brief paper robust control with a terminal state constraint this paper introduces a problem of robust control with a terminal state constraint this problem involves finding an output feedback controller to steer the initial state of a given system into an ellipsoidal bounding set in a specified time the underlying system in this problem is a time varying uncertain linear system in which the uncertainty satisfies an integral quadratic constraint necessary and sufficient conditions are given for the solution to this problem in terms of a pair of parameter dependent riccati differential equations

global stabilization of nonlinear systems with a class of unmatched uncertainties abstract global and asymptotic stabilization of uncertain dynamical systems which violate the matching conditions is investigated a class of unmatched uncertainties called equivalently matched uncertainties is defined a robust controller is proposed to stabilize the uncertain system asymptotically in the large provided that the nominal system is uniformly asymptotically stable and that the unmatched uncertainties are equivalently matched the required information about uncertain dynamics in the system is merely that the uncertainties are bounded in euclidean norm by known functions of the system state

estimation of the mean function with panel count data using monotone polynomial splines we study nonparametric likelihood based estimators of the mean function of counting processes with panel count data using monotone polynomial splines the generalized rosen algorithm proposed by zhang jamshidian 2004 is used to compute the estimators we show that the proposed spline likelihood based estimators are consistent and that their rate of convergence can be faster than n 1 3 simulation studies with moderate samples show that the estimators have smaller variances and mean squared errors than their alternatives proposed by wellner zhang 2000 a real example from a bladder tumour clinical trial is used to illustrate this method

on brockett s condition for smooth stabilizability and its necessity in a context of nonsmooth feedback the necessity of brockett s condition for stabilizability of nonlinear systems by smooth feedback is shown by an argument based on properties of a degree for set valued maps to persist when the class of controls is enlarged to include discontinuous feedback

a smoothness priors state space modeling of time series with trend and seasonality abstract a smoothness priors modeling of time series with trends and seasonalities is shown an observed time series is decomposed into local polynomial trend seasonal globally stationary autoregressive and observation error components each component is characterized by an unknown variance white noise perturbed difference equation constraint the constraints or bayesian smoothness priors are expressed in state space model form trading day factors are also incorporated in the model a kalman predictor yields the likelihood for the unknown variances hyperparameters likelihoods are computed for different constraint order models in different subsets of constraint equation model classes akaike s minimum aic procedure is used to select the best model fitted to the data within and between the alternative model classes smoothing is achieved by using a fixed interval smoother algorithm examples are shown

a nonlinear partially observed differential game with a finite dimensional information state abstract in this paper we present an example of a deterministic nonlinear partially observed differential game for which the information state is finite dimensional the example is of interest because in general the information state is infinite dimensional as is typically the case in stochastic nonlinear filtering the solution is presented in terms of a hamilton jacobi isaacs equation an adjoint information state is also explicitly computed the results are illustrated in the familiar case of linear systems and a new interpretation of the coupling condition of linear h control is given

asymptotic controllability implies feedback stabilization it is shown that every asymptotically controllable system can be globally stabilized by means of some discontinuous feedback law the stabilizing strategy is based on pointwise optimization of a smoothed version of a control lyapunov function iteratively sending trajectories into smaller and smaller neighborhoods of a desired equilibrium a major technical problem and one of the contributions of the present paper concerns the precise meaning of solution when using a discontinuous controller

filtering and smoothing algorithms for state space models abstract the paper reviews and generalizes recent filtering and smoothing algorithms for observations generated by a state model in particular the paper discusses the modified kalman filter derived by ansley and kohn 1985 and kohn and ansley 1986 to deal with state space models having partially diffuse initial conditions and shows how to compute the limiting normalized likelihood of the observations for such models the paper also discusses and generalizes the new smoothing algorithm presented by kohn and ansley 1987c 1989 and extends it to state space models with partially diffuse initial conditions

semiparametric estimation methods for panel count data using monotone b splines we study semiparametric likelihood based methods for panel count data with proportional mean model e t z 0 t exp 0tz where z is a vector of covariates and 0 t is the baseline mean function we propose to estimate 0 t and 0 jointly with 0 t approximated by monotone b splines and to compute the estimators using generalized rosen algorithm proposed by jamshidian 2004 we show that the proposed spline based likelihood estimators of 0 t are consistent with a possibly better than n1 3 convergence rate if 0 t is sufficiently smooth the normality of the estimators of 0 is also established comparisons between the proposed estimators and their alternatives studied in wellner and zhang 2007 are made through simulations studies regarding their finite sample performance and computational complexity a real example from a bladder tumor clinical trial is used to illustrate the methods

