a note on the null condition for quadratic nonlinear klein gordon systems in two space dimensions we consider the cauchy problem for quadratic nonlinear klein gordon systems in two space dimensions with masses satisfying the resonance relation under the null condition in the sense of j m delort d fang and r xue j funct anal 211 2004 no 2 288 323 we show the global existence of asymptotically free solutions if the initial data are sufficiently small in some weighted sobolev space our proof is based on an algebraic characterization of nonlinearities satisfying the null condition 2012 wiley periodicals inc

a compact design scheme of adaptive output feedback control for uncertain nonlinear systems abstractmultiple uncertainties noises frequently exist in a plant usually require multiple compensation techniques which renders feedback controllers highly dynamic and nonlinear this motivates us to search for a compact design scheme of compensation to reduce the complexity of controllers in this paper global output feedback stabilisation is investigated for a class of uncertain nonlinear systems with unknown unmeasured states dependent growth and input matching uncertainty to solve the problem a compact scheme is proposed to design a global adaptive output feedback controller which combines the technique of dynamic gain and extended state observer together particularly only one dynamic gain rather than two dynamic gains is introduced to deal with the unknown polynomial of output growth rate which makes our controller to have lower dynamics than those in the related works moreover the input matching uncertainty is asymptotically estimated by the extended state observer and thus its effec

finite time stability analysis of stochastic switched boolean networks with impulsive effect abstract this paper analyzes the finite time stability of stochastic switched boolean networks sbns with impulsive effect using the algebraic state space representation assr approach the dynamics of sbns with impulsive effect is converted to an algebraic form based on the algebraic form some necessary and sufficient conditions are presented for the finite time stability of stochastic sbns with impulsive effect including probabilistic switching signal case and markov jump switching signal case the study of an illustrative example shows that the obtained new results are effective

approximation based control of nonlinear mimo time delay systems approximation based control is presented for a class of multi input multi output mimo nonlinear systems in block triangular form with unknown state delays neural networks nns are utilized to approximate and compensate for unknown functions in the system dynamics including the unknown bounds of the functions of delayed states the use of a separation technique removes the need for any assumption on the function of delayed states and allows the handling of multiple delays in each function of delayed states by combining the use of lyapunov krasovskii functionals and adaptive nn backstepping the proposed control guarantees that all closed loop signals remain bounded while the outputs converge to a neighborhood of the desired trajectories simulation results demonstrate the effectiveness of the proposed scheme

fuzzy approximation adaptive fault tolerant control for nonlinear pure feedback systems with unknown control directions and sensor failures abstract in this paper the problem of adaptive fuzzy fault tolerant control ftc is investigated for a class of nonlinear pure feedback systems with unknown control directions and sensor failures by utilizing the mean value theorem the considered nonlinear pure feedback system is transformed into a strict feedback structure the unavailability of state variables caused by sensor faults is dealt with by using parameter separation and regrouping technique based on cancelation and decoupled backstepping technique an adaptive fuzzy fault tolerant control method is developed it is proved that the proposed adaptive ftc scheme can guarantee the exponential stabilization of the resulting closed loop system furthermore all the signals of the system remain semi global uniformly ultimately bound sguub the simulation results are provided to illustrate the effectiveness of the proposed control scheme

complex geometry and the asymptotics of harish chandra modules for real reductive lie groups i let g be a connected semisimple real matrix group it is now apparent that the representation theory of g is intimately connected with the complex geometry of the flag variety 9 by studying appropriate orbit structures on 9 we are naturally led to representation theory in the category of harish chandra modules x or the representation theory of category 9 the jacquet functor j f 9 has proved a useful tool in converting yfw problems into 9 problems which are often more tractable in this paper we advance the philosophy that the complex geometry of 9 associated to yf and 9 interacts in a natural way with the functor j leading to deep new information on the structure of jacquet modules this in turn gives new insight into the structure of certain nilpotent cohomology groups associated to harish chandra modules our techniques are based upon many of the ideas present in the proof of the kazhdan lusztig conjectures and bernstein s proof of the jantzen conjecture

