we derive a method to construct a nonlinear state estimator by finding an appropriate feedback input gain using the policy gradient method we tested the proposed method on single pendulum dynamics and show that the joint angle variable could be successfully estimated by observing only the angular velocity and vice versa in addition we show that we could acquire a state estimator for the pendulum swing up task in which a swing up controller is also acquired by reinforcement learning simultaneously furthermore we demonstrate that it is possible to estimate the dynamics of the pendulum itself while the hidden variables are estimated in the pendulum swing up task application of the proposed method to a two linked biped model is also presented

static output feedback and guaranteed cost control of a class of discrete time nonlinear systems with partial state measurements abstract in this paper both the static output feedback issue and the observer based control of a class of discrete time nonlinear systems are considered thanks to a newly developed linearization lemma it is shown that the solution of the discrete time output feedback problem is conditioned by a set of simple convex optimization conditions that are numerically tractable and free from any equality constraint an illustrative example is provided to show the usefulness of the proposed control designs

on a nonlinear multivariable servomechanism problem abstract multivariable nonlinear plants with both measured and unmeasured vector disturbance signals are considered output feedback dynamic control laws are designed for the problem of tracking a constant or slowly varying reference input while rejecting constant or slowly varying disturbances

on the stabilization and observation of nonlinear uncertain dynamic systems the problem of stabilization and observation of uncertain and or nonlinear dynamic systems for which matching conditions are not satisfied is investigated no statistical description of uncertain elements is assumed the uncertain and or nonlinear quantities are described only in terms of bounds on their possible sizes stabilizing feedback controllers and observers are proposed whose design is based on the constructive use of lyapunov functions and the bellman gronwall lemma

observer design for a class of nonlinear systems a viable design methodology to construct observers for a class of nonlinear systems is developed the proposed technique is based on the off line solution of a riccati equation and can be solved using commercially available software packages for globally valid results the class of systems considered is characterized by globally lipschitz nonlinearities local results relax this assumption to only a local requirement for a more general description of nonlinear systems the methodology yields approximate observers locally the proposed theory is used to design an observer for a single link flexible joint robot this observer estimates the robot link variables based on the joint measurements

a general formulation and solvability of the global robust output regulation problem while the output regulation problem for linear systems accommodates both bounded and unbounded exogenous signals the existing formulation of the output regulation problem for nonlinear systems only allows bounded exogenous signals produced by an exosystem with a neutrally stable equilibrium in particular when it comes to the robust output regulation problem the only admissible exogenous signal is a finite combination of step and sinusoidal functions in this paper we give a general formulation of the robust output regulation problem that admits unbounded exogenous signals and contains the previous formulations as special cases when the system is linear or when the exogenous signals are bounded then we give conditions under which the problem can be solved by solving a robust stabilization problem of an augmented system finally we apply our general result to obtain the solvability conditions of the general robust output regulation problem for the class of lower triangular nonlinear systems

a state observer for nonlinear dynamical systems the problem of state observation for nonlinear systems is of main importance in automatic control in recent years many contributions have been presented in literature that solve the design problem for classes of nonlinear systems most works can be roughly classi ed into two categories in one the geometrical properties of vector elds de ning the system are exploited and therefore mathematical tools of the di erential geometry are extensively employed in the other one the functional properties of the input state and state output maps which de ne the system are mainly used while the geometrical methods often provide a general solution of the problem for systems that belong to restricted classes characterized by geometrical properties 1 2 3 4 5 6 7 13 14 17 18 19 the second approach gives solutions for classes of nonlinear systems whose geometrical nature is not investigated and only macroscopic parameters norms gains lipschitz constants and so on are involved in the design procedure 8 9 11 12 21 one main problem in state observation for nonlinear systems is that the property of driftobservability does not imply observability for any input function as shown in 16 19 thus it is interesting to investigate when the drift observability property allows the solution of the state observation problem nding conditions that restricts the class of input functions due to the mathematical tools employed this work may be considered as belonging to both the categories above mentioned in this paper nonlinear systems of the form