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

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

on the certainty equivalence principle and the optimal control of partially observed dynamic games the purpose of this paper is to explain that while in general the certainty equivalence controller does not achieve the optimal value of a dynamic min max game with partial information the optimal controller may be determined using the recently developed information state approach examples are provided illustrating when the certainty equivalence controller is or is not optimal

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

comments on the stabilization of the angular velocity of a rigid body abstract this paper discusses the stabilizability by smooth feedback of the angular velocity of a rigid body first we show how to asymptotically stabilize the system with a single control then it is shown that a single control aligned with a principal axis cannot asymptotically stabilize the system finally we present some new results on stabilization by means of scalar feedback control

feedback minimax sensitivity and optimal robustness in this paper we look for feedbacks that minimize the sensitivity function of a linear single variable feedback system represented by its frequency responses sensitivity to disturbances and robustness under plant perturbations are measured in a weighted h infty norm in an earlier paper zames proposed an approach to feedback design involving the measurement of sensitivity by multiplicative seminorms which have certain advantages over the widely used quadratic norm in problems where there is plant uncertainty or where signal power spectra are not fixed but belong to sets the problem was studied in a general setting and some h infty examples were solved here a detailed study of the single variable case is undertaken the results are extended to unstable plants and explicit formulas for the general situation of a finite number of right half plane rhp plant zeros or poles are provided the q or approximate inverse parametrization of feedbacks that maintain closed loop stability is extended to the ease of unstable plants the h infty and wiener hopf approaches are compared

receding horizon control of nonlinear systems the receding horizon control strategy provides a relatively simple method for determining feedback control for linear or nonlinear systems the method is especially useful for the control of slow nonlinear systems such as chemical batch processes where it is possible to solve sequentially open loop fixed horizon optimal control problems online the method has been shown to yield a stable closed loop system when applied to time invariant or time varying linear systems it is shown that the method also yields a stable closed loop system when applied to nonlinear systems

efficient generalized cross validation for state space models summary for a signal plus noise model with a state space representation an efficient procedure is given for obtaining the trace of the influence matrix where the influence matrix expresses the estimated signal vector as a linear combination of the observed data this allows an 0 n evaluation of the generalized cross validation criterion function our approach is very efficient requiring the addition of only one equation to the ordinary kalman filter and extends to models with linear regressors in the observation equation important applications are to spline smoothing in regression and to variance components models for seasonal time series

stabilization of nonlinear systems in the plane abstract it is shown that every small time locally controllable system in the plane can locally be asymptotically stabilized by employing locally holder continuous feedback laws as essentially was conjectured by e sontag an explicit algorithm for the construction of such feedback laws is given

robust control of mimo nonlinear systems with mismatched uncertainty the problem of the control of multivariable systems in the presence of both modelling and disturbance uncertainties is considered the technique described is not restricted to linear systems nor to systems where the uncertainties satisfy matching conditions only bounds on the uncertainties are required as examples of the technique two practical problems are considered

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

risk sensitive control and dynamic games for partially observed discrete time nonlinear systems solves a finite horizon partially observed risk sensitive stochastic optimal control problem for discrete time nonlinear systems and obtains small noise and small risk limits the small noise limit is interpreted as a deterministic partially observed dynamic game and new insights into the optimal solution of such game problems are obtained both the risk sensitive stochastic control problem and the deterministic dynamic game problem are solved using information states dynamic programming and associated separated policies a certainty equivalence principle is also discussed the authors results have implications for the nonlinear robust stabilization problem the small risk limit is a standard partially observed risk neutral stochastic optimal control problem

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

convergence rate of sieve estimates in this paper we develop a general theory for the convergence rate of sieve estimates maximum likelihood estimates mle s and related estimates obtained by optimizing certain empirical criteria in general parameter spaces in many cases especially when the parameter space is infinite dimensional maximization over the whole parameter space is undesirable in such cases one has to perform maximization over an approximating space sieve of the original parameter space and allow the size of the approximating space to grow as the sample size increases this method is called the method of sieves in the case of the maximum likelihood estimation an mle based on a sieve is called a sieve mle we found that the convergence rate of a sieve estimate is governed by a the local expected values variances and l 2 entropy of the criterion differences and b the approximation error of the sieve a robust nonparametric regression problem a mixture problem and a nonparametric regression problem are discussed as illustrations of the theory we also found that when the underlying space is too large the estimate based on optimizing over the whole parameter space may not achieve the best possible rates of convergence whereas the sieve estimate typically does not suffer from this difficulty