two geometric character formulas for reductive lie groups in this paper we prove two formulas for the characters of representations of reductive groups both express the character of a representation in terms of the same geometric data attached to when specialized to the case of a compact lie group one of them reduces to kirillov s character formula in the compact case and the other to an application of the atiyah bott fixed point formula to the borel weil realization of the representation to set the stage let us first recall the borel weil theorem for a connected compact lie group gr for simplicity we assume that gr is simply connected we let gr denote its lie algebra and g c r gr the complexified lie algebra via the adjoint action gr operates on igr the space of all r linear functions gr ir every gr orbit in igr coadjoint orbit for short carries a canonical grinvariant symplectic structure the orbit is said to be integral if some or equivalently any exponentiates to a character e of the isotropy subgroup gr in that case the one dimensional representation spaces of the characters e fit together into a gr equivariant real algebraic hermitian line bundle l the pair l carries a unique positive polarization a gr invariant complex structure on the manifold and the structure of a gr equivariant holomorphic line bundle on l positive in the sense of algebraic geometry the hypothesis of simple connectivity ensures that the square root k of the canonical bundle k exists as a gr equivariant holomorphic line bundle according to the borel weil theorem the natural action of gr on the space of holomorphic l valued half forms h0 o k l is irreducible moreover the association h0 o k l 1 1

two dimensional dissipative control and filtering for roesser model this paper investigates the problems of two dimensional 2 d dissipative control and filtering for a linear discrete time roesser model first a novel sufficient condition is proposed such that the discrete time roesser system is asymptotically stable and 2 d q s r hbox alpha dissipative special cases such as 2 d passivity performance and 2 d h infty performance and feedback interconnected systems are also discussed based on this condition new 2 d q s r hbox alpha dissipative state feedback and output feedback control problems are defined and solved for a discrete time roesser model the design problems of 2 d q s r hbox alpha dissipative filters of observer form and general form are also considered using a linear matrix inequality lmi approach two examples are given to illustrate the effectiveness and potential of the proposed design techniques

filtration de certains espaces de fonctions sur un espace symetrique reductif we introduce a filtration of a g k module of some space of functions on a reductive symmetric space g h and compute the associated grading as a direct sum of induced representations as an application of this result to the reductive groups viewed as symmetric spaces we are able to realize any harish chandra module as a subquotient of a direct sum of induced representations from parabolic subgroups the inducing representations being trivial on the unipotent radical

adaptive neural control of mimo nonlinear state time varying delay systems with unknown dead zones and gain signs in this paper adaptive neural control is proposed for a class of uncertain multi input multi output mimo nonlinear state time varying delay systems in a triangular control structure with unknown nonlinear dead zones and gain signs the design is based on the principle of sliding mode control and the use of nussbaum type functions in solving the problem of the completely unknown control directions the unknown time varying delays are compensated for using appropriate lyapunov krasovskii functionals in the design the approach removes the assumption of linear functions outside the deadband as an added contribution by utilizing the integral lyapunov function and introducing an adaptive compensation term for the upper bound of the residual and optimal approximation error as well as the dead zone disturbance the closed loop control system is proved to be semi globally uniformly ultimately bounded simulation results demonstrate the effectiveness of the approach

adaptive tracking control of uncertain mimo nonlinear systems with input constraints in this paper adaptive tracking control is proposed for a class of uncertain multi input and multi output nonlinear systems with non symmetric input constraints the auxiliary design system is introduced to analyze the effect of input constraints and its states are used to adaptive tracking control design the spectral radius of the control coefficient matrix is used to relax the nonsingular assumption of the control coefficient matrix subsequently the constrained adaptive control is presented where command filters are adopted to implement the emulate of actuator physical constraints on the control law and virtual control laws and avoid the tedious analytic computations of time derivatives of virtual control laws in the backstepping procedure under the proposed control techniques the closed loop semi global uniformly ultimate bounded stability is achieved via lyapunov synthesis finally simulation studies are presented to illustrate the effectiveness of the proposed adaptive tracking control

