on the structure of h sup infinity control systems and related extensions an existence condition of a h sup infinity controller which achieves a prescribed norm bound of the closed loop transfer function is derived in the frequency domain based on a generalization of the notion of j lossless systems this condition is regarded as a frequency domain representation of the well known existence condition in the state space represented in terms of the two algebraic riccati equations a notion of j orthogonal complement which is introduced as a generalization of the usual orthogonal complement play an important role in clarifying the fundamental frequency domain structure of the model matching problem and simplifying the computation of controllers the results are extended to the nonstandard case where the direct feedthrough from the input to the error or from the exogenous signal to the output is no longer of full rank it is shown that the proper controller achieving the prescribed norm bound exists even in this case in nonstandard cases the controller order can be smaller than the plant order

robust l2 gain control for nonlinear systems with projection dynamics and input constraints an example from traffic control we formulate the l 2 gain control problem for a general nonlinear state space system with projection dynamics in the state evolution and hard constraints on the set of admissible inputs we develop specific results for an example motivated by a traffic signal control problem a state feedback control with the desired properties is found in terms of the solution of an associated hamilton jacobi isaacs equation the storage function or value function of the associated game and the critical point of the associated hamiltonian function discontinuities in the resulting control as a function of the state and due to the boundary projection in the system dynamics lead to hybrid features of the closed loop system specifically jumps of the system description between two or more continuous time models trajectories for the closed loop dynamics must be interpreted as a differential set inclusion in the sense of filippov construction of the storage function is via a generalized stable invariant manifold for the flow of a discontinuous hamiltonian vector field which again must be interpreted in the sense of filippov for the traffic control model example the storage function is constructed explicitly the control resulting from this analysis for the traffic control example is a mathematically idealized averaged control which is not immediately implementable implementation issues for traffic problems will be discussed elsewhere

h controller synthesis by j lossless coprime factorization this paper develops a coprime factorization approach to the synthesis of internally stabilizing controllers for a given system such that the mathcal h infty norm of the closed loop is strictly less than a given bound by the use of coprime factorizations it is shown that the mathcal h infty control problem is fundamentally related to the so called analytic systems considered by helton et al regional conference series in mathematics 68 1987 such problems admit a solution if and only if a certain j lossless factorization exists interpreted in the mathcal h infty control context this means that for a controller of the requisite type to exist the plant must admit a certain j lossless coprime factorization the full mathcal h infty synthesis problem requires that two nested j lossless factorizations exist the results are independent of whether discrete time or continuous time systems are being considered it is then shown that j lossless factorization is equivalent to the existen

a family of nonlinear h sup spl infin output feedback controllers state space formulas are derived for a family of controllers solving the nonlinear h sup spl infin output feedback control problem the formulas given are expressed in terms of the solutions to two hamilton jacobi inequalities in n independent variables these controllers are obtained by interconnecting the central controller with an asymptotically stable free system having l sup 2 gain spl les spl gamma all proofs given are simple and clear and provide deeper insight in the synthesis of the corresponding linear h sup spl infin controllers

on linearization technique in robust nonlinear h control a direct approach of linearization techniques for nonlinear h control is proposed the approach allows to treat both nonsingular and singular as well as robust h control problems of the most general forms without any smoothness assumption

goodness of fit and related inference processes for quantile regression abstract we introduce a goodness of fit process for quantile regression analogous to the conventional r2 statistic of least squares regression several related inference processes designed to test composite hypotheses about the combined effect of several covariates over an entire range of conditional quantile functions are also formulated the asymptotic behavior of the inference processes is shown to be closely related to earlier p sample goodness of fit theory involving bessel processes the approach is illustrated with some hypothetical examples an application to recent empirical models of international economic growth and some monte carlo evidence

j inner outer factorization j spectral factorization and robust control for nonlinear systems the problem of expressing a given nonlinear state space system as the cascade connection of a lossless system and a stable minimum phase system inner outer factorization is solved for the case of a stable system having state space equations affine in the inputs the solution is given in terms of the stabilizing solution of a certain hamilton jacobi equation the stable minimum phase factor is obtained as the solution of an associated nonlinear spectral factorization problem as an application one can arrive at the solution of the nonlinear h sub spl infin control problem for the disturbance feedforward case

a necessary condition for nonlinear h control via measurement feedback abstract in a series of recent papers it was shown that the solution of the problem of disturbance attenuation for nonlinear system is related to the existence of solutions of a pair of hamilton jacobi inequalities in n independent variables associated with state feedback and output injection design the purpose of the present paper is to discuss the necessity of the existence of solutions of the hamilton jacobi inequality which determines the output injection gain

judgment post stratification in finite mixture modeling an example in estimating the prevalence of osteoporosis judgment post stratification is used to supplement observations taken from finite mixture models with additional easy to obtain rank information and incorporate it in the estimation of model parameters to do this sampled units are post stratified on ranks by randomly selecting comparison sets for each unit from the underlying population and assigning ranks to them using available auxiliary information or judgment ranking this results in a set of independent order statistics from the underlying model where the number of units in each rank class is random we consider cases where one or more rankers with different ranking abilities are used to provide judgment ranks the judgment ranks are then combined to produce a strength of agreement measure for each observation this strength measure is implemented in the maximum likelihood estimation of model parameters via a suitable expectation maximization algorithm simulation studies are conducted to evaluate the performance of the estimators with or without the extra rank information results are applied to bone mineral density data from the third national health and nutrition examination survey to estimate the prevalence of osteoporosis in adult women aged 50 and over

