mappings of least dirichlet energy and their hopf differentials the paper is concerned with mappings h colon mathbb x begin array ll rm onto longrightarrow end array mathbb y between planar domains having least dirichlet energy the existence and uniqueness up to a conformal change of variables in mathbb x of the energy minimal mappings is established within the class overline fancyscript h 2 mathbb x mathbb y of strong limits of homeomorphisms in the sobolev space fancyscript w 1 2 mathbb x mathbb y a result of considerable interest in the mathematical models of nonlinear elasticity the inner variation of the independent variable in mathbb x leads to the hopf differential h z overline h bar z rm d z otimes rm d z and its trajectories for a pair of doubly connected domains in which mathbb x has finite conformal modulus we establish the following principle a mapping h in overline fancyscript h 2 mathbb x mathbb y is energy minimal if and only if its hopf differential is analytic in mathbb x and real along partial mathbb x in general the energy minimal mappings may not be injective in which case one observes the occurrence of slits in mathbb x cognate with cracks slits are triggered by points of concavity of mathbb y they originate from partial mathbb x and advance along vertical trajectories of the hopf differential toward mathbb x where they eventually terminate so no crosscuts are created

observer design for nonlinear control systems abstract this paper deals with the observer design problem of a wide class of nonlinear systems subjected to bounded nonlinearities a sufficient liapunovlike condition is provided and the proposed dynamic observer is a direct extension of the one in linear case

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

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

modular design of nonlinear observers for state and disturbance estimation this work studies the problem of design of nonlinear observers in the presence of exogenous disturbances in particular the present work proposes a systematic design method for nonlinear state and disturbance observers in modular form consisting of an observer for the disturbance free part of the system along with a disturbance observer and a state estimate corrector the modular observer is first defined and characterized in a general setting and then a systematic design method is developed on the basis of exact linearization with eigenvalue assignment necessary and sufficient conditions for feasibility of the proposed nonlinear modular observer design are derived the proposed modular nonlinear observer is tested through simulation studies in an illustrative example involving a biochemical reactor

reset adaptive observer for a class of nonlinear systems this technical note proposes a novel kind of state estimator called reset adaptive observer reo a reo is an adaptive observer consisting of an integrator and a reset law that resets the output of the integrator depending on a predefined condition the main contribution of this technical note is that the reset element theory is applied for the first time to the nonlinear adaptive observer framework the introduction of the reset element in the adaptive law can decrease the overshooting and settling time of the estimation process without sacrificing the rising time the stability and convergence lmi based analysis of the proposed reo is addressed and additionally an easily computable method to determine the l2 gain of the reo dealing with noise corrupted systems is presented

brief robust output feedback control of nonlinear singularly perturbed systems in this work we consider nonlinear singularly perturbed systems with time varying uncertain variables for which the fast subsystem is asymptotically stable and the slow subsystem is input output linearizable and possesses input to state stable iss inverse dynamics for these systems we synthesize a robust output feedback controller that ensures boundedness of the state and enforces robust asymptotic output tracking with attenuation of the effect of the uncertain variables on the output of the closed loop system the controller is constructed through combination of a high gain observer with a robust state feedback controller synthesized via lyapunov s direct method the proposed controller enforces the aforementioned properties in the closed loop system for initial conditions uncertainty and rate of change of uncertainty in arbitrarily large compact sets provided that the singular perturbation parameter is sufficiently small and the observer gain is sufficiently large

harmonic maps with defects two problems concerning maps with point singularities from a domain c 3 tos2 are solved the first is to determine the minimum energy of when the location and topological degree of the singularities are prescribed in the second problem is the unit ball and g is given on we show that the only cases in whichg x x minimizes the energy isg const org x rx withr a rotation extensions of these problems are also solved e g points are replaced by holes 3 s2 is replaced by n sn 1 or by n pn 1 the latter being appropriate for the theory of liquid crystals

