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

fine structure of the 2f1 f2 acoustic distortion product changes with primary level the fine frequency structure of the 2f1 f2 acoustic distortion product adp fine structure was examined in ten human subjects with normal hearing primary frequencies f1 and f2 were incremented in steps of 1 32 octave with an f2 f1 ratio of 1 2 the primary levels were kept equal to each other and varied from 45 to 65 db spl in 2 5 db steps the results show that the adp fine structure is characterized by a series of peaks and valleys across frequency with a peak to peak frequency spacing of about 3 32 octave and a peak to valley amplitude ratio of up to 20 db at frequencies below 4000 hz as primary level increases the sharpness of the adp fine structure is not significantly reduced and the pattern gradually shifts to lower frequencies at frequencies above 4000 hz a flattening of the pattern is sometimes observed at high levels a consequence of the underlying process responsible for the fine structure is that adp input output i o functions can be highly variable in shape dramatic shape change

reducing reflected contributions to ear canal distortion product otoacoustic emissions in humans distortion product otoacoustic emission dpoae fine structure has been attributed to the interaction of two cochlear source mechanisms distortion and reflection sources a suppressor presented near the 2f1 f2 frequency reduces the reflection source contribution and therefore dpoae fine structure optimal relationships between stimulus and suppressor conditions however have not been described in this study the relationship between suppressor level l3 and stimulus level l2 was evaluated to determine the l3 that was most effective at reducing fine structure subjects were initially screened to find individuals who produced dpoae fine structure a difference in the prevalence of fine structure in two frequency intervals was observed at 2 khz 11 of 12 subjects exhibited fine structure as compared to 5 of 22 subjects at 4 khz only subjects demonstrating fine structure participated in subsequent measurements dpoae responses were evaluated in 1 3 octave intervals centered at 2 or 4 khz with 4 subjects contributing data at each interval multiple l3 s were evaluated for each l2 which ranged from 20 to 80 db spl the results indicated that one or more l3 s at each l2 were roughly equally effective at reducing dpoae fine structure however no single l3 was effective at all l2 s in every subject

distortion product otoacoustic emission input output characteristics in normal hearing and hearing impaired human ears dpoae input output i o functions were measured at 7f2 frequencies 1 to 8 khz f2 f1 1 22 over a range of levels 5 to 95 db spl in normal hearing and hearing impaired human ears l1 l2 was level dependent in order to produce the largest 2f1 f2 responses in normal ears system distortion was determined by collecting dp data in six different acoustic cavities these data were used to derive a multiple linear regression model to predict system distortion levels the model was tested on cochlear implant users and used to estimate system distortion in all other ears at most but not all f2 s measurements in cochlear implant ears were consistent with model predictions at all f2 frequencies the ears with normal auditory thresholds produced i o functions characterized by compressive nonlinear regions at moderate levels with more rapid growth at low and high stimulus levels as auditory threshold increased dpoae threshold increased accompanied by dpoae amplitude reductions notably over the range of levels where normal ears showed compression the slope of the i o function was steeper in impaired ears the data from normal hearing ears resembled direct measurements of basilar membrane displacement in lower animals data from ears with hearing loss showed that the compressive region was affected by cochlear damage however responses at high levels of stimulation resembled those observed in normal ears

low frequency and high frequency cochlear nonlinearity in humans low and high frequency cochlear nonlinearity was studied by measuring distortion product otoacoustic emission input output dpoae i o functions at 0 5 and 4khz in 103 normal hearing subjects behavioral thresholds at both f2 s were used to set l2 in db sl for each subject primary levels were optimized by determining the l1 resulting in the largest ldp for each l2 for each subject and both f2 s dpoae i o functions were measured using l2 inputs from 10db sl 0 5khz or 20db sl 4khz to 65db sl both frequencies mean dpoae i o functions averaged across subjects differed between the two frequencies even when threshold was taken into account the slopes of the i o functions were similar at 0 5 and 4khz for high level inputs with maximum compression ratios of about 4 1 at both frequencies the maximum slope near dpoae threshold was approximately 1 which occurred at lower levels at 4khz compared to 0 5khz these results suggest that there is a wider dynamic range and perhaps greater cochlear ampl

