global stabilization of high order nonlinear time delay systems by state feedback abstract we consider the problem of global stabilization by state feedback for a class of high order nonlinear systems with time delay by developing a novel dynamic gain based backstepping approach a state feedback controller independent of the time delay is explicitly constructed with the help of appropriate lyapunov krasovskii functionals the precise knowledge even the upper bound of the time delay is not required it is proved that the states of the nonlinear time delay systems can be regulated to the origin while all the closed loop signals are globally bounded finally both physical and academic examples are given to illustrate the applications of the proposed scheme

adaptive regulation of high order lower triangular systems an adding a power integrator technique abstract in this paper a new adaptive control technique called adding a power integrator is proposed for a class of linearly parametrized high order nonlinear systems that are of a lower triangular structure but neither feedback linearizable nor affine in the control input using the adaptive adding a power integrator technique as a basic design tool we show how to explicitly construct in a recursive manner a smooth adaptive controller that solves the problem of adaptive regulation with global stability the development of the adding a power integrator technique leads to a significant relaxation on the system nonlinearities such as feedback linearizability and affineness which are known to be two standard hypotheses made in the existing nonlinear adaptive control schemes

adding one power integrator a tool for global stabilization of high order lower triangular systems a new feedback design tool called adding a power integrator is introduced and used to solve the problem of global robust stabilization for a significant class of uncertain nonlinear systems that are of a lower triangular form but neither necessarily feedback linearizable fully or partially nor affine in the control input and therefore cannot be dealt with via conventional approaches sufficient conditions are presented under which a globally stabilizing smooth state feedback control law can be explicitly constructed using repeatedly the adding one power integrator technique this novel design technique permits removal of the feedback linearizability and linearity of the control input which have been two common assumptions so far in the literature of nonlinear control

robust backstepping control for a class of time delayed systems in this note the problem of robust output feedback control for a class of nonlinear time delayed systems is considered the systems considered are in strict feedback form state observer is first designed then based on the observed states the controller is designed via backstepping method both the designed observer and controller are independent of the time delays based on lyapunov stability theory we prove that the constructed controller can render the closed loop system asymptotically stable simulation results further verify the effectiveness of the proposed approach

derivatives of any order of the gaussian hypergeometric function 2f1 a b c z with respect to the parameters a b and c the derivatives to any order of the gaussian hypergeometric function 2f1 a b c z with respect to the parameters a b and c are expressed in terms of generalizations of multivariable kampe de feriet functions several properties are presented in an application to the two body coulomb scattering problem the usefulness of these derivatives is illustrated with the study of the charge dependence of pollaczek like polynomials

derivatives of any order of the hypergeometric function pfq a1 ap b1 bq z with respect to the parameters ai and bi the derivatives of any order of the general hypergeometric function pfq a1 ap b1 bq z with respect to the parameters ai or bi are expressed in compact form in terms of generalizations of multivariable kampe de feriet functions to achieve this use is made of babister s solution to non homogeneous differential equations for pfq a1 ap b1 bq z an application to hahn polynomials which are 3f2 functions is given as an illustration

optimum sample size determination in stratified case control studies with cost considerations we investigate sample size determination for cochran s test for stratified case control studies when samples of cases and controls are allocated to maximize the asymptotic efficiency of cochran s test subject to fixed total cost with cost per control varying by strata we consider two situations typical of strata matched case control studies when one samples both cases and controls and when cases are given and one samples controls in each situation we develop and study an asymptotic method for finding the sample size required for a specific power under the optimum allocation proposed by nam and fears also for the second situation we investigate an asymptotic method for determining the common ratio k in one to k strata matched case control studies without cost consideration for a given power when cases are given neither the optimum nor the standard control sample sizes appear in a closed form we present numerical methods for calculating these sample sizes and illustrate them with examples we find the reduction in total cost obtained under the optimum allocation compared to standard allocation more pronounced as the differences in stratum specific costs of sampling controls increase