h sup infinity control for nonlinear systems with output feedback the basic question of nonlinear h sup infinity control theory is to decide for a given two port system when feedback that makes the full system dissipative and internally stable exists this problem can also be viewed as a question about circuits and after translation also has a game theoretic statement several necessary conditions for solutions to exist are presented and sufficient conditions for a certain construction to lead to a solution are given

adaptive controller design for tracking and disturbance attenuation in parametric strict feedback nonlinear systems the authors develop a systematic procedure for obtaining robust adaptive controllers that achieve asymptotic tracking and disturbance attenuation for a class of nonlinear systems which are described in the parametric strict feedback form and are subject to additional exogenous disturbance inputs their approach to adaptive control is performance based where the objective for the controller design is not only to find an adaptive controller but also to construct an appropriate cost functional compatible with desired asymptotic tracking and disturbance attenuation specifications with respect to which the adaptive controller is worst case optimal three main issues of the paper are the backstepping methodology worst case identification schemes and singular perturbations analysis closed form expressions have been obtained for an adaptive controller and the corresponding value function a numerical example involving a third order system is given

mixed h 2 h control via state feedback for nonlinear systems this paper studies a mixed h 2 h control problem with internal stability by means of memoryless state feedback for smooth nonlinear control systems the problem consists of combining the performance requirements of quadratic optimal controllers with the robustness properties of h controllers it is shown that under appropriate assumptions the problem is solvable if a pair of cross coupled hamilton jacobi isaacs equations allows smooth solutions our approach to the mixed h 2 h nonlinear control problem is drawn from the concepts of non zero sum differential game lasalle s invariance principle and completion of squares analogous results are also developed for discrete time nonlinear systems by using the taylor expansion argument finally all the results obtained in affine systems are generalized to non affine nonlinear systems

estimating a distribution function based on nomination sampling abstract nomination sampling is a sampling process in which every observation is the maximum of a random sample from some population assuming that all samples are taken from a single underlying distribution f data may be viewed as consisting of pairs xi ki where ki is the size of the ith sample and given ki ki xi is distributed according to f ki willemain 1980 who discussed nomination sampling in the context of health care delivery proposed an estimator for the median of f under the assumption that ki n a fixed integer in this article the assumption of a fixed sample size n from each population is relaxed with k taken as random the problem of nonparametric estimation of the distribution function f is considered the nonparametric maximum likelihood estimator of f is derived its consistency is demonstrated and its asymptotic behavior as a stochastic process is identified conditions are given under which these asymptotic results hold for nonrandom k a by product of this developme

a hamilton jacobi inequality approach to the strict h control problem of nonlinear systems abstract a hamilton jacobi strict inequality approach is developed for the strict h8 control problem of nonlinear systems first a characterization of the strict bounded real condition of nonlinear systems is given by the hamilton jacobi strict inequality next based on the above result some necessary and or sufficient conditions are given for the solvability of the strict h8 control problem via state and output feedback in the case of asymptotic stability

h sub spl infin control for asymptotically stable nonlinear systems this paper deals with the problem of h sub spl infin control for a class of nonlinear systems the system under consideration is assumed to be globally asymptotically stable with a known lyapunov function based on this lyapunov function and using the notion of dissipativeness a state feedback controller is designed which renders the closed loop system globally asymptotically stable with a prescribed bound on the l sub 2 gain from the disturbance input to the controlled output the proposed controller design method is based on the explicit construction of a lyapunov function for the closed loop system which represents a significant advantage over existing methods

robust dissipative control for linear systems with dissipative uncertainty and nonlinear perturbation this paper focuses on the problem of dissipative control for linear systems which are subjected to dissipative uncertainty and matched nonlinear perturbation specifically quadratic dissipative uncertainty is considered which contains norm bounded uncertainty positive real uncertainty and uncertainty satisfying integral quadratic constraints iqcs as special cases we develop a linear matrix inequality lmi approach for designing a robust nonlinear state feedback controller such that the closed loop system is quadratic dissipative for all admissible uncertainties furthermore under some condition on the dissipative uncertainty we show that the controller also guarantees the asymptotic stability of the closed loop system as special cases robust h control and robust passive control problems for systems with nonlinear perturbation and norm bounded uncertainty respectively generalized positive real uncertainty are solved using the lmi approach

bayesian analysis of a tobit quantile regression model this paper develops a bayesian framework for tobit quantile regression our approach is organized around a likelihood function that is based on the asymmetric laplace distribution a choice that turns out to be natural in this context we discuss families of prior distributions on the quantile regression vector that lead to proper posterior distributions with finite moments we show how the posterior distribution can be sampled and summarized by markov chain monte carlo methods a method for comparing alternative quantile regression models is also developed and illustrated the techniques are illustrated with both simulated and real data in particular in an empirical comparison our approach out performed two other common classical estimators

