unknown time varying input delay compensation for uncertain nonlinear systems abstract a tracking controller is developed for a class of uncertain nonlinear systems subject to unknown time varying input delay and additive disturbances a novel filtered error signal is designed using the past states in a finite integral over a constant estimated delay interval the maximum tolerable error between unknown time varying delay and a constant estimate of the delay is determined to establish uniformly ultimately bounded convergence of the tracking error to the origin the controller development is based on an approach which uses lyapunov krasovskii functionals to analyze the effects of unknown sufficiently slowly time varying input delays a stability analysis is provided to prove ultimate boundedness of the tracking error signals numerical simulation results illustrate the performance of the developed robust controller

adaptive planar curve tracking control and robustness analysis under state constraints and unknown curvature we provide adaptive controllers for curve tracking in the plane under unknown curvatures and control uncertainty which is a central problem in robotics the system dynamics include a nonlinear dependence on the curvature and are coupled with an estimator for the unknown curvature to form the augmented error dynamics we prove input to state stability of the augmented error dynamics with respect to an input that is represented by additive uncertainty on the control under polygonal state constraints and under suitable known bounds on the curvature and on the control uncertainty when the uncertainty is zero this gives tracking of the curve and convergence of the curvature estimate to the unknown curvature our curvature identification result is a significant improvement over earlier results which do not ensure parameter identification or which identify the control gain but not the curvature

generating positive and stable solutions through delayed state feedback for time varying forward complete nonlinear systems with delay in the input a new reduction model approach is proposed it presents three advantages first the corresponding control laws do not include distributed terms second it yields closed loop systems with positive solutions that can be easily derived finally the stabilized systems possess some robustness properties that can be estimated

global adaptive controller for linear systems with unknown input delay in this note a switching type delay adaptive predictor feedback controller is proposed to globally stabilize linear systems with unknown input delay the idea of our method is to take advantage of the robustness of feedback laws to delay estimate error that is sufficiently small we first prove that when the delay estimate is sufficiently close to the true delay there is a lyapunov krasovskii functional that is strictly decreasing and asymptotic regulation is achievable then with the help of the lyapunov krasovskii functional as a supervisor the switching logic plays the role of adjusting the estimated delay online to make it sufficiently close to the true delay the result of this note shows that global adaptive stabilization of linear systems with unknown input delay is achievable with a logic based switching control law

the effect of noise on β cell burst period bursting electrical behavior is commonly observed in a variety of nerve and endocrine cells including that in electrically coupled cells located in intact pancreatic islets however individual cells usually display either spiking or very fast bursting behavior and the difference between isolated and coupled cells has been suggested to be due to stochastic fluctuations of the plasma membrane ion channels which are supposed to have a stronger effect on single cells than on cells situated in clusters the channel sharing hypothesis this effect of noise has previously been studied using numerical simulations we show here how the application of two recent methods allows an analytic treatment of the stochastic effects on the location of the saddle node and homoclinic bifurcations which determine the burst period thus the stochastic system can be analyzed similarly to the deterministic system but with a quantitative description of the effect of noise this approach supports previous investigations

non coercive lyapunov functions for infinite dimensional systems abstract we show that the existence of a non coercive lyapunov function is sufficient for uniform global asymptotic stability ugas of infinite dimensional systems with external disturbances provided the speed of decay is measured in terms of the norm of the state and an additional mild assumption is satisfied for evolution equations in banach spaces with lipschitz continuous nonlinearities these additional assumptions become especially simple the results encompass some recent results on linear switched systems on banach spaces finally we derive new non coercive converse lyapunov theorems and give some examples showing the necessity of our assumptions

on the existence of a kazantzis kravaris luenberger observer we state sufficient conditions for the existence on a given open set of the extension to nonlinear systems of the luenberger observer as it has been proposed by kazantzis and kravaris we prove it is sufficient to choose the dimension of the system giving the observer less than or equal to 2 twice the dimension of the state to be observed we show that it is sufficient to know only an approximation of the solution of a pde needed for the implementation we establish a link with high gain observers finally we extend our results to systems satisfying an unboundedness observability property

