on vanishing stability regions in nonlinear systems with high gain feedback when local stabilization of nonlinear systems is achieved by linear feedback the resulting stability region may vanish as the feedback gains increase this is demonstrated by examples in which neglected nonlinearities create an unstable limit cycle around an asymptotically stable equilibrium as the feedback gains tend to infinity the unstable limit cycle shrinks to the equilibrium if a feedback linearization design is applied the same instability mechanism may occur when the nonlinearities are not precisely known

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

on the radius of convergence of interconnected analytic nonlinear input output systems a complete analysis is presented of the radii of convergence of the parallel product cascade and feedback interconnections of analytic nonlinear input output systems represented as fliess operators such operators are described by convergent functional series which are indexed by words over a noncommutative alphabet their generating series are therefore specified in terms of noncommutative formal power series given growth conditions for the coefficients of the generating series for the subsystems the radius of convergence of each interconnected system is computed assuming the subsystems are either all locally convergent or all globally convergent in the process of deriving the radius of convergence for the feedback connection it is shown definitively that local convergence is preserved under feedback this had been an open problem in the literature until recently

adaptive low gain integral control of linear systems with input and output nonlinearities abstract an adaptive low gain integral control framework is developed for tracking constant reference signals in a context of finite dimensional exponentially stable single input single output linear systems with positive steady state gain and subject to locally lipschitz monotone input and output nonlinearities of a general nature the input nonlinearity is required to satisfy an asymptotic growth condition of sufficient generality to accommodate nonlinearities ranging from saturation to exponential growth and the output nonlinearity is required to satisfy a sector constraint in those cases wherein the input nonlinearity is unbounded

faa di bruno hopf algebra of the output feedback group for multivariable fliess operators abstract given two nonlinear input output systems written in terms of chen fliess functional expansions i e fliess operators it is known that the feedback interconnected system is always well defined and in the same class an explicit formula for the generating series of a single input single output closed loop system was provided by the first two authors in earlier work via hopf algebra methods this paper is a sequel it has four main innovations first the full multivariable extension of the theory is presented next a major simplification of the basic setup is introduced using a new type of grading that has recently appeared in the literature this grading also facilitates a fully recursive algorithm to compute the antipode of the hopf algebra of the output feedback group and thus the corresponding feedback product can be computed much more efficiently the final innovation is an improved convergence analysis of the antipode operation namely the radius of convergence of the antipode is computed

robust output feedback regulation of minimum phase nonlinear systems using conditional integrators this paper is on the design of robust output feedback integral control for minimum phase nonlinear systems with a well defined relative degree previous work has shown how to design such controllers to achieve asymptotic regulation by a two step process first robust control is designed to bring the trajectories to a small neighborhood of an equilibrium point within this neighborhood the control then acts as a high gain feedback that stabilizes the equilibrium point the asymptotic regulation achieved by integral action happens at the expense of degrading the transient performance in this paper we present an approach to improve the transient performance the control design is a continuous sliding mode control with integral action however the integrator is introduced in such a way that it provides integral action only conditionally effectively eliminating the performance degradation there are two main results in the paper the first is asymptotic regulation and the second confirms the transient performance improvement by showing that the output feedback continuous sliding mode control with integral action can be tuned to recover the performance of a state feedback ideal sliding mode control without integral action

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

robust design of nonlinear internal models without adaptation we propose a solution to the problem of semiglobal output regulation for nonlinear minimum phase systems driven by uncertain exosystems that does not rely upon conventional adaptation schemes to estimate the frequency of the exogenous signals rather the proposed approach relies upon regression like arguments used to derive a nonlinear internal model able to offset the presence of an unknown number of harmonic exogenous inputs of uncertain amplitude phase and frequency the design methodology guarantees asymptotic regulation if the dimension of the regulator exceeds a lower bound determined by the actual number of harmonic components of the exogenous input if this is not the case a bounded steady state regulation error is ensured whose amplitude though can be arbitrarily decreased by acting on a design parameter of the regulator

dynamic inversion for multivariable non affine in control systems via time scale separation this paper presents a tracking design methodology applicable to multivariable non affine in control systems the main focus is on solving the tracking problem for non linear systems whose dynamics depend non linearly on the control input the latter is designed to be faster than the main system dynamics using singular perturbation theory along with the lyapunov stability theorems it is shown that the proposed controller approximates an unknown dynamic inversion based solution with bounded errors provides closed loop stability and solves the tracking problem with bounded errors simulations illustrate the theoretical results

