optimal and self tuning deconvolution in time domain this paper is concerned with both the optimal minimum mean square error variance and self tuning deconvolution problems for discrete time systems when the signal model measurement model and noise statistics are known a novel approach for the design of the optimal deconvolution filter predictor and smoother is proposed based on projection theory and innovation analysis in the time domain the estimators are given in terms of an autoregressive moving average arma innovation model and one unilateral linear polynomial equation where the arma innovation model is obtained by performing one spectral factorization a self tuning scheme can be incorporated when the noise statistics the input model and or colored noise model are unknown the self tuning estimator is designed by identifying two arma innovation models

regression methods for stochastic control problems and their convergence analysis in this paper we develop several regression algorithms for solving general stochastic optimal control problems via monte carlo this type of algorithm is particularly useful for problems with a high dimensional state space and complex dependence structure of the underlying markov process with respect to some control the main idea behind the algorithms is to simulate a set of trajectories under some reference measure and to use the bellman principle combined with fast methods for approximating conditional expectations and functional optimization theoretical properties of the presented algorithms are investigated and the convergence to the optimal solution is proved under some assumptions finally the presented methods are applied in a numerical example of a high dimensional controlled bermudan basket option in a financial market with a large investor

solution of the h sub infinity optimal linear filtering problem for discrete time systems the solution of l sub 2 minimum variance and h sub infinity estimation problems is considered using a polynomial systems approach the results for the l sub 2 filtering problem which corresponds with wiener or kalman filtering prediction are first presented in polynomial matrix form attention then turns to the solution of the h sub infinity estimation problem for scalar systems numerous examples are presented to illustrate the computational procedures the two types of estimator are appropriate to very different estimation problems and the new h sub infinity devices should be valuable in certain application areas

nonlinear optimal control via occupation measures and lmi relaxations we consider the class of nonlinear optimal control problems ocps with polynomial data i e the differential equation state and control constraints and cost are all described by polynomials and more generally for ocps with smooth data in addition state constraints as well as state and or action constraints are allowed we provide a simple hierarchy of lmi linear matrix inequality relaxations whose optimal values form a nondecreasing sequence of lower bounds on the optimal value under some convexity assumptions the sequence converges to the optimal value of the ocp preliminary results show that good approximations are obtained with few moments

brief papers new results in state estimation and regulation an alternative technique to design linear state estimators and regulators is presented this technique is based on transfer matrix considerations the optimal regulator or estimator gain is obtained via spectral factorization and the solution of a simple equation in polynomial matrices this approach provides further insight displays the duality of estimation and control nicely and bridges the state space and frequency domain techniques the resulting design procedure is computationally attractive and particularly simple for system matrices in the observer or controller canonical form

polynomial equations for the linear mmse state estimation the linear minimum mean square error mmse state estimation problem is solved via spectral factorization and a pair of bilateral diophantine equations detectability and or stability requirements in the riccati based solution context are expressed in terms of the stability of the greatest common right and left divisors of polynomial matrices

mmse deconvolution via polynomial methods and its dual lqg regulation abstract the problem of linear minimum mean square error mmse multichannel deconvolution of sampled signals from noisy observations is approached via matrix polynomial equations the general solution is given in terms of a left spectral factorization and a pair of bilateral diophantine equations the first diophantine equation is obtained by imposing optimality of the deconvolution filter whereas the second ensures stability of the filter should the signal model be unstable the proposed solution encompasses classical wiener as well as stationary kalman filtering prediction and fixed lag smoothing the duality with the polynomial equations for lqg regulation is also discussed

continuous time lq regulator design by polynomial equations abstract the deterministic continuous time lq output regulation problem is solved by polynomial equations as an alternative to the usual riccati equation approach in particular it is shown that riccati based and polynomial methods are fully conceptually equivalent in steady state lq regulation

