generalized controller canonical form for linear and nonlinear dynamics a generalized controller canonical form for linear and nonlinear dynamics is proposed it is obtained using the theorem of the primitive element from differential algebra the derivation of the controller form does not apply to multivariable constant linear systems with the transformations all nonlinear dynamics can be exactly linearized by dynamic feedback the main departure from standard theory is that transformations may depend on input derivatives once differential algebraic tools are introduced the proofs of the results are easy

reinforcement of an inequality due to brascamp and lieb in this paper we obtain a reinforcement of an inequality due to brascamp and lieb and a reinforcement of poincare s inequality for general logarithmical concave measures on rd the formula used in the proof is related to theorems concerning the integration of log concave functions such as results of prekopa and of ball barthe and naor we also obtain a lower bound for the variance of the same family of measures

a polynomial approach to nonlinear system controllability uses a polynomial approach to present a necessary and sufficient condition for local controllability of single input single output siso nonlinear systems the condition is presented in terms of common factors of a noncommutative polynomial expression this result exposes controllability properties of a nonlinear system in the input output framework and gives a computable procedure for examining nonlinear system controllability using computer algebra

observer based h controller design for state delayed linear systems we present two alternative observer based h control design methods for linear dynamic systems with delay in the state based on the riccati equation approach we design observer based feedback control laws that guarantee the asymptotic stability if the closed loop control system and reduce the effect of the disturbance input on the controlled output to a prescribed level

an observer design for linear systems with unknown inputs a method is presented for designing an observer for the state of a linear time invariant system with unknown inputs the structure algorithm developed by silverman is applied to obtain the observer which estimates the maximum estimable subspace of the state it is shown that the observer equation can be derived from the maximum uncontrollable subspace of the original system with the aid of a left inverse for a transposed linear system this leads us to the necessary and sufficient condition for the existence of a state observer an application to the insensitivity observer synthesis is also included

computational observer design techniques for linear systems with unknown inputs using the concept of transmission zeros computational observer design techniques for linear systems subject to unknown inputs are presented complete and intuitive geometric conditions for the solution of the problem which result in design matrix equations are provided these design equations are solved in a computationally efficient way the synthesis of the reduced order observer takes full advantage of the concept of transmission zeros in particular the necessary and sufficient conditions obtained are given in terms of the transmission zeros of the triple a d c

the differential field associated to a general analytic nonlinear dynamical system a rigorous and detailed construction of the differential field k sub sigma u y associated in a differential algebraic context to a nonlinear system sigma described in state space form with analytic coefficients is presented the field k sub sigma u y represents an input output description of sigma and its study is of key importance in problems concerning the input output behavior of sigma technically the basic step of the construction of k sub sigma u y consists in proving that the differential ideal associated to the state evolution equation of sigma is prime

some integral inequalities for l operator and their applications on self shrinkers abstract in this paper we derive a reilly type inequality for the drifting laplacian operator l on a self shrinker of the mean curvature flow using this reilly type inequality we obtain some new poincare type inequalities not only on the self shrinker but more interestingly also on its boundary moreover we get some eigenvalue estimates for l operator on the compact self shrinker and its boundary and also make some global estimates on generalized mean curvature h on the boundary

observer synthesis in the behavioral approach analyzes the observer design problem in the behavioral context observability and detectability notions are first introduced and fully characterized necessary and sufficient conditions for the existence of an observer possibly an asymptotic or an exact one are introduced and a complete parameterization of all admissible observers is given the problem of obtaining observers endowed with a strictly proper transfer matrix and the design of observer based controllers are later addressed and solved finally the above issues are particularized to the case of state space systems thus showing they naturally generalize well known theorems of traditional system theory

brief transfer equivalence and realization of nonlinear higher order input output difference equations two fundamental modelling problems in nonlinear discrete time control systems are studied using the language of differential forms the discrete time nonlinear single input single output systems to be studied are described by input output i o difference equations i e a high order difference equation relating the input the output and a finite number of their time shifts a new definition of equivalence is introduced which generalizes the notion of transfer equivalence well known for the linear case our definition is based upon the notion of an irreducible differential form of the system and was inspired by the analogous definition for continuous time systems the second problem to be addressed is the realization problem the i o difference equation is assumed to be in the irreducible form so that one can obtain an accessible and observable realization necessary and sufficient conditions are given for the existence of a local state space realization of the irreducible i o difference equation these conditions are formulated in terms of the integrability of certain subspaces of one forms classified according to their relative degree the sufficiency part of the proof gives a constructive procedure up to finding the integrating factors and integration of the set of one forms for obtaining a locally observable and accessible state space system if the system is not in the irreducible form one has first to apply the reduction procedure to transform the system into the irreducible form

