adaptive controller for wing flutter with immeasurable excitations and unmodelled dynamics abstract the problem of designing a robust simplified controller for the control of a wing flutter vibration is studied the adaptive control algorithm developed by bar kana et al 1983 is extended to include independent excitations to both the input and the output of the plant those excitations are partitioned into measurable and unmeasurable parts and are incorporated into the ideal trajectory and into the adaptive law the stability of the adaptive law is proved using ultimate bounded ness results the almost strict positive realness property of the plant is examined and related to the minimum phase property to the output stabilizability and to the steady state solution of the riccati equation the numerical simulations of the wing flutter control problem demonstrate stability and robustness over a wide range of variations in both the plant and adaptation parameters

the expressive power of valued constraints hierarchies and collapses in this paper we investigate the ways in which a fixed collection of valued constraints can be combined to express other valued constraints we show that in some cases a large class of valued constraints of all possible arities can be expressed by using valued constraints over the same domain of a fixed finite arity we also show that some simple classes of valued constraints including the set of all monotonic valued constraints with finite cost values cannot be expressed by a subset of any fixed finite arity and hence form an infinite hierarchy

dynamic balancing randomization in controlled clinical trials in the design of randomized clinical trials balancing of treatment allocation across important prognostic factors strata improves the efficiency of the final comparisons whilst randomization methods exist which attempt to balance treatments across the strata permuted blocks minimization biased coin these approaches assign equal importance for all the strata dynamic balancing randomization dbr is a tree based method proposed by signorini et al allowing different levels of imbalance in different strata which ensures a balance for each level of prognostic risk factors conditional balance whilst at the same time preserving randomness we present a simple modification to the original approach to maintain a marginal balance over important strata and examine the properties of this modification two important measures of performance are used to provide comparisons between the approaches a loss function which can be interpreted as the squared norm of the imbalance vector and a forcing index which conveys the degree of randomness a comparison of dbr with minimization and a biased coin design is carried out by simulation on two simulated trials

the asymptotic properties of nonparametric tests for comparing survival distributions the asymptotic distribution under alternative hypotheses is derived for a class of statistics used to test the equality of two survival distributions in the presence of arbitrary and possibly unequal right censoring the test statistics include equivalents to the log rank statistic the modified wilcoxon statistic and the class of rank invariant test procedures introduced by peto peto when there are equal censoring distributions and the hazard functions are proportional the sample size formula for the f test used to compare exponential samples is shown to be valid for the log rank test in certain situations the power of the log rank test falls as the amount of censoring decreases

degrees of freedom of two hop wireless networks everyone gets the entire cake we show that fully connected two hop wireless networks with k sources k relays and k destinations have k degrees of freedom both in the case of time varying channel coefficients and constant channel coefficients in which case the result holds for almost all values of constant channel coefficients our main contribution is a new achievability scheme which we call aligned network diagonalization this scheme allows the data streams transmitted by the sources to undergo a diagonal linear transformation from the sources to the destinations thus being received free of interference by their intended destination in addition we extend our scheme to multihop networks with fully connected hops and multihop networks with mimo nodes for which the degrees of freedom are also fully characterized

robust adaptive control in the presence of bounded disturbances the model reference adaptive control of a linear plant subjected to bounded disturbances is considered by analyzing a set of nonlinear differential equations it is shown that the global behavior of the adaptive system depends upon the persistent excitation of the reference input as well as the amplitude of the external disturbances the principal contribution of the paper is the derivation of sufficient conditions on the persistent excitation of the reference input given the maximum amplitude of disturbance for the signals in the adaptive system to be globally bounded

tuning multitone instabilities and intrinsic differences in robustness of adaptive control systems an example is presented of an adaptive system that becomes unstable when a multitone reference input is applied although it is stable when the spectral components are applied separately it is further shown that another scheme based on an input error instead of an output error in the adaptation does not exhibit the same instability mechanism the technique of averaging is used to analyze this phenomenon the equilibrium points of the averaged system called the tuned values are investigated results are given on the number of tuned values their locations and their stability the analysis is not only valid for a specific plant but for a large class of systems

cut set bound is loose for gaussian relay networks the cut set bound developed by cover and el gamal in 1979 has since remained the best known upper bound on the capacity of the gaussian relay channel we develop a new upper bound on the capacity of the gaussian primitive relay channel which is tighter than the cut set bound our proof uses gaussian measure concentration to establish geometric relations satisfied with high probability between the n letter random variables associated with a reliable code for communicating over this channel we then translate these geometric relations into new information inequalities that cannot be obtained with classical methods combined with a tensorization argument proposed by courtade and ozgur in 2015 our result also implies that the current capacity approximations for gaussian relay networks which have linear gap to the cut set bound in the number of nodes are order optimal and lead to a lower bound on the pre constant