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

the observer follower filter a new approach to nonlinear suboptimal filtering this paper investigates the state estimation problem for a class of stochastic nonlinear differential systems a novel algorithm is proposed denoted as observer follower filter off based on a two steps mixed approach the first step makes use of a high gain observer based estimator for nonlinear systems applied to the system equations in order to provide the trajectory around which a n degree carleman approximation of the stochastic differential system is achieved second step in principle any other high gain estimator can be used but in this note we prove that the one here proposed provides a bounded mean square error numerical simulations show the effectiveness of the proposed methodology and the improvements of the off with respect to the standard extended kalman bucy filter ekbf obtained by increasing the order of the carleman approximation

time varying increasing gain observers for nonlinear systems a full order state observer for a class of nonlinear continuous time systems is presented as generalization of the high gain observer for having a time varying gain that is let to be small in the first time instants increases over time up to its maximum and then is kept constant the global stability of the resulting estimation error is proved by means of a lyapunov functional via a change of coordinate the design of such an observer is obtained by solving a nonlinear programming problem and using series expansions to set the time varying gain

integral action in output feedback for multi input multi output nonlinear systems we address a particular problem of output regulation for multi input multi output nonlinear systems specifically we are interested in making the stability of an equilibrium point and the regulation to zero of an output robust to small unmodelled discrepancies between design model and actual system in particular those introducing an offset we propose a novel procedure which is intended to be relevant to realistic scenarios as illustrated by a non academic example

increasing gain observers for nonlinear systems for the purpose to estimate the state of nonlinear continuous time systems we focus on the increasing gain observer regarded as generalization of the well known high gain observer as compared with the previous results on increasing gain observers the assumptions under which the global asymptotic stability of the estimation error is proved are relaxed the stability analysis is drawn by using a more general type of lyapunov functional where design parameters can be tuned to set the time varying gain a new design method based on such a lyapunov functional is proposed to construct the observer simulation results affirm the effectiveness of the increasing gain approach as compared with the high gain observer

frequency domain analysis and tuning of the algebraic differentiators abstractthe algebraic differentiators introduced by mboup join and fliessare studied in the frequency domain the study complements the time domain developments of the previous reference where a least squares interpretation has allowed to explain the main properties of the method and also to devise efficient differentiators the frequency domain analysis gives answers to the central question of the choice of the algebraic differentiator parameters also an interpretation of the algebraic differentiators in terms of wavelet decomposition is given

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

universal integral control an approach based on mollifiers the universal integral control introduced by h k khalil universal integral controllers for minimum phase nonlinear systems ieee trans autom control vol 45 no 3 is revisited by employing mollifiers instead of a high gain observer for the differentiation of the output signal the closed loop system is a classical functional differential equation with distributed delays on which standard lyapunov arguments are applied to study the stability low pass filtering capability of mollifiers is demonstrated for a high amplitude and rapidly oscillating noise the controller is supported by numerical simulations

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

algebraic differential equations and rational control systems an equivalence is shown between realizability of input output i o operators by rational control systems and high order algebraic differential equations for i o pairs this generalizes to nonlinear systems the equivalence between autoregressive representations and finite dimensional linear realizability

continuous state feedback guaranteeing uniform ultimate boundedness for uncertain dynamic systems we consider a dynamic system containing uncertain elements only the set of possible values of these uncertainties is known based on this information a class of state feedback controls is proposed in order to guarantee uniform ultimate boundedness of every system response within an arbitrarily small neighborhood of the zero state these feedback controls are continuous functions of the state

renormalization in quantum field theory and the riemann hilbert problem i the hopf algebra structure of graphs and the main theorem this paper gives a complete selfcontained proof of our result announced in 6 showing that renormalization in quantum field theory is a special instance of a general mathematical procedure of extraction of finite values based on the riemann hilbert problem we shall first show that for any quantum field theory the combinatorics of feynman graphs gives rise to a hopf algebra which is commutative as an algebra it is the dual hopf algebra of the enveloping algebra of a lie algebra whose basis is labelled by the one particle irreducible feynman graphs the lie bracket of two such graphs is computed from insertions of one graph in the other and vice versa the corresponding lie group g is the group of characters of we shall then show that using dimensional regularization the bare unrenormalized theory gives rise to a loop where c is a small circle of complex dimensions around the integer dimension d of space time our main result is that the renormalized theory is just the evaluation at z d of the holomorphic part of the birkhoff decomposition of we begin to analyse the group g and show that it is a semi direct product of an easily understood abelian group by a highly non trivial group closely tied up with groups of diffeomorphisms the analysis of this latter group as well as the interpretation of the renormalization group and of anomalous dimensions are the content of our second paper with the same overall title