observer based learning control for a class of nonlinear systems with time varying parametric uncertainties in this note a new learning control approach combined with state estimation is developed to perform output tracking problems where the state information is not available by virtue of the learning capability the control mechanism is able to handle a class of rapid time varying parametric uncertainties which are periodic and the only prior knowledge is the periodicity two classes of system nonlinearities are taken into account the first class is the global lipschitz continuous functions of the unknown state variables and the second class is the local lipschitz continuous functions of the accessible output variables to facilitate the learning control design and property analysis the lyapunov like energy function is employed which allows the incorporation of any available system knowledge henceforth the new learning control approach widens the application scope comparing with the repetitive type learning control

some basic structural properties of generalized linear systems abstract this paper shows how to give a kalman state variable realization to generalized linear systems simple characterizations of controllability observability of their duality and of a minimal realization are proposed our techniques based on elementary module theory are applicable to time varying systems as well as constant systems the note ends with a brief discussion of asymptotic observers in the constant case

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

on the robust design of sliding observers for linear systems abstract the restrictive character of well known structural constraints related to the matching conditions for the sliding mode feedforward state reconstruction problem in linear time invariant perturbed systems is critically reexamined from a new perspective it is shown that in generalized state space coordinates a matched canonical state space realization exists which always allows discontinuous asymptotic stabilization of the observation error dynamics the well known structural conditions thus become largely irrelevant and robust asymptotic state estimation is shown to be feasible for any perturbed observable system by means of sliding mode observers

entropy jumps in the presence of a spectral gap it is shown that if x is a random variable whose density satisfies a poincare inequality and y is an independent copy of x then the entropy of x y p 2 is greater than that of x by a fixed fraction of the entropy gap between x and the gaussian of the same variance the argument uses a new formula for the fisher information of a marginal which can be viewed as a local reverse form of the brunn minkowski inequality in its functional form due to prekopa and leindler

classical electrical engineering questions in the light of fliess s differential algebraic framework of non linear control systems this paper addresses two important questions of electrical engineering in the differential algebraic framework introduced by fliess this lead to an intrinsic formulation of the well known park transformation and to a generalized state representation of stand alone electrical generators a mon maitre en hommage respecteux pour son jubile

on designing reduced order observers for linear time invariant systems subject to unknown inputs abstract using the simplest matrix generalized inverse the l inverse a procedure is developed for the construction of a reduced order luenberger observer for a linear time invariant system subjected to immeasurable input disturbances illustrative examples are included

new unified h dynamic observer design for linear systems with unknown inputs in this paper a unified h dynamic observer uo is proposed for a class of linear systems in the presence of unknown inputs and disturbances it generalizes the existing results on the proportional observer po the proportional integral observer pio and the dynamic observer do the design approach of the uo is derived from the solution of the linear matrix inequality lmi based on the new dynamic observer formulation and the solution of the algebraic constraints obtained from the unbiased estimation error a numerical example is provided to show the applicability and the performance of our results

dynamic output feedback linearization and global stabilization abstract we present a class of single input single output nonlinear systems which are globally transformable by a dynamic output feedback control and a time varying state space transformation into a linear observable and minimum phase system we then show how those systems can be globally stabilized by a dynamic output feedback nonlinear control and how global output tracking can be achieved as well

a remark on nonlinear accessibility conditions and infinite prolongations the lie rank condition for strong nonlinear accessibility is interpreted via the differential geometry of jets and prolongations of infinite order it yields to a new lie algebraic criterion and to the consideration of first integrals which apply to nonlinear systems in quite general form the latter characterization in particular is valid without distinguishing between the system variables and is independent of time scalings weak accessibility is also considered

on unknown input observers of linear systems asymptotic unknown input decoupling approach this note presents a new unknown input observer uio with adjustable performances for linear systems it focuses on state estimation in the presence of zeros with slow dynamics it is known that if the system has stable invariant zeros and satisfies the decoupling condition then a uio exists however the invariant zeros constrain the pole placement and consequently the state estimation error convergence rate especially when the zeros dynamics are slow in the proposed uio the exact decoupling condition is relaxed by the introduction of the asymptotic decoupling notion which allows to act on the invariant zeros and then enhance the convergence rate of the state estimation error numerical examples are provided to illustrate the performances of the uio

