linearization of time delay systems by input output injection and output transformation in the present paper necessary and sufficient geometric conditions for the equivalence of a single input single output nonlinear time delay system under bicausal change of coordinates and regular output transformation to a linear weakly observable time delay system up to input output injection are given the obtained results are then applied to the observer design problem

n dimensional superintegrable systems from symplectic realizations of lie coalgebras the construction of n dimensional nd integrable systems from coalgebras is reviewed in the case of poisson coalgebras a necessary condition for the integrability of the nd coalgebra hamiltonian coming from a given coalgebra is obtained in terms of the dimension of the symplectic realization and the number of nonlinear casimir functions from this viewpoint the full set of three four and five dimensional lie poisson coalgebras is analysed and many new families of multiparametric nd integrable systems coming from the cases that fulfil the integrability condition are obtained including the explicit form of the integrals of the motion the superintegrability of these hamiltonians is also emphasized and the generalization of the whole construction to the quantum mechanical case is straightforward

the spin calogero gaudin system and its q deformation the spin calogero gaudin system and its q deformation are exactly solved a complete set of commuting observables is diagonalized and the corresponding eigenvectors and eigenvalues are explicitly calculated the method of solution is purely algebraic and relies on the co algebra symmetry of the model

a linear algebraic framework for dynamic feedback linearization to any accessible nonlinear system we associate a so called infinitesimal brunovsky form this gives an algebraic criterion for strong accessibility as well as a generalization of kronecker controllability indices an output function which defines a right invertible system without zero dynamics is shown to exist if and only if the basis of the brunovsky form can be transformed into a system of exact differential forms this is equivalent to the system being differentially flat and hence constitutes a necessary and sufficient condition for dynamic feedback linearizability

integrability for nonlinear time delay systems in this note the notion of integrability is defined for 1 forms defined in the time delay context while in the delay free case a set of 1 forms defines a vector space it is shown that 1 forms computed for time delay systems have to be viewed as elements of a module over a certain non commutative polynomial ring two notions of integrability are defined strong and weak integrability which coincide in the delay free case necessary and sufficient conditions are given to check if a set of 1 forms is strongly or weakly integrable to show the importance of the topic integrability of 1 forms is used to characterize the accessibility property for nonlinear time delay systems the possibility of transforming a system into a certain normal form is also considered

robust backstepping control for a class of time delayed systems in this note the problem of robust output feedback control for a class of nonlinear time delayed systems is considered the systems considered are in strict feedback form state observer is first designed then based on the observed states the controller is designed via backstepping method both the designed observer and controller are independent of the time delays based on lyapunov stability theory we prove that the constructed controller can render the closed loop system asymptotically stable simulation results further verify the effectiveness of the proposed approach

a new approach to state observation of nonlinear systems with delayed output the article presents a new approach for the construction of a state observer for nonlinear systems when the output measurements are available for computations after a nonnegligible time delay the proposed observer consists of a chain of observation algorithms reconstructing the system state at different delayed time instants chain observer conditions are given for ensuring global exponential convergence to zero of the observation error for any given delay in the measurements the implementation of the observer is simple and computer simulations demonstrate its effectiveness

sliding mode control of retarded nonlinear systems via finite spectrum assignment approach in the present study a sliding mode control design method based on the finite spectrum assignment procedure is proposed the finite spectrum assignment for retarded nonlinear systems can transform retarded nonlinear systems into delay free linear systems via a variable transformation and a feedback which contain the past values of the state this method can be considered to be an extension of both the finite spectrum assignment for retarded linear systems with controllability over polynomial rings of the delay operator and the exact linearization for finite dimensional nonlinear systems the proposed method is to design a sliding surface via the variable transformation used in the finite spectrum assignment and to derive a switching feedback law the obtained surface contains not only the current values of the state variables but also the past values of the state variables in the original coordinates the effectiveness of the proposed method is tested by an illustrative example