a stability instability boundary for disturbance free slow adaptation with unmodeled dynamics the instability of adaptive schemes for small values of parameter adjustment gain has the form of a slow drift of adjustable parameters with an averaging analysis we derive not only a sufficient condition for stability of this drift but also a sufficient condition for it to be unstable a sharp boundary between stability and instability is signal dependent and much less demanding than the usual strict positive realness property the new positivity condition has a simple signal energy interpretation

singularity free adaptive pole placement using periodic controllers a globally convergent adaptive control scheme for nonminimum phase systems is presented the approach is based on a particular periodic pole placement controller an ad hoc parameter estimate correction procedure is used to prevent any possible singularities in the control law computation furthermore a lower bound on the estimated model controllability is ensured the a priori knowledge on the system is reduced to the process order

finite dimensional adaptive observers applied to distributed parameter systems the application of finite dimensional adaptive observers to distributed parameter systems is addressed ultimate boundedness of the parameter and state errors are proved in the case of residuals which have finite energy over a finite time interval provided the plant input is definitely exciting in the absence of definite excitation an error growth rate of proportional to t sup 1 2 is proved the results are obtained without assuming plant stability or input boundedness

submodular functions from discrete to continous domains submodular set functions have many applications in combinatorial optimization as they can be minimized and approximately maximized in polynomial time a key element in many of the algorithms and analyses is the possibility of extending the submodular set function to a convex function which opens up tools from convex optimization submodularity goes beyond set functions and has naturally been considered for problems with multiple labels or for functions defined on continuous domains where it corresponds essentially to cross second derivatives being nonpositive in this paper we show that most results relating submodularity and convexity for set functions can be extended to all submodular functions in particular a we naturally define a continuous extension in a set of probability measures b show that the extension is convex if and only if the original function is submodular c prove that the problem of minimizing a submodular function is equivalent to a typically non smooth convex optimization problem and d propose another convex optimization problem with better computational properties e g a smooth dual problem most of these extensions from the set function situation are obtained by drawing links with the theory of multi marginal optimal transport which provides also a new interpretation of existing results for set functions we then provide practical algorithms to minimize generic submodular functions on discrete domains with associated convergence rates

stability of slow adaptation for non spr systems with disturbances sufficient conditions are given for the existence of a bounded uniformly asymptotically stable u a s solution of the model reference adaptive control system these conditions which do not require any matching assumptions or knowledge of the order of the plant provide an estimate of the region of attraction and a bound on the average squared tracking error for which the u a s property of the solution is preserved

on the optimality of simple schedules for networks with multiple half duplex relays this paper studies networks that consist of n half duplex relays assisting the communication between a source and a destination in isit 12 brahma et al conjectured that in gaussian half duplex diamond networks i e without a direct link between the source and the destination and with n non interfering relays an approximately optimal relay scheduling policy i e achieving the cut set upper bound to within a constant gap uniformly over all channel gains has at most n 1 active states i e at most n 1 out of the 2 n possible relay listen transmit configurations have a strictly positive probability such relay scheduling policies were referred to as simple in itw 13 we conjectured that simple approximately optimal relay scheduling policies exist for any gaussian half duplex multi relay network irrespectively of the topology this paper formally proves this more general version of the conjecture and shows it holds beyond gaussian noise networks in particular for any class of memoryless half duplex n relay networks with independent noises and for which independent inputs are approximately optimal in the cut set upper bound an approximately optimal simple relay scheduling policy exists the key step of the proof is to write the minimum of the submodular cut set function by means of its lovasz extension and use the greedy algorithm for submodular polyhedra to highlight structural properties of the optimal solution this together with the saddle point property of min max problems and the existence of optimal basic feasible solutions for linear programs proves the conjecture as an example for n relay gaussian networks with independent noises where each node is equipped with multiple antennas and where each antenna can be configured to listen or transmit irrespectively of the others the existence of an approximately optimal simple relay scheduling policy with at most n 1 active states irrespectively of the total number of antennas in the system is proved

a robust direct adaptive controller this paper proposes a new direct adaptive control algorithm which is robust with respect to additive and multiplicative plant unmodeled dynamics the algorithm is designed based on the reduced order plant which is assumed to be minimum phase and of known order and relative degree but is analyzed with respect to the overall plant which due to the unmodeled dynamics may be nonminimum phase and of unknown order and relative degree it is shown that if the unmodeled dynamics are sufficiently small in the low frequency range then the algorithm guarantees boundedness of all signals in the adaptive loop and small residual tracking errors for any bounded initial conditions in the absence of unmodeled dynamics the residual tracking error is shown to be zero

analysis of adaptive identifiers in the presence of unmodeled dynamics averaging and tuned parameters the authors analyze the behavior of a standard identifier when the plant contains additional dynamics called unmodeled dynamics which invalidate the known order assumption the first result of the analysis is an input richness condition which does not depend on the order of the unmodeled dynamics to guarantee persistency of excitation of the regressor then it is shown that the persistently exciting pe condition leads to a bibo bounded input bounded output stability property for the identifier the method of averaging is used to formally define the notion of tuned parameters as the equilibrium of the identifier averaged system it is shown that the tuned parameters always exist and that the actual parameters converge to some neighborhood of the tuned parameters from the definition of the tuned parameters an explicit expression to calculate and interpret them as the fixed parameter values that minimize the mean squared output error is derived