backstepping controller synthesis and characterizations of incremental stability incremental stability is a property of dynamical and control systems requiring the uniform asymptotic stability of every trajectory rather than that of an equilibrium point or a particular time varying trajectory similarly to stability lyapunov functions and contraction metrics play important roles in the study of incremental stability in this paper we provide characterizations and descriptions of incremental stability in terms of existence of coordinate invariant notions of incremental lyapunov functions and contraction metrics respectively most design techniques providing controllers rendering control systems incrementally stable have two main drawbacks they can only be applied to control systems in either parametric strict feedback or strict feedback form and they require these control systems to be smooth in this paper we propose a design technique that is applicable to larger classes of control systems including a class of non smooth control systems moreover we propose a recursive way of constructing contraction metrics for smooth control systems and incremental lyapunov functions which have been identified as a key tool enabling the construction of finite abstractions of nonlinear control systems the approximation of stochastic hybrid systems source code model checking for nonlinear dynamical systems and so on the effectiveness of the proposed results in this paper is illustrated by synthesizing controllers rendering two non smooth control systems incrementally stable the first example aims to show how to recursively construct the incremental lyapunov functions the second example aims to show the key role of the computed incremental lyapunov function in constructing a finite abstraction that is equivalent to the system under study

new formulation of predictors for finite dimensional linear control systems with input delay we consider a one dimensional controlled reaction diffusion equation where the control acts on the boundary and is subject to a constant delay such a model is a paradigm for more general parabolic systems coupled with a transport equation we prove that this is possible to stabilize in h 1 norm this process by means of an explicit predictor based feedback control that is designed from a finite dimensional subsystem the implementation is very simple and efficient and is based on standard tools of pole shifting our feedback acts on the system as a finite dimensional predictor we compare our approach with the backstepping method

approximately bisimilar symbolic models for nonlinear control systems control systems are usually modeled by differential equations describing how physical phenomena can be influenced by certain control parameters or inputs although these models are very powerful when dealing with physical phenomena they are less suited to describe software and hardware interfacing with the physical world for this reason there is a growing interest in describing control systems through symbolic models that are abstract descriptions of the continuous dynamics where each symbol corresponds to an aggregate of states in the continuous model since these symbolic models are of the same nature of the models used in computer science to describe software and hardware they provide a unified language to study problems of control in which software and hardware interact with the physical world furthermore the use of symbolic models enables one to leverage techniques from supervisory control and algorithms from game theory for controller synthesis purposes in this paper we show that every incrementally globally asymptotically stable nonlinear control system is approximately equivalent bisimilar to a symbolic model the approximation error is a design parameter in the construction of the symbolic model and can be rendered as small as desired furthermore if the state space of the control system is bounded the obtained symbolic model is finite for digital control systems and under the stronger assumption of incremental input to state stability symbolic models can be constructed through a suitable quantization of the inputs

power characterizations of input to state stability and integral input to state stability new notions of external stability for nonlinear systems are introduced making use of average powers as signal norms and comparison functions as in the input to state stability iss framework several new characterizations of iss and integral iss are presented in terms of the new notions an example is discussed to illustrate differences and similarities of the newly introduced properties

global exponential observers for two classes of nonlinear systems abstract this paper develops sufficient conditions for the existence of global exponential observers for two classes of nonlinear systems i the class of systems with a globally asymptotically stable compact set and ii the class of systems that evolve on an open set in the first class the derived continuous time observer also leads to the construction of a robust global sampled data exponential observer under additional conditions two illustrative examples of applications of the general results are presented one is a system with monotone nonlinearities and the other is a chemostat system

robust exponential input to state stability of impulsive systems with an application in micro grids abstract this paper studies the robust exponential input to state stability robust e iss for impulsive systems new notions of input to state exponent is e and e property are proposed based on the established relation between is e and e property and the method of variation of constants formula the equivalent conditions for robust e iss have been derived then the notion of robust event e iss is defined the sufficient conditions and the robust regions for robust e iss and robust event e iss are also derived by using the is e of every subsystem it shows the whole system may have robust event e iss while every subsystem may have no iss it also shows the external disturbances may lead to relatively small robust regions the results are then specialized to derive the equivalent conditions of interval e iss for interval impulsive systems as an application the result is used to test the iss for a controlled micro grid

a relaxed condition for stability of nonlinear observer based controllers we study certainty equivalence design of observer based controllers and present a new stability condition that exploits state dependent convergence properties of observers this result eliminates the conservatism of treating the observer error as an exogeneous disturbance as an application we show that the reduced order variant of the class of observers in automatica 37 2001 9231 preserves global asymptotic stability in a certainty equivalence implementation in another application we study a nonminimum phase system which cannot be stabilized with the existing output feedback designs

global existence of solutions of differential inclusions abstract in this paper we consider sufficient conditions for global existence of solutions to a differential inclusion dx dt f t x assuming existence of local solutions to it by means of lyapunov s second method our theorem includes as special cases s w seah s theorems 1982 j math anal appl 89 648 663