combinatorial restrictions on the tree class of the auslander reiten quiver of a triangulated category we show that if a connected hom finite krull schmidt triangulated category has an auslander reiten quiver component with dynkin tree class then the category has auslander reiten triangles and that component is the entire quiver this is an analogue for triangulated categories of a theorem of auslander and extends a previous result of scherotzke we also show that if there is a quiver component with extended dynkin tree class then other components must also have extended dynkin class or one of a small set of infinite trees provided there is a non zero homomorphism between the components the proofs use the theory of additive functions

neural networks based adaptive control for nonlinear time varying delays systems with unknown control direction this paper investigates a neural network nn state observer based adaptive control for a class of time varying delays nonlinear systems with unknown control direction an adaptive neural memoryless observer in which the knowledge of time delay is not used is designed to estimate the system states furthermore by applying the property of the function tanh2 e the function can be defined at 0 and introducing a novel type appropriate lyapunov krasovskii functional an adaptive output feedback controller is constructed via backstepping method which can efficiently avoid the problem of controller singularity and compensate for the time delay it is highly proven that the closed loop systems controller designed by the nn basis function property new kind parameter adaptive law and nussbaum function in detecting the control direction is able to guarantee the semi global uniform ultimate boundedness of all signals and the tracking error can converge to a small neighborhood of zero the characteristic of the proposed approach is that it relaxes any restrictive assumptions of lipschitz condition for the unknown nonlinear continuous functions and the proposed scheme is suitable for the systems with mismatching conditions and unmeasurable states finally two simulation examples are given to illustrate the effectiveness and applicability of the proposed approach

classical dynamical systems from q algebras cluster variables and explicit solutions a general procedure to get the explicit solution of the equations of motion for n body classical hamiltonian systems equipped with coalgebra symmetry is introduced by defining a set of appropriate collective variables which are based on the iterations of the coproduct map on the generators of the algebra in this way several examples of n body dynamical systems obtained from q poisson algebras are explicitly solved the q deformed version of the sl 2 calogero gaudin qcg system a q poincare gaudin system and a system of ruijsenaars type arising from the same non coboundary q deformation of the 1 1 poincare algebra while the complete integrability of all these systems was already well known being in fact encoded in their construction no explicit solution was available until now in particular it turns out that there exists an open subset of the whole phase space where the orbits of the qcg system are periodic with the same period also a unified interpretation of all these systems as different poisson lie dynamics on the same three dimensional solvable lie group is given

on observation of time delay systems with unknown inputs causal and non causal observability are discussed in this technical note for nonlinear time delay systems with unknown inputs using the theory of non commutative rings and the algebraic framework introduced by xia the nonlinear time delay system is transformed into a suitable canonical form to solve the problem a necessary and sufficient condition is given to guarantee the existence of a change of coordinates leading to such a form

quadratic stabilization of continuous time systems with state delay and norm bounded time varying uncertainties this paper develops a method for designing a feedback control law to stabilize a class of uncertain linear systems the class of systems under consideration is described by a continuous time model with variable state delay and depends on time varying unknown but bounded uncertain parameters it is shown that the construction of the stabilizing controller involves solving a certain algebraic riccati equation several previous results are derived as interesting special cases finally a simulation example is presented to illustrate the analytical developments

brief analysis of nonlinear time delay systems using modules over non commutative rings the theory of non commutative rings is introduced to provide a basis for the study of nonlinear control systems with time delays the left ore ring of non commutative polynomials defined over the field of meromorphic function is suggested as the framework for such a study this approach is then generalized to a broader class of nonlinear systems with delays that are called generalized roesser systems finally the theory is applied to analyze nonlinear time delay systems a weak observability is defined and characterized generalizing the well known linear result properties of closed submodules are then developed to obtain a result on the accessibility of such systems

comodule algebras and integrable systems a method of constructing both classical and quantum completely integrable systems from jordan lie comodule algebras is introduced several integrable models based on a so 2 1 comodule algebra two non standard schrodinger comodule algebras the classical and quantum q oscillator algebra and the reflection equation algebra are explicitly obtained