a novel error compensation control for a class of high order nonlinear systems with input delay a novel tracking error compensation based adaptive neural control scheme is proposed for a class of high order nonlinear systems with completely unknown nonlinearities and input delay in the tracking errors of existing papers there exist the following difficulties first output curve always lags behind the desired trajectory second some big peak errors cause a decrease in tracking precision and third a big initial value of the modified tracking error can make the closed loop system unstable to tackle them three corresponding error compensation terms are constructed including a prediction and compensation term an auxiliary signal produced by the constructed auxiliary system and a damping term however inequality amplification caused by high order will weaken the effectiveness of the proposed error compensation scheme and the control precision will decrease under an assumption that the lower bounds of the unknown control coefficients should be exactly known to overcome aforementioned difficulties in the derivation of the first virtual control law the radial basis function neural network is used to approximate a hybrid term online constructed by unknown nonlinearities a lumped control coefficient achieved by state transformation and the dynamic of the proposed error compensation terms and desired signal meanwhile input delay is coped with a robust compensation signal constructed based on a finite integral of the past control values finally it is proven that all the closed loop signals are semiglobally uniformly ultimately bounded simulation results demonstrate the effectiveness of the proposed method

optimum allocation of samples in strata matching case control studies when cost per sample differs from stratum to stratum we investigate the allocation of samples over strata in case control studies with consideration of sampling costs we consider two situations typical of strata matched case control studies subject to a fixed total cost we derived optimum allocations that maximize the asymptotic efficiency of cochran s test that is minimize the variance of the maximum likelihood estimator of the common odds ratio when the common odds ratio is one our results show that the standard design with equal numbers of cases and controls in each stratum is inefficient when costs per control differ greatly from stratum to stratum we show that the optimum design suggested in this paper is robust for values of the odds ratio common in epidemiologic studies

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

adaptive approximation based regulation control for a class of uncertain nonlinear systems without feedback linearizability in this paper for a general class of uncertain nonlinear cascade systems including unknown dynamics which are not feedback linearizable and cannot be solved by existing approaches an innovative adaptive approximation based regulation control aarc scheme is developed within the framework of adding a power integrator api by deriving adaptive laws for output weights and prediction error compensation pertaining to single hidden layer feedforward network slfn from the lyapunov synthesis a series of slfn based approximators are explicitly constructed to exactly dominate completely unknown dynamics by the virtue of significant advancements on the api technique an adaptive api methodology is eventually established in combination with slfn based adaptive approximators and it contributes to a recursive mechanism for the aarc scheme as a consequence the output regulation error can asymptotically converge to the origin and all other signals of the closed loop system are uniformly ultimately bounded simulation studies and comprehensive comparisons with backstepping and api based approaches demonstrate that the proposed aarc scheme achieves remarkable performance and superiority in dealing with unknown dynamics

derivatives of the pochhammer and reciprocal pochhammer symbols and their use in epsilon expansions of appell and kampe de feriet functions useful expressions of the derivatives to any order of pochhammer and reciprocal pochhammer symbols with respect to their arguments are presented they are building blocks of a procedure recently suggested for obtaining the expansion of functions of the hypergeometric class related to feynman integrals the procedure is applied to some examples of such kind of functions taken from the literature

control sample size when cases are given in constant ratio stratum matched case control studies strata matched case control studies based on a given number of cases and k times as many controls are common we obtain a necessary and sufficient condition for there to exist a numerical solution for k with a desired level of a power we derive the maximum power of the cochran test which may be less than one when the number of cases is fixed we provide an approximate formula for the minimum number of cases required for a specified power there exists a numerical solution that is convergence of an iterative method for k if the number of cases given is greater than this minimum number and no such a solution otherwise we also show that the incremental gain in relative efficiency of the test with respect to k is diminished as k gets large

derivatives of horn hypergeometric functions with respect to their parameters the derivatives of eight horn hypergeometric functions four appell f1 f2 f3 and f4 and four degenerate confluent 1 2 1 and 1 with respect to their parameters are studied the first derivatives are expressed systematically as triple infinite summations or alternatively as single summations of two variable kampe de feriet functions taking advantage of previously established expressions for the derivative of the confluent or gaussian hypergeometric functions the generalization to the nth derivative of horn s functions with respect to their parameters is rather straightforward in most cases the results are expressed in terms of n 2 infinite summations following a similar procedure mixed derivatives are also treated an illustration of the usefulness of the derivatives of f1 with respect to the first and third parameters is given with the study of autoionization of atoms occurring as part of a post collisional process their evaluation setting the coulomb charge to zero provides the