numerical approximations for stochastic differential games the markov chain approximation method is a widely used robust relatively easy to use and efficient family of methods for the bulk of stochastic control problems in continuous time for reflected jump diffusion type models it has been shown to converge under broad conditions and there are good algorithms for solving the numerical problems if the dimension is not too high versions of these methods have been used in applications to various two player differential and stochastic dynamic games for a long time and proofs of convergence are available for some cases mainly using pde type techniques in this paper purely probabilistic proofs of convergence are given for a broad class of such problems where the controls for the two players are separated in the dynamics and cost function and which cover a substantial class not dealt with in previous works discounted and stopping time cost functions are considered finite horizon problems and problems where the process is stopped on first hitting an a priori given boundary can be dealt with by adapting the methods of h j kushner and p dupuis numerical methods for stochastic control problems in continuous time 2nd ed springer verlag berlin new york 2001 as done in this paper for the treated problems the essential conditions are the weak sense existence and uniqueness of solutions an almost everywhere continuity condition and that a weak local consistency condition holds almost everywhere for the numerical approximations just as for the control problem there are extensions to problems with controlled variance and jumps

computing b stationary points of nonsmooth dc programs motivated by a class of applied problems arising from physical layer based security in a digital communication system in particular by a secrecy sum rate maximization problem this paper studies a nonsmooth difference of convex dc minimization problem the contributions of this paper are i clarify several kinds of stationary solutions and their relations ii develop and establish the convergence of a novel algorithm for computing a d stationary solution of a problem with a convex feasible set that is arguably the sharpest kind among the various stationary solutions iii extend the algorithm in several directions including a randomized choice of the subproblems that could help the practical convergence of the algorithm a distributed penalty approach for problems whose objective functions are sums of dc functions and problems with a specially structured nonconvex dc constraint for the latter class of problems a pointwise slater constraint qualification is introduced that facilitates the ver

a general double proximal gradient algorithm for d c programming the possibilities of exploiting the special structure of d c programs which consist of optimising the difference of convex functions are currently more or less limited to variants of the dca proposed by pham dinh tao and le thi hoai an in 1997 these assume that either the convex or the concave part or both are evaluated by one of their subgradients in this paper we propose an algorithm which allows the evaluation of both the concave and the convex part by their proximal points additionally we allow a smooth part which is evaluated via its gradient in the spirit of primal dual splitting algorithms the concave part might be the composition of a concave function with a linear operator which are however evaluated separately for this algorithm we show that every cluster point is a solution of the optimisation problem furthermore we show the connection to the toland dual problem and prove a descent property for the objective function values of a primal dual formulation of the problem convergence of the iterates is shown if this objective function satisfies the kurdyka ojasiewicz property in the last part we apply the algorithm to an image processing model

numerical approximations for stochastic differential games the ergodic case the markov chain approximation method is a widely used relatively easy to use and efficient family of methods for the bulk of stochastic control problems in continuous time for reflected jump diffusion type models it has been shown to converge under broad conditions and there are good algorithms for solving the numerical problems if the dimension is not too high we consider a class of stochastic differential games with a reflected diffusion system model and ergodic cost criterion and where the controls for the two players are separated in the dynamics and cost function it is shown that the value of the game exists and that the numerical method converges to this value as the discretization parameter goes to zero the actual numerical method solves a stochastic game for a finite state markov chain and ergodic cost criterion the essential conditions are nondegeneracy and that a weak local consistency condition hold almost everywhere for the numerical approximations just as for the control problem

risk sensitive control on an infinite time horizon stochastic control problems on an infinite time horizon with exponential cost criteria are considered the donsker varadhan large deviation rate is used as a criterion to be optimized the optimum rate is characterized as the value of an associated stochastic differential game with an ergodic expected average cost per unit time cost criterion if we take a small noise limit a deterministic differential game with average cost per unit time cost criterion is obtained this differential game is related to robust control of nonlinear systems

open queueing networks in heavy traffic this paper presents heavy traffic limit theorems for the queue length and sojourn time processes associated with open queueing networks these limit theorems state that properly normalized sequences of queue length and sojourn time processes converge weakly to a certain diffusion as the network traffic intensity converges to unity the limit diffusion is reflected brownian motion on the nonnegative orthant this process behaves like brownian motion on the interior of its state space and reflects instantaneously on the boundaries the reflection direction is a constant for each boundary hyperplane

sources of variability in distortion product otoacoustic emissions the goal of this study was to determine the extent to which the variability seen in distortion product otoacoustic emissions dpoaes among ears with normal hearing could be accounted for several factors were selected for investigation including behavioral threshold differences in middle ear transmission characteristics either in the forward or the reverse direction and differences in contributions from the distortion and reflection sources these variables were assessed after optimizing stimulus parameters for individual ears at each frequency a multiple linear regression was performed to identify whether the selected variables either individually or in combination explained significant portions of variability in dpoae responses behavioral threshold at the f2 frequency and behavioral threshold squared at that same frequency explained the largest amount of variability in dpoae level compared to the other variables the combined model explained a small but significant amount of variance in dpoae level at five frequencies a large amount of residual variability remained even at frequencies where the model accounted for significant amounts of variance