stability analysis and fail safe operation of inverters operated in parallel in this paper the stability in the sense of boundedness of inverters operated in parallel is proven and the fail safe operation is achieved for generic linear or nonlinear loads described in the generalised dissipative hamiltonian form the robust droop controller rdc recently proposed in the literature for achieving accurate proportional power sharing and tight voltage regulation is implemented in a nonlinear matrix form to achieve a bounded inverter voltage and inherit a fail safe capability using nonlinear lyapunov methods it is proven that the rdc with fail safe approximates the original rdc generates a bounded inverter output voltage within the given technical limits and guarantees nonlinear closed loop system stability in the sense of boundedness when the prescribed limits are violated e g due to sensor failure the proposed method rapidly shuts down in a continuous time manner thus disconnecting the inverter to prevent a complete system failure even when the protection circuit fails extensive simulation results are presented to demonstrate this approach for two single phase paralleled inverters feeding a linear and a nonlinear load under a sensor failure scenario

lie brackets and local controllability a sufficient condition for scalar input systems we develop a general formalism based on exponential lie series which can be used to study control variations we apply the formalism to prove a result conjectured by h hermes that gives a sufficient condition for small time local controllability for single input systems

a combinatorial hopf algebra for nonlinear output feedback control systems abstract in this work a combinatorial description is provided of a faa di bruno type hopf algebra which naturally appears in the context of fliess operators in nonlinear feedback control theory it is a connected graded commutative and non cocommutative hopf algebra defined on rooted circle trees a cancellation free forest formula for its antipode is given

a quantitative condition for the well posedness of interconnected dynamical systems a sufficient condition for the well posedness of interconnected dynamical systems is reported the condition is stated in terms of the uniform instantaneous gains of subsystems and interconnections and includes vidyasagar s condition 8 as a special case the result is useful for testing the validity of the dynamical model of a large scale system which is obtained by combining the models of subsystems

a high gain nonlinear observer with limited gain power in this note we deal with a new observer for nonlinear systems of dimension n in canonical observability form we follow the standard high gain paradigm but instead of having an observer of dimension n with a gain that grows up to power n we design an observer of dimension 2n 2 with a gain that grows up only to power 2

universal integral controllers for minimum phase nonlinear systems we consider a single input single output siso nonlinear system that has a well defined normal form with asymptotically stable zero dynamics using only knowledge of the relative degree and the sign of the high frequency gain we design an output feedback integral controller that asymptotically regulates the output to a bounded time varying reference signal with a constant limit we give regional as well as semi global results we also show that for relative degree one and two systems the proposed integral controller reduces to the classical pi and pid controllers respectively

observability and controllability for smooth nonlinear systems the definition of a smooth nonlinear system as proposed recently by willems is elaborated as a natural generalization of the more common definitions of a smooth nonlinear input output system mini

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

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

tracking control for a class of unknown nonsquare mimo nonaffine systems a deep rooted information based robust adaptive approach the tracking control problem of multi input multi output mimo nonaffine dynamic systems is studied in this note a globally uniformly ultimately bounded guub stable tracking control solution for non square mimo nonaffine systems with unknown dynamics and disturbances is established different from most existing methods the proposed control design is based on the readily computable deep rooted information on the system and does not involve linearization or approximation and the resultant control algorithms are simple in structure inexpensive in computation user friendly in design and undemanding in implementation both theoretical analysis and numerical simulation verify the effectiveness and benefits of the proposed method

non causal fliess operators and their shuffle algebra fliess operators as a class of non linear operators have been well studied in several respects they have a well developed realization theory and convenient representations in terms of directed infinite products of exponential lie series their interconnection as subsystems has been studied as has their relationship to rational systems they find applications in such diverse areas as discretization methods for controls systems optimal control neural network analysis and the numerical solution of stochastic differential equations one issue concerning fliess operators however that has received little attention is their possible generalization to the non causal case examples of such operators appear implicitly in the literature addressing hilbert adjoints of causal non linear operators and system inversion for the purpose of output tracking but a general systematic treatment of the subject has not appeared in this paper a non causal extension of a fliess operator is developed with the primary focus being on local convergence continuity the associated shuffle algebra and computing adjoint operators