on uniform boundedness of parameterized discrete time systems with decaying inputs applications to cascades a framework for controller design of sampled data nonlinear systems via their approximate discrete time models has been established recently within this framework naturally arises the need to investigate stability properties of parameterized discrete time systems further results that guarantee appropriate stability of the parameterized family of discrete time systems that is used within this framework have been also established for systems with cascaded structure a fundamental condition that is required in this framework is uniform boundedness of solutions of the cascade however this is difficult to check in general in this paper we provide a range of sufficient conditions for uniform boundedness that are easier to check these results further contribute to the toolbox for controller design of sampled data nonlinear systems via their approximate discrete time models

norm controllability of nonlinear systems in this paper we introduce and study the notion of norm controllability for nonlinear systems this property captures the responsiveness of a system with respect to applied inputs which is quantified via the norm of an output as a main contribution we obtain several lyapunov like sufficient conditions for norm controllability some of which are based on higher order derivatives of a lyapunov like function various aspects of the proposed concept and the sufficient conditions are illustrated by several examples including a chemical reactor application furthermore for the special case of linear systems we establish connections between norm controllability and standard controllability

strong iiss for a class of systems under saturated feedback this paper proposes sufficient conditions under which nonlinear input affine systems can be made strongly iiss in the presence of actuator saturation strong iiss was recently proposed as a compromise between the strength of input to state stability iss and the generality of integral input to state stability iiss it ensures in particular that solutions are bounded provided that the disturbance magnitude is below a certain threshold and that they tend to the origin in response to any vanishing disturbance we propose a growth rate condition under which the bounded feedback law proposed by lin and sontag for disturbance free nonlinear systems ensures strong iiss in the presence of perturbations we illustrate our findings on the angular velocity control of a spacecraft with limited power thrusters in the specific case of linear time invariant systems with neutrally stable internal dynamics we provide a simple static state feedback that ensures strong iiss in presence of actuator saturations this second result is illustrated by the robust stabilization of the harmonic oscillator in both cases we provide an estimate of the maximum disturbance amplitude that can be tolerated without compromising solutions boundedness

input output to state stability this work explores lyapunov characterizations of the input output to state stability ioss property for nonlinear systems the notion of ioss is a natural generalization of the standard zero detectability property used in the linear case the main contribution of this work is to establish a complete equivalence between the ioss property and the existence of a certain type of smooth lyapunov function as corollaries one shows the existence of norm estimators and obtains characterizations of nonlinear detectability in terms of relative stability and of finite energy estimates

adaptive control scheme for uncertain time delay systems the paper exposes some of the potential of a recently introduced backstepping transformation for linear uncertain time delay systems to address the classic problems of equilibrium regulation under partial measurements disturbance rejection parameter or delay adaptation for each of these problems an implementable control strategy is proposed it is analyzed through a convergence analysis of infinite dimensional dynamics based on a transport partial differential equation representation of the estimated input delay and the mentioned backstepping transformation the considered controllers contain this representation of the system under the form of a distributed parameter system and use it to determine relevant adaptation strategies an illustration example is proposed

input to state stability and inverse optimality of predictor feedback for multi input linear systems for the exact predictor feedback control design recently introduced by tsubakino krstic and oliveira for multi input linear systems with distinct input delays we establish input to state stability with respect to additive plant disturbances as well as robustness to constant multiplicative uncertainties affecting the inputs we also show that the exact predictor feedback controller is inverse optimal with respect to a meaningful differential game problem our proofs capitalize on the availability of a backstepping transformation which is formulated appropriately in a recursive manner an example computed numerically is provided to illustrate the validity of the developed results

input output to state stability and state norm estimators for switched nonlinear systems in this paper the concepts of input output to state stability ioss and state norm estimators are considered for switched nonlinear systems under average dwell time switching signals we show that when the average dwell time is large enough a switched system is ioss if all of its constituent subsystems are ioss moreover under the same conditions a non switched state norm estimator exists for the switched system furthermore if some of the constituent subsystems are not ioss we show that still ioss can be established for the switched system if the activation time of the non ioss subsystems is not too big again under the same conditions a state norm estimator exists for the switched system however in this case the state norm estimator is a switched system itself consisting of two subsystems we show that this state norm estimator can be constructed such that its switching times are independent of the switching times of the switched system it is designed for