characterization of some gain conditions via the hamilton jacobi inequality abstract this paper gives a characterization of three gain conditions i e l 2 gain l 2 gain subject to an l 2 gain constraint and the hankel gain of nonlinear systems via the hamilton jacobi inequalities it is shown that the obtained results for the l 2 gain and the hankel gain are analog to that derived for the l 2 gain so far

h sub spl infin fuzzy output feedback control design for nonlinear systems an lmi approach addresses the problem of stabilizing a class of nonlinear systems by using an h sub spl infin fuzzy output feedback controller first a class of nonlinear systems is approximated by a takagi sugeno ts fuzzy model then based on a well known lyapunov functional approach we develop a technique for designing an h sub spl infin fuzzy output feedback control law which guarantees the l sub 2 gain from an exogenous input to a regulated output is less or equal to a prescribed value a design algorithm for constructing an h sub spl infin fuzzy output feedback controller is given in contrast to the existing results the premise variables of the h sub spl infin fuzzy output feedback controller are not necessarily to be the same as the premise variables of the ts fuzzy model of the plant a numerical simulation example is presented to illustrate the theory development

continuous state feedback guaranteeing uniform ultimate boundedness for uncertain dynamic systems we consider a dynamic system containing uncertain elements only the set of possible values of these uncertainties is known based on this information a class of state feedback controls is proposed in order to guarantee uniform ultimate boundedness of every system response within an arbitrarily small neighborhood of the zero state these feedback controls are continuous functions of the state

non linear systems stabilization and coprimeness a theory of coprimeness is developed for non linear systems with the intention of constructing analytic tools for the solution of the problem of stabilizing a non linear system through the application of additive non linear feedback the qualitative features of the resulting theory are strikingly similar to the situation in the linear case

stabilisation of nonlinear systems by discontinuous dynamic state feedback in this paper a dynamic state feedback that stabilizes general nonlinear affine in the control systems is proposed it is deduced from the solution of an hamilton jacobi like equality with two boundary conditions the asymptotic stability of the closed loop system is proved and some examples are given an interesting feature of this method is that the so obtained feedback takes the form of a generalised sliding mode control in the sense that it is a dynamic feedback on one half part of the space and a static feedback on the other half with eventually a discontinuity on the surface dividing the space

disturbance attenuation and h sub infinity control via measurement feedback in nonlinear systems a solution to the problem of disturbance attenuation via measurement feedback with internal stability is presented for an affine nonlinear system it is shown that the concept of disturbance attenuation in the sense of truncated l sub 2 norms can be given an interpretation in terms of the response to periodic inputs in the sense of rms amplitude even in the nonlinear setup in the case of state feedback a family of controllers is also provided the proofs of all these results are simple and provide deeper insight even in the analysis of the corresponding linear control problem

an inequality governing nonlinear h control abstract this note gives necessary and sufficient conditions for solving a reasonable version of the nonlinear h control problem the most objectionable hypothesis is elegant and holds in the linear case but every possibly may not be forced for nonlinear systems what we discover in distinction to isidori and astolfi 1992 and ball et al 1993 is that the key formula is not a nonlinear riccati partial differential inequality but a much more complicated inequality mixing partial derivatives and an approximation theoretic construction called the best approximation operator this chebeshev riccati inequality when specialized to the linear case gives the famous solution to the h control problem found in doyle et al 1989 while complicated the chebeshev riccati inequality is modulo a considerable number of hypotheses behind it a solution to the nonlinear h control problem it should serve as a rational basis for discovering new formulas and compromises we follow the conventions of ball et al 1993 and this note adds directly to that paper

disturbance attenuation via state feedback for systems with a saturation nonlinearity in the control channel we study the problem of disturbance attenuation via state feedback for asymptotically stable systems with a saturation nonlinearity in the control channel the disturbance is assumed to be bounded with the bound known this amounts to adding a saturation nonlinearity in the disturbance channel a sufficient condition is derived in terms of algebraic matrix inequalities which are much simpler to solve than the general hamilton jacobi isaacs partial differential inequality a suboptimal control law is given based on the solution to the riccati inequalities the computational complexity of solving the optimal controller is similar to that of liner h controller design

l sub 2 gain analysis of nonlinear systems and nonlinear state feedback h sub infinity control previously obtained results on l2 gain analysis of smooth nonlinear systems are unified and extended using an approach based on hamilton jacobi equations and inequalities and their relation to invariant manifolds of an associated hamiltonian vector field on the basis of these results a nonlinear analog is obtained of the simplest part of a state space approach to linear h sub infinity control namely the state feedback h sub infinity optimal control problem furthermore the relation with h sub infinity control of the linearized system is dealt with

robust nonlinear h filtering this paper investigates the robust nonlinear h filtering problem for nonlinear systems with uncertainties which are described by integral functional constraints the objective is to design a dynamic filter such that the l 2 gain from an exogenous input to an estimation error is minimized or guaranteed to be less or equal to a prescribed value for all admissable uncertainties we establish the interconnection between the robust nonlinear h filtering problem and the nonlinear h filtering problem for known systems i e systems without uncertainties using the existing nonlinear h filtering results for known systems we solve the robust nonlinear h filtering problem in terms of hamilton jacobi inequalities