on feedback invariance properties for systems over a principal ideal domain simple necessary and sufficient conditions for the solvability of many control problems for linear systems over a field are based on the equivalence between the a b invariance property and the a bf invariance or feedback invariance property for systems over a ring this equivalence is no longer true and many results of the geometric control theory cannot be extended we present new algorithmically checkable characterizations of the a bf invariance property for systems defined over a principal ideal domain and a new solvability condition for the disturbance rejection problem

linearization of discrete time systems the algebraic formalism developed in this paper unifies the study of the accessibility problem and various notions of feedback linearizability for discrete time nonlinear systems the accessibility problem for nonlinear discrete time systems is shown to be easy to tackle by means of standard linear algebraic tools whereas this is not the case for nonlinear continuous time systems in which case the most suitable approach is provided by differential geometry the feedback linearization problem for discrete time systems is recasted through the language of differential forms in the event that a system is not feedback linearizable the largest feedback linearizable subsystem is characterized within the same formalism using the notion of derived flag of a pfaffian system a discrete time system may be linearizable by dynamic state feedback though it is not linearizable by static state feedback necessary and sufficient conditions are given for the existence of a so called linearizing output which in turn is a sufficient condition for dynamic state feedback linearizability

robust stability and stabilization methods for a class of nonlinear discrete time delay systems this paper establishes new robust delay dependent stability and stabilization methods for a class of nonlinear discrete time systems with time varying delays the parameter uncertainties are convex bounded and the unknown nonlinearities are time varying perturbations satisfying lipschitz conditions in the state and delayed state an appropriate lyapunov functional is constructed to exhibit the delay dependent dynamics and compensate for the enlarged time span the developed methods for stability and stabilization eliminate the need for over bounding and utilize smaller number of lmi decision variables new and less conservative solutions to the stability and stabilization problems of nonlinear discrete time system are provided in terms of feasibility testing of new parametrized linear matrix inequalities lmis robust feedback stabilization methods are provided based on state measurements and by using observer based output feedback so as to guarantee that the corresponding closed loop system enjoys the delay dependent robust stability with an l 2 gain smaller that a prescribed constant level all the developed results are expressed in terms of convex optimization over lmis and tested on representative examples

a systematic construction of completely integrable hamiltonians from coalgebras a universal algorithm to construct n particle classical and quantum completely integrable hamiltonian systems from representations of coalgebras with casimir elements is presented in particular this construction shows that quantum deformations can be interpreted as generating structures for integrable deformations of hamiltonian systems with coalgebra symmetry in order to illustrate this general method the algebra and the oscillator algebra are used to derive new classical integrable systems including a generalization of gaudin calogero systems and oscillator chains quantum deformations are then used to obtain some explicit integrable deformations of the previous long range interacting systems and a non coboundary deformation of the 1 1 poincare algebra is shown to provide a new ruijsenaars schneider like hamiltonian

finite time and asymptotic left inversion of nonlinear time delay systems in this paper we investigate the left invertibility problem for a class of nonlinear time delay systems in both cases of time delay systems with and without internal dynamics the invertibility conditions are given a new approach based on the use of higher order sliding mode observer is developed for finite time left invertibility and for asymptotic left inversion causal and non causal estimations of the unknown inputs are respectively discussed the results are illustrated by numerical examples in order to show the efficiency of the method and its limits

unknown input observer for linear time delay systems this paper investigates an unknown input observer design for a large class of linear systems with unknown inputs and commensurate delays a luenberger like observer is proposed by involving only the past and actual values of the system output the required conditions for the proposed observer are considerably relaxed in the sense that they coincide with the necessary and sufficient conditions for the unknown input observer design of linear systems without delays

identifiabilty of systems described by convolution equations parameter identifiability is studied for a class of finite and infinite dimensional systems described by convolution equations the notion of sufficiently rich input which enforces identifiability is also addressed and the results are obtained assuming knowledge of solutions on a bounded time interval