feedback stabilization of a 1 d linear reaction diffusion equation with delay boundary control the goal of this paper is to design a stabilizing feedback boundary control for a reaction diffusion partial differential equation pde where the boundary control is subject to a constant delay while the equation may be unstable without any control for this system which is equivalent to a parabolic equation coupled with a transport equation a prediction based control is explicitly computed by splitting the infinite dimensional system into two parts a finite dimensional unstable part and a stable infinite dimensional part a finite dimensional delayed controller is computed for the unstable part and it is shown that this controller stabilizes the whole pde the proof is based on an explicit expression of the classical artstein transformation combined with an adequately designed lyapunov function a numerical simulation illustrates the constructive feedback design method

nonlinear predictor feedback for input affine systems with distributed input delays prediction based transformation is applied to control affine systems with distributed input delays transformed system state is calculated as a prediction of the system s future response to the past input with future input set to zero stabilization of the new system leads to lyapunov krasovskii proven stabilization of the original one conditions on the original system are smooth linearly bounded open loop vector field and smooth uniformly bounded input vectors about the transformed system which turns out to be affine in the undelayed input but with input vectors dependent on the input history and system state we assume existence of a linearly bounded stabilizing feedback and quadratically bounded control lyapunov function if all assumptions hold globally then achieved exponential stability is global otherwise local analytical and numerical control design examples are provided

fast subsystem bifurcations in a slowly varying lie nard system exhibiting bursting a perturbed lienard differential system is examined using local stability and hopf bifurcation analyses asymptotic techniques and melnikov s method the results of these analyses are applied to a simple cubic model that exhibits a variety of different oscillatory behaviors for different parameter values for a bounded region in fast parameter space the model exhibits square wave bursting patterns analogous to the bursting electrical activity observed in pancreatic beta cells under certain hypotheses solutions of the cubic model are known to have square wave patterns by using the theory developed for the more general lienard system each hypothesis is shown to correspond to a curve in parameter space together the curves bound a region in which the model exhibits square wave bursting patterns since the model is simple the curves that bound this region can all be determined analytically

nonsmooth feedback control of time delay nonlinear systems a dynamic gain based approach this technical note addresses the problem of global control for a class of time delay nonlinear systems under a smoothness condition on the system nonlinearities a delay independent non smooth dynamic state compensator is constructed by developing a dynamic gain based design method with the help of appropriate lyapunov krasovskii functionals it is shown that all the states of the time delay nonlinear system can be regulated to the origin while maintaining boundedness of the closed loop system a benchmark example is given to illustrate the effectiveness of the proposed non smooth feedback controller

compensation of wave actuator dynamics for nonlinear systems the problem of stabilization of pde ode cascades has been solved in the linear case for several pde classes whereas in the nonlinear case the problem has been solved only for the transport delay pde namely for compensation of an arbitrary delay at the input of a nonlinear plant motivated by a specific engineering application in off shore drilling we solve the problem of stabilization of the cascade of a wave pde with a general nonlinear ode due to the presence of nonlinearities of arbitrary growth and the time reversibility of the wave pde and due to the possibility of using arguments based on lyapunov functionals or explicit solutions several stability analysis approaches are possible we present stability results in the h 2 times h 1 and c 1 times c 0 norms for general nonlinear odes as well as in the h 1 times l 2 norm for linear odes we specialize our general design for wave pde ode cascades to the case of a wave pde whose uncontrolled end does not drive an ode but is instead governed by a nonlinear robin boundary condition a nonlinear spring as in the friction law in drilling this is the first global stabilization result for wave equations that incorporate non collocated destabilizing nonlinearities of superlinear growth we present two numerical examples one with a nonlinear ode and one with a nonlinear spring at the uncontrolled boundary of the wave pde

symbolic models for nonlinear control systems without stability assumptions finite state models of control systems were proposed by several researchers as a convenient mechanism to synthesize controllers enforcing complex specifications most techniques for the construction of such symbolic models have two main drawbacks either they can only be applied to restrictive classes of systems or they require the exact computation of reachable sets in this paper we propose a new abstraction technique that is applicable to any nonlinear sampled data control system as long as we are only interested in its behavior in a compact set moreover the exact computation of reachable sets is not required the effectiveness of the proposed results is illustrated by synthesizing a controller to steer a vehicle

delay adaptive control for nonlinear systems we present a systematic delay adaptive prediction based control design for nonlinear systems with unknown long actuator delay our approach is based on the representation of the constant actuator delay as a transport partial differential equation pde in which the convective speed is inversely proportional to the unknown delay we study two different frameworks assuming first that the actuator state is measured and relaxing afterward for the full state feedback case we prove global asymptotic convergence of the proposed adaptive controller while in the second case replacing the actuator state by its adaptive estimate we prove local regulation the relevance of the obtained results are illustrated by simulations of a biological activator repressor system