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

a high gain observer with updated gain for a class of mimo non triangular systems a high gain like observer with updated gain is proposed for a class of cascade nonlinear and non triangular systems that are observable for any input the objective of the gain adaptation is to perform an admissible tradeoff between state reconstruction dynamics on the one hand versus noise amplification on the other hand to this end the gain of the proposed observer is tuned through a single scalar time varying parameter governed by an adequate differential riccati equation the involved adaptation process is mainly driven by the power of the output observation error norm computed on a moving horizon window simulation results are given to show the effectiveness of the proposed observer namely its exponential convergence and its insensitivity with respect to noise measurements

lyapunov functions for persistently excited cascaded time varying systems application to consensus we present some results on stability of linear time varying systems with particular structures such systems appear in diverse problems which include the analysis of adaptive systems persistently excited observers and consensus of systems interconnected through time varying links the originality of our statements rely in the fact that we provide smooth strict lyapunov functions hence our proofs are constructive and direct moreover we establish uniform global exponential stability with explicit stability and decay estimates for illustration we address a brief but representative case study of consensus of lagrangian systems interconnected through unreliable links

nonlinear inversion based output tracking an inversion procedure is introduced for nonlinear systems which constructs a bounded input trajectory in the preimage of a desired output trajectory in the case of minimum phase systems the trajectory produced agrees with that generated by hirschorn s inverse dynamic system however the preimage trajectory is noncausal rather than unstable in the nonminimum phase case in addition the analysis leads to a simple geometric connection between the unstable manifold of the system zero dynamics and noncausality in the nonminimum phase case with the addition of stabilizing feedback to the preimage trajectory asymptotically exact output tracking is achieved tracking is demonstrated with a numerical example and compared to the well known byrnes isidori regulator rather than solving a partial differential equation to construct a regulator the inverse is calculated using a picard like interaction when preactuation is not possible noncausal inverse trajectories can be truncated resulting in the tracking error transients found in other control schemes

generating series for interconnected analytic nonlinear systems given two analytic nonlinear input output systems represented as fliess operators four system interconnections are considered in a unified setting the parallel connection product connection cascade connection and feedback connection in each case the corresponding generating series is produced and conditions for the convergence of the corresponding fliess operator are given in the process an existing notion of a composition product for formal power series has its set of known properties significantly expanded in addition the notion of a feedback product for formal power series is shown to be well defined in a broad context and its basic properties are characterized

a faa di bruno hopf algebra for a group of fliess operators with applications to feedback a faa di bruno type hopf algebra is developed for a group of integral operators known as fliess operators where operator composition is the group product such operators are normally written in terms of generating series over a noncommutative alphabet using a general series expansion for the antipode an explicit formula for the generating series of the compositional inverse operator is derived the result is applied to analytic nonlinear feedback systems to produce an explicit formula for the feedback product that is the generating series for the fliess operator representation of the closed loop system written in terms of the generating series of the fliess operator component systems this formula is employed to provide a proof that local convergence is preserved under feedback

observer design for nonlinear triangular systems with unobservable linearisation the article deals with the observer design problem for a wide class of triangular time varying nonlinear systems with unobservable linearisation sufficient conditions are derived for the existence of a luenberger type observer when it is a priori known that the initial state of the system belongs to a given nonempty bounded subset of the state space for the general case the state estimation is exhibited by means of a switching sequence of time varying dynamics

a unified approach to generating series for mixed cascades of analytic nonlinear input output systems the primary goal is to describe in a unified fashion the generating series for the cascade connection of any two analytic nonlinear input output systems in particular it will be shown that a single general definition of a composition product can be formulated in terms of formal power series to describe any possible cascade connection of analytic integral operators fliess operators and analytic functions provided that the composite system is well defined and resides in one of these two classes in each case the radius of convergence of the interconnection is computed

on admissible pairs and equivalent feedback youla parameterization in iterative learning control this paper revisits a well known synthesis problem in iterative learning control where the objective is to optimize a performance criterion over a class of causal iterations the approach taken here adopts an infinite time setting and looks at limit behavior the first part of the paper considers iterations without current cycle feedback ccf term a notion of admissibility is introduced to distinguish between pairs of operators that define a robustly converging iteration and pairs that do not the set of admissible pairs is partitioned into disjoint equivalence classes different members of an equivalence class are shown to correspond to different realizations of a stabilizing feedback controller conversely every stabilizing controller is shown to allow for a non unique factorization in terms of admissible pairs class representatives are introduced to remove redundancy the smaller set of representative pairs is shown to have a trivial parameterization that coincides with the youla parameterization of all stabilizing controllers stable plant case the second part of the paper considers the general family of ccf iterations results derived in the non ccf case carry over with the exception that the set of equivalent controllers now forms but a subset of all stabilizing controllers necessary and sufficient conditions for full generalization are given