submodular function minimization submodular functions often arise in various fields of operations research including discrete optimization game theory queueing theory and information theory in this survey paper we give overview on the fundamental properties of submodular functions and recent algorithmic devolopments of their minimization

examination of the spr condition in output error parameter estimation abstract when the spr condition is not satisfied then there exist input signals for which the considered output error algorithm is locally unstable a condition is given which delimits the sharp stability instability boundary in the case of slow estimation whereas local stability properties are guaranteed by a more conservative signal dependent average spr condition these conditions are also illustrated by an example

stable adaptive regulation of arbitrary nth order plants this paper presents an algorithm for adaptively stabilizing and asymptotically regulating an arbitrary single input single output linear time invariant plant which is controllable and observable of known order n and has unknown parameters no further assumptions are made no external probing signal is required

on morse s new adaptive controller parameter convergence and transient performance some transient and asymptotic performance properties are established for the model reference adaptive controller proposed by a s morse proc us italy joint seminar syst models feedback 1992 it is proved that the l sub 2 norm of the tracking error is uniformly bounded by the initial parameter estimation error further if the initial conditions are sufficiently small it is shown that the l sub infinity norm of the tracking error is uniformly bounded by the l sub m2 norm of the reference signal these transient bounds are independent of the signals richness and the adaptation gain making them arguably the strongest transient results available in the literature second excitation conditions for exponential stability a property which is well known to insure some local performance measures are given to this end it is shown that modulo a signal dependent time scale change morse s estimator is equivalent to a normalized gradient plus filtering identifier

adaptive regulation of mimo linear discrete time systems without requiring a persistent excitation an adaptive regulator which does not require a persistent excitation is developed for multiinput multioutput mimo linear discrete time systems the assumptions on the plant are 1 an upper bound on the system dimension is known 2 the unknown system parameters belong to known bounded intervals 3 the plant is stabilizable for all possible values of the unknown system parameters the stabilizability condition can be tested before the system is put into operation a recursive parameter estimation scheme is given which forces the parameter estimates to converge to the known intervals using this estimator an adaptive regulator is derived which results in a globally stable closed loop system

lattices which are good for almost everything we define an ensemble of lattices and show that for asymptotically high dimension most of its members are simultaneously good as sphere packings sphere coverings additive white gaussian noise awgn channel codes and mean squared error mse quantization codes these lattices are generated by applying construction a to a random linear code over a prime field of growing size i e by lifting the code to spl ropf sup n

sufficiency of excitation in the context of adaptive identification and adaptive control of linear systems the concept of a sufficiently exciting input play a key role in this note necessary and sufficient conditions are presented for an input function of a single input linear stationary system to be sufficiently exciting these conditions are independent of the stability properties of the linear system

a robust indirect adaptive control approach this paper considers the robust design of an indirect adaptive control approach which is applicable when the unknown parameters of a linear time invariant plant lie in a known convex set throughout which no unstable pole zero cancellation occurs in order to achieve the robustness the use of a relative dead zone in the adaptive law is proposed it is shown that with a suitably designed relative dead zone the adaptive control system is globally stable even in the presence of small unmodeled plant uncertainties

robust redesign of adaptive control effects of unmodeled high frequency dynamics on stability and performance of adaptive control schemes are analyzed in the regulation problem global stability properties are no longer guaranteed but a region of attraction exists for exact adaptive regulation the dependence of the region of attraction on unmodeled parasitics is examined first then the general case of model reference adaptive control is considered in which parasitics can destroy stability and boundedness properties a modified adaptive law is proposed guaranteeing the existence of a region of attraction from which all signals converge to a residual set which contains the equilibrium for exact tracking the size of this set depends on design parameters the frequency range of parasitics and the reference input signal characteristics

inefficiency of randomization methods that balance on stratum margins and improvements with permuted blocks and a sequential method stratified permuted blocks randomization is commonly applied in clinical trials but other randomization methods that attempt to balance treatment counts marginally for the stratification variables are able to accommodate more stratification variables when the analysis stratifies on the cells formed by crossing the stratification variables these other randomization methods yield treatment effect estimates with larger variance than does stratified permuted blocks when it is truly necessary to balance the randomization on many stratification variables it is shown how this inefficiency can be improved by using a sequential randomization method where the first level balances on the crossing of the strata used in the analysis and further stratification variables fall lower in the sequential hierarchy copyright 2012 john wiley sons ltd

