oscillations of nonlinear partial difference systems abstract this paper studies the following two dimensional nonlinear partial difference systems t 1 2 x mn b mn g y mn 0 t 1 2 y mn a mn f x mn 0 where m n n0 0 1 2 t 1 2 1 2 i t 1 2 1 2 i 1ymn ym 1 n ymn 2ymn ym n 1 ymn iymn ymn 1ymn ym 1 n ymn 2ymn ym n 1 ymn amn and bmn are real sequences m n n0 and f g r r are continuous with uf u 0 and ug u 0 for all u 0 a solution xmn ymn of the system is oscillatory if both components are oscillatory some sufficient conditions for all solutions of this system to be oscillatory are derived

symplectic topology and hamiltonian dynamics on etudie des applications symplectiques non lineaires capacites symplectiques construction d une capacite symplectique problemes de plongement problemes de rigidite

further results on stabilizability of discrete time nonlinearly parameterized systems with scalar parameters this note advances the work simultaneous identification and stabilization of nonlinearly parameterized discrete time systems by nonlinear least squares algorithm by li and chen by allowing the sensitivity functions of discrete time nonlinearly parameterized systems with scalar parameters admitting arbitrarily many zeros for large outputs stabilizability theorems and impossible theorems have been provided both for time invariant parameter and time varying parameter cases a practical estimation algorithm is also proposed to facilitate the implementation in computations

oscillation of partial difference equations with variable coefficients for the partial difference equations am 1 n am n 1 am n pm nam k n 1 0 and am 1 n am n 1 am n i 1upi m n fi am ki n li 0 we shall obtain sufficient conditions for the oscillation of all solutions

nonexistence of positive solutions of a class of nonlinear delay partial difference equations sufficient conditions are derived for the nonexistence of positive solutions of a class of positive nonlinear delay partial difference equations results are also obtained for the nonexistence of positive solutions of the dual equation

oscillation theorems for second order nonlinear partial difference equations 479 abstract the oscillation of the second order nonlinear partial difference equation t 1 2 c mn 1 y mn i 1 s a i m n f i y m 1 n 1 y mn 0 is investigated some sufficient conditions for the oscillation of all solutions of the above equation are obtained

brief adaptive estimation of discrete time systems with nonlinear parameterization this paper concerns adaptive estimation of dynamic systems which are nonlinearly parameterized a majority of adaptive algorithms employ a gradient approach to determine the direction of adjustment which ensures stable estimation when parameters occur linearly these algorithms however do not suffice for estimation in systems with nonlinear parameterization we introduce in this paper a new algorithm for such systems and show that it leads to globally stable estimation by employing a different regression vector and selecting a suitable step size both concave convex parameterizations as well as general nonlinear parameterizations are considered stable estimation in the presence of both nonlinear parameters and linear parameters which may appear multiplicatively is established for the case of concave convex parameterizations parameter convergence is shown to result under certain conditions of persistent excitation

oscillation criteria for nonlinear partial difference equations with delays abstract we offer sufficient conditions for the oscillation of all solutions of the partial difference equations y m 1 n m n y m n 1 m n y m n p m n y m k n l q m n y m k n l and y m 1 n m n y m n 1 m n y m n i 1 p i m n y m k i n l i i 1 q i m n y m k i n l i several examples which dwell upon the importance of our results are also included

parameter estimation and compensation in systems with nonlinearly parameterized perturbations we consider a class of systems influenced by perturbations that are nonlinearly parameterized by unknown constant parameters and develop a method for estimating the unknown parameters the method applies to systems where the states are available for measurement and perturbations with the property that an exponentially stable estimate of the unknown parameters can be obtained if the whole perturbation is known the main contribution is to introduce a conceptually simple modular design that gives freedom to the designer in accomplishing the main task which is to construct an update law to asymptotically invert a nonlinear equation compensation for the perturbations in the system equations is considered for a class of systems with uniformly globally bounded solutions for which the origin is uniformly globally asymptotically stable when no perturbations are present we also consider the case when the parameters can only be estimated when the controlled state is bounded away from the origin and show that we may still be able to achieve convergence of the controlled state we illustrate the method through examples and apply it to the problem of downhole pressure estimation during oil well drilling