interval observer of minimal error dynamics abstract this paper proposes a simple interval observer which can generate tighter interval estimates of variables in transient states than the standard interval observer the simple nonlinear dynamics shrinks the estimated intervals to true state variables at the maximum velocity in the absence of disturbances in the presence of bounded disturbances ultimate bounds of the interval estimates are given under the standard assumption for interval observer design

stability of stochastic functional differential systems using degenerate lyapunov functionals and applications motivated by the seminal work of dupire 2009 on functional ito formulas this work investigates asymptotic properties of systems represented by stochastic functional differential equations sfdes stability of general delay dependent sfdes is investigated using degenerate lyapunov functionals which are only positive semi definite rather than positive definite as used in the classical work this paper first establishes boundedness and regularity of sfdes by using degenerate lyapunov functionals then moment and almost sure exponential stabilities are obtained based on degenerate lyapunov functionals and the semi martingale convergence theorem as an application of the stability criteria consentability of stochastic multi agent systems with nonlinear dynamics is studied

robust and adaptive observer based partial stabilization for a class of nonlinear systems the problem of adaptive stabilization with respect to a set for a class of nonlinear systems in the presence of external disturbances is considered a novel adaptive observer based solution for the case of noisy measurements is proposed the efficiency of proposed solution is demonstrated via example of swinging a pendulum with unknown parameters

generating and generalizing models of visual objects abstract we report on initial experiments with an implemented learning system whose inputs are images of two dimensional shapes the system first builds semantic network descriptions of shapes based on brady s smoothed local symmetry representation it learns shape models from them using a substantially modified version of winston s analogy program a generalization of gray coding enables the representation to be extended and also allows a single operation called ablation to achieve the effects of many standard induction heuristics the program can learn disjunctions and can learn concepts using only positive examples we discuss learnability and the pervasive importance of representational hierarchies

global exponential sampled data observers for nonlinear systems with delayed measurements abstract this paper presents new results concerning the observer design for certain classes of nonlinear systems with both sampled and delayed measurements by using a small gain approach we provide sufficient conditions which involve both the delay and the sampling period ensuring exponential convergence of the observer system error the proposed observer is robust with respect to measurement errors and perturbations of the sampling schedule moreover new results on the robust global exponential state predictor design problem are provided for wide classes of nonlinear systems

symbolic models for nonlinear control systems affected by disturbances in the last few years there has been a growing interest in the use of symbolic models for the formal verification and control design of purely continuous or hybrid systems symbolic models are abstract descriptions of continuous systems where one symbol corresponds to an aggregate of continuous states in this article we face the problem of deriving symbolic models for nonlinear control systems affected by disturbances the main contribution of this article is in proposing symbolic models that can be effectively constructed and that approximate nonlinear control systems affected by disturbances in the sense of alternating approximate bisimulation

constructing arrangements of lines and hyperplanes with applications a finite set of lines partitions the euclidean plane into a cell complex similarly a finite set of d 1 dimensional hyperplanes partitions d dimensional euclidean space an algorithm is presented that constructs a representation for the cell complex defined by n hyperplanes in optimal o n d time in d dimensions it relies on a combinatorial result that is of interest in its own right the algorithm is shown to lead to new methods for computing lambda matrices constructing all higher order voronoi diagrams halfspatial range estimation degeneracy testing and finding minimum measure simplices in all five applications the new algorithms are asymptotically faster than previous results and in several cases are the only known methods that generalize to arbitrary dimensions the algorithm also implies an upper bound of 2 cn d c a positive constant for the number of combinatorially distinct arrangements of n hyperplanes in e d

robustness of nonlinear predictor feedback laws to time and state dependent delay perturbations much recent progress has been achieved for stabilization of linear and nonlinear systems with input delays that are long and dependent on either time or the plant state provided the dependence is known in this paper we consider the delay variations as unknown and study robustness of nominal constant delay predictor feedbacks under delay variations that depend on time and the state we show that when the delay perturbation and its rate have sufficiently small magnitude the local asymptotic stability of the closed loop system under the nominal predictor based design is preserved for the special case of linear systems and under only time varying delay perturbations we prove robustness of global exponential stability of the predictor feedback when the delay perturbation and its rate are small in any one of four different metrics we present two examples one that is concerned with the control of a dc motor through a network and one of a teleoperation like system