a behavioral approach to estimation and dead beat observer design with applications to state space models the observer design problem is investigated in the context of linear left shift invariant discrete behaviors whose trajectories have supports on z necessary and sufficient conditions for the existence of a dead beat observer of some relevant variables from some measured ones in the presence of some unmeasured and irrelevant variables are introduced and a complete parametrization of all dead beat observers is given equivalent conditions for the existence of causal dead beat observers are then derived finally several classical problems addressed for state space models like state estimation the design of unknown input observers or the design of fault detectors and identifiers possibly in the presence of disturbances are cast in this general framework and the aforementioned equivalent conditions and parametrizations are specialized to these cases

dynamical pulse width modulation control of nonlinear systems abstract the design of dynamical stabilizing pulse width modulated controllers is addressed in full generality for the class of analytical nonlinear single input single output systems expressible in fliess local generalized observability canonical form

brief paper some examples and remarks on quasi static feedback of generalized states three simple nonlinear examples with physical background are considered they illustrate how generalized state representations which depend on time derivatives of the input occur it is shown with these examples how quasi static feedback of such generalized states may be used for input output decoupling disturbance rejection and linearization and thus for trajectory tracking

a normal form approach to approximate input output linearization for maximum phase nonlinear siso systems a control synthesis scheme is presented for nonlinear single input single output systems which have completely unstable antistable zero dynamics the approach is similar in spirit to linear approaches for nonminimum phase systems and involves the derivation of an input output linearizing controller for a suitably defined nonlinear minimum phase approximation to the original system the linearizing controller achieves an approximately linear input output response and internal stability

new algebraic geometric conditions for the linearization by input output injection the goal of this paper is twofold it unifies and generalizes existing results on input output injection linearization of nonlinear systems the problem is solved as a realization problem since it is based on the analysis of the structure of the input output differential equation the necessary and sufficient conditions are derived from a simplified and constructive procedure for clarity the paper is limited to the case of single output systems exterior differential systems are extensively used throughout the paper giving constructive conditions

differential flatness and absolute equivalence of nonlinear control systems this paper presents a formulation of differential flatness a concept originally introduced by fliess levine martin and rouchon in terms of absolute equivalence between exterior differential systems systems that are differentially flat have several useful properties that can be exploited to generate effective control strategies for nonlinear systems the original definition of flatness was given in the context of differential algebra and required that all mappings be meromorphic functions the formulation of flatness presented here does not require any algebraic structure and allows one to use tools from exterior differential systems to help characterize differentially flat systems in particular it is shown that under regularity assumptions and in the case of single input control systems i e codimension 2 pfaffian systems a system is differentially flat if and only if it is feedback linearizable via static state feedback in higher codimensions our approach does not allow one to prove that feedback linearizability about an equilibrium point and flatness are equivalent one must be careful with the role of time as well as the use of prolongations that may not be realizable as dynamic feedback in a control setting applications of differential flatness to nonlinear control systems and open questions are also discussed

exact feedforward linearization based on differential flatness this article deals with the trajectory aspect of differential flatness from a feedforward point of view the notion of exact feedforward linearization based on differential flatness is introduced a differentially flat system to which a nominal feedforward deduced from flatness is applied is equivalent by change of coordinates to a linear multivariable brunovsk form if the initial condition is consistent with the one considered in the design of the nominal trajectory in its second part the new notion states that there exist unique solutions in the vicinity of the desired trajectory when applying a nominal feedforward to the corresponding flat system to the end of stabilizing the desired trajectory the information from the brunovsk form is used to design the combination of the nominal feedforward and an additional feedback part in the case of extended pid controls for the latter stability is proven using a theorem by kelemen thus the overall control structure turns out to be quite simple and e

technical communique reduced order kalman filter with unknown inputs this paper presents an optimal reduced order kalman filter for discrete time dynamic stochastic linear systems with unknown inputs the problem is to estimate a part of the state vector in the case where none of the observations are assumed to be noise free the proposed filter is obtained by minimizing the trace of the estimation error covariance matrix with respect to the remaining degrees of freedom after noninteresting state and unknown inputs decoupling the necessary and sufficient conditions for stability and convergence of the filter are established

exact differentiation and sliding mode observers for switched lagrangian systems abstract the main topic of this paper is the problem of constructing observers for switched mechanical systems which includes as a specific case the design of observers based on the high order sliding mode technique the high order sliding mode is used to overcome the chattering phenomena occurring which induce some irrelevant and undesirable phenomena for mechanical systems the proposed approach based on the fliess canonical form also allows observers to give an estimate of the discrete location of the system which indicates the dynamic evolution the convergence of the observers is proved and a stick mass friction system is used to illustrate the efficiency of the proposed hybrid observers