state and input simultaneous estimation for a class of nonlinear systems this paper addresses the problem of estimating simultaneously the state and input of a class of nonlinear systems here the systems nonlinear part comprises a lipschitz nonlinear function with respect to the state and input and a state dependent unknown function including additive disturbance as well as uncertain nonlinear time varying terms upon satisfying some conditions the observer design problem can be solved via a riccati inequality or a lmi based technique with asymptotic estimation guaranteed a numerical example is included for illustration

h synthesis of unknown input observers for non linear lipschitz systems the problem of unknown input observer design for non linear lipschitz systems is considered a new dynamic framework which is a generalization of previously used linear unknown input observers is introduced the additional degrees of freedom offered by this dynamic framework are used to deal with the lipschitz non linearity the necessary and sufficient condition that ensures asymptotic convergence of the new observer is presented and the equivalence between this condition and an h optimal control problem which satisfies the standard regularity assumptions in the h optimization theory is shown based on these results a design procedure that is solvable using commercially available software is presented a simulation example is given to illustrate the proposed design

fuzzy control theory a nonlinear case abstract sources of nonlinearity in a fuzzy controller include the fuzzification algorithm used for the controller inputs fuzzy control rules type of fuzzy logic used for evaluating the fuzzy control rules and the defuzzification algorithm used for the controller output we analyze the performance of a simple fuzzy controller with linear and nonlinear defuzzification algorithms we prove theoretically that such a fuzzy controller the smallest possible with two inputs error and rate change of error and a nonlinear defuzzification algorithm is equivalent to a nonfuzzy nonlinear proportional integral pi controller with proportional gain and integral gain changing with error and rate change of error about a setpoint furthermore this fuzzy controller is precisely equivalent to a conventional linear pi controller if a linear defuzzification algorithm is employed computer simulation showed that the performance of the fuzzy controller was almost the same as that of the pi controller when first order and second order linear processes were used furthermore the fuzzy controller was significantly better when a first order with a time delay model was used more importantly the simulated result illustrated that the fuzzy controller was stable when a nonlinear process model was controlled but the pi controller was unstable

robust output regulation with nonlinear exosystems for over a decade the solvability of the nonlinear robust output regulation problem relies on the assumption that the exosystem is linear and neutrally stable thus the only exogenous signal that can be accommodated by the existing theory is a combination of finitely many step functions and sinusoidal functions in this paper we will show that it is possible to find controllers that can admit exogenous signals produced by nonlinear exosystems an example with the well known van der pol oscillator as the exosystem is given to illustrate our approach

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

observer design for systems with multivariable monotone nonlinearities globally convergent observers are designed for a class of systems with multivariable nonlinearities the approach is to represent the observer error system as the feedback interconnection of a linear system and a state dependent multivariable nonlinearity we first extend an earlier design automatica 37 12 2001 1923 to multivariable nonlinearities satisfying an analog of the scalar nondecreasing property next we exploit the structure of the nonlinearity to relax the positive real restriction on the linear part of the observer error system this relaxed design renders the feasibility conditions less restrictive and widens the applicability of the observer as illustrated with examples finally output nonlinearities are studied and the design is extended to be adaptive in the presence of unknown parameters

online exact differentiation and notion of asymptotic algebraic observers in recent years the availability of computer based methods has created a revival of interests in exploring algebraic methods in nonlinear context this paper proposes a new approach to algebraic nonlinear observer design after giving the notion of algebraic observability and based on a novel algorithm of exact differentiation the formulation of the nonlinear observer is realized via the construction of a set of linear time varying differentiators an example of a chemical reaction is given to show the effectiveness of our approach