stabilization of discrete time linear systems with an unknown time varying delay by switched low gain feedback in this note we investigate the stabilization of discrete time linear systems with an unknown time varying delay existing literature on the stabilization of time delay systems require some knowledge such as an upper bound of the delay in this paper by proposing a switched low gain feedback control law we are able to achieve asymptotic stabilization of the system without any knowledge of the delay in addition the proposed switched low gain feedback law also significantly improves the closed loop system performance in terms of overshoot and convergence speed in comparison with the traditional fixed gain design simulation study illustrates the effectiveness of our theoretical results

a note on the stability of single frequency laser diode models a formal proof of the stability of a widely applicable form of the laser diode rate equations is presented the conditions under which this proof holds provide guidance to designers and modellers of laser diodes in the identification of ranges of parameter values that preserve stability the proof requires that there is some non zero threshold for gain in order to guarantee stability laser models incorporating purcell enhancement factors are found to be stable for all physically allowed values of the factor

compensation of transport actuator dynamics with input dependent moving controlled boundary we introduce and solve the stabilization problem of a transport partial differential equation pde nonlinear ordinary differential equation ode cascade in which the pde state evolves on a domain whose length depends on the boundary values of the pde state itself in particular we develop a predictor feedback control design which compensates such transport pde dynamics we prove local asymptotic stability of the closed loop system in the c 1 norm of the pde state employing a lyapunov like argument and introducing a backstepping transformation we also highlight the relation of the pde ode cascade to a nonlinear system with input delay that depends on past input values and present the predictor feedback control design for this representation as well

nonuniform in time input to state stability and the small gain theorem for time varying control systems various equivalent characterizations of the nonuniform in time input to state stability iss property are established these characterizations enable us to derive sufficient conditions for nonuniform in time iss concerning composite time varying systems our main result generalizes the well known small gain theorem due to jiang teel praly for autonomous systems under the presence of uniform in time iss

on the representation of switched systems with inputs by perturbed control systems this paper provides representations of switched systems described by controlled differential inclusions in terms of perturbed control systems the control systems have dynamics given by differential equations and their inputs consist of the original controls together with disturbances that evolve in compact sets their sets of maximal trajectories contain as a dense subset the set of maximal trajectories of the original system several applications to control theory dealing with properties of stability with respect to inputs and of detectability are derived as a consequence of the representation theorem 2004 elsevier ltd all rights reserved

robust synchronization for multistable systems in this note we study a robust synchronization problem for multistable systems evolving on manifolds within an input to state stability iss framework based on a recent generalization of the classical iss theory to multistable systems a robust synchronization protocol is designed with respect to a compact invariant set of the unperturbed system the invariant set is assumed to admit a decomposition without cycles that is with neither homoclinic nor heteroclinic orbits numerical simulation examples illustrate our theoretical results

a converse lyapunov theorem for nonuniform in time global asymptotic stability and its application to feedback stabilization lyapunov like characterizations for the concepts of nonuniform in time robust global asymptotic stability and input to state stability for time varying systems are established the main result of our work enables us to derive 1 necessary and sufficient conditions for feedback stabilization for affine in the control systems and 2 sufficient conditions for the propagation of the input to state stability property through integrators

observation and stabilization of ltv systems with time varying measurement delay abstract this work deals with observer based output feedback stabilization of linear time varying ltv systems with time varying measurement delay the delay is modeled by a first order hyperbolic partial differential equation pde whose boundary condition evolves according to an ordinary differential equation ode namely the plant the overall system is thus represented by an ode pde cascade which is also the structure of the proposed observer the exponential stability of the estimation error is established for arbitrarily large time varying delays an observer based controller is also introduced and the closed loop stability is proved the separation principle holds and the design of both the observer and controller gains can be done as if there was no delay some simulations illustrate the feasibility of this approach

adaptive sinusoidal disturbance cancellation for unknown lti systems despite input delay solutions exist for the problems of canceling sinusoidal disturbances and compensating input delays in this paper two problems are considered simultaneously and an adaptive controller is designed to cancel unknown sinusoidal disturbances forcing an unknown linear time invariant system in controllable canonical form despite input delay the design is based on three steps 1 parametrization of the sinusoidal disturbance as the output of a known feedback system with an unknown output vector that depends on unknown disturbance parameters 2 representation of the delay as a transport pde 3 design of the adaptive controller by using the backstepping boundary control technique for pdes it is proven that the equilibrium of the closed loop system is stable and the state of the considered system converges to zero as t with perfect disturbance estimation the effectiveness of the controller is illustrated with a simulation example of a second order system

adaptive tuning to bifurcation for time varying nonlinear systems adaptive output feedback control algorithm providing exact tuning of adjustable parameters to unknown values which ensure desired bifurcation properties of the system is proposed design of the algorithm is based on passification and adaptive observer application examples like neural integrator resonant pendulum and three dimensional oscillator are presented and illustrated by simulation results