oscillation for nonlinear delay partial difference equations with positive and negative coefficients abstract we construct an important transform to obtain sufficient conditions for the oscillation of all solutions of the delay partial difference equations with positive and negative coefficients of the form m n a m n a m u n v a m 1 n a m n 1 a mn pa m k n l qa m k n l 0 and mn m n a m n a m u n v a m 1 n a m n 1 a mn p mn a m k n l q mn a m k n l 0 where m n 0 1 and k k l l are nonnegative integers p q 0 and u v are positive integers the coefficients mn qmn and pmn are assumed to be positive

the stability of certain partial difference equations abstract this paper is concerned with the linear delay partial difference equation where and are positive integers a i j b i j p i j are real sequences defined on i j sufficient conditions for this equation to be stable are derived stability of certain nonlinear partial difference equations is studied also

convergence and logarithm laws of self tuning regulators abstract this paper starts with a survey of some recent results on least squares ls and ls based self tuning regulators str several long standing problems concerning the basic properties of ls based str such as stability optimality consistency and the best convergence rate are solved within a unified framework some previously related results are also subsumed and extended various new techniques for analysing ls based adaptive tracking systems are presented which may also be useful for analysing other adaptive control problems

on critical stability of discrete time adaptive nonlinear control in this paper we examine the global stability and instability problems for a class of discrete time adaptive nonlinear stochastic control the systems to be controlled may exhibit chaotic behavior and are assumed to be linear in unknown parameters but nonlinear in output dynamics which are characterized by a nonlinear function say f x it is found and proved that in the scalar parameter case there is a critical stability phenomenon for least squares ls based adaptive control systems to be specific let the growth rate of f x be f x o spl par x spl par sup 6 with b spl ges 0 then it is found that b 4 is a critical value for global stability i e the closed loop adaptive system is globally stable if b 4 and is unstable in general if b spl ges 4 as a consequence we find an interesting phenomenon that the linear case does not have for some ls based certainty equivalence adaptive controls even if the ls parameter estimates are strongly consistent the closed loop systems may still be unstable this paper also indicates that adaptive nonlinear stochastic control that is designed based on e g taylor expansion or weierstrass approximation for nonlinear models may not be feasible in general

on the oscillation of two partial difference equations abstract this paper is concerned with two partial difference equations of the form a m 1 n a m n 1 a m n p m n a m k n l 0 and a m 1 n a m n 1 a m n i 1 u p i m n f i a m k i n l i 0 respectively we obtain sufficient conditions for the oscillation of all solutions of these equations

oscillation of certain partial difference equations in this paper we consider a class of nonlinear delay partial difference equations and a class of linear delay partial difference equations with variable coefficients which may change sign we obtain oscillation criteria for these equations there are no results for the oscillation of these equations up to now

a combined multiple model adaptive control scheme and its application to nonlinear systems with nonlinear parameterization a combined multiple model adaptive control cmmac scheme which is a proper combination of the estimator based mmac scheme and the unfalsified mmac scheme has been proposed with the aim of taking advantage of the strength of each scheme while avoiding their weaknesses the major novelty of the cmmac scheme lies in the fact that it monitors not only the adequacy of candidate models in terms of their estimation performances but also the performance of the active candidate controller as an application of the cmmac scheme and one example of such new multiple model adaptive controllers a cmmac based controller has been designed for a class of nonlinear systems with nonlinear parameterization under some sufficient conditions a strong finite time switching result which provides a characterization on the maximum number of switching and the closed loop stability have been established a constructive design based on back stepping is provided for the adaptive control problem of a special class of nonlinearly parameterized systems which can satisfy all the sufficient conditions to ensure closed loop stability

