brief paper a dual optimization procedure for linear quadratic robust control problems this paper considers the problem of choosing a single constant linear state feedback control law which produces satisfactory performance for each of several operating points of a system the model for each operating point is assumed to be linear and the criterion for satisfactory performance is taken to be an infinite horizon quadratic cost functional this problem is reformulated as a finite dimensional optimization over the linear feedback gains which can be readily solved using standard nonlinear optimization techniques provided a stabilizing initial value of the gains can be found although the direct solution of this problem will be discussed briefly the major portion of the paper will be devoted to solution techniques when an initial stabilizing guess is not available

monotone discriminant functions and their applications in rheumatology abstract some applications of discriminant analysis e g in rheumatology naturally require that the discriminator satisfies certain monotonicity constraints in terms of the measurements on which the classification is based this article presents a dynamic programming approach to the problem of finding the monotone function that minimizes the total misclassification cost incurred when classifying two types of cases on the basis of two variables measured on each case questions of uniqueness and convexity are explored and the way in which the solution varies with choice of misclassification costs is investigated the use of the bootstrap to estimate the accuracy of summary statistics of interest is discussed the methodology is illustrated using data on rheumatology patients some comparisons with linear discriminant functions and classification tree methods are made

multiple well invasion percolation when the invasion percolation model is applied as a simplified model for the displacement of a viscous fluid by a less viscous one the distribution of displaced mass follows two distinct universality classes depending on the criteria used to stop the displacement here we study the distribution of mass for this process in the case where four extraction wells are placed around a single injection well in the middle of a square lattice our analysis considers the limit where the pressure of the extraction well p e is zero in other words an extraction well is capped as soon as less viscous fluid reaches that extraction well our results show that as expected the probability of stopping the production with small amounts of displaced mass is greatly reduced we also investigate whether or not creating extra extraction wells is an efficient strategy we show that the probability of increasing the amount of displaced fluid by adding an extra extraction well depends on the total recovered mass obtained before adding this well the results presented here could be relevant to determine efficient strategies in oil exploration

random walk percolation based modeling of two phase flow in porous media breakthrough time and net to gross ratio estimation abstract fluid flow modeling in porous media has many applications in waste treatment hydrology and petroleum engineering in any geological model flow behavior is controlled by multiple properties these properties must be known in advance of common flow simulations when uncertainties are present deterministic modeling often produces poor results percolation and random walk rw methods have recently been used in flow modeling their stochastic basis is useful in dealing with uncertainty problems they are also useful in finding the relationship between porous media descriptions and flow behavior this paper employs a simple methodology based on random walk and percolation techniques the method is applied to a well defined model reservoir in which the breakthrough time distributions are estimated the results of this method and the conventional simulation are then compared the effect of the net to gross ratio on the breakthrough time distribution is studied in terms of shannon entropy use of the entropy plot allows one to assign the appropriate net to gross ratio to any porous medium

output feedback pole placement in the design of suboptimal linear quadratic regulators a design oriented methodology is presented for the construction of low order suboptimal output feedback compensators the design is suboptimal in the sense that it retains an l dimensional eigenspace from a reference optimal state feedback linear quadratic regulator problem if r is the number of outputs then for fixed l r it is known that the design requires a dynamic compensator of dimension l r the parameters of the compensator are determined by the solution of an associated output feedback pole placement problem using iterative dyadic pole placement a procedure is given which determines the solution of this problem without a priori assumptions on the dimension of the compensator the design is also extended to the class of stabilizable systems and the resulting compensator is shown to possess a separation property

water propagation in two dimensional petroleum reservoirs abstract in the present paper we investigate the problem of water propagation in 2 dimensional 2d petroleum reservoir in which each site has the probability p of being occupied we first analyze this propagation pattern described by darcy equations by focusing on its geometrical features we find that the domain walls of this model at p p c 0 59 are schramm loewner evolution sle curves with 3 05 0 1 consistent with the ising universality class we also numerically show that the fractal dimension of these domain walls at p p c is d f 1 38 consistent with sle 3 along with this analysis we introduce a self organized critical soc model in which the water movement is modeled by a chain of topplings taking place when the water saturation exceeds the critical value we present strong indications that it coincides with the reservoir simulation described by darcy equation we further analyze the soc model and show numerically that for this model the spanning cluster probability has a maximum around p 0 65