smooth neuroadaptive pi tracking control of nonlinear systems with unknown and nonsmooth actuation characteristics this paper considers the tracking control problem for a class of multi input multi output nonlinear systems subject to unknown actuation characteristics and external disturbances neuroadaptive proportional integral pi control with self tuning gains is proposed which is structurally simple and computationally inexpensive different from traditional pi control the proposed one is able to online adjust its pi gains using stability guaranteed analytic algorithms without involving manual tuning or trial and error process it is shown that the proposed neuroadaptive pi control is continuous and smooth everywhere and ensures the uniformly ultimately boundedness of all the signals of the closed loop system furthermore the crucial compact set precondition for a neural network nn to function properly is guaranteed with the barrier lyapunov function allowing the nn unit to play its learning approximating role during the entire system operation the salient feature also lies in its low complexity in computation and effectiveness in dealing with modeling uncertainties and nonlinearities both square and nonsquare nonlinear systems are addressed the benefits and the feasibility of the developed control are also confirmed by simulations

robust control for a nonlinear servomechanism problem this paper deals with the design of output feedback control to achieve asymptotic tracking and disturbance rejection for a class of nonlinear systems when the exogenous signals are generated by a known linear exosystem the system under consideration is single input single output input output linearizable minimum phase and modelled by an input output model of the form of an nth order differential equation we assume that at steady state the nonlinearities of the system can only introduce a finite number of harmonics of the original exosystem modes this assumption enables us to identify a linear servo compensator which is augmented with the original system moreover we augment a series of m integrators at the input side where m is the highest derivative of the input and then represent the augmented system by a state model the augmented system is stabilized via a separation approach in which a robust state feedback controller is designed first to ensure boundedness of all state variables and track

distributed moving horizon state estimation of two time scale nonlinear systems abstract in this paper we focus on distributed moving horizon estimation dmhe for a class of two time scale nonlinear systems described in the framework of singularly perturbed systems by taking advantage of the time scale separation property a two time scale system is first decomposed into a reduced order fast system and a reduced order slow system the slow system is further decomposed into several interconnected slow subsystems in the proposed distributed state estimation scheme a local estimator is designed for each slow subsystem and for the reduced order fast system the slow subsystem estimators communicate with each other to exchange information and they are only required to send information to the fast system one directionally the fast system estimator does not send out any information the local estimators are designed as observer enhanced moving horizon estimators sufficient conditions on the convergence of the estimation error of the dmhe are derived the application of the proposed dmhe to a chemical process example demonstrates its applicability and effectiveness

tracking and disturbance rejection of mimo nonlinear systems with pi controller we study tracking and disturbance rejection of a class of mimo nonlinear systems with linear proportional plus integral pi compensator roughly speaking we show that if the given nonlinear plant is exponentially stable and has a strictly increasing dc steady state i o map then a simple pi compensator can be used to yield a stable unity feedback closed loop system which asymptotically tracks reference inputs that tend to constant vectors and asymptotically rejects disturbances that tend to constant vectors

performance recovery of a class of uncertain non affine systems with unmodelled dynamics an indirect dynamic inversion method abstractthis paper presents an output feedback indirect dynamic inversion idi approach for a class of uncertain nonaffine systems with input unmodelled dynamics compared with previous approaches to achieve performance recovery the proposed method aims at dealing with a broader class of nonaffine in control systems with triangular structure an idi state feedback law is designed first in which less knowledge of the model plant is needed compared to earlier approximate dynamic inversion methods thus yielding more robust performance after that an extended high gain observer is designed to accomplish the task with output feedback finally we prove that the designed idi controller is equivalent to an adaptive proportional integral pi controller with respect to both time response equivalence and robustness equivalence the conclusion implies that for the studied strict feedback non affine systems with unmodelled dynamics there always exits a pi controller to stabilise the systems the effectiveness

discontinuous integral action for arbitrary relative degree in sliding mode control abstract for uncertain minimum phase systems with arbitrary and well defined relative degree we propose the implementation of a sliding mode control through a homogeneous discontinuous integral action the output sliding variable will track exactly and in finite time any sufficiently smooth reference while rejecting smooth perturbations with an absolutely continuous control signal this controller generalizes the well known super twisting algorithm to arbitrary order continuous and homogeneous integral controllers are also proposed approximating the behaviour of the discontinuous controller smooth lyapunov functions are derived to show the convergence and robustness properties of all controllers the performance is illustrated by means of experimental results on a magnetic suspension system

optimum weighted stack for multiple suppression in water deeper than about 300 m common midpoint stack is moderately effective at suppressing multiple reflections the stacking process acts as a low pass multiple filter rejecting to some extent frequencies greater than the reciprocal of the multiple s residual moveout on the farthest offset trace a weighted stack can often be even more effective at attenuating multiples if the weights are chosen such that the multiple filter response has low amplitudes at those frequencies where the multiple is strong a least squares technique is developed to determine optimum weights based on the multiple s frequency content the water depth the primary velocity and on a stabilization factor equivalent to white noise in deconvolution filter design to be truly optimum the weights must vary both spatially to account for water depth changes and temporally to account for sediment velocity changes and mute patterns but the filter responses are not very sensitive to the input parameters and need to be redesigned only infrequently the superiority of weighted stacks to uniform stacks is demonstrated by application to three deep water examples in all cases weighted stacks attenuate multiples more effectively than do conventional uniform stacks