a digital interface for gaussian relay and interference networks lifting codes from the discrete superposition model for every gaussian network there exists a corresponding deterministic network called the discrete superposition network we show that this discrete superposition network provides a near optimal digital interface for operating a class consisting of many gaussian networks in the sense that any code for the discrete superposition network can be naturally lifted to a corresponding code for the gaussian network while achieving a rate that is no more than a constant number of bits lesser than the rate it achieves for the discrete superposition network this constant depends only on the number of nodes in the network and not on the channel gains or snr moreover the capacities of the two networks are within a constant of each other again independent of channel gains and snr we show that the class of gaussian networks for which this interface property holds includes relay networks with a single source destination pair interference networks multicast networks and the counterparts of these networks with multiple transmit and receive antennas the code for the gaussian relay network can be obtained from any code for the discrete superposition network simply by pruning it this lifting scheme establishes that the superposition model can indeed potentially serve as a strong surrogate for designing codes for gaussian relay networks we present similar results for the k k gaussian interference network mimo gaussian interference networks mimo gaussian relay networks and multicast networks with the constant gap depending additionally on the number of antennas in case of mimo networks

earliest arrival flows with multiple sources earliest arrival flows capture the essence of evacuation planning given a network with capacities and transit times on the arcs a subset of source nodes with supplies and a sink node the task is to send the given supplies from the sources to the sink as quickly as possible the latter requirement is made more precise by the earliest arrival property which requires that the total amount of flow that has arrived at the sink is maximal for all points in time simultaneously it is a classical result from the 1970s that for the special case of a single source node earliest arrival flows do exist and can be computed by essentially applying the successive shortest path algorithm for min cost flow computations although it has previously been observed that an earliest arrival flow still exists for multiple sources the problem of computing one efficiently has been open for many years we present an exact algorithm for this problem whose running time is strongly polynomial in the input plus output size of the problem

stable pole placement direct adaptive control for systems with arbitrary zeros this paper extends a recently proposed adaptive regulation algorithm to the general case where a non zero bounded reference signal is allowed the desired control objectives are asymptotically satisfied in the sense that the estimated plant together with the adaptive controller yield a characteristic polynomial arbitrarily close to the desired one furthermore in the case of a zero reference signal the regulation objective is asymptotically achieved

brief paper on the stabilizability condition in indirect adaptive control many recent studies on overall stability of adaptive control systems require among other conditions that the identified model be stabilizable at least asymptotically in fact the usual identification methods do not guarantee this property in the passive approach without exciting extra signals or if the model order is subject to over estimation in order to solve this problem it is shown in this paper that certain classical identification algorithms can be easily modified in order to ensure the above stabilizability condition without affecting the other properties

robust model reference adaptive control we propose a new model reference adaptive control algorithm and show that it provides the robust stability of the resulting closed loop adaptive control system with respect to unmodeled plant uncertainties the robustness is achieved by using a relative error signal in combination with a dead zone and a projection in the adaptive law the extra a priori information needed to design the adaptive law are bounds on the plant parameters and an exponential bound on the impulse response of the inverse plant transfer function

network simplification in half duplex building on submodularity this paper explores the network simplification problem in the context of gaussian half duplex diamond networks specifically given an n relay diamond network this problem seeks to derive fundamental guarantees on the capacity of the best k relay subnetwork as a function of the full network capacity simplification guarantees are presented in terms of a particular approximate capacity termed independent gaussian ig approximate capacity that characterizes the network capacity to within an additive gap which is independent of the channel coefficients and operating snr the main focus of this work is when k n 1 relays are selected out of n relays in a diamond network first a simple algorithm is proposed which selects all relays except the one with the minimum ig approximate half duplex capacity it is shown that the selected n 1 relay subnetwork has an ig approximate half duplex capacity that is at least 1 2 of the ig approximate half duplex capacity of the full network and that for the proposed algorithm this guarantee is tight furthermore this work proves the following tight fundamental guarantee there always exists a subnetwork of k n 1 relays that have an ig approximate half duplex capacity that is at least equal to n 1 n of the ig approximate half duplex capacity of the full network finally these results are extended to derive lower bounds on the fraction guarantee when k in 1 n relays are selected the key steps in the proofs lie in the derivation of properties of submodular functions which provide a combinatorial handle on the network simplification problem for gaussian half duplex diamond networks

reduced order adaptive observation with nonspecific adaptive law the robustness of adaptive observers whose order is less than that of the plant is addressed it is shown that residuals unmodeled states with finite energy over a finite time interval together with a definitely exciting plant input are sufficient to insure ultimate boundedness of the parameter and state errors regardless of the plant stability or input boundedness the residuals are assumed to be strongly observable at the output

a faster scaling algorithm for minimizing submodular functions combinatorial strongly polynomial algorithms for minimizing submodular functions have been developed by iwata fleischer and fujishige iff and by schrijver the iff algorithm employs a scaling scheme for submodular functions whereas schrijver s algorithm achieves strongly polynomial bound with the aid of distance labeling subsequently fleischer and iwata have described a push relabel version of schrijver s algorithm to improve its time complexity this paper combines the scaling scheme with the push relabel framework to yield a faster combinatorial algorithm for submodular function minimization the resulting algorithm improves over the previously best known bound by essentially a linear factor in the size of the underlying ground set