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

the extended luenberger observer for nonlinear systems abstract for nonlinear single input single output systems dot x f x u y h x u the relationships for a state transformation into the nonlinear observer canonical form are developed it is possible to dimension a nonlinear observer by an eigenvalue assignment without solving the nonlinear partial differential equations for the transformation if the transformed nonlinearities are linearized about the reconstructed state with reference to the extended kalman filter algorithm this nonlinear observer design is called the extended luenberger observer

disturbance decoupled observer design a unified viewpoint this paper is concerned with the observer design for linear systems with unknown inputs an equivalent system which is free of unknown inputs is derived for the purpose of the observer design based on the equivalent system description one can design an observer full order reduced order minimal order or functional for linear systems with unknown inputs using well known techniques it is shown that the equivalent system exists as long as there exists a disturbance decoupled observer two sets of the known existence conditions of disturbance decoupled observers are proved to be equivalent

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

on dynamic feedback linearization abstract we address the problem of transforming a nonlinear multi input system into a linear controllable one via nonsingular dynamic feedback and extended state space diffeomorphism we show that in the single input case if a system is dynamic feedback linearizable it is also static feedback linearizable we then give sufficient conditions for a class of multi input systems to be dynamic feedback linearizable all three dimensional systems with two controls and a controllable linear approximation about the origin are shown to belong to such a class

dynamic input output decoupling of nonlinear control systems the problem of dynamic input output decoupling of nonlinear control systems is studied based on an analytic algorithm the authors obtain necessary and sufficient conditions for the solvability of this problem the solution of the problem is constructed by applying a series of simple precompensations and linking maps some interesting connections with other approaches in nonlinear control theory are discussed the authors also give a few simple examples to illustrate the methods used

brief paper h observers design for a class of nonlinear singular systems the present paper is devoted to the h observer or filter design problem for a class of lipschitz nonlinear singular systems the approach is based on the parameterization of the obtained algebraic constraints from the estimation errors sufficient conditions for the existence of the observers which guarantee stability and the worst case observers error energy over all bounded energy disturbances is minimized are given the method also unifies the design for the full order reduced order minimal order observers for continuous time systems it can be seen that the obtained conditions when applied to linear systems are also necessary a numerical example is given to show the applicability of our results

linearization by generalized input output injection abstract the problem under interest is the linearization of nonlinear mimo systems by generalized input output injection in order to design observers with linear error dynamics the method is based on the study of the structure of the input output differential equations thus the problem is solved as a realization problem in this note one considers the linearization under two kinds of inout output injection in the first case the transformation depends on the output and time derivatives of the input whereas in the second case derivatives of both the input and the output are considered necessary and sufficient conditions are obtained which generalize the ones on standard input output injection linearization

reduced order observer design for descriptor systems with unknown inputs a new method for the design of reduced order observers for descriptor systems with unknown inputs is presented the approach is based on the generalized constrained sylvester equation sufficient conditions for the existence of the observer are given

the b conjecture for the gaussian measure of dilates of symmetric convex sets and related problems we show that given a symmetric convex set k rd the function t etk is log concave on r where denotes the standard d dimensional gaussian measure we also comment on the extension of this property to unconditional log concave measures and sets and on the complex case

canonical decomposition of non linear systems the construction of a canonical or normal representation for non linear systems similar to the morse canonical form in the linear case is obtained the problem considered consists in particular of studying the existence of generalized transformations that achieve a desired block decoupling such transformations generalize the notions of state transformation state feedback and output injection a sufficient condition is given in terms of a separability condition which in turn is completely characterized by using differential forms and their properties

technical communique dynamic observers for linear time invariant systems an alternative state estimator structure for linear time invariant systems named for dynamic observer is presented which can be considered as an extension of the usual observer in its configuration as a possible design method for the dynamic observer an efficient and plausible design algorithm is also provided the mechanism of the proposed dynamic observer design is the dual of the output feedback controller design the essential characteristics of the dynamic observer to be qualified as an effective observer are addressed