a j spectral factorization approach to h control it is shown that necessary and sufficient conditions for the existence of sub optimal solutions to the model matching problem associated with h control are that two coupled j spectral factorizations exist the second j spectral factor provides a parameterization of all solutions to the model matching problem the existence of the j spectral factors is then shown to be equivalent to the existence of stabilizing non negative definite solutions to two algebraic riccati equations allowing a state space formula for a linear fractional representation of all controllers to be given

nonlinear h control and estimation of optimal h gain abstract the structure of nonlinear h controller and the estimation of optimal h gain are investigated in this paper the essential problem boils down to the existence of semipositive solution to the hamilton jacobi isaacs inequality further the solvability of this first order fully nonlinear differential inequality is discussed we look for one kind of special semipositive radial solution to the hamilton jacobi isaacs inequality an explicit estimation of optimal h gain and explicit formulas of semipositive radial solutions to the hamilton jacobi isaacs inequality are obtained the results are quite simple and intuitive they even shed a new insight on the linear h theory

nonlinear h almost disturbance decoupling the l2 gain almost disturbance decoupling problem for siso nonlinear systems is formulated sufficient conditions are identified for the existence of a parametrized state feedback controller such that the l2 gain from disturbances to output can be made arbitrarily small by increasing its gain the controller is explicity constructed using a lyapunov based recursive scheme sufficient conditions for the solvability of the h almost disturbance decoupling problem and the explicit construction of teh controller are given for a more restrictive class of nonlinear systems

weighted optimization theory for nonlinear systems in this paper the solution of a nonlinear version of the weighted sensitivity h infty optimization problem is discussed it is shown that the natural object to be considered in this context is a certain sensitivity operator which will be optimized locally in a given energy ball see 5 for the details in the linear case the authors are reduced again to the classical sensitivity minimization technique of zames 21 the methods were very strongly influenced by the complex analytic power series ideas of 3 4 5 see also the recent results of ball and helton 6 for another approach to this subject

criticality condition of the fully anisotropic ising model with next nearest neighbour interaction abstract we derive an analytical expression for the criticality condition of the fully anisotropic ising model with next nearest neighbour interaction for that behalf a recently published method h j w zandvliet eur phys lett 73 2006 747 to calculate the free energy of a boundary between two areas of opposite magnetisation is generalised to systems without reflection symmetry with respect to the boundary line for the anisotropic triangular model and related special cases without crossing bonds the method provides the exact criticality conditions in polynomial form which is shown to be a factor of the exactly known criticality condition the other factor is related to the first one by a reciprocal transformation for systems with crossing bonds the method is not exact but it may be useful as a closed form approximation in a wide parameter range

quantile regression methods for reference growth charts estimation of reference growth curves for children s height and weight has traditionally relied on normal theory to construct families of quantile curves based on samples from the reference population age specific parametric transformation has been used to significantly broaden the applicability of these normal theory methods non parametric quantile regression methods offer a complementary strategy for estimating conditional quantile functions we compare estimated reference curves for height using the penalized likelihood approach of cole and green statistics in medicine 1992 11 1305 1319 with quantile regression curves based on data used for modern finnish reference charts an advantage of the quantile regression approach is that it is relatively easy to incorporate prior growth and other covariates into the analysis of longitudinal growth data quantile specific autoregressive models for unequally spaced measurements are introduced and their application to diagnostic screening is illustrated copyright 2005 john wiley sons ltd

inner outer factorization of nonlinear operators abstract a fundamental result in the theory of hardy spaces of analytic matrix and operator valued functions on the unit disk is inner outer factorization for the case of rational matrix functions explicit formulas for the inner and outer factors have recently been obtained in these formulas the functions are presented in terms of a collection of finite matrices as the transfer function of a linear system the key ingredient in the construction is the solution of a linear matrix equation called a stein equation in this paper we obtain extensions of these results to the setting of input output maps of nonlinear discrete time systems a particaular computable class of examples is presented for illustration

spl hscr sub spl infin control of nonlinear systems a convex characterization the nonlinear spl hscr sub spl infin control problem is considered with an emphasis on developing machinery with promising computational properties the solutions to spl hscr sub spl infin control problems for a class of nonlinear systems are characterized in terms of nonlinear matrix inequalities which result in convex problems the computational implications for the characterization are discussed

a j spectral factorization approach to control necessary and sufficient conditions for the existence of suboptimal solutions to the standard model matching problem associated with mathcal h infty control j control are derived using j spectral factorization theory the existence of solutions to the model matching problem is shown to be equivalent to the existence of solutions to two coupled j spectral factorization problems with the second factor providing a parametrization of all solutions to the model matching problem the existence of the j spectral factors is then shown to be equivalent to the existence of nonnegative definite stabilizing solutions to two indefinite algebraic riccati equations allowing a state space formula for a linear fractional representation of all controllers to be given a virtue of the approach is that a very general class of problems may be tackled within a conceptually simple framework and no additional auxiliary riccati equations are required