convergence acceleration for observers by gain commutation increasing convergence rates of observers and differentiators for a class of nonli near systems in the output canonical form under presence of bounded matched disturbances lipschitz uncertainties and measurement noises is investigated a supervisory algorithm is designed that switches among different values of observer gains to accelerate the estimation in the noise free case the presented switched gain observer ensures global uniform time of convergence of the estimation error to the origin in the presence of noise the goals of overshoot reducing for the initial phase acceleration of convergence and improvement of asymptotic precision of estimation are achieved efficiency of the proposed switching gain observer is demonstrated by numerical comparison with a sliding mode and linear high gain observers

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

the state observer as a tool for the estimation of gene expression abstract in this paper a mathematical tool is presented to estimate unknown variables of transcription networks according to a set of measurements of the transcriptional activity of promoters the approach is based on the use of the mathematical model of the network under investigation and on the state reconstruction technique known as state observer borrowed from the control theory to this aim besides the general case the network motif of the multi output feed forward loop mo ffl will be investigated in details simulations show the effectiveness of the proposed approach in a wide range of possible critical frameworks such as only one target gene measurements non smooth input perturbations noisy measurements and model parameter uncertainties

lmi based integral fuzzy control of dc dc converters in this paper we propose a t s fuzzy controller which combines the merits of i the capability for dealing with nonlinear systems ii the powerful lmi approach to obtain control gains iii the high performance of integral controllers iv the workable rigorous proof for exponential convergence of error signals and v the flexibility on tuning decay rate the output regulation problems of a basic buck converter and a zero voltage transition zvt buck converter are used as application examples to illustrate the control performance of the proposed methodology first we consider a general nonlinear system which can represent the large signal models of the converters after introducing an added integral state of output regulation error and taking coordinate translation on an equilibrium point the resulting augmented system is represented into a takagi sugeno t s fuzzy model then the concept of parallel distributed compensation is applied to design the control law whereby the control gains are obtained by solving linear matrix inequalities lmis an interesting result is that the obtained control law is formed only by the linear state feedback signals weighted by grade functions in addition the robustness analysis is carried out when uncertainty and disturbance are taken into consideration the performance of numerical simulations and practical experiments results is satisfactory

hopf algebras renormalization and noncommutative geometry we explore the relation between the hopf algebra associated to the renormalization of qft and the hopf algebra associated to the ncg computations of tranverse index theory for foliations

continuously implemented sliding mode adaptive unknown input observers under noisy measurements we propose an estimator for nonlinear systems with unmatched unknown inputs and under measurement noise the estimator design is based on the combination of observer design for descriptor systems sliding modes theory and adaptive control the estimation of the measurement noise is achieved thanks to the transformation of the original system into a singular form where the measurement noise makes part of the augmented state two adaptive parameters are updated online one to compensate for the unknown bounds on the states the unknown inputs and the measurement noise and a second one to compensate for the effect of the nonlinearities to join robust state estimation and unknown inputs reconstruction our approach borrows inspiration from sliding mode theory however all signals are continuously implemented we demonstrate that both state and unknown inputs estimation are achieved up to arbitrarily small tolerance the utility of our theoretical results is illustrated through simulation case studies

robust disturbance attenuation of nonlinear systems using output feedback and state dependent scaling this paper presents an approach to output feedback stabilization with l 2 disturbance attenuation for nonlinear systems in the presence of dynamic uncertainties a new formulation of state dependent scaling is introduced into the output feedback design which unifies treatment of nonlinear and linear gains the effect of disturbance on the controlled output which is allowed to be any function of output measurements can be always attenuated to an arbitrarily small level with global asymptotic stability if the plant belongs to a wide class of triangular systems whose uncertainties do not necessarily have finite linear gains the uncertain dynamics is not limited to input to state stable systems either the approach is not only a natural extension of popular approaches in robust linear control but also advantageous to numerical computation which is applicable to non triangular systems as well as triangular systems

robust nonlinear integral control it is well known from linear systems theory that an integral control law is needed for asymptotic set point regulation under parameter perturbations the note presents a similar result fur a class of nonlinear systems in the presence of an unknown equilibrium due to uncertain nonlinearities and dynamic uncertainties both partial state and output feedback cases are considered sufficient small gain type conditions are identified for existence of linear and nonlinear control laws a procedure for robust nonlinear integral controller design is presented and illustrated via a practical example of fan speed control