induction automorphe pour gl n c for f r or c isomorphism classes of irreducible g k modules for gl n f are parametrized by n dimensional representations of the weil group wf of f we can induce to wr a representation of wc which has index 2 in wr that gives a process of automorphic induction which to an irreducible g k module for gl n c associates an irreducible g k module c r for gl 2n r in the present paper we show that if is unitary and generic then is determined by up to isomorphism via a character identity entirely analogous to the character identity occurring in the automorphic induction process for p adic fields this completes the theory of automorphic induction for local and global representations of gl n over number fields

final state problem for a quadratic nonlinear schrodinger system in two space dimensions with mass resonance abstract we consider the asymptotic behavior of a solution to a quadratic nonlinear schrodinger system in two space dimensions we construct a particular solution which describes the charge dissipation phenomenon in spite of the mass preserving structure of the system this is a consequence of a new explicit solution to a system of ordinary differential equation which approximates asymptotic behavior of a solution to the system

small data global existence for a class of quadratic derivative nonlinear schrodinger systems in two space dimensions abstract this paper provides a small data global existence result for a class of quadratic derivative nonlinear schrodinger systems in two space dimensions this is an extension of the previous results by li 2012 25 and ikeda katayama sunagawa 2015 14

asymptotic behavior of matrix coefficients of admissible representations introduction 869 1 generalities on reductive groups 873 2 the infinitesimal cartan decomposition 876 3 the t radial components 880 4 differential equations satisfied by sphereical functions 885 5 asymptotic behavior of spherical functions on a 888 6 asymptotic behavior of spherical functions along the walls of a 892 7 leading characters and growth estimates on the group 898 8 admissible representations and their matrix coefficients 906 appendix 917

finite frequency memory output feedback controller design for t s fuzzy dynamical systems in this paper we will investigate the problem of finite frequency memory fixed order output feedback controller design for takagi sugeno t s fuzzy affine systems it is assumed that the disturbances reside in a finite frequency range i e the low middle or high frequency range the objective is to design a memory piecewise affine pwa controller by using past output measurements to guarantee the asymptotic stability of the resulting closed loop system with a prescribed finite frequency mathscr h infty performance via the system state input augmentation a novel descriptor system approach is proposed to facilitate the controller design all the design conditions are formulated in the form of linear matrix inequalities it is also proven that the mathscr h infty performance can be improved with the memory control strategy finally simulation studies are presented to show the effectiveness of the proposed design method

fuzzy adaptive decentralized output feedback control for large scale nonlinear systems with dynamical uncertainties in this paper an adaptive fuzzy decentralized robust output feedback control approach is proposed for a class of large scale strict feedback nonlinear systems with the unmeasured states the large scale nonlinear systems in this paper are assumed to possess the unstructured uncertainties unmodeled dynamics and unknown high frequency gain sign fuzzy logic systems are used to approximate the unstructured uncertainties k filters are designed to estimate the unmeasured states and a dynamical signal and a special nussbaum gain function are introduced into the control design to solve the problem of unknown high frequency gain sign and dominate unmodeled uncertainties respectively based on the backstepping design and adaptive fuzzy control methods an adaptive fuzzy decentralized robust output feedback control scheme is developed it is proved that the proposed adaptive fuzzy control approach can guarantee that all the signals in the closed loop system are uniformly and ultimately bounded and the tracking errors converge to a small neighborhood of the origin the effectiveness of the proposed approach is illustrated by using simulation results