on sontag s formula for the input to state practical stabilization of retarded control affine systems abstract in this paper input to state practically stabilizing control laws for retarded control affine nonlinear systems with actuator disturbance are investigated the developed methodology is based on artstein s theory of control lyapunov functions and related sontag s formula extended to retarded systems if the actuator disturbance is bounded then the controller yields the solution of the closed loop system to achieve an arbitrarily fixed neighborhood of the origin by increasing a control tuning parameter the considered systems can present an arbitrary number of discrete as well as distributed time delays of any size as long as they are constant and in general known

text ad _ f g text ad _ f g and locally text ad _ f g invariant and controllability distributions in the study of nonlinear control systems the concepts of an invariant foliation and an invariant distribution play important roles in this paper we explore various forms of these concepts and show how they occur in the study of controllability observability and decoupling of nonlinear systems

controllability of nonlinear discrete time systems a lie algebraic approach this paper presents a geometric study of controllability for discrete time nonlinear systems various accessibility properties are characterized in terms of lie algebras of vector fields some of the results obtained are parallel to analogous ones in continuous time but in many respects the theory is substantially different and many new phenomena appear

locally finite triangulated categories abstract a k linear triangulated category a is called locally finite provided x ind a dim k hom a x y for any indecomposable object y in a it has auslander reiten triangles in this paper we show that if a connected triangulated category has auslander reiten triangles and contains loops then its auslander reiten quiver is of the form l n download download full size image by using this we prove that the auslander reiten quiver of any locally finite triangulated category a is of the form z g where is a dynkin diagram and g is an automorphism group of z for most automorphism groups g the triangulated categories with z g as their auslander reiten quivers are constructed in particular a triangulated category with l n as its auslander reiten quiver is constructed

solvable quantum version of an integrable hamiltonian system solvable quantum versions of the classical dynamical system characterized by the hamiltonian h nj k 1 pjpk cos qj qk are presented the eigenvalues of the quantum hamiltonians are exhibited as well as the corresponding eigenfunctions

observability of linear systems with commensurate delays and unknown inputs this paper investigates the observability analysis for linear time systems whose outputs are affected by unknown inputs three different definitions of observability are proposed by introducing the smith form and comparing the invariant factors a sufficient condition is deduced for each proposed definition observability several examples are given for the purpose of highlighting the effectiveness of the proposed approach

exact solution of the quantum calogero gaudin system and of its q deformation a complete set of commuting observables for the calogero gaudin system is diagonalized and the explicit form of the corresponding eigenvalues and eigenfunctions is derived we use a purely algebraic procedure exploiting the coalgebra invariance of the model with the proper technical modifications this procedure can be applied to the q deformed version of the model which is then also exactly solved

h tracking based adaptive fuzzy neural control for mimo uncertain robotic systems with time delays in this paper a novel adaptive fuzzy neural control afnc scheme for multi input multi output uncertain robotic systems is proposed for h tracking performance and to suppress the effects caused by multiple time delayed state uncertainties unmodeled dynamics and disturbances each delayed uncertainty is assumed to be bounded by an unknown gain a reference model with the desired amplitude and phase properties is given to construct an error model a fuzzy neural fn system is used to approximate an unknown controlled system from the strategic manipulation of the model following tracking errors the proposed afnc scheme uses two on line estimations which allows for the inclusion of identifying the gains of the delayed state uncertainties and training the weights of the fn system simultaneously stability and robustness of the afnc scheme is analyzed in lyapunov sense it is shown that the proposed control scheme can guarantee parameter estimation convergence and stability robustness of the closed loop system with h tracking performance for the overall system without a priori knowledge on the upper bounds of the delayed state uncertainties the performance of the proposed scheme is evaluated through the simulation results simulations are given to show the validity and confirm the performance of the proposed scheme

