a cohomological obstruction to the hasse principle for homogeneous spaces for a homogeneous space with connected or abelian stabilizer of a connected linear algebraic group defined over a number field a cohomological obstruction to the hasse principle is defined in terms of galois hypercohomology with coefficients in a complex of two abelian algebraic groups this obstruction is proved to be the only obstruction to the hasse principle it is proved that up to sign this cohomological obstruction coincides with the brauer manin obstruction

nonlinearities enhance parameter convergence in output feedback systems while the parameter convergence properties of standard adaptive algorithms for linear systems are well established there are no similar results on the parameter convergence of adaptive controllers for nonlinear systems which have gained popularity in recent years in this paper we focus on a recently developed class of adaptive schemes for output feedback nonlinear systems and show that parameter convergence is guaranteed if and only if an appropriately defined signal vector which does not depend on closed loop signals is persistently exciting then we develop an analytic procedure which allows us given a specific nonlinear system and a specific reference signal to determine a priori whether or not this vector is persistently exciting pe and hence whether or not the parameter estimates will converge in the process we show that the presence of nonlinearities usually reduces the sufficient richness sr requirements on the reference signals and hence enhances parameter convergence this is the first result on the relationship between pe and sr for adaptive nonlinear control systems

prediction based stabilization of linear systems subject to input dependent input delay of integral type in this paper it is proved that a predictor based feedback controller can effectively yield asymptotic convergence for a class of linear systems subject to input dependent input delay this class is characterized by the delay being implicitly related to past values of the input via an integral model this situation is representative of systems where transport phenomena take place as is frequent in the process industry the sufficient conditions obtained for asymptotic stabilization bring a local result and require the magnitude of the feedback gain to be consistent with the initial conditions scale arguments of proof for this novel result include general halanay inequalities for delay differential equations and build on recent advances of backstepping techniques for uncertain or varying delay systems

adaptive observers with arbitrary exponential rate of convergence for nonlinear systems concerns the same class of linearly parameterized single output nonlinear systems that the authors previously identified in 1992 in terms of differential geometric conditions when persistency of excitation conditions are satisfied the adaptive observers presented in this note guarantee arbitrarily fast exponential convergence both of parameter and state estimates to actual parameters and states while previous adaptive observers guarantee only exponential not arbitrarily fast convergence this extends earlier results for linear systems

robust adaptive uniform exact tracking control for uncertain euler lagrange system abstractthis paper offers a solution to the robust adaptive uniform exact tracking control for uncertain nonlinear euler lagrange el system an adaptive finite time tracking control algorithm is designed by proposing a novel nonsingular integral terminal sliding mode surface moreover a new adaptive parameter tuning law is also developed by making good use of the system tracking errors and the adaptive parameter estimation errors thus both the trajectory tracking and the parameter estimation can be achieved in a guaranteed time adjusted arbitrarily based on practical demands simultaneously additionally the control result for the el system proposed in this paper can be extended to high order nonlinear systems easily finally a test bed 2 dof robot arm is set up to demonstrate the performance of the new control algorithm

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 to state stability and inverse optimality of linear time varying delay predictor feedbacks for linear systems with time varying input delay and additive disturbances we show that the basic predictor feedback control law is inverse optimal with respect to a meaningful differential game problem and establish its robustness to constant multiplicative perturbations appearing at the system input both of these properties of the basic predictor feedback controller have not been established so far even for the constant delay case we then show that the basic predictor feedback controller when applied through a low pass filter is again inverse optimal and study its input to state stability as well as its robustness to the low pass filter time constant properties all of the stability and inverse optimality proofs are based on the infinite dimensional backstepping transformation which allows us to construct appropriate lyapunov functionals a numerical example is also provided

finite time stability of sets for hybrid dynamical systems abstract notions and tools for finite time stability of closed sets for hybrid dynamical systems modeled as hybrid inclusions are introduced finite time stability of a closed set is defined as the following two properties lyapunov stability namely the property that solutions that start close to the set stay close to it and finite time convergence in the latter property the amount of time required to converge to the set of interest is captured by a settling time function that depends on hybrid time namely the time elapsed during flows and the number of jumps or events of the hybrid system various sufficient conditions for such properties to hold for a given closed set are established conditions involving lyapunov like functions that strictly decrease during flows that strictly decrease during jumps and that strictly decrease along both regimes are proposed these functions are only required to be locally lipschitz a link between non finite time asymptotic stability and the proposed notion is also established in addition sufficient conditions for finite time attractivity involving properties at jumps of the system the second derivative of a lyapunov like function and a property of nested sets are provided throughout the paper examples exercise the results in addition an application to finite time parameter estimation is provided and results are applied to it