nonlinear observers with approximately linear error dynamics the multivariable case exact error linearization uses nonlinear input output injection to design observers with linear error dynamics in certain coordinates this approach can only be applied nongenerically we propose an observer for a wider class of multivariable systems which uniformly minimizes the nonlinear part of the system that cannot be canceled by nonlinear input output injection our approach is numerical constructive and provides locally exponentially stable error dynamics an example compares our design with a high gain method

output feedback control of switched nonlinear systems using multiple lyapunov functions abstract this work presents a hybrid nonlinear control methodology for a broad class of switched nonlinear systems with input constraints the key feature of the proposed methodology is the integrated synthesis via multiple lyapunov functions of lower level bounded nonlinear feedback controllers together with upper level switching laws that orchestrate the transitions between the constituent modes and their respective controllers both the state and output feedback control problems are addressed under the assumption of availability of full state measurements a family of bounded nonlinear state feedback controllers are initially designed to enforce asymptotic stability for the individual closed loop modes and provide an explicit characterization of the corresponding stability region for each mode a set of switching laws are then designed to track the evolution of the state and orchestrate switching between the stability regions of the constituent modes in a way that guarantees asymptotic stability of the overall switched closed loop system when complete state measurements are unavailable a family of output feedback controllers are synthesized using a combination of bounded state feedback controllers high gain observers and appropriate saturation filters to enforce asymptotic stability for the individual closed loop modes and provide an explicit characterization of the corresponding output feedback stability regions in terms of the input constraints and the observer gain a different set of switching rules based on the evolution of the state estimates generated by the observers is designed to orchestrate stabilizing transitions between the output feedback stability regions of the constituent modes the differences between the state and output feedback switching strategies and their implications for the switching logic are discussed and a chemical process example is used to demonstrate the proposed approach

mappings of finite distortion monotonicity and continuity we study mappings f f1 fn rn in the sobolev space w loc r n where is a connected open subset of rn with n 2 thus for almost every x we can speak of the linear transformation d f x rn rn called differential of f at x its norm is defined by d f x sup d f x h h sn 1 we shall often identify d f x with its matrix and denote by j x f det d f x the jacobian determinant thus using the language of differential forms we can write

radial symmetry of p harmonic minimizers it is still not known if the radial cavitating minimizers obtained by ball philos trans r soc lond a 306 557 611 1982 and subsequently by many others are global minimizers of any physically reasonable nonlinearly elastic energy this quotation is from sivaloganathan and spector ann inst henri poincare anal non lineaire 25 1 201 213 2008 and seems to be still accurate the model case of the p harmonic energy is considered here we prove that the planar radial minimizers are indeed the global minimizers provided we prescribe the admissible deformations on the boundary in the traction free setting however even the identity map need not be a global minimizer

nonlinear observers with linearizable error dynamics we present a new method for designing asymptotic observers for a class of nonlinear systems the error between the state of the system and the state of the observer in appropriate coordinates evolves linearly and can be made to decay arbitrarily exponentially fast

observer linearization by output dependent time scale transformations we study the problem of observer linearization for single output dynamical systems in the presence of output dependent time scaling changes an alternative algorithm for the solution of the observer linearization problem is introduced the algorithm employs an exterior calculus approach that provides a simple procedure for the solution of the observer linearization problem by means of an output dependent time scale transformation

neohookean deformations of annuli in the higher dimensional euclidean space abstract let n 2 be an integer and assume that a x r n 1 x r and a y r n 1 y r be two annuli in euclidean space r n assume that f a a resp r a a be the class of all orientation preserving resp radial homeomorphisms h a a in the sobolev space w 1 n a a which keep the boundary circles in the same order in this paper we extended the corresponding results of iwaniec and onninen which was published in math ann vol 348 2010