spl hscr sub spl infin control of nonlinear systems via output feedback controller parameterization the standard state space solutions to the spl hscr sub spl infin control problem for linear time invariant systems are generalized to nonlinear time invariant systems a class of local nonlinear output feedback spl hscr sub spl infin controllers are parameterized as nonlinear fractional transformations on contractive stable nonlinear parameters as in the linear case the spl hscr sub spl infin control problem is solved by its reduction to state feedback and output estimation problems together with a separation argument sufficient conditions for spl hscr sub spl infin control problem to be locally solved are also derived with this machinery

critical binder cumulant in two dimensional anisotropic ising models the binder cumulant at the phase transitions of ising models on square lattices with various ferromagnetic nearest and next nearest neighbour couplings is determined using mainly monte carlo techniques we discuss the possibility of relating the value of the critical cumulant in the isotropic nearest neighbour and in the anisotropic cases to each other by means of a scale transformation in rectangular geometry to pinpoint universal and nonuniversal features

h control of nonlinear time varying systems with finite time horizon the finite time horizon h control problems for nonlinear time varying systems are considered where the initial state is unknown they are solved by using both static state feedback and dynamic output feedback controllers a class of nonlinear h controllers is parameterized as nonlinear fractional transformation on contractive nonlinear parameters the solvability for nonlinear finite time horizon h control problem requires suitable solutions to some hamilton jacobi inequalities equations

backstepping design with local optimality matching in nonlinear h sup spl infin optimal control design for strict feedback nonlinear systems our objective is to construct globally stabilizing control laws to match the optimal control law up to any desired order and to be inverse optimal with respect to some computable cost functional our recursive construction of a cost functional and the corresponding solution to the hamilton jacobi isaacs equation employs a new concept of nonlinear cholesky factorization when the value function for the system has a nonlinear cholesky factorization we show that the backstepping design procedure can be tuned to yield the optimal control law

on a state space approach to nonlinear h control we study the standard h optimal control problem using state feedback for smooth nonlinear control systems the main theorem obtained roughly states that the l2 induced norm from disturbances to inputs and outputs can be made smaller than a constant 0 if the corresponding h norm for the system linearized at the equilibrium can be made smaller than by linear state feedback necessary and sufficient conditions for the latter problem are by now well known e g from the state space approach to linear h optimal control our approach to the nonlinear h optimal control problem generalizes the state space approach to the linear h problem by replacing the hamiltonian matrix and corresponding riccati equation as used in the linear context by a hamiltonian vector field together with a hamiltonian jacobi equation corresponding to its stable invariant manifold

nonlinear h method for volterra systems nonlinear systems with convergent volterra series representations are considered new definitions of stability and stabilizability and the h norm for nonlinear systems will be presented via the laplace transform of the corresponding volterra kernel second order and bilinear systems are used as examples to deal with the stability in detail in particular the h norm for some bilinear systems and the boundary of the h norm for nonlinear separable systems are given explicitly finally the stabilizability of the second order system via dynamic output feedback is analysed

analytical approximation methods for the stabilizing solution of the hamilton jacobi equation in this paper two methods for approximating the stabilizing solution of the hamilton jacobi equation are proposed using symplectic geometry and a hamiltonian perturbation technique as well as stable manifold theory the first method uses the fact that the hamiltonian lifted system of an integrable system is also integrable and regards the corresponding hamiltonian system of the hamilton jacobi equation as an integrable hamiltonian system with a perturbation caused by control the second method directly approximates the stable flow of the hamiltonian systems using a modification of stable manifold theory both methods provide analytical approximations of the stable lagrangian submanifold from which the stabilizing solution is derived two examples illustrate the effectiveness of the methods

fuzzy observer based fuzzy control design for nonlinear systems with persistent bounded disturbances to date nonlinear l gain control problems have not been solved by the conventional control methods for the nonlinear dynamic systems with persistent bounded disturbances this study introduces a fuzzy control design to deal with the nonlinear l gain output feedback control problem first the takagi and sugeno t s fuzzy model is employed to approximate the nonlinear dynamic system next based on the fuzzy model a fuzzy observer based fuzzy controller is developed to minimize the upper bound of l gain of the closed loop system under some linear matrix inequality lmi constraints therefore the nonlinear l gain control problem is transformed into a suboptimal control problem i e to minimize the upper bound of the l gain of the closed loop system subject to some lmi constraints in this situation the nonlinear l gain output feedback control problem can be easily solved by a lmi based optimization method the proposed methods which efficiently attenuate the peak of perturbation due to persistent bounded disturbances extend the l gain control problems from linear dynamic systems to nonlinear dynamic systems

brief solutions of nonlinear optimal and robust control problems via a mixed collocation dae s based algorithm a new algorithm for computing the solutions of nonlinear optimal and robust h control problems is proposed the algorithm is based on the use of the collocation method to transform the pde s into ode s some convergence results are given and several examples are presented

brief a transformation approach for solving the hamilton jacobi bellman equation in h2 deterministic and stochastic optimal control of affine nonlinear systems in this paper we present a transformation approach for solving the hamilton jacobi bellman equations hjbes arising in h 2 or quadratic cost control of nonlinear deterministic and stochastic systems we show that the hjbe can be solved analogously to a scalar quadratic equation and we give a parameterization of solutions to the hjbe characterizing the solution of the optimal control problem the procedure is also generalized to include nonsmooth or viscosity solutions of the s hjbe