analysis and synthesis of low gain integral controllers for nonlinear systems relaxed conditions are given for stability of a feedback system consisting of an exponentially stable multi input multi output nonlinear plant and an integral controller roughly speaking it is shown that if the composition of the plant equilibrium input output map and the integral feedback gain is infinitesimally contracting then the closed loop system is exponentially stable if the integral gain is sufficiently low the main result is illustrated with an application arising in frequency control of ac power systems we demonstrate how the contraction condition can be checked computationally via semidefinite programming and how integral gain matrices can be synthesized via convex optimization to achieve robust performance in the presence of nonlinearity and uncertainty

robust moving horizon estimation based output feedback economic model predictive control abstract in this work we develop an economic model predictive control scheme for a class of nonlinear systems with bounded process and measurement noise in order to achieve fast convergence of the state estimates to the actual system state as well as the robustness of the observer to measurement and process noise a deterministic high gain observer is first applied for a small time period with continuous output measurements to drive the estimation error to a small value after this initial small time period a robust moving horizon estimation scheme is used on line to provide more accurate and smoother state estimates in the design of the robust moving horizon estimation scheme the deterministic observer is used to calculate reference estimates and confidence regions that contain the actual system state within the confidence regions the moving horizon estimation scheme is allowed to optimize its estimates the output feedback economic model predictive controller is designed via lyapunov techniques based on state estimates provided by the deterministic observer and the moving horizon estimation scheme the stability of the closed loop system is analyzed rigorously and conditions that ensure the closed loop stability are derived extensive simulations based on a chemical process example illustrate the effectiveness of the proposed approach

multiple suppression using a local coherence filter generally when velocity filters are applied to prestack seismic data they can suppress long period multiples but they can also deteriorate the primary amplitudes since the apparent velocity differences between primaries and multiples can be negligible within the near offset regions of data gathers a velocity filter will be ineffective in these regions tending to remove or distort primary signal the normal solution to this problem is to mute or remove near offset data but this approach is detrimental to low fold data in this paper we derive a filter that can be used to address the problem by responding to average apparent velocity differences rather than to instantaneous apparent velocity differences between primaries and multiples the filter called a local coherence filter is essentially a finite difference operator whose step size is equivalent to a spatial prediction distance within the local coherence filter s small application window an nmo corrected multiple is predictable while an overcorrected primary is not predictable the step size of its difference operator gives the filter the ability to discriminate between primaries and long period multiples in regions of a data gather where velocity filters fail this paper derives the local coherence filter and compares it to the f k filter in both model and real data applications results demonstrate that the local coherence filter is more effective in suppressing long period multiples without distorting the primary reflections

ray tracing based prediction and subtraction of water layer multiples many methods of multiple suppression break down when the structure that produces the reverberation possesses significant lateral variation a common example of this situation occurs in marine data with the multiple reflections that are generated by seafloor topography such multiples may be suppressed by techniques based upon wave equation extrapolation the recorded seismic data are mathematically propagated through a simulated water layer to generate a set of multiple arrivals which may after data matching be subtracted however the computational effort required to propagate prestack data to a laterally varying datum is very large in this paper a method of suppressing selected multiples with arbitrary moveout is presented in order to reduce the computational cost prediction of the multiple arrival times is performed by ray tracing through a model of the laterally varying water layer and possibly the subsurface an estimate of the multiple waveform on each trace is obtained by stacking a window of data about the calculated arrival times the multiple arrival can then be attenuated by subtracting this wavelet from each trace in the prestack gather from which the estimate is derived in practice calculations of the variation in multiple amplitude and of any errors in the moveout correction require the multiple reflections to be of comparable or higher amplitude than contemporary primary events a situation that is often the case where multiple contamination is a problem

bounded integral control of input to state practically stable nonlinear systems to guarantee closed loop stability a fundamental problem in control systems theory is that stability is not always guaranteed for a closed loop system even if the plant is open loop stable with the only knowledge of the input to state practical stability isps of the plant in this note a bounded integral controller bic is proposed which generates a bounded control output independently from the plant parameters and states and guarantees closed loop system stability in the sense of boundedness when a given bound is required for the control output an analytic selection of the bic parameters is proposed and its performance is investigated using lyapunov methods extending the result for locally isps plant systems additionally it is shown that the bic can replace the traditional integral controller ic and guarantee asymptotic stability of the desired equilibrium point under certain conditions with a guaranteed bound for the solution of the closed loop system simulation results of a dc dc buck boost power converter system are provided to compare the bic with the ic operation