the state vector reconstruction for linear systems with unknown inputs necessary and sufficient conditions for the existence of an observer for linear multivariable systems with unknown inputs are presented in theorem 1 proof of the theorem gives an algorithm of full order observer matrices calculation

state observers for discrete time linear systems with unknown inputs in the paper the problem of designing a full order state observer for a general discrete time linear system with unknown inputs is analyzed necessary and sufficient conditions for the existence either of an asymptotic or of a deadbeat observer are provided and a constructive design procedure together with some examples are discussed finally the equivalence of these conditions for problem solvability with those derived in previous contributions by means of different approaches is explicitly proved

technical communique robust h observer design of linear state delayed systems with parametric uncertainty the discrete time case in this note we consider the problem of h observer design for a class of uncertain linear discrete time systems with delayed state and parameter uncertainties the goal of this problem is to design a linear state observer such that for the positive integer state time delay and all admissible norm bounded parameter uncertainties the observation process remains robustly stable and the transfer function from exogenous disturbances to error state outputs meets the prespecified h norm upper bound constraint the observer structure does not depend on the parameter uncertainties a simple effective algebraic methodology is developed to derive the conditions for the existence of the desired robust h observers and the analytical expression of these observers is then characterized in terms of the matrix riccati like equations inequalities we provide a numerical example to demonstrate the validity and the applicability of the proposed approach

reversible linear and nonlinear discrete time dynamics it is shown that any causal discrete time system can be realized with a reversible or invertible state variable representation this bridges the gap with continuous time where flows always satisfy this property and settles an old debate on the relevance of invertibility in nonlinear discrete dynamics as the result applies to the linear case it is shown how the classic approach should be slightly modified and several examples of the benefits that can be obtained are given difference algebra is employed for nonlinear systems it leads to a most elegant characterization of causality which enables reversibility to be demonstrated module theory suffices in the linear case which is supplemented by elementary matrix manipulations

canonical forms of generic piecewise linear continuous systems this technical note reports a simple but effective strategy to derive a single coordinate transformation of a generic n dimensional piecewise linear continuous vector field that puts both of its subsystems into the same observer or control canonical form the only hypothesis required is that both subsystems are either observable or controllable to derive the result the structure of the system is used in order to prove that it suffices to consider the same transformation for both subsystems the theoretical results are illustrated by means of the colpitts oscillator as a practical case of study

the differential algebraic approach in nonlinear dynamical feedback controlled landing maneuvers a differential algebraic approach is proposed for the synthesis of a dynamical feedback controller regulating a spacecraft smooth descent toward the surface of a planet which exhibits nonnegligible atmospheric resistance an exact linearization based controller is synthesized using fliess generalized observability canonical form of the controller system the smooth controlled trajectory is regulated by means of assumed amplitude modulated thrusting capabilities of the spacecraft the robustness of the regulator is tested in the presence of significant unmodelled spatial changes in the coefficient of atmospheric resistance a simulation example is provided

continuous time non linear flatness based predictive control an exact feedforward linearisation setting with an induction drive example a general flatness based framework for non linear continuous time predictive control is presented it extends the results of fliess and marquez 2000 to the non linear case the mathematical setting which is valid for multivariable systems is provided by the theory of flatness based exact feedforward linearisation introduced by the authors hagenmeyer and delaleau 2003b thereby differential flatness does not only yield an easy calculation of the predicted trajectories considering the respective system constraints but allows to use simple linear feedback parts in a two degree of freedom control structure moreover this formalism permits one to handle non minimum phase systems and furthermore to deal with parameter uncertainties and exogenous perturbations respective robustness analysis tools are available finally an induction drive example is discussed in detail and experimental results for this fast electro mechanical system are presented

observers for linear systems with unknown inputs a direct design procedure of a full order observer for a linear system with unknown inputs is presented using straightforward matrix calculations some examples are given in these examples a reduced order observer is also derived it is shown that this may restrict the rate of convergence of some state estimates