h control stabilization and input output stability of nonlinear systems with homogeneous properties new relations are established between h control and stabilization and between input output stability and lyapunov stability of nonlinear systems with homogeneous properties these results can be applied to h controller design and stability analysis

the simple quadratic ising model with crossing bonds abstract we investigate the ferromagnetic critical line of the simple quadratic ising model with nearest neighbour and next nearest neighbour interactions by means of monte carlo renormalisation group and analytic methods a comparison of the monte carlo results with the renormalisation group trajectories yields the asymptotic behaviour of the critical line in the strong coupling limit a number of figures of spin configurations is included to illustrate the physical behaviour of the model

right coprime factorizations and stabilization for nonlinear systems the problem of constructing right coprime factorizations which are based on the graph of an input output map instead of the bezout identity of nonlinear input output maps is considered the map is assumed to arise from a state variable realization with a fixed initial state the main result is that the existence of a stabilizing state feedback implies the existence of a right coprime factorization for the map the technique is illustrated by application to nonlinear systems which are affine in the control and have a controllable linear past and nonlinear systems which are feedback linearizable a notion of input output stability that requires a bound on the magnitude of the input signals is introduced methods of constructing such bounds are developed for a locally feedback linearizable system the problem of input bounds is transferred to the equivalent linear system this leads to a technique that allows state and input constraints for a feedback linearizable system to be mapped to the equivalent linear system

state space formulae for all stabilizing controllers that satisfy and h norm bound and relations to risk sensitivity abstract given a linear system all stabilizing controllers such that a specified closed loop transfer function has h norm less than a given scalar are parametrized this characterization involves the solution to two algebraic riccati equations each with the same order as the system and further gives gives feasible controllers also with this order the relationship to the risk sensitive lqg stochastic control problem is established giving an equivalence between robust and stochastic control

a chain scattering matrix approach to the h output feedback control for state delayed systems a state space coprime factorization approach to the h controllers design for state delayed systems is developed the coprime factors that are generated by the present factorization possess the same delayed state as that of the original system this property together with the well known youla parameterization and the chain scattering matrix description provides a relatively simple method to obtain a family of the internally stabilizing h output feedback controllers a numerical example is given to demonstrate the validity and the applicability of the proposed approach

a robust control framework for option pricing a new approach is taken to the problem of option pricing in the standard framework the option pricing problem involves determining a price such that the option writer can guarantee a certain bound on the cost almost surely due to this form the problem may be reformulated in terms of deterministic differential games of the type employed in robust and h control different models yield different prices the standard model yields the black and scholes price both a deterministic model and the standard model with the ito integral replaced by the stratonovich integral yield the price corresponding to a stop loss hedging technique with these methods it can also easily be shown that for the standard model with a bounded stochastic volatility the black and scholes price corresponding to the upper bound for volatility is sufficient to hedge the option

global l 2 gain design for a class of nonlinear systems abstract it is known that the so called h control problem of a nonlinear system is locally solvable if the corresponding problem for the linearized system can be solved by linear feedback in this paper we prove that this condition suffices to solve also a global h control problem for a fairly large class of nonlinear systems if one is free to choose a state dependent weight of the control input using a two way backward and forward recursive induction argument we simultaneously construct starting from a solution of the riccati algebraic equation a global solution of the hamilton jacobi isaacs partial differential equation arising in the nonlinear h control as well as a state feedback control law that achieves global disturbance attenuation with internal stability for the nonlinear systems

nonlinear h sub spl infin control a j dissipative approach this paper applies the chain scattering approach for linear h sub spl infin control to input affine nonlinear plants with general output structure the nonlinear h sub spl infin control problem is reformulated in terms of the chain representation of a given plant the state space characterization of j dissipative j lossless systems together with two special types of coprime factorizations are used to provide a class of controllers which solve locally the h sub spl infin control problem the problems considered correspond to the general two and four block problems in the linear case the results are given in terms of two uncoupled nonlinear partial differential inequalities with a coupling condition on their solutions

brief paper robust h control of uncertain nonlinear systems this paper discusses the robust l 2 gain performance synthesis problem for a class of uncertain nonlinear systems it is shown that the hamilton jacobi equation approach to robust h performance synthesis can be extended to solve this problem based on a positive definite solution of a hamilton jacobi inequality a sufficient condition is given such that the uncertain nonlinear system is robust and stable and its l 2 gain is less than or equal to a prescribed value using this condition a state feedback law and an output feedback law which ensure robust l 2 gain performance of the closed loop system are derived finally an example is given