predictive fuzzy pid control theory design and simulation abstract predictive fuzzy pid control theory is developed in this paper which offers a new approach for robust control of time delay systems the paper describes the functional structure design principle and stability analysis of a new predictive fuzzy pid controller sufficient computer simulations are provided for illustration and verification first the structure of the controller is derived from both the fuzzy pid control and the generalized predictive control concepts then on line model identification optimal cost index fuzzification rule base and defuzzification of the representative predictive fuzzy pd i controller are discussed in detail lyapunov asymptotic stability analysis is conducted then many computer simulations are performed to compare with several closely related controllers such as the fuzzy pd i controller and the smith type predictive fuzzy pd i controller in the simulations second order linear systems with without time delays nonlinear systems with without time delays uncertain linear systems with time delays and uncertain nonlinear systems with time delays are used to confirm the advantages of the new predictive fuzzy pd i controller finally this method is applied to control some chaotic systems with success this predictive fuzzy control method provides a new way for controlling uncertainty and complex linear and nonlinear systems even with significant time delay

geometric steady states of nonlinear systems the analytic concept of steady states for nonlinear systems was introduced by isidori and byrnes and its geometric properties were also given implicitly mixed with the solvability of the output regulation problem for nonlinear systems with neutrally stable exogenous signals in this technical note a geometric definition of steady states for nonlinear systems which is named as geometric steady state is formulated independent of the output regulation problem so that it can be applied to many problems other than output regulation and the exogenous system can be unstable too some sufficient conditions for the existence of geometric steady states and a practical application in robotics are also provided

a state observer for nonlinear systems a state observer design methodology for a class of nonlinear systems is proposed the nonlinear observer design methodology is in fact an extension of linear observer design techniques using transformations related to linear observability matrices

on the solvability of the regulator equations for a class of nonlinear systems regulator equations arise in studying the output regulation problem for nonlinear systems the solvability of the regulator equations is the necessary condition for that of the output regulation problem it has been shown under various assumptions that the solvability of the regulator equations can be reduced to that of a center manifold equation defined by the zero dynamics of a composite system consisting of the plant and exosystem in this paper we further show that for a quite general class of nonlinear systems the solvability of the regulator equations can be reduced to that of a center manifold equation if the relative degree of the composite system at the origin exists

observability through delayed measurements a new approach to state observers design an original approach for the construction of state observers for dynamic systems is presented in this article new notions of observability delay observability and delay drift observability useful for the development of the observer equations and for the convergence proof are introduced and compared with other standard observability concepts in particular it is shown that delay drift observability is an extension of the well known drift observability property the construction of the proposed observer is straightforward and does not require any coordinate transformation of the system into a canonical form which is a common feature of many other approaches a numerical example is reported where a system that is not drift observable is considered in this case the proposed observer is easily constructed and performs well

observer based control of discrete time lipschitzian non linear systems application to one link flexible joint robot the problem of designing asymptotic observers along with observer based feedbacks for a class of discrete time non linear systems is considered we assume that the system non linearity is globally lipschitz and the system is supposed to be stabilizable by a linear controller sufficient linear matrix inequality condition is derived to ensure the stability of the considered system under the action of feedback control based on the reconstructed states a numerical example of a single link flexible joint robot is presented to illustrate the efficacy of the theoretical developments

brief paper robust h observer design for sampled data lipschitz nonlinear systems with exact and euler approximate models an lmi approach is proposed for the design of robust h observers for a class of lipschitz nonlinear systems two type of systems are considered lipschitz nonlinear discrete time systems and lipschitz nonlinear sampled data systems with euler approximate discrete time models observer convergence when the exact discrete time model of the system is available is shown then practical convergence of the proposed observer is proved using the euler approximate discrete time model as an additional feature maximizing the admissible lipschitz constant the solution of the proposed lmi optimization problem guaranties robustness against some nonlinear uncertainties the robust h observer synthesis problem is solved for both cases the maximum disturbance attenuation level is achieved through lmi optimization

nonlinear observers a circle criterion design and robustness analysis globally convergent observers are designed for a class of systems with monotonic nonlinearities the approach is to represent the observer error system as the feedback interconnection of a linear system and a time varying multivariable sector nonlinearity using lmi software observer gain matrices are computed to satisfy the circle criterion and hence to drive the observer error to zero in output feedback design the observer is combined with control laws that ensure input to state stability with respect to the observer error robustness to unmodeled dynamics is achieved with a small gain assignment design as illustrated on a jet engine compressor example