passivity based controllers for the stabilization of dc to dc power converters abstract passivity based feedback controllers are derived for the indirect stabilization of the average output voltage in pulse width modulation pwm controlled dc to dc power converters of the boost buck boost and buck types the controller design is carried out on the basis of well known average pwm models of such circuits the average models are first shown to be euler lagrange systems corresponding to a suitable set of average euler lagrange parameters the proposed regulators are based on an energy shaping plus damping injection scheme achievable through nonlinear dynamical feedback the performance of the proposed passivity based duty ratio synthesis policies is tested for the boost converter case the regulating feedback law derived on the basis of a boost model composed of ideal switches and ideal circuit components is assessed via computer simulations on a realistic stochastically perturbed switched converter model including parasitic resistances and parasitic voltage sources

dynamical discontinuous feedback control of nonlinear systems the problem of analyzing dynamical discontinuous feedback nonlinear controlled plants is addressed the continuous feedback scheme is assumed to be constituted by a dynamical feedback plant of nonlinear nature and a controlled switch obeying a pulse width modulation pwm type of switching strategy with sufficiently high sampling rate it is found that the actual closed loop controlled responses of the system exhibit chattering motions constituting nonideal sliding regimes which converge continuously toward certain average manifolds as the sampling frequency is increased these manifolds are immersed in the regions of the composite state space where the duty ratio function is not acting under saturation conditions the average system is simply obtained by an infinite sampling frequency assumption on the pwm process a pwm feedback interconnection scheme with general duty ratio function is shown to be easily analyzable in terms of an average model which captures the essential features of the discontinuously feedback controlled system

global transformations of nonlinear systems recent results have established necessary and sufficient conditions for a nonlinear system of the form dot x t f x t u t g x t with f 0 0 to be locally equivalent in a neighborhood of the origin in rnto a controllable linear system we combine these results with several versions of the global inverse function theorem to prove sufficient conditions for the transformation of a nonlinear system to a linear system in doing so we introduce a technique for constructing a transformation under the assumptions that g ldot f dotg ad n 1 f ldotg span an n dimensional space and that g ldot f ldot g ad n 2 f ldotg is an involutive set

new delay dependent non fragile h observer based control for continuous time delay systems the problem of the delay dependent non fragile h observer based control for a class of continuous time delay systems is investigated in this paper the additive gain variations under consideration are contained in both the controller gain and obhsiunserver gain delay dependent criteria are derived to guarantee the stability of the non fragile h observer based control system using the lyapunov functional approach the controller and observer gains are given from the lmi feasible solutions based on the result of this paper the constraint of matrix equality is not necessary for designing the non fragile h observer based controls computer software matlab can be applied to solve all the proposed results finally a numerical example is illustrated to show the improvement of this paper

low order state estimators and compensators for dynamical systems with unknown inputs abstract we propose a new type of state estimator for a class of dynamical systems with unknown inputs we synthesize the combined low order estimator controller compensator and show the stability of the closed loop system the results are illustrated with a numerical example

reduced order disturbance observer for discrete time linear systems in the paper an output based disturbance observer of reduced order is presented for a class of discrete time linear systems first a general form of a disturbance observer is proposed when full states are available then by combining a state function estimator of minimal order an output based disturbance observer is derived the existence condition will be formulated in the form of a static output feedback through examples the effectiveness and advantages of the proposed approach will be demonstrated a servo control problem in practice is addressed to show the validity of the approach furthermore it will be shown that the proposed approach does provide a smaller order of disturbance observer than that of conventional approaches while maintaining satisfactory performances

necessary conditions for asymptotic tracking in nonlinear systems in the literature it has been shown that if a single input single output analytic nonlinear plant 1 has a well defined relative degree and 2 is minimum phase it is possible to achieve asymptotic tracking for an open set of output trajectories containing the origin in c sup n 0 spl infin the space of n times continuously differentiable functions taking values in r when either of these sufficient conditions is not met various authors have investigated approximate analytic solutions discontinuous solutions and solutions for restricted sets of trajectories in this paper it is shown that conditions 1 and 2 are necessary for the existence of an analytic compensator which yields asymptotic tracking for an open set of output trajectories analogous results are established for multi input multi output systems

identification of the delay parameter for nonlinear time delay systems with unknown inputs using the theory of non commutative rings this paper studies the delay identification of nonlinear time delay systems with unknown inputs a sufficient condition is given in order to deduce an output delay equation from the studied system then necessary and sufficient conditions are proposed to judge whether the deduced output delay equation can be used to identify delay involved in this equation two different cases are discussed for the dependent and independent outputs respectively the presented result is applied to identify delay in a biological system