robust stabilization of the angular velocity of a rigid body the problem of robust control for the angular velocity of a rigid body subject to external disturbances is addressed it is shown that if the disturbances are matched there exists a control law attenuating the effect of the disturbances whereas in the case of non matched disturbances no such a feedback law generically exists hence a new concept of disturbance attenuation is introduced and it is proved that the aforementioned problem is solvable in this weaker sense explicit expressions of the control laws solving the proposed robust stabilization problems are given

a fast algorithm for signal extraction influence and cross validation in state space models summary a fast algorithm is developed for computing the conditional mean and variance of the signal given the observations in a signal plus noise model the resulting recursions can be applied immediately to provide new and efficient formulae for smoothing part or all of the state vector the ideas of studentized residuals and leverage from regression analysis are generalized to state space models and the new algorithm is used to compute the various measures the results are also applied to obtain a new efficient algorithm for polynomial spline smoothing suppose observations are generated by a gaussian signal plus noise process with the signal described by a state space model such a model for the signal occurs often in practice for example when the signal is the output of a stochastic difference or differential equation this paper presents a new algorithm for signal extraction that is the computa tion of the conditional mean and variance of the signal given the observations the usual method for signal extraction is to use the kalman filter see for example anderson moore 1979 p 105 followed by a smoothing step using an algorithm such as the fixed interval smoothing algorithm anderson moore 1979 p 187 our approach also uses the kalman filter but for the smoothing step introduces a new set of recursions which are more efficient than those for the fixed interval smoothing algorithm as for the fixed interval smoothing algorithm recursions for estimating the signal and its variance are carried out separately so that considerable additional savings can be made if the signal estimate alone is required the development uses ideas introduced by ansley kohn 1987a a remarkable property of the new recursions is that they can be applied immediately

a reliable data based bandwidth selection method for kernel density estimation we present a new method for data based selection of the bandwidth in kernel density estimation which has excellent properties it improves on a recent procedure of park and marron which itself is a good method in various ways first the new method has superior theoretical performance second it also has a computational advantage third the new method has reliably good performance for smooth densities in simulations performance that is second to none in the existing literature these methods are based on choosing the bandwidth to approximately minimize good quality estimates of the mean integrated squared error the key to the success of the current procedure is the reintroduction of a non stochastic term which was previously omitted together with use of the bandwidth to reduce bias in estimation without inflating variance

estimation prediction and interpolation for arima models with missing data abstract we show how to define and then compute efficiently the marginal likelihood of an arima model with missing observations the computation is carried out by using the univariate version of the modified kalman filter introduced by ansley and kohn 1985a which allows a partially diffuse initial state vector we also show how to predict and interpolate missing observations and obtain the mean squared error of the estimate

two estimators of the mean of a counting process with panel count data we study two estimators of the mean function of a countingprocess based on panel count data the setting for panel count data is one in which n independent subjects each with a counting process with common mean function are observed at several possibly different times duringa study following a model proposed by schick and yu we allow the number of observation times and the observation times themselves to be random variables our goal is to estimate the mean function of the counting process we show that the estimator of the mean function proposed by sun and kalbfleisch can be viewed as a pseudo maximum likelihood estimator when a non homogeneous poisson process model is assumed for the counting process we establish consistency of both the nonparametric pseudo maximum likelihood estimator of sun and kalbfleisch and the full maximum likeli hood estimator even if the underlying counting process is not a poisson process we also derive the asymptotic distribution of both estimators at a fixed time t and compare the resulting theoretical relative efficiency with finite sample relative efficiency by way of a limited monte carlo study

on robust stabilization on nonlinear control systems abstract a robust stabilization problem for general mimo nonlinear systems is formulated in a banach space setting in the time domain existence and uniqueness theorems are established a general procedure for solving the problem is illustrated and a simple example is included to show how the results can be applied

regression analysis of panel count data with dependent observation times panel count data often occur in long term studies that concern occurrence rate of a recurrent event methods have been proposed for regression analysis of panel count data but most of the existing research focuses on situations where observation times are independent of longitudinal response variables and therefore rely on conditional inference procedures given the observation times this article considers a different situation where the independence assumption may not hold that is the observation times and the response variable may be correlated for inference estimating equation approaches are proposed for estimation of regression parameters and both large and finite sample properties of the proposed estimates are established an illustrative example from a cancer study is provided