newton s method for solving parametric linear quadratic control problems newton s method is applied to parametric linear quadratic control problems including the optimal output feedback problem and the optimal decentralized control problem newton s equations are obtained as a system of coupled linear matrix equations they are solved iteratively using the conjugate gradient method in order to reduce the amount of work associated with the procedure an inexact newtonian algorithm is also considered in this algorithm an approximate solution of the newton equations is computed in such a way that the asymptotic convergence rate is quadratic

interactive learning of monotone boolean functions this paper presents some optimal interactive algorithms for some problems related to learning of monotone boolean functions these algorithms are based on the fundamental hansel theorem the advantage of the algorithms is that they are not heuristics as is often the case of many known algorithms for general boolean functions but they are optimal in the sense of the shannon function this paper also formulates a new problem for the joint restoration of two nested monotone boolean functions f1 and f2 this formulation allows one to further decrease the dialogue with an expert and restore nonmonotone functions of the form f2 f1 the effectiveness of the proposed approaches is demonstrated by some illustrative computational experiments

guided inference of nested monotone boolean functions this paper addresses the problem of minimizing the average query complexity of inferring a pair of nested monotone boolean functions defined on 0 1 n using a pair of oracles here nested refers to the case when one of the functions is always greater than or equal to the other function it is shown that the nested case is equivalent to inferring the single function case defined on 0 1 n 1 when access to the two oracles is unrestricted two common examples of restricted oracles namely sequential oracles and a single three valued oracle are also analyzed the most efficient known approach to minimizing the average query complexity in inferring a single monotone boolean function is based on a query selection criterion it is shown that the selection criterion approach is easily modified for use with restricted oracles several real world examples illustrate the necessity and sufficiency of the nested monotone boolean function model extensive computational results indicate that the nestedness assumption reduces the average query complexity by a few percent this is a dramatic improvement considering the fact that this complexity is exponential in n

the optimal projection equations for model reduction and the relationships among the methods of wilson skelton and moore first order necessary conditions for quadratically optimal reduced order modeling of linear time invariant systems are derived in the form of a pair of modified lyapunov equations coupled by an oblique projection which determines the optimal reduced order model this form of the necessary conditions considerably simplifies previous results of wilson 1 and clearly demonstrates the quadratic extremality and nonoptimality of the balancing method of moore 2 the possible existence of multiple solutions of the optimal projection equations is demonstrated and a relaxation type algorithm is proposed for computing these local extrema a component cost analysis of the model error criterion similar to the approach of skelton 3 is utilized at each iteration to direct the algorithm to the global minimum

polynomial time recognition of 2 monotonic positive boolean functions given by an oracle we consider the problem of identifying an unknown boolean function f by asking an oracle the functional values f a for a selected set of test vectors a in 0 1 n furthermore we assume that f is a positive or monotone function of n variables it is not yet known whether or not the whole task of generating test vectors and checking if the identification is completed can be carried out in polynomial time in n and m where m min t f max f f and min t f respectively max f f denotes the set of minimal true respectively maximal false vectors of f to partially answer this question we propose here two polynomial time algorithms that given an unknown positive function f of n variables decide whether or not f is 2 monotonic and if f is 2 monotonic output both sets min t f and max f f the first algorithm uses o nm 2 n 2 m time and o nm queries while the second one uses o n 3 m time and o n 3 m queries

a theory of state covariance assignment for discrete systems in many regulation control problems it is desired to design the controller so that various system states have acceptable root mean squared values this is a multiple objective problem one way to satisfy these objectives is to assign a specified state covariance to the system this paper introduces and solves the following problem 1 characterize the entire set of state covariances which may be assigned to a linear discrete time system by state feedback and 2 find the set of all state feedback gains which will assign an admissible state covariance to the system extensions are also presented for state estimate feedback

a note on the location of the roots of a polynomial two new theorems and two corollaries are presented which give sufficient conditions for a polynomial to have all its roots inside the unit circle these results unify and extend certain earlier stability tests for discrete time systems the significance of the new results is illustrated by a couple of examples