subsolutions of an isaacs equation and efficient schemes for importance sampling it was established in dupuis and wang dupuis p h wang 2004 importance sampling large deviations and differential games stoch stoch rep 76 481 508 dupuis p h wang 2005 dynamic importance sampling for uniformly recurrent markov chains ann appl probab 15 1 38 that importance sampling algorithms for estimating rare event probabilities are intimately connected with two person zero sum differential games and the associated isaacs equation this game interpretation shows that dynamic or state dependent schemes are needed in order to attain asymptotic optimality in a general setting the purpose of the present paper is to show that classical subsolutions of the isaacs equation can be used as a basic and flexible tool for the construction and analysis of efficient dynamic importance sampling schemes there are two main contributions the first is a basic theoretical result characterizing the asymptotic performance of importance sampling estimators based on subsolutions the second is an explicit method for constructing classical subsolutions as a mollification of piecewise affine functions numerical examples are included for illustration and to demonstrate that simple nearly asymptotically optimal importance sampling schemes can be obtained for a variety of problems via the subsolution approach

an iterative procedure for constructing subsolutions of discrete time optimal control problems an iterative procedure for constructing subsolutions of deterministic or stochastic optimal control problems in discrete time with continuous state space is introduced the procedure generates a nondecreasing sequence of subsolutions giving true lower bounds on the minimal costs convergence of the values at any fixed initial state is shown

on the polynomial equations for the mimo lq stochastic regulator the role played by three polynomial equations in the lq stochastic regulation problem is discussed the emphasis is on establishing conditions under which the lq regulator can be obtained via the solution of a single uncoupled diophantine equation nevertheless the authors do not claim that there is any advantage in solving a single uncoupled equation in place of two coupled diophantine equations

optimal deconvolution based on polynomial methods the problem of estimating the input to a known linear system is treated in a shift operator polynomial formulation the mean square estimation error is minimized the input and a colored measurement noise are described by independent arma autoregressive moving average processes the filter is calculated by performing a spectral factorization and solving a polynomial equation the approach can be applied to input prediction filtering and smoothing problems as well as to the use of prefilters in the quadratic criterion it applies to nonminimum phase as well as unstable systems as illustrated by two examples

robust filter design for uncertain systems defined by both hard and soft bounds a new approach to robust linear filter design is described that attempts to combine the advantages of h sub spl infin robust linear synthesis with a probabilistic method of system and noise modeling the signal and measurement noise model parameters are assumed to be subject to perturbations represented by random variables with known covariances the system is represented in polynomial form and the uncertainty can be described by both soft and hard bounds an h sub spl infin cost function is minimized and averaged with respect to model errors in signal and noise descriptions the polynomial solution is no more complicated than the usual h sub spl infin optimal filter and involves averaged spectral factorizations and linear equations both usual and deconvolution filtering problems are considered

distributed dynamic programming for discrete time stochastic control and idempotent algorithms idempotent methods have been found to be extremely fast for the solution of dynamic programming equations associated with deterministic control problems the original methods exploited the idempotent e g max plus linearity of the associated semigroup operator it is now known that curse of dimensionality free idempotent methods do not require this linearity instead it is sufficient that certain solution forms are retained through application of the associated semigroup operator here we see that idempotent methods may be used to solve some classes of stochastic control problems the key is the use of the idempotent distributive property we demonstrate this approach for a class of nonlinear discrete time stochastic control problems

an information based approximation scheme for stochastic optimization problems in continuous time dynamic stochastic optimization problems with a large possibly infinite number of decision stages and high dimensional state vectors are inherently difficult to solve in fact scenario tree based algorithms are unsuitable for problems with many stages while dynamic programming type techniques are unsuitable for problems with many state variables this paper proposes a stage aggregation scheme for stochastic optimization problems in continuous time thus having an extremely large i e uncountable number of decision stages by perturbing the underlying data and information processes we construct two approximate problems that provide bounds on the optimal value of the original problem moreover we prove that the gap between the bounds converges to zero as the stage aggregation is refined if massive aggregation of stages is possible without sacrificing too much accuracy the aggregate approximate problems can be addressed by means of scenario tree based methods the suggested approach applies to problems that exhibit randomness in the objective and the constraints while the constraint functions are required to be additively separable in the decision variables and random parameters