on adaptive state regulation an indirect adaptive state regulator consisting of an adaptive observer and an asymptotic feedback matrix synthesis is discussed in a rigorous analysis lyapunov stability of the resulting closed loop system without the need for external excitation possible global instabilities as well as global convergence subject to sufficient excitation are shown moreover the behavior of the closed loop system is analyzed for cases in which the true plant differs from the assumed linear time invariant model in that it is of higher order contains slight nonlinearities and time variation effects and is subject to plant and measurement disturbances

determining optimal rates for communication for omniscience this paper considers the communication for omniscience problem a set of users observe a discrete memoryless multiple source and want to recover the entire multiple source via noise free broadcast communications we study the problem of how to determine an optimal rate vector that attains omniscience with the minimum sum rate the total number of communications the results cover both asymptotic and non asymptotic models where the transmission rates are real and integral respectively we propose a modified decomposition algorithm mda and a sum rate increment algorithm sia for the asymptotic and non asymptotic models respectively both of which determine the value of the minimum sum rate and a corresponding optimal rate vector in polynomial time for the coordinate saturation capacity algorithm a nesting algorithm in mda and sia we propose to implement it by a fusion method and show by experimental results that this fusion method contributes to a reduction in computation complexity finally we show that the separable convex minimization problem over the optimal rate vector set in the asymptotic model can be decomposed by the fundamental partition the optimal partition of the user set that determines the minimum sum rate so that the problem can be solved more efficiently

design of adaptive pole placement controllers for plants of unknown order by an indirect control approach an adaptive pole placement control problem is considered for a scalar discrete time linear plant assuming the knowledge of an upper bound of the plant order a class of models that can be regarded to be input output equivalent to the plant is first constructed based on the parameter estimate generated by a least squares type identification scheme a minimization problem is then derived that enables one to determine the model s coefficients and the pole placing feedback gains so that the desired closed loop poles are assigned in a limit

integral manifolds of slow adaptation conditions are given under which an integral manifold slow manifold exists for a nonlinear system representing a broad class of adaptive algorithms the parameter update equation restricted to the manifold is an exact description of the slow adaptation process which can be approximately analyzed by averaging stability properties of the slow motion in the manifold are extended off the manifold by a set of conditions under which the manifold is shown to be attractive this two time scale analysis provides a geometrical visualization of instability phenomena observed in adaptive systems and generalizes earlier local stability results

global convergence for adaptive one step ahead optimal controllers based on input matching this paper establishes global convergence for adaptive one step ahead optimal controllers applied to a class of linear discrete time single input single output systems the class of systems includes all stable systems whether they are minimum phase or not all minimum phase systems whether they are stable or not and some unstable nonminimum phase systems the key substantive assumption is that the one step ahead optimal controller designed using the true system parameters leads to a stable closed loop system subject to this natural restriction it is shown that a simple adaptive control algorithm based on input matching is globally convergent in the sense that the system inputs and outputs remain bounded for all time and the input converges to the one step ahead optimal input both deterministic and stochastic cases are treated

a new adaptive law for robust adaptation without persistent excitation a new adaptive law motivated by the work of loannou and kokotovic 1983 is proposed for the robust adaptive control of plants with unknown parameters in this adaptive law the output error plays a dual role in the adjustment of the control parameter vector the advantages of using the adaptive law over others proposed in the literature are discussed in the ideal case the adaptive system has bounded solutions in addition the origin of the error equations is exponentially stable when the reference input is persistently exciting and has a sufficiently large amplitude the adaptive system is also shown to be robust under bounded external disturbances finally it is shown that by suitably modifying the adaptive law the overall system can be made robust in the presence of a class of unmodeled dynamics of the plant simulation results are presented throughout the paper to complement the theoretical developments

appointment scheduling with discrete random durations we consider the problem of determining an optimal appointment schedule for a given sequence of jobs e g medical procedures on a single processor e g operating room examination facility physician to minimize the expected total underage and overage costs when each job has a random processing duration given by a joint discrete probability distribution simple conditions on the cost rates imply that the objective function is submodular and l convex then there exists an optimal appointment schedule that is integer and can be found in polynomial time our model can handle a given due date for the total processing e g end of day for an operating room after which overtime is incurred as well as no shows and some emergencies

paper an approach to stable indirect adaptive control stable indirect adaptive control of minimum and nonminimum phase plants is established for cases where a priori bounds on the unknown plant parameters are known and where for each set of parameter values within these bounds the plant has no unstable pole zero cancellation by incorporating this partial parameter knowledge in the adaptive law and using a nonminimal representation of the plant it is shown that the adaptive closed loop control system can be written as an exponentially stable system driven by the identification error the stability of the adaptive control system is then shown using techniques similar to those known from the model reference adaptive control approach