a finite time convergent observer with robustness to piecewise constant measurement noise motivated by the design of observers with good performance and robustness to measurement noise the problem of estimating the state of a linear time invariant system in finite time and robustly with respect to measurement noise is considered using a hybrid systems framework a hybrid observer producing an estimate that converges to the plant state in finite time even under unknown piecewise constant noise is presented the stability and robustness properties of the observer are shown analytically and validated numerically

fliess operators on lp spaces convergence and continuity fliess operators as input output mappings are particularly useful in a number of fundamental problems concerning nonlinear realization theory in the classical analysis of these operators certain growth conditions on the coe3cients in their series representations insure uniform and absolute convergence provided every input is uniformly bounded by some 4xed upperbound in some emerging applications however it is more natural to consider other classes of inputs in this paper lp function spaces are considered in particular it is shown that the classic growth conditions also provide su3cient conditions for convergence and continuity when the admissible inputs are from a ball in lp t0 t 0 t where t is bounded and p 1 in addition stronger global growth conditions are given that apply even for the case where t is unbounded when the coe3cients of a fliess operator have a state space representation it is shown that the state space model will always locally realize the correspondinginput output map on lp t0 t 0 t for su3ciently small t 0 if certain well posedness conditions are satis4ed then the state space model will globally realized the input output mapping for unbounded t when the coe3cients satisfy the global growth condition c 2002 elsevier science b v all rights reserved

robust event triggered state estimation a risk sensitive approach in this work we investigate a robust event triggered remote state estimation problem for linear gaussian systems with a stochastic event triggering condition the reference measure approach is used to obtain a robust event triggered estimate that minimizes the so called risk sensitive criterion which refers to the expectation of the exponential of the sum of the squared estimation error we introduce the reference measure under which the measurements are identically independently distributed i i d and independent of the states and propose a map to link the real world measure to the reference measure so that the recursions of the information states under the reference measure can be obtained based on these results the risk sensitive criteria are reformulated under the reference measure and closed form expressions of the risk sensitive event triggered posterior and prior estimates are presented which are shown to evolve in simple recursive kalman like structures moreover two sufficient stability conditions for the proposed estimators are given where the first requires the solution of a time varying riccati equation to be positive definite and satisfy a specific inequality which can be further extended to the scenario when the weighting matrix in the risk sensitive criterion is time variant the second gives the range of values of the risk sensitive parameter and covariance of the initial state for which the proposed estimators are stable comparative simulation results demonstrate that the proposed risk sensitive event triggered estimator is more robust to model uncertainties compared with a typical minimum mean squared error mmse estimator with stochastic event triggered sensor scheduling

proportional integral controllers for minimum phase nonaffine in control systems we show that stabilizing tracking proportional integral pi controllers can be constructed for minimum phase nonaffine in control systems the constructed pi controller is an equivalent realization of an approximate dynamic inversion controller this equivalence holds only for the time response when applied to the unperturbed system even when restricted to unperturbed minimum phase linear time invariant systems their closed loop robustness properties differ this shows that in general properties that do not define the equivalence relation for systems controllers are not preserved under such equivalence transformations

left inversion of analytic nonlinear siso systems via formal power series methods given a single input single output siso system f and a function y in the range of f the left inversion problem is to determine an input u such that y f u the goal of this paper is to provide an exact and explicit analytical solution to this problem in the case where f is an analytic mapping in the sense that it has a convergent chen fliess functional expansion and y is a real analytic function in particular it will be shown that given a certain condition on the generating series c of f a corresponding unique analytic u can always be determined via operations on formal power series the condition on c turns out to be equivalent to having a well defined relative degree when f has an input affine analytic state space realization with finite dimension but the method is applicable even when f does not have such a realization the technique is demonstrated on four examples including a continuous stirred chemical reactor

universal integral controllers with non linear integral gains we consider a single input single output minimum phase non linear system which has a normal form in previous work integral control and high gain observers were used to achieve robust regulation under output feedback to improve the transient performance we propose the use of integrators with non linear gains we prove that the controller achieves regional and semiglobal regulation simulation results are presented showing the improved overshoot and settling time

high gain observers with limited gain power for systems with observability canonical form we consider the problem of state observation for systems having a well defined observability canonical form gauthier and kupka 2004 by means of high gain observers the main goal is to show that for this class of systems observers can be designed with the high gain parameter powered just up to the order 2 regardless the dimension of the state system in this way we substantially overtake the main limitations of standard design procedures in which the high gain parameter is powered up to the order of the system the observer structure which generalizes the ideas presented in astolfi and marconi 2015 can be used in all those contexts where fast state observation is required such as in the design of output feedback stabilizers by means of the nonlinear separation principle that is also specifically addressed in the paper