estimation of states faults and unknown disturbances in non linear systems in this paper we extend existing theory on non linear unknown input observer design to a wider class of non linear systems where the systems are subject to unknown input and output disturbances and experience faults the approach used is to decouple the faults and unknown disturbances from the rest of the system through a series of transformations on state and output equations once total disturbance decoupling is achieved an appropriate observer for the disturbance free part of the non linear system is proposed and designed the designed observer is subsequently used for estimation of unknown inputs outputs and fault signals two examples are given for illustration

circle criterion based ℋ observer design for lipschitz and monotonic nonlinear systems enhanced lmi conditions and constructive discussions a new lmi design technique is developed to address the problem of circle criterion based mathcal h infty observer design for nonlinear systems the developed technique applies to both locally lipschitz as well as monotonic nonlinear systems and allows for nonlinear functions in both the process dynamics and output equations the lmi design condition obtained is less conservative than all previous results proposed in the literature for these classes of nonlinear systems by judicious use of a modified young s relation additional degrees of freedom are included in the observer design these additional decision variables enable improvements in the feasibility of the obtained lmi several recent results in the literature are shown to be particular cases of the more general observer design methodology developed in this paper illustrative examples are given to show the effectiveness of the proposed methodology the application of the method to slip angle estimation in automotive applications is discussed and experimental results are presented

unknown input observers for switched nonlinear discrete time descriptor systems in this paper a linear matrix inequality technique for the state estimation of discrete time nonlinear switched descriptor systems is developed the considered systems are composed of linear and nonlinear parts an observer giving a perfect unknown input decoupled state estimation is proposed sufficient conditions of global convergence of observers are proposed numerical examples are given to illustrate this method

brief mixed internal model based and feedforward control for robust tracking in nonlinear systems the purpose of this paper is to compare different features of two approaches to the problem of tracking prescribed trajectories in a nonlinear system and to propose a possible merger of these approaches in what is called here the problem of asymptotically robust perfect tracking the latter is the problem of designing a feedforward error feedback control law achieving perfect tracking in case the initial conditions of the system exosystem are known and compatible with perfect tracking and asymptotic tracking in all other cases

observers for lipschitz non linear systems in an interesting paper r rajamani and y m cho have proposed a systematic methodology to design observers they have introduced a new problem relation between distance to unobservability and convergence of luenberger like observers a result for the convergence of the observer has also been given they have presented a quantity denoted by i claimed as the distance to unobservability we show that this number is not actually the distance from the system to the set of unobservable systems moreover the result for the observer is incorrect we provide a counterexample for the result of convergence in this paper results for convergence are obtained with additional strengthened hypothesis to correct rajamani and cho s result the results are used to design an observer for a now classical single link flexible robot joint the behaviour of the observer to noisy output is quite satisfactory

on designing observers for time delay systems with non linear disturbances in this paper the observer design problem is studied for a class of time delay non linear systems the system under consideration is subject to delayed state and non linear disturbances the time delay is allowed to be time varying and the non linearities are assumed to satisfy global lipschitz conditions the problem addressed is the design of state observers such that for the admissible time delay as well as non linear disturbances the dynamics of the observation error is globally exponentially stable an effective algebraic matrix inequality approach is developed to solve the non linear observer design problem specifically some conditions for the existence of the desired observers are derived and an explicit expression of desired observers is given in terms of some free parameters a simulation example is included to illustrate the practical applicability of the proposed theory