how exciting can a signal really be abstract the rate of parameter convergence in a number of adaptive estimation schemes is related to the smallest eigenvalue of the average information matrix determined by the regression vector using a very simple examples we illustrate that the input signals that maximize this minimum eigenvalue may be quite different from the input signals that optimize more classical input design criteria e g d optimal criterion

decentralized adaptive control of interconnected systems the adaptive control of a class of large scale systems formed of an arbitrary interconnection of subsystems with unknown parameters nonlinearities and bounded disturbances is investigated it is first shown that no matter how weak the interconnections are a decentralized adaptive control scheme can become unstable approaches are then developed for stabilization and tracking using new decentralized adaptive controllers in the case where the relative degree n of the transfer function of each decoupled subsystem is less than or equal to two sufficient conditions are established which guarantee boundedness and exponential convergence of the state and parameter errors to bounded residual sets in the absence of disturbances and interconnections the decentralized adaptive control schemes guarantee exact convergence of the tracking errors to zero the effectiveness of the proposed adaptive schemes is demonstrated using a simple example

adaptive state regulation in the presence of disturbances of known frequency range adaptive state regulation via adaptive observation and asymptotic feedback matrix synthesis in the presence of bounded disturbances of known frequency range is considered the adaptive observer uses a filtered output error to adapt parameter and state estimates the filter is designed to attenuate in the disturbance frequency range it is shown that with persistent excitation parameter and feedback gain errors are bounded by a quantity which is proportional directly to the attenuated disturbance magnitudes and inversely to the degree of persistent excitation closed loop stability is proven when the ratio of filtered disturbance magnitude to degree of persistent excitation is sufficiently small a computer simulation demonstrates the method

lattice coding and decoding for multiple antenna ergodic fading channels for ergodic fading a lattice coding and decoding strategy is proposed and its performance is analyzed for the single input single output siso and multiple input multiple output mimo point to point channel as well as the multiple access channel mac with channel state information available only at the receiver csir at the decoder a novel strategy is proposed consisting of a time varying equalization matrix followed by decision regions that depend only on channel statistics not individual realizations our encoder has a similar structure to that of erez and zamir for the siso channel the gap to capacity is bounded by a constant under a wide range of fading distributions for the mimo channel under rayleigh fading the rate achieved is within a gap to capacity that does not depend on the signal to noise ratio snr and diminishes with the number of receive antennas the analysis is extended to the k user mac where similar results hold achieving a small gap to capacity while limiting the use of csir to the equalizer highlights the scope for efficient decoder implementations since decision regions are fixed i e independent of channel realizations

efficient capacity computation and power optimization for relay networks the capacity or approximations to capacity of various single source single destination relay network models has been characterized in terms of the cut set upper bound in principle a direct computation of this bound requires evaluating the cut capacity over exponentially many cuts we show that the minimum cut capacity of a relay network under some special assumptions can be cast as a minimization of a submodular function and as a result can be computed efficiently we use this result to show that the capacity or an approximation to the capacity within a constant gap for the gaussian wireless erasure and avestimehr diggavi tse deterministic relay network models can be computed in polynomial time we present some empirical results showing that computing constant gap approximations to the capacity of gaussian relay networks with around 300 nodes can be done in order of minutes for gaussian networks cut set capacities are also functions of the powers assigned to the nodes we consider a family of power optimization problems and show that they can be solved in a polynomial time in particular we show that the minimization of the sum of powers assigned to the nodes subject to a minimum rate constraint measured in terms of cut set bounds can be computed in the polynomial time we propose a heuristic algorithm to solve this problem and measure its performance through simulations on random gaussian networks we observe that in the optimal allocations most of the power is assigned to a small subset of relays which suggests that network simplification may be possible without excessive performance degradation

the approximate capacity of half duplex line networks this paper investigates the problem of characterizing the capacity of half duplex hd line networks where a source node communicates to a destination node through a multi hop path of n relays if the relays operate in full duplex fd it is well known that the capacity of the line network equals the minimum among the point to point link capacities in the path in contrast this paper considers a different case where the relays operate in hd in the first part of the paper it is shown that the approximate capacity optimal up to a constant additive gap that only depends on the number of nodes in the network of an hd n relay line network equals half the minimum of the harmonic means of the point to point link capacities of each two consecutive links in the path it is then proved that the n 1 listen transmit states out of the 2 n possible ones sufficient to characterize the approximate capacity can be found in linear time in the second part of the paper it is shown that the problem of finding the path that has the largest hd approximate capacity in a network that can be represented as a graph is np hard however if the number of cycles in the network is polynomial in the number of nodes then a polynomial time algorithm can indeed be designed

parameter identification in the presence of non parametric dynamic uncertainty abstract this paper provides identification laws which yield monotonic parameter error reduction in the absence of external noise inputs but in the presence of non parametric dynamic uncertainty unmodelled dynamics this paper considers two non parametric uncertainty sets motivated by robust control the weighted ball in h and the weighted ball in the induced l2 norm the non parametric uncertainty produces signals which corrupt the signals used in identification this paper shows that the corruption is non conservatively bounded in an l2 sense this l2 bound is then compared with the signal energy with the result used to enable disable the parameter adjustment of a gradient least squares adjustment mechanism it is proved that the resulting parameter adjustment yields non increasing parameter errors with strictly decreasing parameter errors whenever the parameter errors are distinguishable from zero given the system input and output histories