on auslander reiten components of blocks and self injective biserial algebras we investigate the existence of auslander reiten components of euclidean type for special biserial self injective algebras and for blocks of group algebras in particular we obtain a complete description of stable auslander reiten quivers for the tame self injective algebras considered here

brief paper state elimination and identifiability of the delay parameter for nonlinear time delay systems the identifiability of the delay parameter for nonlinear systems with a single constant time delay is analyzed we show the existence of input output equations and relate the identifiability of the delay parameter to their form explicit criteria based on rank calculations are formulated the identifiability of the delay parameter is shown not to be directly related to the well characterized identifiability observability of the other system parameters states

parameters estimation of systems with delayed and structured entries this paper deals with on line identification of continuous time systems with structured entries such entries which may consist of inputs perturbations or piecewise polynomial time varying parameters can be defined as signals that can be easily annihilated the proposed cancellation method allows to obtain non asymptotic estimators for the unknown coefficients application to delayed and switching hybrid systems are proposed numerical simulations with noisy data but also experimental results on a delay process are provided

feedback linearization of discrete time systems abstract we give necessary and sufficient conditions for a nonlinear discrete time system to be locally linearizable by a change of state coordinates and a feedback the conditions are expressed in terms of controllability distributions associated to the system

on saturation discontinuities and delays in iiss and iss feedback control redesign this paper addresses input to state stability iss and integral iss iiss redesign to enhance robustness of feedback control systems in the face of actuator disturbances the idea of the redesign is to modify control laws available for disturbance free systems a priori in order to achieve robustness against the disturbance in practice control system design often encounters time delays discontinuities and actuator limitations at the same time the purpose of this paper is to propose a unified treatment of these issues in the redesign for actuator disturbances for the new class of systems we pursue lgv type formulas which are widely used for ordinary differential equations in addition we incorporate saturation into the lgv type control for implementation in the presence of actuator limitations to derive such a redesign formula we develop a framework of iss iiss lyapunov krasovskii functionals allowing for the krasovskii solutions this paper demonstrates that the notion of invariantly differentiable functionals is useful for deriving lgv type control laws and dealing with discontinuities directly the iiss formulation which includes the iss as a special case allows us to address actuator limitations in the redesign problem in a flexible manner

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

input to state stabilization of stabilizable time delay control affine nonlinear systems in this technical note state feedback control laws which provide input to state stability of the closed loop system with respect to a disturbance adding to the control input are investigated for state feedback globally stabilizable time delay systems

output transformations and separation results for feedback linearisable delay systems abstractthe class of strict feedback systems enjoys special properties that make it similar to linear systems this paper proves that such a class is equivalent under a change of coordinates to the wider class of feedback linearisable systems with multiplicative input when the multiplicative terms are functions of the measured variables only we apply this result to the control problem of feedback linearisable nonlinear mimo systems with input and or output delays in this way we provide sufficient conditions under which a separation result holds for output feedback control and moreover a predictor based controller exists when these conditions are satisfied we obtain that the existence of stabilising controllers for arbitrarily large delays in the input and or the output can be proved for a wider class of systems than previously known

input output linearization of retarded non linear systems by using an extension of lie derivative this paper considers the input output linearization problem for retarded non linear systems which have time delays in the state by using an extension of the lie derivative for functional differential equations we derive a coordinates transformation and a static state feedback to obtain linear input output behaviour for a class of retarded non linear systems the obtained coordinates transformation is allowed to contain not only the current value of the state variables but also the past values of ones in addition we show that the coordinates transformation is invertible in a neighbourhood of the origin and examine the stability condition of the closed loop system with the static state feedback the effectiveness of the proposed technique is demonstrated through numerical simulations