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

nonlinear observer design for state and disturbance estimation a new systematic framework for nonlinear observer design that allows the concurrent estimation of the process state variables together with key unknown process or sensor disturbances is proposed the nonlinear observer design problem is addressed within a similar methodological framework as the one introduced in n kazantzis c kravaris nonlinear observer design using lyapunov s auxiliary theorem systems control lett 34 1998 241 a j krener m xiao nonlinear observer design in the siegel domain siam j control optim 41 2002 932 for state estimation purposes only from a mathematical standpoint the problem under consideration is addressed through a system of first order singular pdes for which a rather general set of solvability conditions is derived a nonlinear observer is then designed with a state dependent gain that is computed from the solution of the system of singular pdes under the aforementioned conditions both state and disturbance estimation errors converge to zero with assignable rates the convergence properties of the proposed nonlinear observer are tested through simulation studies in an illustrative example involving a biological reactor

extremal mappings of finite distortion the theory of mappings of finite distortion has arisen out of a need to extend the ideas and applications of the classical theory of quasiconformal mappings to the degenerate elliptic setting where one finds concrete applications in non linear elasticity and the calculus of variations in this paper we initiate the study of extremal problems for mappings with finite distortion and extend the theory of extremal quasiconformal mappings by considering integral averages of the distortion function instead of its supremum norm for instance we show the following suppose that f o is a homeomorphism of the circle with f o 1 in cal w 1 2 2 then there is a unique extremal extension to the disk which is a real analytic diffeomorphism with non vanishing jacobian determinant the condition on f o is sharp classically the mapping f o is assumed to be quasisymmetric then there is an extremal quasiconformal mapping with boundary values f o but it is not always unique and it is seldom smooth indeed even when f o is quasisymmetric the cal l 1 minimiser for the distortion function will almost never be quasiconformal we further find that there are many new and unexpected phenomena concerning existence uniqueness and regularity for these extremal problems where the functionals are polyconvex but typically not convex these seem to differ markedly from phenomena observed when studying multi well type functionals

adaptive redesign of nonlinear observers to estimate unmeasured states in dynamical systems with parametric uncertainties one can use adaptive observers in this technical note a new method for adaptive redesign of reduced order observers for nonlinear systems is presented the redesign makes the observer robust as it guarantees that the state estimation error converges to zero in the presence of parametric uncertainties to enable parameter adaption a new type of update law is derived using lyapunov analysis and a nonlinear coordinate transformation the uniqueness of the approach is that it allows terms containing both uncertainty and nonlinearity in the unmeasured states to appear in the dynamics of the unmeasured states and still achieves convergence of the state estimate without requiring persistent excitation two examples are presented that demonstrate these properties

observer design based on immersion technics and canonical form abstract a crucial problem in immersion based observer design is the case where the dimension of the immersed system is greater than that of the original system and the analytical expression of the inverse of the immersion is unknown in this paper we have proposed a method for constructing observers for such autonomous nonlinear systems

a unified h adaptive observer synthesis method for a class of systems with both lipschitz and monotone nonlinearities abstract this paper investigates the problem of the h adaptive observer design for a class of nonlinear dynamical systems the main contribution consists in providing a unified synthesis method for systems with both lipschitz and monotone nonlinearities not necessarily lipschitz thanks to the innovation terms into the nonlinear functions m arcak p kokotovic observer based control of systems with slope restricted nonlinearities ieee transactions on automatic control 46 7 2001 1146 1150 and to the differential mean value theorem a zemouche m boutayeb g i bara observers for a class of lipschitz systems with extension to h performance analysis systems and control letters 57 1 2008 18 27 the stability analysis leads to the solvability of a linear matrix inequality lmi with several degrees of freedom for simplicity we start by presenting the result in an h adaptive free context furthermore we propose an h adaptive estimator that extends easily the obtained results to systems with unknown parameters in the presence of disturbances we show in particular that the matching condition in terms of an equality constraint required in several works is not necessary and therefore allows reducing the conservatism of the existing conditions performances of the proposed approach are shown through a numerical example with a polynomial nonlinearity