fuzzy adaptive output feedback control of mimo nonlinear systems with partial tracking errors constrained in this paper a partial tracking error constrained fuzzy output feedback dynamic surface control dsc scheme is proposed for a class of uncertain multi input and multi output mimo nonlinear systems the considered mimo nonlinear systems contain unknown functions and without the requirement of their states being available for the controller design with the help of fuzzy logic systems identifying the mimo unknown nonlinear systems a fuzzy adaptive observer is established to estimate the unmeasured states by transforming the tracking errors into new virtual error variables and based on the dsc backstepping recursive design technique a new adaptive fuzzy output feedback control method is developed it is proved that the proposed control approach can guarantee that all the signals of the resulting closed loop system are bounded and the partial state tracking errors are confined all times within the prescribed bounds the simulation results and comparisons with the previous control approaches confirm the effectiveness and utility of the proposed scheme

primitive ideals and representations certain theorems of joseph and king relating primitive ideals to characters in category o are extended to the case of arbitrary g modules with finite dimensional n cohomology a derived functor construction analogous to a construction of zuckerman in the case of a nilpotent lie algebra is used to extend the results applications to harish chandra modules are also given

well posedness for a quadratic derivative nonlinear schrodinger system at the critical regularity abstract we consider the cauchy problem for a quadratic derivative nonlinear schrodinger system in sobolev space h s in this paper under the null condition and the mass resonance relation we prove large data local well posedness if the space dimension d 3 and s s c d 2 and s s c or d 1 and s 0 where s c is the scaling critical regularity moreover under the same assumptions we also prove small data global well posedness and scattering in h s if d 3 and s s c our proof is based on a contraction argument using the u p and v p type function spaces

decentralized adaptive neural control for high order stochastic nonlinear strongly interconnected systems with unknown system dynamics abstract this paper studies the problem of decentralized adaptive neural backstepping control for a class of high order stochastic nonlinear systems with unknown strongly interconnected nonlinearity during the control of the high order nonlinear interconnected systems only one adaptive parameter is used to overcome the over parameterization problem and radial basis function rbf neural networks are employed to tackle the difficulties brought about by completely unknown system dynamics and stochastic disturbances in addition to address the problem arising from high order strongly interconnected nonlinearities with full states of the overall system the variable separation technique is introduced based on the monotonically increasing property of the bounding functions next a decentralized adaptive neural control method is proposed based on lyapunov stability theory in which the controller is designed to decrease the number of learning parameters it is shown that the designed controller can ensure that all the signals in the closed loop system are 4 moment or 2 moment semi globally uniformly ultimately bounded sguub and the tracking error converges to a small neighborhood of the origin finally two simulation examples are offered to illustrate the effectiveness of the proposed control scheme

global small amplitude solutions for two dimensional nonlinear klein gordon systems in the presence of mass resonance we consider a nonlinear system of two dimensional klein gordon equations with masses m1 m2 satisfying the resonance relation m2 2m1 0 we introduce a structural condition on the nonlinearities under which the solution exists globally in time and decays at the rate o t 1 as t in l in particular our new condition includes the yukawa type interaction which has been excluded from the null condition in the sense of j m delort d fang and r xue j m delort d fang r xue global existence of small solutions for quadratic quasilinear klein gordon systems in two space dimensions j funct anal 211 2004 288 323

adaptive tracking control for a class of uncertain switched nonlinear systems this paper is concerned with the problem of tracking control for a class of switched nonlinear systems in lower triangular form with unknown functions and arbitrary switchings two classes of state feedback controllers are constructed by adopting the adaptive backstepping technique and both of them are designed by using the common lyapunov function clf method the first controller is designed under multiple adaptive laws then the second one is designed based on constructing a maximum common adaptive parameter which can overcome the problem of over parameterization of the first controllers it is shown that the designed state feedback controllers can ensure that all the signals remain bounded and the tracking error converges to a small neighborhood of the origin finally simulation results are presented to show the effectiveness of the proposed approaches

small data blow up for a system of nonlinear schrodinger equations abstract we give examples of small data blow up for a three component system of quadratic nonlinear schrodinger equations in one space dimension our construction of the blowing up solution is based on the hopf cole transformation which allows us to reduce the problem to getting suitable growth estimates for a solution to the transformed system amplification in the reduced system is shown to have a close connection with the mass resonance