partially observed differential games infinite dimensional hamilton jacobi isaacs equations and nonlinear h_ infty control this paper presents new results for partially observed nonlinear differential games using the concept of information state we solve this problem in terms of an infinite dimensional partial differential equation which turns out to be the hamilton jacobi isaacs hji equation for partially observed differential games we give definitions of smooth and viscosity solutions and prove that the value function is a viscosity solution of the hji equation we prove a verification theorem which implies that the optimal controls are separated in that they depend on the observations through the information state this constitutes a separation principle for partially observed differential games we also present some new results concerning the certainty equivalence principle under certain standard assumptions our results are applied to a nonlinear output feedback h infty robust control problem

signal extraction for finite nonstationary time series summary for a signal plus noise model where both signal and noise are generated by nonstation ary arima autoregressive integrated moving average models we use the transformation approach of ansley kohn 1985 to construct an estimate of the signal and obtain its mean squared error given a finite number of observations a method for efficient computa tion of the signal estimate and its mean squared error is also presented consider observations z t generated by the signal plus noise nmodel z t s t n t 1s1 where both signal s t and noise n t follow nonstationary arima processes we give a solution to the finite sample signal extraction problem by defining an estimate of the signal s t given observations z 1 z n and finding its mean squared error the major difficulty in handling the model with nonstationary components is that the distribution of the observations is not defined unless assumptions are made about the initial values of the series moreover it is usually very difficult to formulate reasonable assumptions about the initial values because they affect the correlation structure of the whole series see for example the discussion of bell 1984 p 652 kohn ansley 1986 use a transformation approach to overcome the initial value problem in defining the likelihood and obtaining predittors and interpolators for an arima model which may have missing values this approach does not require any assumptions about the initial values and generalizes the usual differencing approach of box jenkins 1976 for the case where there are no missing observations in the present paper we apply the transformation approach of kohn ansley 1986 and ansley kohn 1985 to solve the signal extraction problem we define a linear estimator a t of s t so that s t sa t is invariant to the initial values and furthermore is unbiased in the sense that e s t s t 0 moreover it has minimum mean squared error amongst all such estimators our approach allows missing observations and extends to signal extraction for several additive signals when each is an arima process we also show how to compute the signal estimate and its mean squared error efficiently by writing the model in state space form placing a diffuse prior on the initial values of the process and then using the modified kalman filter and the modified smoothing algorithm of ansley kohn 1985 and kohn ansley 1986 gersch kitagawa 1983 kitagawa gersch 1984 and harvey todd 1983 use

finite dimensional optimal controllers for nonlinear plants abstract optimal risk sensitive feedback controllers are now available for very general stochastic nonlinear plants and performance indices they consist of nonlinear static feedback of so called information states from an information state filter in general these filters are linear but infinite dimensional and the information state feedback gains are derived from doubly infinite dimensional dynamic programming the challenge is to achieve optimal finite dimensional controllers using finite dimensional calculations for practical implementation this paper derives risk sensitive optimality results for finite dimensional controllers the controllers can be conveniently derived for linearized approximate models applied to nonlinear stochastic systems performance indices for which the controllers are optimal for the nonlinear plants are revealed that is inverse risk sensitive optimal control results for nonlinear stochastic systems with finite dimensional linear controllers are generated it is instructive to see from these results that as the nonlinear plants approach linearity the risk sensitive finite dimensional controllers designed using linearized plant models and risk sensitive indices with quadratic cost kernels are optimal for a risk sensitive cost index which approaches one with a quadratic cost kernel also even far from plant linearity as the linearized model noise variance becomes suitably large the index optimized is dominated by terms which can have an interesting and practical interpretation limiting versions of the results as the noise variances approach zero apply in a purely deterministic nonlinear h setting risk neutral and continuous time results are summarized more general indices than risk sensitive indices are introduced with the view to giving useful inverse optimal control results in non gaussian noise environments

disturbance attenuation and h optimization a design method based on the algebraic riccati equation this note presents a method for designing a state feedback control law to reduce the effect of disturbances on the output of a given linear system the problem under consideration involves attenuating the disturbances to a prespecified level the construction of the state feedback control law requires the solution of a certain algebraic riccati equation by applying the procedure with successively smaller values of the prespecifled disturbance level the result also provides an approach to the h infty optimization problem for the state feedback case