canonical form observer design for non linear time variable systems an observer of canonical phase variable form for non linear time variable systems is introduced the development of this non linear time variable form requires regularity of the non linear time variable observability matrix of the system from the relationships derived during the development it follows that a non linear time variable observer can be dimensioned by an eigenvalue assignment with respect to the canonical state coordinates if a linearization of system non linearities about the reconstructed state trajectories is permissible this is an assumption similar to that of the extended kalman filter based on a linearization about the current estimate

adaptive control of chaotic continuous time systems with delay a simple delay system governed by a first order differential delay equation may behave chaotically but the conditions for the system to have such behaviors have not been well recognized in this paper a set of rules is postulated first for the conditions for the delay system to display chaos a model reference adaptive control scheme is then proposed to control the chaotic system state to converge to an arbitrarily given reference trajectory with certain and uncertain system parameters numerical examples are given to analyze the chaotic behaviors of the delay system and to demonstrate the effectiveness of the proposed adaptive control scheme

hyperelastic deformations and total combined energy of mappings between annuli abstract we consider the so called combined energy of a deformation between two concentric annuli and minimize it provided that it keep order of the boundaries it is an extension of the corresponding result of euclidean energy it is interesting that the minimizers are certain radial mappings and they exist if and only if the annulus on the image domain is not too thin provided that the original annulus is fixed this in turn implies a nitsche type phenomenon next we consider the combined distortion and obtain certain related results which are dual to the results for combined energy which also involve some nitsche type phenomenon the main part of the paper is concerned with the total combined energy a certain integral operator defined as a convex linear combination of the combined energy and combined distortion of diffeomorphisms between two concentric annuli a 1 r and b 1 r first we construct radial minimizers of total combined energy then we prove that those radial minimizers are absolute minimizers on the class of all mappings between the annuli under certain constraint this extends the main result obtained by iwaniec and onninen in 9

the nitsche conjecture the nitsche conjecture is deeply rooted in the theory of doubly connected minimal surfaces however it is commonly formulated in slightly greater generality as a question of existence of a harmonic homeomorphism between circular annuli h a a r r onto a r r a in the early 1960s while attempting to describe all doubly connected minimal graphs over a given annulus a j c c nitsche observed that their conformal modulus cannot be too large then he conjectured in terms of isothermal coordinates even more a harmonic homeomorphism h a onto a exists if an only if r r 1 2 r r r r this fascinating and engaging problem remained open for almost a half of a century in the present paper we provide among further generalizations an affirmative answer to his conjecture

local observer for infinitesimally observable nonlinear systems in this article we present a local observer based on infinitesimal observability along trajectories the gain of this observer derives from a dynamical lyapunov equation the inputs for which the observer converges are those which render the system observable at each point of the limit of the unknown trajectory infinitesimal observability at infinity along trajectories the performance of the proposed observer is illustrated with an application to dc machine

erratum nonlinear observer design in the siegel domain there is an error in the proof of the main result of our paper siam j control optim 41 2002 pp 932 953 an additional assumption is needed for the main result to hold in this erratum we supply a corrected version of the main result

on conservation laws and necessary conditions in the calculus of variations it is well known from the work of noether that every variational symmetry of an integral functional gives rise to a corresponding conservation law in this paper we prove that each such conservation law arises directly as the euler lagrange equation for the functional on taking suitable variations around a minimizer

a luenberger like observer for nonlinear systems a state observer is proposed for nonlinear continuous time systems which extends the well known luenberger observer in particular on the basis of simple assumptions on the regularity of the system equations observability and the global holder condition for suitable functions which are generally satisfied for physically meaningful dynamic systems the global asymptotic convergence of the estimated state towards the true state is shown finally some examples of applications are also reported showing the effectiveness of the proposed observer