convex duality approach to the optimal control of diffusions an alternative to the usual dynamic programming approach to the optimal control of markov processes is considered it is based on duality of convex analysis the control problem is embedded in a convex mathematical programming problem on a space of measures the dual problem is to find the supremum of smooth subsolutions to the hamilton jacobi bellman equation

pathwise stochastic optimal control this paper approaches optimal control problems for discrete time controlled markov processes by representing the value of the problem in a dual lagrangian form the value is expressed as an infimum over a family of lagrangian martingales of an expectation of a pathwise supremum of the objective adjusted by the lagrangian martingale term this representation opens up the possibility of numerical methods based on monte carlo simulation which may be advantageous in high dimensional problems or in problems with complicated constraints

h deconvolution filtering of 2 d digital systems this paper deals with the problem of two dimensional 2 d digital system deconvolution under the h performance specification the 2 d digital system under consideration is expressed by the fornasini marchesini local state space fm lss model for a given 2 d digital system a 2 d deconvolution filter is designed to reconstruct the 2 d signal to meet a prescribed h performance specification a key analytical means for the deconvolution filter design is the 2 d bounded realness property derived in this paper applying this property the 2 d h deconvolution filter design is formulated into a convex optimization problem characterized by linear matrix inequalities lmis a procedure for the design of an h deconvolution filter for a given 2 d digital system with measurement noise is developed first the lmi approach to the 2 d h deconvolution filtering problem is further extended to the 2 d h robust deconvolution filtering problem with polytopic modeling uncertainties in the 2 d system the obtained results on the 2 d deconvolution filtering and robust deconvolution filtering problems are demonstrated with examples

wiener filter design using polynomial equations a simplified way of deriving realizable and explicit wiener filters is presented discrete time problems are discussed in a polynomial equation framework optimal filters predictors and smoothers are calculated by means of spectral factorizations and linear polynomial equations a tool for obtaining these equations for a given problem structure is described it is based on the evaluation of orthogonality in the frequency domain by means of canceling stable poles with zeros comparisons are made to previously known derivation methodologies such as completing the squares for the polynomial systems approach and the classical wiener solution the simplicity of the proposed derivation method is particularly evident in multistage filtering problems to illustrate two examples are discussed a filtering and a generalized deconvolution problem a new solvability condition for linear polynomial equation appearing in scalar problems is also presented

a direct approach to h sub 2 optimal deconvolution of periodic digital channels this paper studies the h sub 2 optimal deconvolution problem for periodic finite impulse response fir and infinite impulse response iir channels it shows that the h sub 2 norm of a periodic filter can be directly quantified in terms of periodic system matrices and linear matrix inequalities lmis without resorting to the commonly used lifting technique the optimal signal reconstruction problem is then formulated as an optimization problem subject to a set of matrix inequality constraints under this framework the optimization of both the fir and iir periodic deconvolution filters can be made convex solved using the interior point method and computed by using the matlab lmi toolbox the robust deconvolution problem for periodic fir and iir channels with polytopic uncertainties are further formulated and solved also by convex optimization and the lmis compared with the lifting approach to the design of periodic filters the proposed approach is simpler yet more powerful in dealing with multiobjective deconvolution problems and channel uncertainties especially for iir deconvolution filter design the obtained solutions are applied to the design of an optimal filterbank yielding satisfactory performance

a general polynomial solution to the mmse deconvolution problem it is shown that in order to solve the minimum mean square error mmse deconvolution problem under general conditions two coupled polynomial equations must be used this is constructively proved by satisfying both the orthogonality principle and mean square boundedness of the estimation error

coupling coefficients for lie algebra representations and addition formulas for special functions representations of the lie algebra su 1 1 and of a generalization of the oscillator algebra b 1 are considered the paper then introduces polynomials which are related by the coupling or clebsch gordan coefficients of the lie algebra in question by making a proper choice these polynomials themselves are related to known special functions the coupling of two or three representations of the lie algebra then leads to interesting addition formulas for these special functions the polynomials appearing here are generalized laguerre and jacobi polynomials for the su 1 1 case and hermite polynomials for the b 1 algebra