quantile regression with nominated samples an application to a bone mineral density study this paper studies quantile regression analysis with maxima or minima nomination sampling designs these designs are often used to obtain more representative samples from the tails of the underlying distribution using the easy to access rank information during the sampling process we propose new loss functions to incorporate the rank information of nominated samples in the estimation process also we provide an alternative approach that translates estimation problems with nominated samples to corresponding problems under simple random sampling srs strategies are given to choose proper nomination sampling designs for a given population quantile numerical studies show that quantile regression models with maxima or minima nominated samples have higher relative efficiencies compared with their counterparts under srs for analyzing the upper or lower tail quantiles of the distribution of the response variable results are then implemented on a large cohort study in the canadian province of manitoba to analyze quantiles of bone mineral density using available covariates we show that in some cases methods based on nomination sampling designs require about one tenth of the sample used in srs to estimate the lower or upper tail conditional quantiles with comparable mean squared errors this is a dramatic reduction in time and cost compared with the usual srs approach

robust h sub spl infin control for linear discrete time systems with norm bounded nonlinear uncertainties this paper studies the problem of robust control of a class of uncertain discrete time systems the class of uncertain systems is described by a state space model with linear nominal parts and norm bounded nonlinear uncertainties in the state and output equations the authors address the problem of robust h sub spl infin control in which both robust stability and a prescribed h sub spl infin performance are required to be achieved irrespective of the uncertainties it has been shown that instead of the nonlinear uncertain system one may only consider a related linear uncertain system and thus a linear static state feedback control law is designed which is in terms of a riccati inequality

simplifying the h theory via loop shifting matrix pencil and descriptor concepts the 2 riccati h controller formulae and derivations are simplified via various loop shifting transformations that are naturally expressed in terms of a degree one polynomial system matrix psm closely related to the luenberger descriptor form of a system the technique enables one without loss of generality to restrict attention to the simple case in which d 11 0 d 22 0 d t 12 0 l d 21 0 l d l 12 c1 0 and b 1 d t 21 0 matrix fraction descriptions mfds for the algebraic riccati equation solutions afford another change of variables which brings the 2 riccati h controller formulae into a cleaner more symmetric descriptor form having the important practical advantage that it eliminates the numerical difficulties that can occur in cases where one or both of the riccati solutions pi and q blow up and in cases where l qp is nearly singular numerical difficulties previously associated with verifying the existence conditions p 0 q 0 and maxlpar qp 1 are largely eliminated by e

a separation result for systems with feedback constraints in this paper we propose a certainty equivalence principle for the stabilization of nonlinear systems via measurement feedback which clarifies the connection between the solution of a couple of hamilton jacobi inequalities hjis and the design constraints imposed on the control and the estimation error fed back in the control loop by the observer itself once a solution of these hjis has been found a measurement feedback controller can be directly implemented this controller has different features with respect to classical controllers in classical control scheme s an observer consists of a copy of the system plus a term proportional to the error between the actual measurement and the estimated measurement here we allow a term which is a nonlinear function of this error this result is particularly powerful in conjunction with step by step strategies as illustrated by an application to feedforward systems 2005 elsevier b v all rights reserved

h sub spl infin tuning for task space feedback control of robot with uncertain jacobian matrix the h sub spl infin tuning problem for task space feedback control of a robot with uncertain kinematics and jacobian matrix from joint space to task space is formulated and solved h sub spl infin tuning methods are presented for two task space feedback controllers when the systems are subject to external disturbance it is shown that the conditions for the establishment of h sub spl infin tuning can be obtained in simple forms without solving the hamilton jacobi inequalities even in the presence of kinematics uncertainty

factorization and feedback stabilization for nonlinear systems we establish the equivalence of internal input out stability for two feedback configurations of a nonlinear time varying plant p for which a related plant g is assumed to have a factorization g r with both r and r 1 incrementally stable this extends a factorization principle for stabilizability previously given only for the linear time invariant case as an application of a special case we recover a version of the youla parametrization of stabilizing compensators for the nonlinear case previously presented in the literature we use degree theory to parametrize a collection of solutions of the h control problem for the case of a 1 gain stable or lossless plant in the case of a plant g having a j inner outer factorization this last result combined with the above mentioned factorization principle leads to results on the h control problem for p

brief h controller reduction for nonlinear systems sufficient conditions are proposed for the existence of reduced order fixed order controllers solving the standard nonlinear h output feedback control problem state space formulas for such reduced order h controllers are also derived in terms of the solutions of two hamilton jacobi inequalities the development uses only elementary concepts of dissipativity and differential game thus the proofs given are simple and clear

robust h sub spl infin output feedback control for nonlinear systems in this paper we present a new approach to the solution of the output feedback robust h sub spl infin control problem we employ the recently developed concept of information state for output feedback dynamic games and obtain necessary and sufficient conditions for the solution to the robust control problem expressed in terms of the information state the resulting controller is an information state feedback controller and is intrinsically infinite dimensional stability results are obtained using the theory of dissipative systems and our results are expressed in terms of dissipation inequalities