neohookean deformations of annuli existence uniqueness and radial symmetry let mathbb x x in mathbb r 2 r x r and mathbb y y in mathbb r 2 r ast y r ast be annuli in the plane we consider the class fancyscript f mathbb x mathbb y of all orientation preserving homeomorphisms h mathbb x overset textnormal tiny onto longrightarrow mathbb y in the sobolev space fancyscript w 1 2 mathbb x mathbb y which keep the boundary circles in the same order this means that lim x searrow r h x r ast and lim x nearrow r h x r ast we study the neohookean energy integral mathcal e h int limits mathbb x dh 2 phi rm det dh quad rm for h in fancyscript f mathbb x mathbb y quad quad quad 1 where phi in fancyscript c infty 0 infty is positive and strictly convex we assume in addition that the function psi z 1 ddot phi z and its derivative extend continuously to 0 with 0 0 then we prove

myriad radial cavitating equilibria in nonlinear elasticity it is shown that every bounded strictly increasing smooth positive function of sufficiently slow growth is the jacobian of a radial hole creating equilibrium deformation for an appropriately constructed compressible nonlinearly elastic energy

regularity of the inverse of a planar sobolev homeomorphism let be a domain suppose that f w1 1loc r2 is a homeomorphism such that df x vanishes almost everywhere in the zero set of j f we show that f 1 w1 1loc f r2 and that df 1 y vanishes almost everywhere in the zero set of sharp conditions to quarantee that f 1 w1 q f r2 for some 1 q 2 are also given

uniqueness of regular and singular equilibria for spherically symmetric problems of nonlinear elasticity introduction 97 constitutive assumptions 99 0 the stored energy function and weak equilibrium solutions 101 1 properties of radial equilibrium solutions 105 2 uniqueness of solutions to boundary value problems for shells 111 3 uniqueness of cavitating solutions 117 4 existence of radial equilibria 121 5 asymptotic behaviour of equilibria for shells 128 6 concluding remarks 132 7 appendix 133 references 135

nonlinear observer design using lyapunov s auxiliary theorem abstract the present work proposes a new approach to the nonlinear observer design problem based on the early ideas that influenced the development of the linear luenberger observer theory the proposed approach develops a nonlinear analogue the formulation of the observer design problem is realized via a system of singular first order linear pdes and a rather general set of necessary and sufficient conditions for solvability is derived by using lyapunov s auxiliary theorem the solution to the above system of pdes is locally analytic and this enables the development of a series solution method that is easily programmable with the aid of a symbolic software package

nonlinear observers for autonomous lipschitz continuous systems this paper considers the state observation problem for autonomous nonlinear systems an observation mapping is introduced which is defined by applying a linear integral operator rather than a differential operator to the output of the system it is shown that this observation mapping is well suited to capture the observability nature of smooth as well as nonsmooth systems and to construct observers of a remarkably simple structure a linear state variable filter followed by a nonlinearity the observer is established by showing that observability and finite complexity of the system are sufficient conditions for the observer to exist and by giving an explicit expression for its nonlinearity it is demonstrated that the existence conditions are satisfied and hence our results include a new observer which is not high gain for the wide class of smooth systems it is shown that the observer can as well be designed to realize an arbitrary finite accuracy rather than ultimate exactness on a compact region of the state space this requires only observability of the system a corresponding numerical design procedure is described which is easy to implement and computationally feasible for low order systems

pacemaker induced coherence in cortical networks a simple mathematical model of cortical tissue is introduced and the system s dynamics is monitored when a small subset of neurons is submitted to oscillatory inputs of various frequency and wavefo

maximal smoothness of solutions to certain euler lagrange equations from nonlinear elasticity we investigate the maximal smoothness of stationary states for the multiple integral such variational problems are motivated by the study of nonlinear elasticity assuming certain structure conditions for and given a stationary state we derive an a priori l p estimate for for any p and where as a consequence we show that a c 1 stationary state necessarily satisfies det and is of class c 2 in nevertheless singular stationary states do exist we construct a nonsmooth c 1 solution for a particular in two dimensions such that det in and det vanishes at precisely one point in

