structural properties of minimax controllers for a class of differential games arising in nonlinear h control abstract this paper introduces in precise mathematical terms two properties named certainty equivalence and generalized certainty equivalence that nonlinear minimax controller problems might possess the certainty equivalence is a generalization of the one introduced earlier by basar and bernhard 1991 and bernhard 1990 which applies to problems where the worst case disturbance may not be unique but the worst case state trajectory is the generalized certainty equivalance on the other hand extends this to accomodate nonunique worst case state trajectories and leads to the constrollers that guarantee a bounded upper value for the underlying game the paper also shows that for a large class of games and under certain conditions certainty equivalent as well as generalized certainty equivalent controllers admit infinite dimensional estimator kalman filter structures where the estimator gain depends on the state of the estimator

on anstreicher s combined phase i phase ii projective algorithm for linear programming anstreicher has proposed a variant of karmarkar s projective algorithm that handles standard form linear programming problems nicely we suggest modifications to his method that we suspect will lead to better search directions and a more useful algorithm much of the analysis depends on a two constraint linear programming problem that is a relaxation of the scaled original problem

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

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

an implementation of karmarkar s algorithm for linear programming this paper describes the implementation of power series dual affine scaling variants of karmarkar s algorithm for linear programming based on a continuous version of karmarkar s algorithm two variants resulting from first and second order approximations of the continuous trajectory are implemented and tested linear programs are expressed in an inequality form which allows for the inexact computation of the algorithm s direction of improvement resulting in a significant computational advantage implementation issues particular to this family of algorithms such as treatment of dense columns are discussed the code is tested on several standard linear programming problems and compares favorably with the simplex codeminos 4 0

on the expected condition number of linear programming problems let a be an n m real matrix and consider the linear conic system in cheung and cucker 2001 a condition number a for this system is defined in this paper we let the coefficients of a be independent identically distributed random variables with standard gaussian distribution and we estimate the moments of the random variable ln a in particular when n is sufficiently larger than m we obtain for its expected value e ln a max ln m ln ln n 1 bounds for the expected value of the condition number introduced by renegar 1994b 1995a 1995b follow

stack filters the median and other rank order operators possess two properties called the threshold decomposition and the stacking properties the first is a limited superposition property which leads to a new architecture for these filters the second is an ordering property which allows an efficient vlsi implementation of the threshold decomposition architecture motivated by the success of rank order filters in a wide variety of applications and by the ease with which they can now be implemented we consider in this paper a new class of filters called stack filters they share the threshold decomposition and stacking properties of rank order filters but are otherwise unconstrained they are shown to form a very large class of easily implemented nonlinear filters which includes the rank order operators as well as all compositions of morphological operators the convergence properties of these filters are investigated using techniques similar to those used to determine root signal behavior of median filters the results obtained include necessary conditions for a stack filter to preserve monotone regions or edges in signals the output distribution for these filters is also found all the stack filters of window width 3 are determined along with their convergence properties among these filters are found two which we have named asymmetric median filters they share all the properties of median filters except that they remove impulses of one sign only that is one removes only positive going edges the other removes only negative going edges while the median filter removes impulses of both signs this investigation of the properties of stack filters thus produces several new useful and easily implemented filters

coverage processes on spheres and condition numbers for linear programming this paper has two agendas firstly we exhibit new results for coverage processes let p n m alpha be the probability that n spherical caps of angular radius alpha in s m do not cover the whole sphere s m we give an exact formula for p n m alpha in the case alpha in pi 2 pi and an upper bound for p n m alpha in the case alpha in 0 pi 2 which tends to p n m pi 2 when alpha to pi 2 in the case alpha in 0 pi 2 this yields upper bounds for the expected number of spherical caps of radius alpha that are needed to cover s m secondly we study the condition number mathscr c a of the linear programming feasibility problem exists x in mathbb r m 1 ax le0 x ne0 where a in mathbb r n times m 1 is randomly chosen according to the standard normal distribution we exactly determine the distribution of mathscr c a conditioned to a being feasible and provide an upper bound on the distribution function in the infeasible case using these results we show that mathbf e ln mathscr c a le2 ln m 1 3 31 for all n m the sharpest bound for this expectancy as of today both agendas are related through a result which translates between coverage and condition