a stable adaptive implementation of the internal model principle an adaptive implementation of the internal model principle for linear time invariant systems that allows for rejection of unknown deterministically modeled disturbances is provided the minimal representation of the system model is used for parameter estimation and the global convergence and stability of the algorithm are investigated with unmodeled dynamics with proper modification of the parameter estimation algorithm global convergence and stability for the algorithm are obtained without the requirement of persistent excitation some simulation results are given to support the analysis

paper some design guidelines for discrete time adaptive controllers there have been many algorithms proposed for adaptive control which will provide globally asymptotically stable controllers if some stringent conditions on the plant are met the conditions on the plant cannot be met in practice as all plants will contain high frequency unmodeled dynamics this paper uses a linearization analysis of a nonlinear adaptive controller to demonstrate analytically some design guidelines which alleviate some of the problems associated with adaptive control in the presence of unmodeled dynamics the points made are further demonstrated by simulation results

persistent excitation in adaptive systems the importance of the concept of persistent excitation pe in adaptive identification and control has been recognized for some time recently it has become evident that it also plays a central role in many questions related to the robustness of adaptive systems there is every reason to believe that arguments involving this concept will continue to feature prominently in the analysis of most of the important problems of adaptive control hence there is a real need for a deeper understanding of the concept the paper is written with three objectives the first which is tutorial in nature is to provide a general framework for the discussion of persistent excitation and to collect results in the area which are scattered throughout the adaptive literature the second objective is to present some new results related to the uniform asymptotic stability u a s and robustness of adaptive systems and the relation of pe to the stability properties of a class of non linear systems the final objective is to di

design issues in adaptive control an integrated approach to the design of practical adaptive control algorithms is presented many existing ideas are brought together and the effect of various design parameters available to a user is explored the theory is extended by showing how the problem of stabilizability of the estimated model can be overcome by running parallel estimators it is shown how asymptotic tracking of deterministic set points can be achieved in the presence of unmodeled dynamics

wireless network simplification the gaussian n relay diamond network we consider the gaussian n relay diamond network where a source wants to communicate to destination node through a layer of n relay nodes we investigate the following question what fraction of the capacity can we maintain using only k out of the n available relays we show that independent of the channel configurations and operating snr we can always find a subset of k relays which alone provide a rate k k 1 c over bar g where c over bar is the information theoretic cutset upper bound on the capacity of the whole network and g is independent of the channel coefficients and the snr and depends only on n and k logarithmic in n and linear in k in particular for k 1 this means that half of the capacity of any n relay diamond network can be approximately achieved by routing information over a single relay we also show that this fraction is tight there are configurations of the n relay diamond network where every subset of k relays alone can at most provide approximately a fraction k k 1 of the total capacity these high capacity k relay subnetworks can be also discovered efficiently we propose an algorithm that computes a constant gap approximation to the capacity of the gaussian n relay diamond network in o n log n running time and discovers a high capacity k relay subnetwork in o kn running time this result also provides a new approximation to the capacity of the gaussian n relay diamond network which is hybrid in nature it has both multiplicative and additive gaps in the intermediate snr regime this hybrid approximation is tighter than existing purely additive or purely multiplicative approximations to the capacity of this network

nonlinear averaging theorems and the determination of parameter convergence rates in adaptive control abstract the paper presents nonlinear averaging theorems for two time scale systems where the dynamics of the fast system are allowed to vary with the slow system the results are applied to the narendra valavani adaptive control algorithm and estimates of the parameter convergence rates are obtained which do not rely on a linearization of the system around the equilibrium and therefore are valid in a larger region in the parameter space

capacity of gaussian channels with duty cycle and power constraints in many wireless communication systems radios are subject to a duty cycle constraint that is a radio can only actively transmit signals over a fraction of the time for example it is desirable to have a small duty cycle in some low power systems a half duplex radio cannot keep transmitting if it wishes to receive useful signals and a cognitive radio needs to listen and detect primary users frequently this paper studies the capacity of point to point scalar discrete time gaussian channels subject to a duty cycle constraint as well as an average transmit power constraint an idealized duty cycle constraint is first studied which can be regarded as a requirement on the minimum fraction of nontransmissions or zero symbols in each codeword independent input with a unique discrete distribution is shown to achieve the channel capacity in many situations numerically optimized on off signaling can achieve much higher rate than gaussian signaling over a deterministic transmission schedule this is in part because the positions of nontransmissions in a codeword can convey information a more realistic duty cycle constraint is also studied where the extra cost of transitions between transmissions and nontransmissions due to pulse shaping is accounted for the capacity achieving input is correlated over time and is hard to compute a lower bound of the achievable rate as a function of the input distribution is shown to be maximized by a first order markov input process whose stationary distribution is also discrete and can be computed efficiently the results in this paper suggest that under various duty cycle constraints departing from the usual paradigm of intermittent packet transmissions may yield substantial gain