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

linear systems with delayed controls a reduction linear systems with delayed control action are transformed into systems without delays under an absolute continuity condition the new system is an ordinary differential control equation in the general case the new system is a measure differential control system it is shown how the controllability stabilization and various optimization problems can be analyzed via the reduced systems

compensation of actuator dynamics governed by quasilinear hyperbolic pdes we present a methodology for stabilization of general nonlinear systems with actuator dynamics governed by a certain class of quasilinear first order hyperbolic pdes since for such pde ode cascades the speed of propagation depends on the pde state itself which implies that the prediction horizon cannot be a priori known analytically the key design challenge is the determination of the predictor state we resolve this challenge and introduce a pde predictor feedback control law that compensates the transport actuator dynamics due to the potential formation of shock waves in the solutions of quasilinear first order hyperbolic pdes which is related to the fundamental restriction for systems with time varying delays that the delay rate is bounded by unity we limit ourselves to a certain feasibility region around the origin and we show that the pde predictor feedback law achieves asymptotic stability of the closed loop system providing an estimate of its region of attraction our analysis combines lyapunov like arguments and iss estimates since it may be intriguing as to what is the exact relation of the cascade to a system with input delay we highlight the fact that the considered pde ode cascade gives rise to a system with input delay with a delay that depends on past input values defined implicitly via a nonlinear equation the developed control design methodology is applied to the control of vehicular traffic flow at distant bottlenecks

robust stability of input output systems with initial conditions we consider the development of a general nonlinear input output theory which encompasses systems with initial conditions systems are defined in a set theoretic manner from input output pairs on a doubly infinite time axis and a general construction of the initial conditions is given in terms of an equivalence class of trajectories on the negative time axis input output operators are then defined for given initial conditions and a suitable notion of input output stability on the positive time axis with initial conditions is given this notion of stability is closely related to the iss ios concepts of sontag a fundamental robust stability theorem is derived which represents a generalization of the input output operator robust stability theorem of georgiou and smith to include the case of initial conditions this includes a suitable generalization of the nonlinear gap metric some applications are given to show the utility of the robust stability theorem

approximately bisimilar symbolic models for randomly switched stochastic systems in the past few years there has been a growing interest in the use of symbolic models for control systems the main reason is the possibility to leverage algorithmic techniques over symbolic models to synthesize controllers that are valid for the concrete control systems such controllers can enforce complex logical specifications that are otherwise hard if not impossible to establish on the concrete models with classical control techniques examples of such specifications include those expressible via linear temporal logic or as automata on infinite strings a relevant goal in this research line is in the identification of classes of systems that admit symbolic models in particular continuous time systems with stochastic or hybrid dynamics have been only recently considered due to their rather general and complex dynamics in this work we make progress in this direction by enlarging the class of stochastic hybrid systems admitting finite symbolic models specifically we show that randomly switched stochastic systems satisfying some incremental stability assumption admit such models

non uniform in time robust global asymptotic output stability abstract the notions of non uniform in time robust global asymptotic output stability and robust forward completeness for time varying systems are introduced necessary and sufficient conditions and lyapunov like characterizations are given for these notions

separation principles for input output and integral input to state stability we present new characterizations of input output to state stability this is a notion of detectability formulated in the iss input to state stability framework equivalent properties are presented in terms of asymptotic estimates of the state trajectories based on the magnitudes of the external input and output signals these results provide a set of separation principles for input output to state stability characterizations of the property as conjunctions of weaker stability notions when applied to the notion of integral iss these characterizations yield analogous results

gruff 3 generalizing the domain of a function based recognition system abstract representation systems which support generic object recognition offer promising advantages over current model based vision systems applying function based reasoning are one such approach in this approach specific geometric or structural models are disregarded in favor of analyzing the shape to determine functional requirements for category membership this paper presents an explanation of the ideas behind function based modeling and a description of the extensions made to create the generic representation using form and function 3 gruff 3 system this system analyzes the 3d shape of an object and classifies the object according to its possible function as some sub category of the superordinate category dishes the initial gruff system implementation was restricted to the furniture domain and required five knowledge primitives clearance relative orientation proximity dimensions and stability to realize the functional requirements of the categories represented the important contribution of our current work is that a significantly larger domain of objects can now be recognized with the addition of just one new knowledge primitive enclosure an evaluation of the performance of the system is presented for a database of over 200 3d shapes