nonexistence of unbounded nonoscillatory solutions of partial difference equations abstract we develop criteria for the nonexistence of eventually positive negative and nondecreasing nonincreasing solutions of the partial difference equation m n y m n p m n y m k n l q m n y m k n l and m n y m n i 1 p i m n y m k i n l i i 1 q i m n y m k i n l i several examples which dwell upon the importance of our results are also included

simultaneous identification and stabilization of nonlinearly parameterized discrete time systems by nonlinear least squares algorithm this paper addresses the challenging problem of designing an adaptive feedback strategy for simultaneous identification and stabilization for a class of nonlinearly parameterized uncertain systems in discrete time the nonlinear least squares nls algorithm is applied to estimate the unknown parameters and it turns out to be the standard least squares ls algorithm whenever the model is linearly parameterized based on this algorithm both the strong consistency of the estimator and the global stability of the system are achieved with the output feedback design for the scalar parameter case

adaptive control of nonlinearly parameterized systems the smooth feedback case studies global adaptive control of nonlinearly parameterized systems with uncontrollable linearization using a parameter separation technique and the tool of adding a power integrator we develop a feedback domination design approach for the explicit construction of a smooth adaptive controller that solves the problem of global state regulation in contrast to the existing results in the literature a key feature of our adaptive regulator is its minimum order property namely no matter how big the number of unknown parameters is the order of the dynamic compensator is identical to one and is therefore minimal as a consequence global state regulation of feedback linearizable systems with nonlinear parameterization is achieved by one dimensional adaptive controllers without imposing any extra e g convex concave conditions on the unknown parameters

hofer zehnder symplectic capacity for two dimensional manifolds in this paper we show that the hofer zehnder symplectic capacity of a two dimensional manifold is same as the area of the manifold using this fact we also get a result on the symplectic capacity of the cotangent bundle of the torus with its canonical symplectic form

oscillation criteria of a class of partial difference equations with delays this paper is concerned with the linear delay partial difference equation aa m 1 n 1 ba m 1 n ca n m n l da m n p m na m s n t 0 where s and t are two nonnegative integers a b c and d are positive constants and p i j i j e n 0 is a double real sequence sufficient conditions for this equation to be oscillatory are derived

oscillations of two dimensional nonlinear partial difference systems abstract this paper studies the following nonlinear two dimensional partial difference system 1 x mn b mn g y mn 0 t 1 2 y mn a mn f x mn 0 where m n n i i i 1 i is a nonnegative integer t 1 2 1 2 i 1 y mn y m 1 n y mn 2 y mn y m n 1 y mn i mn y mn y mn a mn and b mn are real sequences m n n 0 and f g r r are continuous with of uf u 0 and ug u 0 for all u 0 a solution x mn y mn of this system is oscillatory if both components are oscillatory some sufficient conditions are derived for all solutions of this system to be oscillatory

fundamental limitations of discrete time adaptive nonlinear control a particular polynomial is introduced which can be used to determine under what conditions a typical class of discrete time nonlinear systems with uncertainties in both parameters and noises is not stabilizable by feedback thus demonstrating the fundamental limitations of discrete time adaptive nonlinear control as a consequence it is shown that for nonlinear systems with unknown parameters and noises the systems may indeed be nonstabilizable in general whenever the usual linear growth condition is relaxed and the number of unknown parameters is large even though the corresponding noise free systems are globally stabilizable

oscillatory behavior of delay partial difference equations with positive and negative coefficients abstract we construct an important transform to obtain sufficient conditions for the oscillation of all solutions of delay partial difference equations with positive and negative coefficients of the form a m 1 n a m n 1 a mn p mn a m k 1 q mn a m k n l 0 where m n 0 1 and k k l l are nonnegative integers p q 0 the coefficients q mn and p mn are sequences of nonnegative real numbers