a dynamical variable structure control strategy in asymptotic output tracking problems a dynamical discontinuous feedback strategy of the sliding mode type is presented for asymptotic output tracking problems in nonlinear dynamical systems n fliess 1989 1990 generalized observability canonical form gocf is used in the derivation of the dynamical variable structure feedback controller for a large class of nonlinear systems a truly effective smoothing of the sliding mode controlled responses is possible while substantially reducing the chattering for the control output for this reason the technique is especially suitable for the control of some mechanical and electromechanical systems an example including simulations is provided

a local characterization of observability abstract we consider time dependent linear systems of the form x ax bu y cx with state x rn control input u rm and output y rp the main results are local characterizations of observability and strong observability or observability with unknown inputs of a c and a b c these criteria are pointwise rank conditions on a certain matrix which is explicitly built up from the first n 2 derivatives of a and b and the first n 1 derivatives of c the results generalize well known theorems for time invariant systems the proofs lead also to observers with and without the input and the main tool is a generalized product rule for the differentiation of a product of matrices where only one factor and the product itself are known to be differentiable

rank invariants of nonlinear systems a linear algebraic framework for the analysis of rank properties of nonlinear systems is introduced this framework gives a high level interpretation of several existing algorithms built around the recursive computation of certain algebraic ranks associated with right invertibility left invertibility and dynamic decoupling furthermore it can be used to establish links between these algorithms and the differential algebraic approach as well as to solve some static and dynamic noninteracting control problems

pseudospectral methods for optimal motion planning of differentially flat systems the article presents some preliminary results on combining two new ideas from nonlinear control theory and dynamic optimization we show that the computational framework facilitated by pseudospectral methods applies quite naturally and easily to fliess implicit state variable representation of dynamical systems the optimal motion planning problem for differentially flat systems is equivalent to a classic bolza problem of the calculus of variations we exploit the notion that derivatives of flat outputs given in terms of lagrange polynomials at legendre gauss lobatto points can be quickly computed using pseudospectral differentiation matrices additionally the legendre pseudospectral method approximates integrals by gauss type quadrature rules the application of this method to the two dimensional crane model reveals how differential flatness may be readily exploited

expectation propagation in the large data limit summary expectation propagation ep is a widely successful algorithm for variational inference ep is an iterative algorithm used to approximate complicated distributions typically to find a gaussian approximation of posterior distributions in many applications of this type ep performs extremely well surprisingly despite its widespread use there are very few theoretical guarantees on gaussian ep and it is quite poorly understood to analyse ep we first introduce a variant of ep averaged ep which operates on a smaller parameter space we then consider averaged ep and ep in the limit of infinite data where the overall contribution of each likelihood term is small and where posteriors are almost gaussian in this limit we prove that the iterations of both averaged ep and ep are simple they behave like iterations of newton s algorithm for finding the mode of a function we use this limit behaviour to prove that ep is asymptotically exact and to obtain other insights into the dynamic behaviour of ep e g that it may diverge under poor initialization exactly like newton s method ep is a simple algorithm to state but a difficult one to study our results should facilitate further research into the theoretical properties of this important method

flatness and quasi static state feedback in non linear delay systems two notions from the theory of non linear systems without time delays are generalized to non linear delay systems flatness and quasi static state feedback depending on the generality of the relations considered flatness properties of increasing generality are obtained flatness flatness flatness and difference differential flatness it is then shown that difference differentially flat delay systems are linearizable by a certain class of predictive quasi static state feedback i e that they are equivalent by such feedback to a linear controllable system the mathematical framework is difference differential algebra

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

robust observer design for unknown inputs takagi sugeno models this paper deals with the observer design for takagi sugeno t s fuzzy models subject to unknown inputs and disturbance affecting both states and outputs of the system sufficient conditions to design an unknown input t s observer are given in linear matrix inequality lmi terms both continuous time and discrete time cases are studied relaxations are introduced by using intermediate variables extension to the case of unmeasured decision variables is also given a numerical example is given to illustrate the effectiveness of the given results

technical communique two stage kalman estimator with unknown exogenous inputs this paper presents a two stage estimator for bias and state filtering in discrete time stochastic linear systems affected by unknown inputs or disturbances we show that the state estimate can be expressed as x k k x k k b k kb k k where x k k is a bias free state estimate and b k k the optimal estimate of constant bias the proposed two stage estimator is based on an alternate derivation of the unbiased minimum variance estimator with unknown exogenous inputs developed by darouach and zasadzinski 1997 automatica 33 717 719