observer based perturbation extremum seeking control with input constraints for direct contact membrane distillation process abstractan observer based perturbation extremum seeking control is proposed for a direct contact membrane distillation dcmd process the process is described with a dynamic model that is based on a 2d advection diffusion equation model which has pump flow rates as process inputs the objective of the controller is to optimise the trade off between the permeate mass flux and the energy consumption by the pumps inside the process cases of single and multiple control inputs are considered through the use of only the feed pump flow rate or both the feed and the permeate pump flow rates a nonlinear lyapunov based observer is designed to provide an estimation for the temperature distribution all over the designated domain of the dcmd process moreover control inputs are constrained with an anti windup technique to be within feasible and physical ranges performance of the proposed structure is analysed and simulations based on real dcmd process parameters for each control input are provided

parameterization of decoupling control laws for affine nonlinear systems the problem of parameterizing all the decoupling feedbacks is investigated and applied to the design of a stable noninteracting control for affine nonlinear systems an algebraic study of controlled invariance is presented it covers a new criterion for controlled invariance parameterization and novel properties of the friend set and computational aspects of the maximal controlled invariant distribution this analysis is used to derive falb wolovich like conditions for general decoupling including disturbance decoupling and noninteracting control problems it is shown that to determine all the decoupling feedbacks one usually needs infinitely many sets of controlled invariant or controllability distributions that can arise as solutions to the problems it is also shown that under certain conditions stable noninteracting design based on first parameterizing the decoupling feedbacks is still a feasible approach in the sense that a feedback can be chosen from the friend set of the maximal solution for the exponentially stable and noninteracting design problem

nonlinear estimation in a class of gene transcription process in this work the goodwin model applied to gene transcription is employed as a benchmark system for estimation purposes considering two dynamic behaviors monotone decreasing and sustained oscillations each one under a specific parameter s set the preceding observability analysis of the goodwin model was done via linear observability and the differential algebraic framework where is proved that the system is fully observable from mrna concentration measurements therefore a class of nonlinear observer which considers a class of sigmoid and linear functions of the output feedback considering model uncertainties is proposed and a sketch of proof of the observer s convergence is provided under the background of the lyapunov theory in order to demonstrate asymptotic convergence numerical experiments are carrying out in order to show the performance of the proposed methodology which is compared with a standard luenberger proportional observer and a proportional sliding mode observer psmo

sliding mode estimators for a class of non linear systems affected by bounded disturbances the problem of state estimation for a class of non linear systems with lipschitz non linearities is addressed using sliding mode estimators stability conditions have been found to guarantee asymptotic convergence to zero of the estimation error in the absence of noise and non divergence if the state perturbations and measurement noise are bounded a method is proposed to find a suitable solution to the algebraic riccati equation on which the design of the estimator is based the performance of the resulting sliding mode filter minimizes an upper bound on the asymptotic estimation error based on such an approach a sliding mode estimator may be designed so as to outperform the extended kalman filter in practical applications with models affected by uncertainty and strong possibly unknown non linearities as shown by means of simulations

global finite time observers for lipschitz nonlinear systems this technical note presents a global finite time observer design for a class of systems with lipschitz nonlinearity by applying a finite time stability theorem and a careful selection of the homogeneity powers and weights the problem of global and finite time stable observers is studied an observer design procedure is given and a numerical example is provided to illustrate the design method

brief paper asymptotic rejection of asymmetric periodic disturbances in output feedback nonlinear systems this paper deals with asymptotic rejection of periodic disturbances which may have asymmetric basic wave patterns this class of disturbances covers asymmetric wave forms in the half period such as alternating sawtooth wave form some disturbances which are generated from nonlinear oscillation such as van de pol oscillators as well as disturbances with symmetric half period wave forms such as sinusoidal disturbances and triangular disturbances etc the systems considered in this paper can be transformed to the nonlinear output feedback form the amplitude and phase of the disturbances are unknown the novel concept of integral phase shift is introduced together with the newly introduced half period integration operator to investigate the invariant properties of asymmetric periodic disturbances they are used for the estimation of unknown disturbances in the systems together with observer design techniques to deal with nonlinearity the proposed control design with the disturbance estimation asymptotically rejects the unknown disturbance and ensures the overall stability of the system