extended lie brackets for nonlinear time delay systems in this note the extended lie bracket operator is introduced for the analysis and control of nonlinear time delay systems nltds this tool is used to characterize the integrability conditions of a given submodule the obtained results have two fundamental outcomes first they define the necessary and sufficient conditions under which a given set of nonlinear one forms in the n dimensional delayed variables x t x t sd with d constant but unknown are integrable thus generalizing the well known fundamental frobenius theorem to delay systems secondly they set the basis for the extension to this context of the geometric approach used for delay free systems the effectiveness of the results is shown by solving the problem of the equivalence of a nltds to an accessible linear time delay system ltds by bicausal change of coordinates

relations for the grothendieck groups of triangulated categories a class of triangulated categories with a finiteness condition is singled out these triangulated categories have auslander reiten triangles it is proved that the relations of the grothendieck group of a triangulated category in this class are generated by all auslander reiten triangles moreover the auslander reiten quivers of certain triangulated categories in this class are described in terms of dynkin diagrams 2002 elsevier science usa all rights reserved

a finite spectrum assignment for retarded non linear systems and its solvability condition this paper considers a finite spectrum assignment problem for retarded non linear systems first using extensions of the lie derivative and the lie bracket for differential difference equations we propose a finite spectrum assignment procedure for a class of retarded non linear systems then we derive a necessary and sufficient condition for the solvability of a class of finite spectrum assignment problems for retarded non linear systems the obtained condition is an extension of the condition for the exact linearization of finite dimensional non linear systems and the finite spectrum assignment of retarded linear systems with controllability over polynomial rings

controllability of driftless nonlinear time delay systems the controllability of a class of nonlinear driftless time delay systems is fully characterized for the first time this result is obtained within a newly introduced geometric approach moreover all those possible autonomous or non controllable elements which can depend on the delayed variables are also characterized when the system is not controllable and in consequence a canonical form of those systems is derived

the disturbance decoupling problem for systems over a ring up to now the use of geometric methods in the study of disturbance decoupling problems ddps for systems over a ring has provided only necessary conditions for the existence of solutions in this paper we study such problems considering separately the case in which only static feedback solutions are allowed and the one in which dynamic feedback solutions are admitted in the first case we give a complete geometric characterization of the solvability conditions of such problems for injective systems with coefficients in a commutative ring practical procedures for testing the solvability conditions and for constructing solutions if any exist are given in the case of systems with coefficients in a principal ideal domain pid in the second case we give a complete geometric characterization of the solvability conditions for systems with coefficients in a pid

delay identification for a class of nonlinear systems abstractthe problem of state estimation for nonlinear systems with unknown state delays is still an open problem in this paper we propose to add a delay identifier to suitable high gain observers in order to achieve simultaneous estimation of state and delay in the case of one constant delay in the state we provide sufficient conditions to guarantee the exponential convergence to zero of the errors globally with respect to the initial choice of the system state variables and locally with respect to the initial delay estimation we validate the method through an example concerning chaotic oscillators

delay estimation via sliding mode for nonlinear time delay systems this paper deals with delay identifiability and delay estimation for a class of nonlinear time delay systems the theory of non commutative rings is used to analyze the identifiability in order to estimate the delay a sliding mode technique and a classical newton method are combined to show the possibility to have a local or global delay estimation for periodic or aperiodic delay signals

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

exact solution to a supersymmetric gaudin model we investigate a special case of the gaudin model related to the superalgebra osp 1 2 we present an exact solution to that system diagonalizing a complete set of commuting observables and providing the corresponding eigenvectors and eigenvalues the approach used in this paper is based on the co algebra symmetry of the model already known from the calogero gaudin system

h sub spl infin memoryless control with an spl alpha stability constraint for time delay systems an lmi approach focuses on the design of h sub spl infin memoryless state feedback controllers satisfying some spl alpha stability constraints on the closed loop poles for a class of linear systems with delayed state subject to disturbance inputs a sufficient condition for feasibility is derived in terms of linear matrix inequalities furthermore we also consider a particular optimization problem the maximal bound allowed on time delay such that the prescribed level on disturbance attenuation and the spl alpha stability constraints are still preserved this problem is converted into a linear matrix inequality lmi optimization problem and we give a suboptimal bound on the delay

disturbance decoupling with closed loop modes stability in switched linear systems this work deals with the problem of rendering the output of a switched linear system insensitive to a disturbance input with the requirement that the dynamics of the closed loop system be exponentially stable for all switching signals with a sufficiently large dwell time a necessary and sufficient condition for the problem to have a solution is shown a complete computational procedure to check the solvability condition and to synthesize the compensation scheme is provided a worked out example is presented with the aim of showing the effectiveness of the devised method