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

robustness analysis of uncertain linear singular systems with output feedback control the robustness analysis for a linear singular system with uncertain parameters and static output feedback control is considered the problem is transformed into a robust nonsingularity problem based on the linear fractional transformation lft approach the robustness bounds to preserve regularity impulse immunity and stability are found in terms of the structured singular value spl mu with respect to parametric uncertainties the lft approach provides a unified framework for robustness analysis of both uncertain linear continuous discrete time singular systems

time varying parameter identification algorithms finite and fixed time convergence in this paper the problem of time varying parameter identification is studied to this aim two identification algorithms are developed in order to identify time varying parameters in a finite time or prescribed time fixed time the convergence proofs are based on a notion of finite time stability over finite intervals of time i e short finite time stability homogeneity for time varying systems and lyapunov based approach the results are obtained under injectivity of the regressor term which is related to the classical identifiability condition the case of bounded disturbances noise of measurements is analyzed for both algorithms simulation results illustrate the feasibility of the proposed algorithms

le groupe fondamental etale d un espace homogene d un groupe algebrique lineaire let x be a homogeneous space of a connected linear algebraic group g defined over an algebraic closed field k of characteristic exponent p let x in x k we denote by h the stabilizer of x in g and we assumed that h is connected or abelian in this text we compute explicitely the prime to p part of the etale fundamental group pi 1 acute mathrm e mathrm t x x in terms of the character groups of g and h as an application we prove a variant of the section conjecture for homogeneous spaces

the elementary obstruction and homogeneous spaces let k be a field of characteristic zero and let k be an algebraic closure of k for a geometrically integral variety x over k we write k x for the function field of x x k k if x has a smooth k point the natural embedding of multiplicative groups k k x admits a galois equivariant retraction in the first part of this article equivalent conditions to the existence of such a retraction are given over local and then over global fields those conditions are expressed in terms of the brauer group of x in the second part of the article we restrict attention to varieties that are homogeneous spaces of connected but otherwise arbitrary algebraic groups with connected geometric stabilizers for k local or global and for such a variety x in many situations but not all the existence of a galois equivariant retraction to k k x ensures the existence of a k rational point on x for homogeneous spaces of linear algebraic groups the technique also handles the case where k is the function field of a complex surface resume soient k un corps de caracteristique nulle et k une cloture algebrique de k pour une k variete x geometriquement integre on note k x le corps des fonctions de x x k k si x possede un k point lisse le plongement naturel de groupes multiplicatifs k k x admet une retraction equivariante pour l action du groupe de galois de k sur k dans la premiere partie de l article sur les corps locaux puis sur les corps globaux on donne des conditions equivalentes a l existence d une telle retraction equivariante ces conditions s expriment en terme du groupe de brauer de la variete x dans la seconde partie de l article on considere le cas des espaces homogenes de groupes algebriques connexes non necessairement lineaires avec groupes d isotropie duke mathematical journal vol 141 no 2 c 2008 received 6 november 2006 revision received 23 april 2007 2000 mathematics subject classification primary 14g05 11g99 12g05 secondary 11e72 14f22 14k15

brief paper parameter convergence in adaptive extremum seeking control this paper addresses the problem of parameter convergence in adaptive extremum seeking control design an alternate version of the popular persistence of excitation condition is proposed for a class of nonlinear systems with parametric uncertainties the condition is translated to an asymptotic sufficient richness condition on the reference set point since the desired optimal set point is not known a priori in this type of problem the proposed method includes a technique for generating perturbation signal that satisfies this condition in closed loop this demonstrates its superiority in terms of parameter convergence the method guarantees parameter convergence with minimal but sufficient level of perturbation the effectiveness of the proposed method is illustrated with a simulation example

finite time parameter estimation in adaptive control of nonlinear systems this note presents a parameter estimation routine that allows exact reconstruction of the unknown parameters in finite time provided a given excitation condition is satisfied the robustness of the routine to an unknown bounded disturbance or modeling error is also shown the result is independent of the control and identifier structures employed the true parameter value is obtained without requiring the measurement or computation of the velocity state vector moreover the technique provides a direct solution to the problem of removing auxiliary perturbation signals when parameter convergence is achieved

stabilization of a system of n 1 coupled first order hyperbolic linear pdes with a single boundary input we solve the problem of stabilization of a class of linear first order hyperbolic systems featuring n rightward convecting transport pdes and one leftward convecting transport pde we design a controller which requires a single control input applied on the leftward convecting pde s right boundary and an observer which employs a single sensor on the same pde s left boundary we prove exponential stability of the origin of the resulting plant observer controller system in the spatial l2 sense