return map characterizations for a model of bursting with two slow variables various physiological systems display bursting electrical activity bea there exist numerous three variable models to describe this behavior however higher dimensional models with two slow processes have recently been used to explain qualitative features of the bea of some experimentally observed systems t chay and d cook math biosci 90 1988 pp 139 153 p smolen and j keizer j memb biol 127 1992 pp 9 19 r bertram et al biophys j 79 2000 pp 2880 2892 r bertram et al biophys j 68 1995 pp 2323 2332 j keizer and p smolen proc nat acad sci usa 88 1991 pp 3897 3901 in this paper we present a model with two slow and two fast variables for some parameter values the system has stable equilibria while for other values there exist bursting solutions singular perturbation methods are used to define a one dimensional return map wherein fixed points correspond to singular bursting solutions we analytically demonstrate that bursting solutions may exist

global stabilization by output feedback examples and counterexamples abstract we show by means of examples that global complete observability and global stabilizability by state feedback are not sufficient to guarantee global stabilizability by dynamic output feedback we show that a main obstruction is related to unboundedness unobservability this is that some unmeasured state components may escape in finite time whereas the measurements remain bounded

lyapunov conditions for input to state stability of impulsive systems this paper introduces appropriate concepts of input to state stability iss and integral iss for impulsive systems i e dynamical systems that evolve according to ordinary differential equations most of the time but occasionally exhibit discontinuities or impulses we provide a set of lyapunov based sufficient conditions for establishing these iss properties when the continuous dynamics are iss but the discrete dynamics that govern the impulses are not the impulses should not occur too frequently which is formalized in terms of an average dwell time adt condition conversely when the impulse dynamics are iss but the continuous dynamics are not there must not be overly long intervals between impulses which is formalized in terms of a novel reverse adt condition we also investigate the cases where i both the continuous and discrete dynamics are iss and ii one of these is iss and the other only marginally stable for the zero input while sharing a common lyapunov function in the former case we obtain a stronger notion of iss for which a necessary and sufficient lyapunov characterization is available the use of the tools developed herein is illustrated through examples from a micro electro mechanical system mems oscillator and a problem of remote estimation over a communication network

a lyapunov based small gain theorem for interconnected switched systems abstract stability of an interconnected system consisting of two switched systems is investigated in the scenario where in both switched systems there may exist some subsystems that are not input to state stable non iss we show that providing the switching signals neither switch too frequently nor activate non iss subsystems for too long a small gain theorem can be used to conclude global asymptotic stability gas of the interconnected system for each switched system with the constraints on the switching signal being modeled by an auxiliary timer a correspondent hybrid system is defined to enable the construction of a hybrid iss lyapunov function apart from justifying the iss property of their corresponding switched systems these hybrid iss lyapunov functions are then combined to establish a lyapunov type small gain condition which guarantees that the interconnected system is globally asymptotically stable

forward completeness unboundedness observability and their lyapunov characterizations a finite dimensional continuous time system is forward complete if solutions exist globally for positive time this paper shows that forward completeness can be characterized in a necessary and sufficient manner by means of smooth scalar growth inequalities moreover a version of this fact is also proved for systems with inputs and a generalization is also provided for systems with outputs and a notion unboundedness observability of relative completeness we apply these results to obtain a bound on reachable states in terms of energy like estimates of inputs

stabilization by means of approximate predictors for systems with delayed input sufficient conditions for global stabilization of nonlinear systems with delayed input by means of approximate predictors are presented an approximate predictor is a mapping which approximates the exact values of the stabilizing input for the corresponding system with no delay a systematic procedure for the construction of approximate predictors is provided for globally lipschitz systems the resulting stabilizing feedback can be implemented by means of a dynamic distributed delay feedback law illustrative examples show the efficiency of the proposed control strategy

relationships between subclasses of integral input to state stability a certain qualitative equivalence has been recently demonstrated between integral input to state stability iiss and a nonlinear mathcal l 2 gain property furthermore it has been observed that the properties of strong iiss and nonlinear mathcal l 2 gain are preserved when multiple systems satisfying the respective property are connected in cascade this technical note clarifies the relationships between various input to state stability and non linear mathcal l p gain properties