a game theoretic approach to a finite time disturbance attenuation problem a disturbance attenuation problem over a finite time interval is considered by a game theoretic approach where the control restricted to a function of the measurement history plays against adversaries composed of the process and measurement disturbances and the initial state a zero sum game formulated as a quadratic cost criterion subject to linear time varying dynamics and measurements is solved by a calculus of variation technique by first maximizing the quadratic cost criterion with respect to the process disturbance and initial state a full information game between the control and the measurement residual subject to the estimator dynamics results the resulting solution produces an n dimensional compensator which expresses the controller as a linear combination of the measurement history a disturbance attenuation problem is solved based on the results of the game problem for time invariant systems it is shown that under certain conditions the time varying controller becomes time invariant on the infinite time interval the resulting controller satisfies an h sub infinity norm bound

sieve estimation for the proportional odds failure time regression model with interval censoring abstract estimation of the proportional odds failure time regression model with interval censoring is considered conditions that allow for positive information for the regression parameter are discussed the efficient score is characterized by a fredholm equation of the second kind the sieve maximum likelihood estimator for the finite dimensional regression parameter is shown to be asymptotically normal with n convergence rate and to achieve the information bound data analysis and simulations assist in clarifying our thoughts regarding the choice of sieve for finite sample problems

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

analysis of gap times based on panel count data with informative observation times and unknown start time abstractin biomedical studies one is often interested in repeat events with longitudinal observations occurring only intermittently resulting in panel count data the first stage of labor measured through unit increments of cervical dilation in pregnant women provides such an example obstetricians are interested in assessing the gap time distribution of per unit increments of cervical dilation for better management of labor process typically only intermittent medical examinations for cervical dilation occur after already dilated women get admitted to hospital the observation frequency is very likely correlated to how fast slow she dilates thus one could view such data as panel count data with informative observation times and unknown start time here we propose semiparametric proportional rate models for the event process and the observation process with a multiplicative subject specific frailty variable capturing the correlation between the two processes inference procedures for the gap ti

optimal control of partially observable stochastic systems with an exponential of integral performance index the stochastic control problem with linear stochastic differential equations driven by brownian motion processes and as cost functional the exponential of a quadratic form is considered the soluti

further comments on the stabilizability of the angular velocity a rigid body abstract we prove that the angular velocity equations can be smoothly stabilized with a single torque controller for bodies having an axis of symmetry this complements a recent result of aeyels and szafranski

feedback and optimal sensitivity model reference transformations multiplicative seminorms and approximate inverses in this paper the problem of sensitivity reduction by feedback is formulated as an optimization problem and separated from the problem of stabilization stable feedback schemes obtainable from a given plant are parameterized salient properties of sensitivity reducing schemes are derived and it is shown that plant uncertainty reduces the ability of feedback to reduce sensitivity the theory is developed for input output systems in a general setting of banach algebras and then specialized to a class of multivariable time invariant systems characterized by n times n matrices of h infty frequency response functions either with or without zeros in the right half plane the approach is based on the use of a weighted seminorm on the algebra of operators to measure sensitivity and on the concept of an approximate inverse approximate invertibility of the plant is shown to be a necessary and sufficient condition for sensitivity reduction an indicator of approximate invertibility called a measure of singularity is introduced the measure of singularity of a linear time invariant plant is shown to be determined by the location of its right half plane zeros in the absence of plant uncertainty the sensitivity to output disturbances can be reduced to an optimal value approaching the singularity measure in particular if there are no right half plane zeros sensitivity can be made arbitrarily small the feedback schemes used in the optimization of sensitivity resemble the lead lag networks of classical control design some of their properties and methods of constructing them in special cases are presented

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

stabilizability of the angular velocity of a rigid body revisited abstract we prove that the jurdjevic quinn techniques for smooth stabilization can be applied to the equation of the angular velocity of a rigid body an explicit polynomial control is given for the symmetric case

estimation filtering and smoothing in state space models with incompletely specified initial conditions on definit la vraisemblance pour un modele d espace d etats avec des conditions initiales incompletement specifiees par transformation des donnees pour eliminer la dependance sur des conditions non specifiees on etend cette approche pour obtenir des estimations sur les vecteurs d etat les predicteurs et les interpolateurs pour des observations manquantes