optimal adaptive control and consistent parameter estimate for deterministic systems with quadratic cost in this paper an adaptive control is designed for deterministic systems on the basis of the projection algorithm so that the quadratic loss function approaches its minimum at a rate of n e e 0 and the parameter estimate converges to its true value with a near exponential rate

a globally convergent algorithm for the optimal constant output feedback problem a dual version of the levine athans algorithm for solving the optimal constant output feedback gain for continuous time systems is studied global convergence of the procedure to a stationary point of the loss function is proved a global convergence property of the levine athans algorithm is also obtained

parametric lq control the parametric linear quadratic plq control problem is considered for discrete time stochastic systems the control problem consists of a non linear optimization problem in the parameters of a linear regulator results on global convergence and on rate of convergence are given for the linear descent mapping method for solving the optimal regulator parameter values furthermore a non linear mapping method based on the solution of a generalized discrete riccati equation is given the plq control problem is a useful extension of the optimal output feedback problem with applications to the design of low order regulators decentralized control and adaptive control

persistence of excitation conditions and the convergence of adaptive schemes in the study of the behavior of adaptive filtering algorithms persistence of excitation of the input process arises as a sufficient condition for convergence and perhaps more importantly for convergence rate of the parameter estimates in this paper the underlying nature of the persistence requirement is presented and discussed relating its normal specification in terms of moment conditions with covariance decays etc to sample path properties deterministic and stochastic persistence conditions and persistence measures are treated as well as persistence conditions for output error equation error and adaptive control schemes

exponential convergence of adaptive identification and control algorithms output and equation error adaptive identification algorithms are shown to be exponentially convergent under a deterministic or stochastic persistently exciting or spanning condition on the system inputs together with several other standard conditions an adaptive control algorithm is shown to be exponentially convergent under a deterministic or stochastic persistently exciting condition on the reference trajectory together with some standard conditions

a geometric approach to stabilization by output feedback in this paper we present a geometric approach to the stabilizability of linear systems by output feedback the geometric approach is completely analysed for both discrete time and continuous time single input single output systems two examples are worked out in detail to illustrate the theoretical development we also show how our approach can be extended to dyadic systems the simplicity of the geometric approach in the special case when the number of inputs or outputs is one less than the order of the system is illustrated with the help of examples present address bell laboratories south plainfield new jersey 07080 u s a

paper optimal output feedback design of systems with ill conditioned dynamics singular perturbation concepts are exploited to develop a procedure for designing a constant gain output feedback control system it is assumed that the original system is ill conditioned in the sense that the plant contains widely separated dynamics and that an accurate description for the high frequency behavior may not be available the design procedure attempts to stabilize the system by minimizing a quadratic cost function made up of the control and states associated with a reduced order low frequency model for the plant and a measure of stability for the neglected fast dynamics the resulting design procedure does not require knowledge of the fast dynamics

convergence rate of least squares identification and adaptive control for stochastic systems the strong consistency and the convergence rate of least squares identification for the multidimensional armax model are established under some decaying excitation conditions which are satisfied if both input and output do not grow too fast and the attenuating excitation technique is applied the parameter identification results are applied to adaptive control systems with a quadratic loss function the rate of convergence of the loss function to its minimum is also obtained

invasion percolation between two sites in two three and four dimensions abstract the mass distribution of invaded clusters in non trapping invasion percolation between an injection site and an extraction site has been studied in two three and four dimensions this study is an extension of the recent study focused on two dimensions by araujo et al a d araujo t f vasconcelos a a moreira l s lucena j s andrade jr phys rev e 72 2005 041404 with respect to higher dimensions the mass distribution exhibits a power law behavior p m m it has been found that the index for p e p c p c being the percolation threshold of a regular percolation appears to be independent of the value of p e and is also independent of the lattice dimensionality when p e p c appears to depend marginally on the lattice dimensionality and the relation 1 being the exponent associated with cluster size distribution of a regular percolation via n s s appears to be valid