adaptive fuzzy finite time stability of uncertain nonlinear systems based on prescribed performance abstract the semi globally practical finite time stability sgpfs problem for a class of uncertain strict feedback nonlinear systems is discussed in this paper a novel performance function called finite time performance function ftpf is first defined moreover this paper is the first to solve an adaptive semi globally practical finite time control issue by combining with backstepping prescribed performance control ppc and fuzzy logic systems furthermore it is proven that the designed control law not only guarantees that all the states converge to a predefined zone in finite time but also all the signals of the closed loop systems are sgpf stable simulation examples are worked out to illustrate the superiority and feasibility of the proposed design method

stochastic stability analysis for 2 d roesser systems with multiplicative noise this paper is concerned with the robust stochastic stability analysis for two dimensional 2 d discrete state multiplicative noisy systems smnss in the roesser form we first derive a new sufficient condition under which linear discrete 2 d smnss are 2 d robustly stochastically stable the underlying problem can then be recast as a convex problem expressed by linear matrix inequalities which can be facilitated using existing numerical algorithms we then apply the obtained result to examine the 2 d robust stochastic stability for 2 d digital filters in the roesser form with random coefficient variation and saturation overflow arithmetic based on free weighting matrices and diagonally dominant matrices an illustrative example is presented to verify the usefulness and potential of the proposed results

brief paper backstepping design for global stabilization of switched nonlinear systems in lower triangular form under arbitrary switchings this paper is concerned with the global stabilization problem for switched nonlinear systems in lower triangular form under arbitrary switchings two classes of state feedback controllers and a common lyapunov function clf are simultaneously constructed by backstepping the first class uses the common state feedback controller which is independent of switching signals the other class utilizes individual state feedback controllers for the subsystems as an extension of the designed method the global stabilization problem under arbitrary switchings for switched nonlinear systems in nested lower triangular form is also studied an example is given to show the effectiveness of the proposed method

adaptive output feedback control design with prescribed performance for switched nonlinear systems abstract in this paper an output feedback control method with prescribed performance is proposed for single input and single output siso switched non strict feedback nonlinear systems it is assumed that nonlinear functions of the concerned systems are unknown switching signals are unknown and arbitrary and the states are unmeasured a linear state observer is designed to estimate the unmeasured states and an observer based output feedback control scheme is developed the key advantages of the proposed control strategy are that virtual control gains of the concerned non strict feedback nonlinear systems are not required to be known and only one tuning parameter is needed based on lyapunov stability theory it is shown that all the signals in the resulting closed loop system are semi globally uniformly ultimately bounded and the tracking error converges to a small residual set with the prescribed performance bound the effectiveness of the proposed control approach is verified by a numerical example

semilinear hyperbolic systems violating the null condition we consider systems of semilinear wave equations in three space dimensions with quadratic nonlinear terms not satisfying the null condition we prove small data global existence of the classical solution under a new structural condition related to the weak null condition for two component systems satisfying this condition we also observe a new kind of asymptotic behavior only one component is dissipated and the other one behaves like a non trivial free solution in the large time

prescribed performance adaptive fuzzy output feedback dynamic surface control for nonlinear large scale systems with time delays the adaptive fuzzy decentralized output feedback control method is proposed for a class of nonlinear large scale systems the considered nonlinear systems contain unstructured uncertainties unknown time varying delays and immeasurable states fuzzy logic systems are used to approximate the unstructured uncertainties and a fuzzy state observer is designed to estimate the unmeasured states based on the backstepping recursive design technique and the prescribed performance technique a new adaptive fuzzy output feedback control method is developed in order to overcome the problem of explosion of complexity inherent in the backstepping control design the dynamic surface control dsc technique is introduced into the control scheme based on lyapunov krasovskii functional it is proved that all the signals in the closed loop system are bounded and the tracking errors remain an adjustable neighborhood of the origin with the prescribed performance bounds the simulation examples and comparison with the previous control methods are provided to show the effectiveness of the proposed control approach