a modified algorithm for invertibility in nonlinear systems the algorithm of hirschorn 1 for the construction of inverses of nonlinear systems is modified and new sufficient conditions for invertibility and inverse system for a larger class of systems are obtained for the systems which do not satisfy the invertibility conditions a characterization of input space on which the input output map is injective is derived

nonlinear morgan s problem case of p 1 inputs and p outputs noninvertible static state feedback solutions of the row by row decoupling problem are investigated for the class of nonlinear systems having one more input component than output components the analysis involves a combination of geometric and algebraic tools but notably avoids the use of regular or degenerate controllability distribution subspaces the main tools used to date for the class of linear systems the main idea is finding within the system a chain of integrators that may be attached to one of the inputs in order to appropriately modify the system s structure at infinity

a polynomial approach to discrete time non linear system controllability this paper uses a polynomial approach to present a necessary and sufficient condition for local controllability of single input single output siso discrete time non linear systems the condition is presented in terms of common factors of a non commutative polynomial expression this extends the result on controllability of linear systems and the recent result on controllability of continuous time non linear systems to expose controllability of discrete time non linear systems in the input output framework the controllability condition yields a finite step computing procedure for examining controllability of discrete time input output non linear systems

adaptive dynamical feedback regulation strategies for linearizable uncertain systems abstract in this paper we address the design of adaptive dynamical feedback strategies of the continuou s and discontinuous types for the output stabilization of nonlinear systems the class of systems considered corresponds to nonlinear controlled systems exhibiting linear parametric uncertainty dynamical feedback controllers ideally achieving output stabilization via exact linearization are obtained by means of repeated output differentiation and either pole placement or sliding mode control techniques the adaptive versions of the dynamical stabilizing controllers are then obtainable through standard direct overparamemzed adaptive control strategies available for linearizable systems illustrative examples are provided which deal with the regulation of electro mechanical systems keywordk exact linearization adaptive control variable structure systemls electromechanical systems preferre d mailing address dr hebertt sira ramirez avenida la s ambricas edificio residencias el roble piso 6 apartamento d 6 mdrida 5101 venezuela this work was supported by the consejo de desarrollo cientifico humanistico y tecnol6gico of the universid ad de los andes mdrida venezulea under research grant 1 325 90 and by a grant from shin meiwa industries japan

a lie backlund approach to equivalence and flatness of nonlinear systems a new system equivalence relation using the framework of differential geometry of jets and prolongations of infinite order is studied in this setting two systems are said to be equivalent if any variable of one system may be expressed as a function of the variables of the other system and of a finite number of their time derivatives this is a lie backlund isomorphism the authors prove that although the state dimension is not preserved the number of input channels is kept fixed they also prove that a lie backlund isomorphism can be realized by an endogenous feedback the differentially flat nonlinear systems introduced by the authors 1992 via differential algebraic techniques are generalized and the new notion of orbitally flat systems is defined they correspond to systems which are equivalent to a trivial one with time preservation or not the endogenous linearizing feedback is explicitly computed in the case of the vtol aircraft to track given reference trajectories with stability

nonlinear control of a shunt dc motor the problem of controlling a shunt dc motor is considered recent methods for nonlinear control are compared including feedback linearization generalized controller canonical forms and input output linearization connections between the approaches as well as their respective advantages are discussed in detail

survey approximate linearization via feedback an overview fostered by a growing interest in nonlinear control theory and catalyzed by the discovery in the early 1980s of the exact conditions under which a nonlinear plant can be linearized by static state feedback and coordinate transformation in the last decades there has been a rapid increase of interest in the search for approximate solutions to the problem of linearizing nonlinear systems by state or output feedback main reason for that is the limited applicability of the rigorous methods and the complexity sensitivity and design difficulties of the exact linearizing compensators if any in the present paper the literature on the subject is reviewed and organized in what is believed to be a new and consistent perspective recent works especially in the area of data based techniques are in fact described and related whenever possible to fundamental results previously obtained by model based differential geometric methods this is expected to bring modern system linearization methods closer to the needs of practicing control engineers and to stimulate further research eventually able to fill visible gaps in this direction

rational systems and observation fields we give a new setting for rational input output systems i e systems on real affine varieties with the dynamics defined by rational vector fields and with rational output functions we characterize conditions under which a c system may be immersed into a rational system the problem of minimal dimension and uniqueness of immersions is also studied the observation field of the system is the main tool in our considerations