distortion product otoacoustic emission measured with continuously varying stimulus level distortion product otoacoustic emissions dpoae are measured by stimulating the ear with two simultaneous tones a novel method for measuring dpoaes has been developed in which the tone levels vary continuously instead of in discrete steps varying the tone levels continuously may offer advantages for characterizing dpoae level as a function of stimulus level for equivalent primary levels dpoae levels measured with the continuous level method were the same as levels obtained with the discrete level method thus validating the new method continuous level measurements were used to determine the optimal l1 for each l2 in individual subjects n 20 at f2 1 2 4 and 8 khz by using a lissajous path that covered a wide range of stimulus levels the optimal l1 defined as the l1 that resulted in the largest dpoae for each l2 varied across subjects and across frequency the optimal difference between l1 and l2 decreased with increasing l2 at all frequencies and increased with frequency when l2 was low whe

a boundary property of semimartingale reflecting brownian motions we consider a class of reflecting brownian motions on the non negative orthant inr k in the interior of the orthant such a process behaves like brownian motion with a constant covariance matrix and drift vector at each of the k 1 dimensional faces that form the boundary of the orthant the process reflects instantaneously in a direction that is constant over the face we give a necessary condition for the process to have a certain semimartingale decomposition and then show that the boundary processes appearing in this decomposition do not charge the set of times that the process is at the intersection of two or more faces this boundary property plays an essential role in the derivation performed in a separate work of an analytical characterization of the stationary distributions of such semimartingale reflecting brownian motions

convergence of new inertial proximal methods for dc programming we present iterative methods for finding the critical points and or the minima of extended real valued functions of the form phi psi g h where psi is a differentiable function and g and h are convex proper and lower semicontinuous the underlying idea relies upon the discretization of a first order dissipative dynamical system which allows us to preserve the local feature and to obtain some convergence results the main theorems not only recover known convergence results in this field but also provide a theoretical basis for the development of new iterative methods

the gauss seidel numerical procedure for markov stochastic games consider the problem of value iteration for solving markov stochastic games one simply iterates backward via a jacobi like procedure the convergence of the gauss seidel form of this procedure is shown for both the discounted and ergodic cost problems under appropriate conditions with extensions to problems where one stops when a boundary is hit or if any one of the players chooses to stop with associated costs generally the gauss seidel procedure accelerates convergence

comparing the optimal signal conditions for recording cubic and quadratic distortion product otoacoustic emissions odd and even order distortion products dps evoked by two primary tones f1 f2 f1 f2 represent different aspects of cochlear nonlinearity the cubic and quadratic difference tones cdt 2f1 f2 and qdt f2 f1 are prominent representatives of the odd and even dps distortion product otoacoustic emissions dpoaes were measured within a primary level l1 l2 space over a wide range of f2 f1 ratios to compare the optimal signal conditions for these dps for cdt the primary level difference decreased as l1 increased with a rate proportional to the f2 f1 ratio moreover the optimal ratio increased with l1 a set of two formulas is proposed to describe the optimal signal conditions however for a given level of a primary increasing the other tone level could maximize the qdt amplitude the frequency ratio at the maximal qdt was about 1 3 and quite constant across different primary levels a notch was found in the qdt amplitude at the f2 f1 ratio of about 1 22 1 25 these opposite behaviors suggest that the optimal recording conditions are different for cdt and qdt due to the different aspects in the cochlear nonlinearity optimizing the dpoae recordings could improve the reliability in clinical or research practices

accelerating the dc algorithm for smooth functions we introduce two new algorithms to minimise smooth difference of convex dc functions that accelerate the convergence of the classical dc algorithm dca we prove that the point computed by dca can be used to define a descent direction for the objective function evaluated at this point our algorithms are based on a combination of dca together with a line search step that uses this descent direction convergence of the algorithms is proved and the rate of convergence is analysed under the ojasiewicz property of the objective function we apply our algorithms to a class of smooth dc programs arising in the study of biochemical reaction networks where the objective function is real analytic and thus satisfies the ojasiewicz property numerical tests on various biochemical models clearly show that our algorithms outperform dca being on average more than four times faster in both computational time and the number of iterations numerical experiments show that the algorithms are globally convergent to a non equilibrium steady state of various biochemical networks with only chemically consistent restrictions on the network topology