adaptive neural control of high order uncertain nonaffine systems a transformation to affine systems approach abstract this brief investigates the adaptive neural network nn control of a class of high order nonaffine nonlinear systems with completely unknown dynamics since the control terms appear within the unknown nonlinearity traditional control schemes and stability analysis are usually rendered extremely complicated our main contribution includes a novel system transformation that converts the nonaffine system into an affine system through a combination of a low pass filter and state transformation as a result the state feedback control of the nonaffine system can be viewed as the output feedback control of an affine system in normal form the transformed system becomes linear with respect to the new input while the traditional backstepping approach is not needed thus allowing the synthesis to be extremely simplified it is theoretically proven that all the signals in the closed loop system are uniformly ultimately bounded uub simulation results are provided to demonstrate the performance of the developed controller

adaptive fuzzy control of switched nonlinear time varying delay systems with prescribed performance and unmodeled dynamics abstract this paper considers the problem of adaptive prescribed performance control for a class of switched nonlinear systems with time varying delays and unmodeled dynamics fuzzy logic systems are introduced to deal with the unknown nonlinear terms utilizing dynamic surface control and convex combination method a state feedback controller is constructed it is proven that all signals of the closed loop system are bounded finally simulation results are given to show that the proposed scheme is effective

global existence of small solutions for quadratic quasilinear klein gordon systems in two space dimensions consider a quasi linear system of two klein gordon equations with masses m1 m2 we prove that when m1a2m2 and m2a2m1 such a system has global solutions for small smooth compactly supported cauchy data this extends a result proved by sunagawa j differential equations 192 2 2003 308 in the semi linear case moreover we show that global existence holds true also when m1 2m2 and a convenient null condition is satisfied by the nonlinearities

global solutions of nonlinear hyperbolic equations for small initial data on considere des systemes quasilineaires d equations hyperboliques d ordre 2 qui sont des deformations non lineaires de l equation d onde on etudie l existence globale et le comportement asymptotique des solutions du probleme de cauchy quand la donnee initiale est suffisamment petite

switched adaptive control of switched nonlinearly parameterized systems with unstable subsystems this paper investigates the problem of adaptive stabilization for a class of switched nonlinearly parameterized systems where the solvability of the adaptive stabilization problem for subsystems is unnecessary a new switched adaptive control technique for the problem studied is set up by exploiting the generalized multiple lyapunov functions method and the parameter separation technique different update laws are designed to reduce the conservativeness caused by adoption of a common update law for all subsystems also the proposed technique permits removal of a common restriction in which the parameterization in the switched systems is restricted to a linear parameterization as an application of the proposed design technique stabilization for a class of non triangular switched systems with nonlinear parameterization is achieved by design of adaptive controllers since no subsystem of such a switched system is assumed to be adaptively stabilizable the problem under study cannot be handled by the existing methods a two inverted pendulums as a practical example is also provided to demonstrate the effectiveness of the proposed design method

jacquet modules and dirac cohomology abstract we show that dirac cohomology of the jacquet module of a harish chandra module is a harish chandra module for the corresponding levi subgroup we obtain an explicit formula of dirac cohomology of the jacquet module for most of the principal series based on our determination of dirac cohomology of irreducible generalized verma modules with regular infinitesimal characters

a simplified adaptive neural network prescribed performance controller for uncertain mimo feedback linearizable systems in this paper the problem of deriving a continuous state feedback controller for a class of multiinput multioutput feedback linearizable systems is considered with special emphasis on controller simplification and reduction of the overall design complexity with respect to the current state of the art the proposed scheme achieves prescribed bounds on the transient and steady state performance of the output tracking errors despite the uncertainty in system nonlinearities contrary to the current state of the art however only a single neural network is utilized to approximate a scalar function that partly incorporates the system nonlinearities furthermore the loss of model controllability problem typically introduced owing to approximation model singularities is avoided without attaching additional complexity to the control or adaptive law simulations are performed to verify and clarify the theoretical findings