a differential vector space approach to nonlinear system regulation nonlinear system regulation is an active research area and is important for disturbance rejection and reference signal tracking existing results using differential geometry or lyapunov theory are restricted to bounded exogenous signals the paper uses a differential vector space approach to develop solutions for nonlinear system regulation with both bounded and unbounded exogenous signals the solutions are given in terms of observable dual state spaces in the differential vector space of the system and are well suited to symbolic and numerical computation

a note on observer design for one sided lipschitz nonlinear systems in this note observer design of a class of nonlinear systems is considered based on the one sided lipschitz condition sufficient conditions for the existence of observers of the class of nonlinear systems are presented a design method of the observer that is dependent on the solution of the linear matrix inequality is then presented furthermore a gain matrix of the observer is given the method given in this note makes the applicable class larger than that given in the literature it should be noticed that the proposed method is applicable not only to the monotone nonlinearities and lipschitz nonlinearities but also to the one sided lipschitz nonlinearities which are neither monotone nonlinearities nor usual lipschitz nonlinearities finally we use the proposed method to design observers for three simulative examples and the effect of each state trajectory tracking is very satisfactory

cal h _ infty filter for bilinear systems using lpv approach the aim of this technical note is to present a linear paramater varying lpv approach for the design of a functional filter for bilinear systems with a disturbance attenuation specification the unbiasedness requirement on the observation error is guaranteed by the solution of sylvester equations obtained by parametrizing the filter gain matrix this parametrization leads to a non convex optimization problem which is overcome by introducing a constraint on the gain matrix to take into account the whole set of the inputs in the filter design an lpv approach is used to obtain the gain matrix guaranteeing the quadratic stability of the observation error and a given level of disturbance attenuation this approach is then applied to the high gain observer design in order to consider the level of disturbance attenuation

robust h control of a nonlinear uncertain system via a stable nonlinear output feedback controller a new approach to solving a nonlinear robust h control problem using a stable nonlinear output feedback controller is presented in this article the class of nonlinear uncertain systems being considered is characterised in terms of integral quadratic constraints and global lipschitz conditions describing the admissible uncertainties and nonlinearities respectively the nonlinear controller is able to exploit the plant nonlinearities through the inclusion of a copy of the known plant nonlinearities in the controller the h control objective is to obtain an absolutely stable closed loop system with a specified disturbance attenuation level the solution to this control problem involves stabilising solutions to parametrised algebraic riccati equations we apply a differential evolution algorithm to solve a non convex nonlinear optimisation problem arising in the controller synthesis

brief paper geometric characterization on the solvability of regulator equations the solvability of the regulator equation for a general nonlinear system is discussed in this paper by using geometric method the feedback part of the regulator equation that is the feasible controllers for the regulator equation is studied thoroughly the concepts of minimal output zeroing control invariant submanifold and left invertibility are introduced to find all the possible controllers for the regulator equation under the condition of left invertibility useful results such as a necessary condition for the output regulation problem and some properties of friend sets of controlled invariant manifolds are also obtained

brief an observer for systems with nonlinear output map a nonlinear observer with the feedback gain weighted by the sensitivity of the output with respect to the state is developed for systems with nonlinear output map the observer can be obtained from the extended kalman filter by a special choice of time varying weighting matrices it is shown that the estimation error dynamics are asymptotically stable and a region of attraction is derived the observer is applied to the top blown converter process for estimating the content of impurities in the liquid metal using plant data from the converter at ssab oxelosund ab the observer is shown to provide accurate estimates of the carbon content

robust stabilization of uncertain linear systems quadratic stabilizability and h sup infinity control theory the problem of robustly stabilizing a linear uncertain system is considered with emphasis on the interplay between the time domain results on the quadratic stabilization of uncertain systems and the frequency domain results on h sup infinity optimization a complete solution to a certain quadratic stabilization problem in which uncertainty enters both the state and the input matrices of the system is given relations between these robust stabilization problems and h sup infinity control theory are explored it is also shown that in a number of cases if a robust stabilization problem can be solved via lyapunov methods then it can be also be solved via h sup infinity control theory based methods