influence of primary level and primary frequency ratios on human distortion product otoacoustic emissions the combined influence of primary level differences l1 l2 and primary frequency ratio f2 f1 on distortion product otoacoustic emission dpoae level was investigated in 20 normal hearing subjects dpoaes were recorded with continuously varying stimulus levels neely et al j acoust soc am 117 1248 1259 2005 for the following stimulus conditions f2 1 2 4 and 8 khz and f2 f1 1 05 to 1 4 various l1 l2 including one individually optimized to produce the largest dpoae for broadly spaced primary frequencies at low l2 levels the largest dpoaes were recorded when l1 was much higher than l2 with l1 remaining relatively constant as l2 increased as f2 fl decreased the largest dpoaes were observed when l1 was closer to l2 and increased as l2 increased optimal values for l1 l2 and f2 f1 were derived from these data in general average dpoae levels for the new l1 l2 and f2 f1 were equivalent to or larger than those observed for other stimulus combinations including the l1 l2 described by kummer et al j acoust soc am 103 3431 3444 1998 and those defined by neely et al in which l1 l2 was evaluated but f2 f1 was fixed at 1 2

dependence of distortion product otoacoustic emissions on primary levels in normal and impaired ears i effects of decreasing l2 below l1 the 2f1 f2 distortion product otoacoustic emission dpoae is evoked by two primary tones of frequencies f1 f2 and levels l1 and l2 previous reports indicate that decreasing l2 below l1 l2 can 1 increase dpoae amplitude in normal ears and 2 increase the degree to which dpoae amplitudes are reduced by cochlear trauma although both of these factors could be advantageous for clinical applications of dpoaes neither has been explored in detail in the present study 2f1 f2 dpoae amplitude frequency functions were collected from normal and impaired ears of rabbits and humans with l1 l2 and with l2 l1 at each of three values of l1 in rabbits controlled tonal or noise overexposures were used to produce permanent reductions of dpoae amplitudes comparison of pre and postexposure dpoae amplitude frequency functions demonstrated that the frequency specific reductions of dpoaes were enhanced by decreasing l2 below l1 in humans dpoae amplitude frequency functions obtained with the various l1 and l2 c

admission control for combined guaranteed performance and best effort communications systems under heavy traffic communications systems often have many types of users since the users share the same resource there is a conflict in their needs this conflict leads to the imposition of controls on admission or elsewhere in this paper there are two types of customers gp guaranteed performance and be best effort we consider an admission control of gp customer which has two roles first to guarantee the performance of the existing gp customers and second to regulate the congestion for the be users the optimal control problem for the actual physical system is difficult a heavy traffic approximation is used with optimal or nearly optimal controls it is shown that the optimal values for the physical system converge to that for the limit system and that good controls for the limit system are also good for the physical system this is done for both the discounted and average cost per unit time cost criteria additionally asymptotically the pathwise average not mean costs for the physical system are nearly minimal when good nearly optimal controls for the limit system are used numerical data show that the heavy traffic optimal control approach can lead to substantial reductions in waiting time for be with only quite moderate rejections of gp under heavy traffic it also shows that the controls are often linear in the state variables the approach has many advantages it is robust simplifies the analysis both analytical and numerical and allows a more convenient study of the parametric dependencies even if optimal control is not wanted the approach is very convenient for a systematic exploration of the possible tradeoffs among the various cost components this is done by numerically solving a series of problems with different weights on the costs we can then get the best tradeoffs and the control policies which give them

nash equilibrium approximation of some class of stochastic differential games a combined chebyshev spectral collocation method with policy iteration abstract this study relates to nonzero sum stochastic games with perfect information it proposes an efficient combined chebyshev spectral collocation method cscm with the policy iteration pi algorithm for solving nonlinear coupled hamilton jacobi hj equations the proposed approach is comprised of two steps first the pi algorithm is used to reduce the nonlinear coupled hj equations to a sequence of linear uncoupled pdes then these equations are approximated by the cscm the cscm pi is especially useful when the cscm fails due to the increasing number of collocation points for solving the associated system of nonlinear algebraic equations the main advantage of the resulting method is that it converts nonlinear coupled hj equations to the systems of linear algebraic equations which can be solved readily convergence analysis of this method is also provided in detail to confirm the accuracy and validity of the proposed computational algorithm several illustrative examples are presented

zero sum risk sensitive stochastic differential games we study zero sum risk sensitive stochastic differential games on the infinite horizon with discounted and ergodic payoff criteria under certain assumptions we establish the existence of values and saddle point equilibria we obtain our results by studying the corresponding hamilton jacobi isaacs equations finally we show that the value of the ergodic payoff criterion is a constant multiple of the maximal eigenvalue of the generators of the associated nonlinear semigroups