robust optimal parametric lq control with a guaranteed cost bound and applications for an optimal parametric linear quadratic lq control problem a design objective is to determine a controller of constrained structure such that the closed loop system is asymptotically stable and an associated performance measure is optimized in the presence of system uncertainty the system via a parametric lq design is further required to be robust in terms of maintaining the closed loop stability with a guaranteed cost bound this problem is referred to as robust optimal parametric lq control with a guaranteed cost bound and is addressed in this work a new design method is proposed to find an optimal controller for simultaneously guaranteeing robust stability and performance over a specified range of parameter variations the results presented generalize some previous work in this area a versatile numerical algorithm is also given for computing the robust optimal gains the usefulness of the design method is demonstrated by numerical examples and a design of the robust control of a vtol helico

the design of optimal output regulators for linear multivariable systems with constant disturbances a method recently developed for solving the output regulator problem is extended to linear systems with constant disturbances the design of static and low order dynamic regulators for linear systems based on the use of projective controls is reviewed first the proposed method determines through a unified procedure the order and the parameters of the compensator together with the feedback parameters this methodology is then applied to systems with external disturbances and various control structures incorporating integral action are investigated in the light of the proposed methodology

the optimal projection equations for fixed order dynamic compensation first order necessary conditions for quadratically optimal steady state fixed order dynamic compensation of a linear time invariant plant in the presence of disturbance and observation noise are derived in a new and highly simplified form in contrast to the pair of matrix riccati equations for the full order lqg case the optimal steady state fixed order dynamic compensator is characterized by four matrix equations two modified riccati equations and two modified lyapunov equations coupled by a projection whose rank is precisely equal to the order of the compensator and which determines the optimal compensator gains the coupling represents a graphic portrayal of the demise of the classical separation principle for the reduced order controller case

computational methods for parametric lq problems a survey iterative methods for finding the optimal constant feedback gains for parametric lq problems notably for optimal constant output feedback problems are surveyed the connections of several methods to loss function expansions are discussed with important implications to the understanding of their convergence properties especially the descent anderson moore method levine athans like methods and the newton method are considered convergence results are also included the initialization problem and the output feedback stabilization problem are also discussed furthermore it is shown that the concepts and methods surveyed in this paper are useful in solving many realistic generalized parametric lq problems as well notably so called robust parametric lq problems

on the anderson moore method for solving the optimal output feedback problem a descent anderson moore method for solving the optimal constant output feedback gains for the stochastic discrete time optimal output feedback problem is discussed an efficient descent mapping algorithm is given in detail the algorithm involves a partial line search mapping implemented as a finite search process to determine a step length parameter so as to guarantee global convergence of the algorithm to a stationary point of the loss function under very mild assumptions furthermore the algorithm involves a scheme to bound the condition numbers of certain critical matrix inverses in the anderson moore method so that the algorithm can be applied to a wider class of control problems

optimal low order controller design via lqg like parametrization abstract a new lqg like parametrization scheme is introduced for low order controller design descent based design methodologies are developed for optimizing an h 2 cost with respect to the controller design parameters in this case the reduced order regulator and estimator gain matrices in a modified version the reduced order model of the plant is also updated numerical experiments using large space structure models show the efficacy of this approach

invasion percolation between two sites we investigate the process of invasion percolation between two sites injection and extraction sites separated by a distance r in two dimensional lattices of size l our results for the nontrapping invasion percolation model indicate that the statistics of the mass of invaded clusters is significantly dependent on the local occupation probability pressure p e at the extraction site for p e 0 we show that the mass distribution of invaded clusters p m follows a power law p m ensuremath sim m ensuremath ensuremath alpha for intermediate values of the mass m with an exponent ensuremath alpha 1 39 ifmmode pm else textpm fi 0 03 when the local pressure is set to p e p c where p c corresponds to the site percolation threshold of the lattice topology the distribution p m still displays a scaling region but with an exponent ensuremath alpha 1 02 ifmmode pm else textpm fi 0 03 this last behavior is consistent with previous results for the cluster statistics in standard percolation in spite of these differences the results of our simulations indicate that the fractal dimension of the invaded cluster does not depend significantly on the local pressure p e and it is consistent with the fractal dimension values reported for standard invasion percolation finally we perform extensive numerical simulations to determine the effect of the lattice borders on the statistics of the invaded clusters and also to characterize the self organized critical behavior of the invasion percolation process