a note on observers for lipschitz nonlinear systems this note deals with the design of reduced order observers for lipschitz nonlinear systems it shows that the conditions under which a full order observer exists also guarantee the existence of a reduced order observer a design method of the reduced order observer that is dependent on the solution of the riccati equation is then presented and an example is given to illustrate effects of the design method

the dynamics of weakly reversible population processes near facets this paper concerns the dynamical behavior of weakly reversible deterministically modeled population processes near the facets codimension one faces of their invariant manifolds and proves that the facets of such systems are repelling it has been conjectured that any population process whose network graph is weakly reversible has strongly connected components is persistent we prove this conjecture to be true for the subclass of weakly reversible systems for which only facets of the invariant manifold are associated with semilocking sets or siphons an important application of this work pertains to chemical reaction systems that are complex balancing for these systems it is known that within the interior of each invariant manifold there is a unique equilibrium the global attractor conjecture states that each of these equilibria is globally asymptotically stable relative to the interior of the invariant manifold in which it lies our results pertaining to weakly reversible systems imply that thi

a riccati equation approach to the stabilization of uncertain linear systems this paper presents a method for designing a feedback control law to stabilize a class of uncertain linear systems the systems under consideration contain uncertain parameters whose values are known only to within a given compact bounding set furthermore these uncertain parameters may be time varying the method used to establish asymptotic stability of the closed loop system obtained when the feedback control is applied involves the use of a quadratic lyapunov function the main contribution of this paper involves the development of a computationally feasible algorithm for the construction of a suitable quadratic lyapunov function once the lyapunov function has been obtained it is used to construct the stabilizing feedback control law the fundamental idea behind the algorithm presented involves constructing an upper bound for the lyapunov derivative corresponding to the closed loop system this upper bound is a quadratic form by using this upper bounding procedure a suitable lyapunov function can be found by solving a certain matrix riccati equation another major contribution of this paper is the identification of classes of systems for which the success of the algorithm is both necessary and sufficient for the existence of a suitable quadratic lyapunov function

gaussian groups and garside groups two generalisations of artin groups it is known that a number of algebraic properties of the braid groups extend to arbitrary finite coxeter type artin groups here we show how to extend the results to more general groups that we call garside groups define a gaussian monoid to be a finitely generated cancellative monoid where the expressions of a given element have bounded lengths and where left and right lowest common multiples exist a garside monoid is a gaussian monoid in which the left and right lowest common multiples satisfy an additional symmetry condition a gaussian group is the group of fractions of a gaussian monoid and a garside group is the group of fractions of a garside monoid braid groups and more generally finite coxeter type artin groups are garside groups we determine algorithmic criteria in terms of presentations for recognizing gaussian and garside monoids and groups and exhibit infinite families of such groups we describe simple algorithms that solve the word problem in a gaussian group show that these algorithms have a quadratic complexity if the group is a garside group and prove that garside groups have quadratic isoperimetric inequalities we construct normal forms for gaussian groups and prove that in the case of a garside group the language of normal forms is regular symmetric and geodesic has the 5 fellow traveller property and has the uniqueness property this shows in particular that garside groups are geodesically fully biautomatic finally we consider an automorphism of a finite coxeter type artin group derived from an automorphism of its defining coxeter graph and prove that the subgroup of elements fixed by this automorphism is also a finite coxeter type artin group that can be explicitly determined 1991 mathematics subject classification primary 20f05 20f36 secondary 20b40 20m05

an approximation method for the nonlinear servomechanism problem an analysis of the nonlinear servomechanism problem by the authors 1992 is shown to lead naturally to a straightforward and practical method for solving the problem in an approximate sense the results are based on a kth order approximate solution for the plant zero error manifold and corresponding control law constructions are shown to yield kth order asymptotic tracking and disturbance rejection properties for the closed loop system the approach is illustrated by application to the ball and beam system