control of chaos in delay differential equations in a network of oscillators and in model cortex abstract we extend the ott grebogi yorke method to the stabilization of unstable orbits in a network of oscillators exhibiting spatiotemporal chaotic activity wherein the perturbation is applied to the variables of the system with the help of numerical simulations we show that a method developed by pyragas can stabilize unstable orbits in a one variable delay differential equation and in a model cortical network with delay we discuss the relevance of these results in the physiological processes of the brain

an existence theory for nonlinear elasticity that allows for cavitation in this paper the existence of minimizers in nonlinear elasticity is established under assumptions on the stored energy that permit the formation of new holes in the body such cavities have been observed in experiments on elastomers and a mathematical theory for radially symmetric cavities has been developed by ball here the full three dimensional problem is considered and an additional physically motivated energy term that is proportional to the area of the boundary of the deformed body is included the minimizers lie in a subclass of those maps in w1 p 2 p 3 that are one to one almost everywhere and preserve orientation roughly speaking this subclass consists of those maps in which cavities in one part of the body are not filled by material from other parts of the body such maps are shown to be much more regular than expected in particular some ideas of sverak are used to show that each map in this subclass has a representative which is continuous outside a set of hausdorff dimension 3 p and that this representative also satisfies lusin s condition n i e it maps lebesgue null sets onto such sets it is also shown that the distributional jacobian of such a map is a measure which is the sum of a measure that is absolutely continuous with respect to lebesgue measure and at most a countable number of dirac measures

on the symmetry of energy minimising deformations in nonlinear elasticity ii compressible materials let a bf x in mathbb r n a 0 be the region occupied by an incompressible nonlinearly hyperelastic material in its reference configuration deformations bf u it a rightarrow mathbb r n are therefore isochoric maps and so satisfy the incompressibility constraint rm det nabla bf u 1 the displacement and the mixed displacement zero traction boundary value problems are considered here a displacement boundary condition of the form bf u bf x sigma bf x is prescribed on one of the boundary components where 0 is a given constant and the displacement on the remaining boundary component is either prescribed in the same form in the case of the pure displacement boundary value problem or left unspecified in the case of the mixed boundary value problem in this paper isoperimetric arguments are used to prove that the radially symmetric solutions to these problems are global energy minimisers in various classes of possibly non symmetric isochoric deformations of the region a

nonlinear observer design in the siegel domain we extend the method of kazantzis and kravaris systems control lett 34 1998 pp 241 247 for the design of an observer to a larger class of nonlinear systems the extended method is applicable to any real analytic observable nonlinear system it is based on the solution of a first order singular nonlinear pde this solution yields a change of state coordinates which linearizes the error dynamics under very general conditions the existence and uniqueness of the solution is proved lyapunov s auxiliary theorem and siegel s theorem are obtained as corollaries the technique is constructive and yields a method for constructing approximate solutions

hyperelastic deformations of smallest total energy throughout this article mathbb x and mathbb y will be nonempty bounded domains in mathbb r n n geqq 2 the term deformation of mathbb x subset mathbb r n onto mathbb y subset mathbb r n refers to an orientation preserving homeomorphism h mathbb x overset textnormal tiny onto longrightarrow mathbb y in the sobolev class fancyscript w 1 1 mathbb x mathbb y whose inverse f mathbb y overset textnormal tiny onto longrightarrow mathbb x lies in fancyscript w 1 1 mathbb y mathbb x the general law of hyperelasticity asserts that there exists an energy integral mathcal e mathbb x h int mathbb x e x h dh rm dx such that the elastic deformations have the smallest energy we assume here that e is conformally coerced and polyconvex some additional regularity conditions are also imposed under those conditions we establish the existence and global invertibility of the minimizers the key tools in obtaining an extremal deformation h mathbb x overset textnormal tiny onto longrightarrow mathbb y regardless of its boundary values are the free lagrangians finding suitable free lagrangians and using them for a specific stored energy function e is truly a work of art we have done it here for the so called total harmonic energy and a pair of annuli in the plane in fact this challenging problem illustrates rather clearly the strength of the concept of free lagrangians