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

a game theoretic approach to h control for time varying systems a representation formula for all controllers that satisfy an mathcal l infty type constraint is derived for time varying systems it is now known that a formula based on two indefinite algebraic riccati equations may be found for time invariant systems over an infinite time support see j c doyle et al ieee trans automat control ac 34 1989 pp 831 847 k glover and j c doyle systems control lett 11 1988 pp 167 172 k glover et al siam j control optim 29 1991 pp 283 324 m green et al siam j control optim 28 1990 pp 1350 1371 d j n limebeer et al in proc ieee conf on decision and control austin tx 1988 g tadmor math control systems signal processing 3 1990 pp 301 324 in the time varying case two indefinite riccati differential equations are required a solution to the design problem exists if these equations have a solution on the optimization interval the derivation of the representation formula illustrated in this paper mak

h optimal feedback controllers for linear multivariable systems this paper treats the problem of designing for a linear multivariable plant a feedback controller which minimizes the h infty norm of a weighted sensitivity matrix there exists a family of optimal improper feedbacks this family is determined by application of a theory of ball and helton a method for computing optimal feedbacks is described in detail and a numerical example is included it is shown that an optimal improper feedback can be approximated by a proper one under certain conditions on the weighting matrices

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

systematic design of robust controllers for nonlinear uncertain systems the design problem of robust stabilizing controllers for nonlinear uncertain systems is considered in this paper the nominal system is input output linearizable and the uncertainty is assumed to be either generalized matching or mismatched the control design combines differential geometric feedback linearization with the deterministic approach in which no statistical property of the uncertainty is assumed and used the only information on the uncertainty which is needed for the design is its possible bound two robust stabilizing controllers for generalized matching uncertain systems are given for mismatched uncertain systems a systematic design procedure is first presented then four robust stabilizing controllers are given the robust controllers which are given in forms of explicit feedback laws based on the nominal system and are parametrized by the robust design parameters related to the bounds of uncertainties are more practicable than the existing ones in the literature numerical example

successive galerkin approximation algorithms for nonlinear optimal and robust control nonlinear optimal control and nonlinear h infinity control are two of the most significant paradigms in nonlinear systems theory unfortunately these problems require the solution of hamilton jacobi equations which are extremely difficult to solve in practice to make matters worse approximation techniques for these equations are inherently prone to the so called curse of dimensionality while there have been many attempts to approximate these equations solutions resulting in closed loop control with well defined stability and robustness have remained elusive this paper describes a recent breakthrough in approximating the hamilton jacobi bellman and hamilton jacobi isaacs equations successive approximation and galerkin approximation methods are combined to derive a novel algorithm that produces stabilizing closed loop control laws with well defined stability regions in addition we show how the structure of the algorithm can be exploited to reduce the amount of computation from exponential to po

robust control of set valued discrete time dynamical systems this paper presents results obtained for the control of set valued discrete time dynamical systems such systems model nonlinear systems subject to persistent bounded noise a robust control problem for such systems is introduced the problem is formulated as a dynamic game wherein the controller plays against the set valued system both necessary and sufficient conditions in terms of stationary dynamic programming equalities are presented the output feedback problem is solved using the concept of an information state where a decoupling between estimation and control is obtained the methods yield a conceptual approach for constructing controlled invariant sets and stabilizing controllers for uncertain nonlinear systems

on the stability of the information state system abstract the purpose of this paper is to present some preliminary results on the stability of the information state system the information state system underlies the infinite dimensional dynamics of an h controller for a nonlinear system thus it is important to understand its stability and the structure of its equilibrium points we analyse the important case corresponding to the mixed sensitivity problem we prove the existence of an equilibrium information state convergence under very general conditions to such an equilibrium state p e and uniqueness of this state up to an irrelevant constant in this case the equilibrium p e is usually singular in the sense that it takes on the value except on a low dimensional subset of its domain this meshes with the article 9 which analysed the effect of using p e to initialize the information state controller and gave explicit formulas which in many cases produce a dramatic reduction in the amount of computation required to implement the controller what this article suggests is that indeed p e is the only equilibrium initialization possible

analysing panel count data with informative observation times in this paper we study panel count data with informative observation times we assume nonparametric and semiparametric proportional rate models for the underlying event process where the form of the baseline rate function is left unspecified and a subject specific frailty variable inflates or deflates the rate function multiplicatively the proposed models allow the event processes and observation times to be correlated through their connections with the unobserved frailty moreover the distributions of both the frailty variable and observation times are considered as nuisance parameters the baseline rate function and the regression parameters are estimated by maximising a conditional likelihood function of observed event counts and solving estimation equations large sample properties of the proposed estimators are studied numerical studies demonstrate that the proposed estimation procedures perform well for moderate sample sizes an application to a bladder tumour study is presented