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

convergence results and numerical experiments on a linear programming hybrid algorithm abstract a modification of karmarkar s algorithm for linear programming successively generates column scaled equivalents of the original linear program and in the scaled coordinates obtains improvements according to steepest descent directions as an interior feasible preserving algorithm termination requires a purification algorithm to obtain a dual basic optimal solution together the two algorithms comprise a hybrid procedure for solving linear programs in this paper we present some convergence results on the phase ii and phase i portions of the scaling algorithm we also present results of numerical experiments on examples of klee minty type which show sensitivity to the starting interior feasible point and steepest descent step size

parallel algorithms and vlsi architectures for stack filtering using fibonacci p codes a parallel decompositional algorithm and vlsi architecture is proposed for computation of the output of a stack filter over a single window of input samples using fibonacci p codes for a subclass of positive boolean functions a more efficient parallel algorithm and vlsi architecture for running stack filtering is also presented the area time complexities of the proposed designs are estimated

adaptive stack filtering with application to image processing with the aid of threshold decomposition it is shown that optimal stack filters under the mean absolute error mae criterion are equal to optimal or bayesian classifiers subject to stacking constraints under the mean classification error mce criterion nonadaptive and adaptive constrained least mean absolute lma algorithms are developed for the esti mation of stack filters through the linearization of the unit step function in the objective function the convergence of the al gorithms is proven under certain conditions although the methods do not generally give optimal stack filters under the mae criterion these algorithms have several distinct merits compared to other stack filter optimization methods 1 the op timization problem has a unique solution that approximates the optimal stack filters in the least mean square sense 2 the meth ods can be implemented in the binary and real domains and 3 for stack filters defined by linearly separable positive boolean functions pbf s or weighted order statistic wos filters the number of the parameters to be estimated is reduced to the window width of the filter a comparison between images re stored by the new algorithms and the stack filtering algorithm optimal under the mae criterion confirms the effectiveness of the proposed algorithms

a dantzig wolfe like variant of karmarkar s interior point linear programming algorithm we show that a variant of karmarkar s projective algorithm for linear programming can be viewed as following the approach of dantzig wolfe decomposition at each iteration the current primal feasible solution generates prices which are used to form a simple subproblem the solution to the subproblem is then incorporated into the current feasible solution with a suitable choice of stepsize a constant reduction in potential function is achieved at each iteration we also use our analysis to motivate a new primal simplex pivot rule that is closely related to rules used by e klotz and l schrage

on the average condition of random linear programs we give an cal o log n bound for the expectation of the logarithm of the condition number cal k a b c introduced in solving linear programs with finite precision i condition numbers and random programs math program 99 2004 pp 175 196 this bound improves the previously existing bound which was of cal o n and yields average case bounds for both the required precision and the complexity of computing an optimal basis or a pair of primal dual optimizers

characterizations bounds and probabilistic analysis of two complexity measures for linear programming problems this note studies a a condition number used in the linear programming algorithm of vavasis and ye 14 whose running time depends only on the constraint matrix a m n and a a variant of another condition number due to ye 17 that also arises in complexity analyses of linear programming problems we provide a new characterization of a and relate a and a furthermore we show that if a is a standard gaussian matrix then e ln a o min mlnn n thus the expected running time of the vavasis ye algorithm for linear programming problems is bounded by a polynomial in m and n for any right hand side and objective coefficient vectors when a is randomly generated in this way as a corollary of the close relation between a and a we show that the same bound holds for e ln a

a variation on karmarkar s algorithm for solving linear programming problems the algorithm described here is a variation on karmarkar s algorithm for linear programming it has several advantages over karmarkar s original algorithm in the first place it applies to the standard form of a linear programming problem and produces a monotone decreasing sequence of values of the objective function the minimum value of the objective function does not have to be known in advance secondly in the absence of degeneracy the algorithm converges to an optimal basic feasible solution with the nonbasic variables converging monotonically to zero this makes it possible to identify an optimal basis before the algorithm converges

a combined phase i phase ii projective algorithm for linear programming we devise a projective algorithm which explicitly considers the constraint that an artificial variable be zero at the solution inclusion of such a constraint allows the algorithm to be applied to a possibly infeasible standard form linear program without the addition of any bigm terms or conversion to a primal dual problem

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

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

analysis of the properties of median and weighted median filters using threshold logic and stack filter representation the deterministic properties of weighted median wm filters are analyzed threshold decomposition and the stacking property together establish a unique relationship between integer and binary domain filtering the authors present a method to find the weighted median filter which is equivalent to a stack filter defined by a positive boolean function because the cascade of wm filters can always be expressed as a single stack filter this allows expression of the cascade of wm filters as a single wm filter a direct application is the computation of the output distribution of a cascade of wm filters the same method is used to find a nonrecursive expansion of a recursive wm filter as applications of theoretical results several interesting deterministic and statistical properties of wm filters are derived

minimum mean absolute error stack filtering with structural constraint and goals a theory for the structural behavior of stack filters is developed this theory provides a test which can determine if a given stack filter has any root signals a method for classifying the root signal behavior of any stack filter found to have roots and perhaps most important a method for designing stack filters with specific root signals or other structural behavior this theory of root signals for stack filters is then combined with the theory of minimum mean absolute error stack filtering this unified theory allows the designer to pick a filter which minimizes noise subject to constraints on its structural behavior

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