sample size for case control studies using cochran s statistic sample size determination for case control studies of chronic disease are often based on the simple 2 x 2 tabular cross classification of exposure and disease thereby ignoring stratification which may be considered in the analysis one consequence of this approach is that the sample size may be inadequate to attain a specified power and size when performing a statistical analysis on j 2 x 2 tables using cochran s 1954 biometrics 10 417 451 statistic or the mantel haenszel 1959 journal of the national cancer institute 22 719 748 statistic a sample size formula is derived from cochran s statistic and it is compared with the corresponding one derived when the data are treated as unstratified and also with two other formulas proposed for stratified data analysis the formula developed yields values slightly higher than one recently proposed by munoz and rosner 1984 biometrics 40 995 1004 which assumes that both margins of each 2 x 2 table are fixed while the present study considers only the case control margin to be fixed

brief paper observer based control of a class of time delay nonlinear systems having triangular structure time delay systems constitute a special class of dynamical systems that are frequently present in many fields of engineering it has been shown in the literature that the existence of a stabilizing observer based controller is related to delay dependent conditions that are generally satisfied for a small time delay motivating works towards reducing the conservatism of the results are among the on going research topics especially when partial state measurements are imposed this paper investigates the problem of observer based stabilization of a class of time delay nonlinear systems written in triangular form first we show that a delay nonlinear observer is globally convergent under the global lipschitz condition of the system nonlinearity then it is shown that a parameterized linear feedback that uses the observer states can stabilize the system whatever the size of the delay an illustrative example is provided to approve the theoretical results

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

mathematical properties of generalized sturmian functions we study some mathematical properties of generalized sturmian functions which are solutions of a schr odinger like equation supplemented by two boundary conditions these generalized functions for any value of the energy are defined in terms of the magnitude of the potential one of the boundary conditions is imposed at the origin of the coordinate where regularity is required the second point is at large distances for negative energies boundlike conditions are imposed for positive or complex energies incoming or outgoing boundary conditions are imposed to deal with scattering problems in this case since scattering conditions are complex the sturmian functions themselves are complex since all of the functions solve a sturm liouville problem they allow us to construct a sturmian basis set which must be orthogonal and complete this is the case even when they are complex here we study some properties of generalized sturmian functions associated with the hulth en potential in particular the spatial organization of their nodes and demonstrate explicitly their orthogonality we also show that the overlap matrix elements which are generally required in scattering or bound state calculations are well defined many of these mathematical properties are expressed in terms of uncommon multivariable hypergeometric functions finally applications to the scattering of a particle by a yukawa and by a hulth en potential serve as

the continuum schrodinger coulomb and dirac coulomb sturmian functions spherical continuum sturmian functions for the schrodinger coulomb and dirac coulomb problems are constructed by solving appropriate sturm liouville systems it is proved that in the non relativistic case a spectrum of potential strengths is continuous and covers the whole real axis in the relativistic case two sturmian sets may be derived for the relativistic sturm liouville problems their eigenvalue spectra consist of the real axes with zero excluded plus circumferences in the complex plane centred at zero it is shown that as a consequence of a relationship existing between the two families of the continuum dirac coulomb sturmians each family obeys two orthogonality and two closure relations

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

sample size determination for case control studies and the comparison of stratified and unstratified analyses woolson bean and rojas 1986 biometrics 42 927 932 present a simple approximation of sample size for cochran s 1954 biometrics 10 417 451 test for detecting association between exposure and disease it is useful in the design of case control studies we derive a sample size formula for cochran s statistic with continuity correction which guarantees that the actual type i error rate of the test does not exceed the nominal level the corrected sample size is necessarily larger than the uncorrected one given by woolson et al and the relative difference between the two sample sizes is considerable allocation of equal number of cases and controls within each stratum is asymptotically optimal when the costs per case and control are the same when any effect of stratification is absent cochran s stratified test although valid is less efficient than the unstratified one except for the important case of a balanced design

derivatives of any order of the confluent hypergeometric function f11 a b z with respect to the parameter a or b the derivatives to any order of the confluent hypergeometric kummer function f f11 a b z with respect to the parameter a or b are investigated and expressed in terms of generalizations of multivariable kampe de feriet functions various properties reduction formulas recurrence relations particular cases and series and integral representations of the defined hypergeometric functions are given finally an application to the two body coulomb problem is presented the derivatives of f with respect to a are used to write the scattering wave function as a power series of the sommerfeld parameter