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

estimating missing observations in economic time series abstract two related problems are considered the first concerns the maximum likelihood estimation of the parameters in an arima model when some of the observations are missing or subject to temporal aggregation the second concerns the estimation of the missing observations both problems can be solved by setting up the model in state space form and applying the kalman filter

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

fixed interval estimation in state space models when some of the data are missing or aggregated summary ansley kohn s 1982 geometrical derivation of the kalman filter fixed interval smoothing algorithm is extended to the case where some of the observations are missing or aggregated and the state covariance matrix may be singular estimates of missing observations are also obtained the theory is then applied to the interpolation of missing data in multivariate autoregressive moving average models

sieve maximum likelihood regression analysis of dependent current status data current status data occur in contexts including demographic studies and tumorigenicity experiments in such cases each subject is observed only once and the failure time of interest is either left or right censored kalbfleisch prentice 2002 many methods have been developed for the analysis of such data huang 1996 sun 2006 most of which assume that the failure time and the observation time are independent completely or given covariates in this paper we present a sieve maximum likelihood approach for current status data when independence does not hold a copula model and monotone i splines are used and the asymptotic properties of the resulting estimators are established in particular the estimated regression parameters are shown to be semiparametrically efficient an illustrative example is provided

robust stabilization of nonlinear systems by h state feedback abstract this paper is concerned with robust stabilization of nonlinear systems with unstructured uncertainty via state feedback first a robust stability condition is given for a closed loop system which is composed of a nonlinear nominal system and an unstructured uncertainty second based on the obtained robust stability condition a sufficient condition for robust stabilization by state feedback is given in terms of the solvability of some h state feedback control

robustness analysis of nonlinear feedback systems an input output approach this paper presents an approach to robustness analysis for nonlinear feedback systems we pursue a notion of model uncertainty based on the closeness of input output trajectories which is not tied to a particular uncertainty representation such as additive parametric structured etc the basic viewpoint is to regard systems as operators on signal spaces we present two versions of a global theory where stability is captured by induced norms or by gain functions we also develop local approaches over bounded signal sets and give a treatment for systems with potential for finite time escape we compute the relevant stability margin for several examples and demonstrate robustness of stability for some specific perturbations e g small time delays we also present examples of nonlinear control systems which have zero robustness margin and are destabilized by arbitrarily small gap perturbations the paper considers the case where uncertainty is present in the controller as well as the plant and the generalization of the approach to the case where uncertainty occurs in several subsystems in an arbitrary interconnection

hybrid dynamical systems robust control synthesis problems the paper presents a new approach to robust control synthesis problems for hybrid dynamical systems the hybrid system under consideration is a composite of a continuous plant and a discrete event controller state and output feedback problems are considered the main results are given in terms of the existence of suitable solutions to a dynamic programming equation and a riccati differential equation of the h filtering type these results show a connection between the theories of hybrid dynamical systems and robust and nonlinear control

reduced complexity nonlinear h sup spl infin control of discrete time systems in this note we describe a reduced complexity solution to the nonlinear h sup spl infin control problem this reduction applies to systems where some of the states are perfectly known and is an intermediate problem between full state feedback and the standard measurement feedback problem the reduction of computational complexity is significant and of practical importance online implementation is feasible with 2003 computer technology for a range of practical engineering design problems

robustness and risk sensitive filtering this paper gives a precise meaning to the robustness of risk sensitive filters for problems in which one is uncertain as to the exact value of the probability model it is shown that risk sensitive estimators including filters enjoy an error bound which is the sum of two terms the first of which coincides with an upper bound on the error that one would obtain if one knew exactly the underlying probability model while the second term is a measure of the distance between the true and design probability models the paper includes a discussion of several approaches to estimation including h sub spl infin filtering

on the dissipativity of nonlinear systems fuzzy control approach a controller with large dissipativity is designed and implemented the stability margin is increased in order to tolerate the uncertainties and the disturbance in the nonlinear system in this study the dissipativity of a nonlinear system is facilitated via fuzzy control method first the nonlinear system is represented by an takagi and sugeno fuzzy model if the state variables of the nonlinear system are available then a state feedback fuzzy control is developed to guarantee that the nonlinear control system is dissipative this design problem becomes a linear matrix inequality lmi problem the maximum dissipativity design is obtained by solving an eigenvalue problem evp if the state variables are not available a fuzzy observer based state feedback controller will be used to solve the dissipative problem of the nonlinear system simulation examples are given to illustrate the design procedures and performances of the proposed method