performance improvement in adaptive control of linearly parameterized nonlinear systems this technical note demonstrates how the finite time identification procedure can be used to improve the overall performance of adaptive control systems first we develop an adaptive compensator which guarantees exponential convergence of the estimation error provided the integral of a filtered regressor matrix is positive definite the approach does not involve online checking of matrix invertibility and computation of matrix inverse nor switching between parameter estimation methods the convergence rate of the parameter estimator is directly proportional to the adaptation gain and a measure of the system s excitation the adaptive compensator is then combined with existing adaptive controllers to guarantee exponential stability of the closed loop system the effectiveness of the proposed method is illustrated with a simulation example

nonlinear adaptive control system design with asymptotically stable parameter estimation error abstractthe paper presents a new general method for nonlinear adaptive system design with asymptotic stability of the parameter estimation error the advantages of the approach include asymptotic unknown parameter estimation without persistent excitation and capability to directly control the estimates transient response time the method proposed modifies the basic parameter estimation dynamics designed via a known nonlinear adaptive control approach the modification is based on the generalised prediction error a priori constraints with a hierarchical parameter projection algorithm and the stable data accumulation concepts the data accumulation principle is the main tool for achieving asymptotic unknown parameter estimation it relies on the parametric identifiability system property introduced necessary and sufficient conditions for exponential stability of the data accumulation dynamics are derived the approach is applied in a nonlinear adaptive speed tracking vector control of a three phase induc

output feedback adaptive control of a wave pde with boundary anti damping abstract we develop an adaptive output feedback controller for a wave pde in one dimension with actuation on one boundary and with an unknown anti damping term on the opposite boundary this model is representative of a torsional stick slip instability in drillstrings in deep oil drilling as well as of various acoustic instabilities the key feature of the proposed controller is that it requires only the measurements of boundary values and not of the entire distributed state of the system our approach is based on employing riemann variables to convert the wave pde into a cascade of two delay elements with the first of the two delay elements being fed by control and the same element in turn feeding into a scalar ode this enables us to employ a prediction based design for systems with input delays suitably converted to the adaptive output feedback setting the result s relevance is illustrated with simulation example

parameter and state estimation of nonlinear systems using a multi observer under the supervisory framework we present a hybrid scheme for the parameter and state estimation of nonlinear continuous time systems which is inspired by the supervisory setup used for control state observers are synthesized for some nominal parameter values and a criterion is designed to select one of these observers at any given time instant which provides state and parameter estimates assuming that a persistency of excitation condition holds the convergence of the parameter and state estimation errors to zero is ensured up to a margin which can be made as small as desired by increasing the number of observers to reduce the potential computational complexity of the scheme we explain how the sampling of the parameter set can be dynamically updated using a zoom in procedure this strategy typically requires a fewer number of observers for a given estimation error margin compared to the static sampling policy the results are shown to be applicable to linear systems and to a class of nonlinear systems we illustrate the applicability of the approach by estimating the synaptic gains and the mean membrane potentials of a neural mass model

control of transport pde nonlinear ode cascades with state dependent propagation speed in this paper we deal with the control of a transport partial differential equation nonlinear ordinary differential equation pde nonlinear ode cascade system in which the transport coefficient depends on the ode state we develop a pde based predictor feedback boundary control law which compensates the transport dynamics of the actuator and guarantees global asymptotic stability of the closed loop system the stability proof is based on an infinite dimensional backstepping transformation and a lyapunov like argument the relation of the pde ode cascade with a state dependent propagation speed to an ode system with a state dependent input delay which is defined implicitly via an integral of past values of the ode state is also highlighted and the corresponding equivalent predictor feedback design is presented together with an alternative proof of global asymptotic stability of the closed loop system based on the construction of a lyapunov functional the practical relevance of our control framework is illustrated in an example that is concerned with the control of a metal rolling process

compensation of input delay that depends on delayed input abstract for nonlinear systems we develop a pde based predictor feedback control design which compensates actuator dynamics governed by a transport pde with outlet boundary value dependent propagation velocity global asymptotic stability under the predictor feedback control law is established assuming spatially uniform strictly positive transport velocity the stability proof is based on a lyapunov like argument and employs an infinite dimensional backstepping transformation that is introduced an equivalent representation of the transport pde nonlinear ode cascade via a nonlinear system with an input delay that is defined implicitly through an integral of the past input is also provided and the equivalent predictor feedback control design for the delay system is presented the validity of the proposed controller is illustrated applying a predictor feedback bang bang boundary control law to a pde model of a production system with a queue consistent simulation results are provided that support the theoretical developments

robust finite time parameter estimation using a hybrid systems framework this technical note investigates the problem of parameter estimation for a class of nonlinear systems we show that by placing a member of this class of systems into a hybrid dynamical system we can identify its parameter exactly and in finite time furthermore by using tools developed for hybrid systems we show that the estimation has robust properties in particular the hybrid system contains a compact globally asymptotically stable set where the stability is robust to small perturbations we also present conditions that ensure convergence of the parameter estimate