diversity of critical behavior within a universality class we study spatial anisotropy effects on the bulk and finite size critical behavior of the mathrm o n symmetric anisotropic ensuremath varphi 4 lattice model with periodic boundary conditions in a d dimensional hypercubic geometry above at and below t c the absence of two scale factor universality is discussed for the bulk order parameter correlation function the bulk scattering intensity and for several universal bulk amplitude relations the anisotropy parameters are observable by scattering experiments at t c for the confined system renormalization group theory within the minimal subtraction scheme at fixed dimension d for 2ldl4 is employed in contrast to the ensuremath epsilon 4 ensuremath d expansion the fixed d finite size approach keeps the exponential form of the order parameter distribution function unexpanded for the case of cubic symmetry and for n 1 our perturbation approach yields excellent agreement with the monte carlo mc data for the finite size amplitude of the free energy of the three dimensional ising model at t c by mon phys rev lett 54 2671 1985 the ensuremath epsilon expansion result is in less good agreement below t c a minimum of the scaling function of the excess free energy is found we predict a measurable dependence of this minimum on the anisotropy parameters the relative anisotropy effect on the free energy is predicted to be significantly larger than that on the binder cumulant our theory agrees quantitatively with the nonmonotonic dependence of the binder cumulant on the ferromagnetic next nearest neighbor nnn coupling of the two dimensional ising model found by mc simulations of selke and shchur j phys a 38 l739 2005 our theory also predicts a nonmonotonic dependence for small values of the antiferromagnetic nnn coupling and the existence of a lifshitz point at a larger value of this coupling the nonuniversal anisotropy effects in the finite size scaling regime are predicted to satisfy a kind of restricted universality the tails of the large l behavior at t ensuremath ne t c violate both finite size scaling and universality even for isotropic systems as they depend on the bare four point coupling of the ensuremath varphi 4 theory on the cutoff procedure and on subleading long range interactions

state space solutions to standard h sub 2 and h sub infinity control problems simple state space formulas are derived for all controllers solving the following standard h sub infinity problem for a given number gamma 0 find all controllers such that the h sub infinity norm of the closed loop transfer function is strictly less than gamma it is known that a controller exists if and only if the unique stabilizing solutions to two algebraic riccati equations are positive definite and the spectral radius of their product is less than gamma sup 2 under these conditions a parameterization of all controllers solving the problem is given as a linear fractional transformation lft on a contractive stable free parameter the state dimension of the coefficient matrix for the lft constructed using the two riccati solutions equals that of the plant and has a separation structure reminiscent of classical lqg i e h sub 2 theory this paper is intended to be of tutorial value so a standard h sub 2 solution is developed in parallel

normalized coprime factorizations and balancing for unstable nonlinear systems in this paper we first study the normalized right and left coprime factorizations of a nonlinear system from a state space point of view in order to do so we introduce the notion of inner and co inner nonlinear systems secondly we deal with balancing for unstable nonlinear systems for linear systems there are several ways to approach this problem and we generalize the ideas of balancing the normalized coprime factorization and of lqg balancing to the nonlinear case lqg balancing can be seen as measuring the influence of a state component on a certain future and past energy function we extend this interpretation to the nonlinear case furthermore we use the normalized coprime factorization to give another way of balancing the unstable nonlinear system we give the relation between these two methods of balancing which is similar to the relation in the linear case

nonlinear l 2 gain suboptimal control abstract a method of solving the nonlinear local l2 gain suboptimal control problem based on the chain scattering approach is proposed this problem requires the l2 gain of the closed loop to be less than one and closed loop internal stability defined in the small signal input output sense we obtained sufficient conditions for the existence of a suboptimal controller in terms of a state space description of the plant as well as a local state space parameterization of a class of controllers solving the local l2 gain suboptimal problem the design procedure is demonstrated with a numerical example 1997 elsevier science ltd

robust stabilization of nonlinear systems with pointwise norm bounded uncertainties a control lyapunov function approach the authors give a necessary and sufficient condition for globally stabilizing a nonlinear system robustly with respect to unstructured uncertainties spl phi spl tilde u x t norm bounded for each fixed x and u this condition requires one to find a smooth proper and positive definite solution v x of a suitable partial differential inequality depending only on the system data a procedure based on the knowledge of v x is outlined for constructing almost smooth robustly stabilizing controllers our approach based on lyapunov functions generalizes previous results for linear uncertain systems and establishes a precise connection between robust stabilization on one hand and h sub spl infin control sector conditions and input to state stabilization on the other

h sub spl infin control via measurement feedback for general nonlinear systems this paper shows how the problem of local disturbance attenuation via measurement feedback with internal stability can be solved for a nonlinear system of rather general structure the solution of the problem is shown to be related to the existence of solutions of a pair of hamilton jacobi inequalities in n independent variables which are associated with state feedback and respectively output injection design

nonlinear output feedback tracking with almost disturbance decoupling addresses the design of global output feedback controls for a class of uncertain nonlinear single input single output systems which are globally transformable into an observable minimum phase system whose nonlinearities depend on the output only they may be affected by unknown time varying disturbances or parameter variations entering linearly in the state equations the proposed dynamic controller is of order spl rho 1 spl rho is the relative degree of the given system and ensures that the closed loop system enjoys for any initial condition and for any smooth bounded output reference signal with bounded time derivatives up to order spl rho the following properties input to state stability with respect to disturbance inputs and almost disturbance decoupling i e the influence of disturbances both on the l sub 2 and on the l sub spl infin norm of the output tracking error is arbitrarily attenuated by increasing a positive scalar control parameter when disturbances are zero the reference signal is exponentially tracked by the output and the equilibrium point corresponding to the reference signal is globally asymptotically stable