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

online identification of continuous time systems with unknown time delay in this note we present a recursive algorithm for online identification of systems with unknown time delay the proposed algorithm can be interpreted as an approximate nonlinear least squares corresponding to modified normalized or un normalized least squares when the normalizing factor spl gamma 0 or spl gamma 0 respectively both algorithms are essentially extensions to general least squares methodology simulation studies demonstrate the characteristics and performance of these algorithms

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

parameter estimation for nonlinear time delay systems with noisy output measurements this paper considers the problem of using noisy output data to estimate unknown time delays and unknown system parameters in a general nonlinear time delay system we formulate the problem as a dynamic optimization problem in which the unknown quantities are decision variables to be chosen optimally with the cost function penalizing the mean and variance of the least squares error between actual and predicted system output since the time delays and system parameters influence the cost function implicitly through the governing time delay system the cost function s gradient which is required to solve the problem using gradient based optimization techniques cannot be computed analytically using standard differentiation rules we instead develop two computational methods for evaluating this gradient one involves solving an auxiliary time delay system forward in time the other involves solving an auxiliary time advance system backward in time on this basis we propose an efficient optimization algorithm for determining optimal estimates for the time delays and system parameters we conclude the paper by examining the performance of this algorithm on a dynamic model of a continuously stirred tank reactor

gaudin models and bending flows a geometrical point of view in this paper we discuss the bi hamiltonian formulation of the rational xxx gaudin models of spin spin interaction generalized to the case of sl r valued spins we only consider the classical case using recent results concerning the quantum models as guiding principles in particular we focus on the so called homogeneous xxx models we find a pencil of poisson brackets that recursively define a complete set of integrals of the motion alternative to the set of integrals associated with the standard lax representation of the gaudin model these integrals in the case of su 2 coincide with the hamiltonians of the bending flows in the moduli space of polygons in the euclidean space introduced by kapovich and millson we finally address the problem of separability of these flows and explicitly find separation coordinates and separation relations for the sl 2 case

the disturbance decoupling problem for time delay nonlinear systems in this paper the disturbance decoupling problem ddp for a class of siso nonlinear systems with multiple delays in the input and the state is studied a pioneering mathematical approach is introduced for this class of systems and is claimed to be the cornerstone of the problem necessary and sufficient conditions are given for the existence of a bicausal feedback that solves the ddp sufficient conditions for the existence of a solution within other classes of compensators are included as well

new insights on the analysis of nonlinear time delay systems application to the triangular equivalence in this paper we present recent advances towards an algebraic framework for the analysis and control of nonlinear systems with delays we show the usefulness of these results by applying them to obtain a constructive characterization of the equivalence of a given system to the so called triangular form

noetherian hereditary abelian categories satisfying serre duality norwegian univ sci technol dept math sci n 7491 trondheim norway limburgs univ ctr dept wni b 3590 diepenbeek belgium reiten i norwegian univ sci technol dept math sci n 7491 trondheim norway

accessibility of nonlinear time delay systems a full characterization of accessibility is provided for nonlinear time delay systems it generalizes the rank condition which is known for weak controllability of linear time delay systems as well as the celebrated geometric approach for delay free nonlinear systems and the characterization of their accessibility besides fundamental results are derived on integrability and basis completion which are of major importance for a number of general control problems for nonlinear time delay systems they are shown to impact preconceived ideas about canonical forms for nonlinear time delay systems