a connection between h control and the absolute stabilizability of uncertain systems abstract this paper considers a stabilization problem for a class of uncertain systems in which the uncertainty satisfies a certain integral quadratic constraint such uncertain systems have been previously studied in the theory of absolute stability with most publications in this area being in the russian literature the paper introduces a notion of absolute stabilizability and shows that an uncertain system is absolutely stabilizable if and only if there exists a solution to a corresponding h control problem the paper also shows that if an uncertain system can be absolutely stabilized via nonlinear output feedback control then it can be absolutely stabilized via linear output feedback control

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

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

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

stabilization of a class of nonlinear systems by a smooth feedback control we consider the stabilizability problem for systems of the form x f x ub in the neighborhood of an equilibrium point of f x first by means of center manifold theory a lower order system is introduced if this system is stabilizable then so is the original system results on the stabilization of the low order system are presented no resort is taken to liapunov theory the relation between stabilizability and controllability is discussed

control of constrained discrete time systems with bounded ell_ 2 gain we consider the problem of designing a control law for a constrained linear system with bounded disturbances that ensures constraint satisfaction over an infinite horizon while also guaranteeing that the closed loop system has bounded lscr2 gain to this end we propose a receding horizon control strategy based on the repeated calculation of optimal finite horizon feedback policies we parameterize these policies such that the input at each time is an affine function of current and prior states and minimize a worst case quadratic cost where the disturbance energy is negatively weighted as in h infin control we show that the resulting receding horizon controller has two advantages over previous results for this problem first the policy optimization problem to be solved at each time step can be rendered convex concave with a number of decision variables and constraints that grows polynomially with the problem size thereby making its solution amenable to standard techniques in convex optimization second the achievable lscr2 gain of the resulting closed loop system is bounded and non increasing with increasing control horizon a numerical example is included to demonstrate the improvement in achievable lscr2 gain relative to existing methods

on graphs conic relations and input output stability of nonlinear feedback systems this paper presents necessary and sufficient conditions for the stability of general interconnected dynamical systems the results are expressed in terms of the graphs of the interconnection s subsystems conditions for robustness of stability for an interconnection with additive disturbances are also provided finally the paper gives sufficient conditions for stability using conic sector conditions that generalize earlier conditions and that incorporate a recent nonlinear small gain idea

optimal control of discrete time uncertain systems with imperfect measurement we consider a discrete time optimal control problem in the presence of uncertainties in the dynamics and in the measurement an optimal in min max sense output feedback controller is derived from a discrete bellman equation we propose a formulation of the last equation in the estimation space which allows approximation by a reduced order equation corresponding to a prescribed collection of estimation sets the approach is illustrated up to numerical experiments by a pursuit evasion game on the plane with incomplete information of the current state of the evader

a risk sensitive maximum principle the case of imperfect state observation the risk sensitive maximum principle for optimal stochastic control derived by the author in an earlier work system control letters vol 15 1990 is restated this is an immediate generalization of the classic pontryagin principle to which it reduces in the deterministic case and is expressed immediately in terms of observables it is derived on the assumption that the criterion function is the exponential of an additive cost function and is exact under linear quadratic gaussian assumptions but is otherwise valid as a large deviation approximation the principle is extended to the case of imperfect state observation after preliminary establishment of a certainty equivalence principle the derivation yields as byproduct a large deviation version of the updating equation for nonlinear filtering the development is heuristic it is believed that the mathematical arguments given are the essential ones and provide a self contained treatment at this level

galerkin approximations of the generalized hamilton jacobi bellman equation in this paper we study the convergence of the galerkin approximation method applied to the generalized hamilton jacobi bellman ghjb equation over a compact set containing the origin the ghjb equation gives the cost of an arbitrary control law and can be used to improve the performance of this control the ghjb equation can also be used to successively approximate the hamilton jacobi bellman equation we state sufficient conditions that guarantee that the galerkin approximation converges to the solution of the ghjb equation and that the resulting approximate control is stabilizing on the same region as the initial control the method is demonstrated on a simple nonlinear system and is compared to a result obtained by using exact feedback linearization in conjunction with the lqr design method