a framework of discrete dc programming by discrete convex analysis a theoretical framework of difference of discrete convex functions discrete dc functions and optimization problems for discrete dc functions is established standard results in continuous dc theory are exported to the discrete dc theory with the use of discrete convex analysis a discrete dc algorithm which is a discrete analogue of the continuous dc algorithm concave convex procedure in machine learning is proposed the algorithm contains the submodular supermodular procedure as a special case exploiting the polyhedral structure of discrete convex functions the algorithms tailored to specific types of discrete dc functions are proposed

a combinatorial strongly polynomial algorithm for minimizing submodular functions this paper presents a combinatorial polynomial time algorithm for minimizing submodular functions answering an open question posed in 1981 by grotschel lovasz and schrijver the algorithm employs a scaling scheme that uses a flow in the complete directed graph on the underlying set with each arc capacity equal to the scaled parameter the resulting algorithm runs in time bounded by a polynomial in the size of the underlying set and the length of the largest absolute function value the paper also presents a strongly polynomial version in which the number of steps is bounded by a polynomial in the size of the underlying set independent of the function values

robust adaptive control conditions for global stability an input output approach is presented for analyzing the global stability and robustness properties of adaptive controllers to unmodeled dynamics the concept of a tuned system is introduced i e the control system that could be obtained if the plant were known comparing the adaptive system to the tuned system results in the development of a generic adaptive error system passivity theory is used to derive conditions which guarantee global stability of the error system associated with the adaptive controller and ensure boundedness of the adaptive gains specific bounds are presented for certain significant signals in the control systems limitations of these global results are discussed particularly the requirement that a certain operator be strictly positive real spr a condition that is unlikely to hold due to unmodeled dynamics

a note on appointment scheduling with piecewise linear cost functions we consider the problem of determining the optimal schedules for a given sequence of jobs on a single processor the objective is to minimize the expected total cost incurred by job waiting and processor idling where the job processing times are random variables it is known in the prior literature that if the processing times are integers and the costs are linear functions satisfying a mild condition then the problem can be solved in a polynomial number of expected cost evaluations in this work we extend the result to piecewise linear cost functions which include many useful objective functions in practice our analysis explores the hidden dual network flow structure of the appointment scheduling problem and thus greatly simplifies that of prior work we also find the number of samples needed to compute a near optimal solution when only some independent samples of processing times are known

paper instability analysis and improvement of robustness of adaptive control the effects of unmodeled high frequency dynamics and bounded disturbances on stability and performance of adaptive control schemes are analyzed five possible types of instability mechanisms parameter drift linear instability fast adaptation instability high frequency instability and throughput instability are analyzed using simple examples a procedure is used to construct lyapunov like functions for a modified adaptive controller applied to a dominant plant of relative degree one in the presence of parasitics and disturbances and obtain sufficient conditions under which none of the five types of instability can occur the modified scheme is robust in the sense that it guarantees the existence of a large region of attraction from which all the trajectories remain bounded and the state errors converge exponentially to a much smaller residual set the size of the region of attraction depends on the speed of parasitics in such a way that as the parasitics become infinitely fast the region of attraction becomes the whole space

achieving 1 2 log 1 snr on the awgn channel with lattice encoding and decoding we address an open question regarding whether a lattice code with lattice decoding as opposed to maximum likelihood ml decoding can achieve the additive white gaussian noise awgn channel capacity we first demonstrate how minimum mean square error mmse scaling along with dithering lattice randomization techniques can transform the power constrained awgn channel into a modulo lattice additive noise channel whose effective noise is reduced by a factor of spl radic 1 snr snr for the resulting channel a uniform input maximizes mutual information which in the limit of large lattice dimension becomes 1 2 log 1 snr i e the full capacity of the original power constrained awgn channel we then show that capacity may also be achieved using nested lattice codes the coarse lattice serving for shaping via the modulo lattice transformation the fine lattice for channel coding we show that such pairs exist for any desired nesting ratio i e for any signal to noise ratio snr furthermore for the modulo lattice additive noise channel lattice decoding is optimal finally we show that the error exponent of the proposed scheme is lower bounded by the poltyrev exponent

a stable adaptive control design for discrete plants with unmodelled dynamics this paper presents a simple discrete model reference adaptive control design which maintains stability around the equilibrium of the tracking error in the presence of unmodelled dynamics only a weak a priori knowledge namely upper bounds of the absolute value of the unmodelled parameters and orders of the unmodelled dynamics is required for the implementation the adaptive controller has an additional parameter to protect the scheme against instability

robust adaptive controller with zero residual tracking errors the adaptive control of a plant whose dominant part has transfer function with relative degree n ast 1 has been considered in the presence of parasitics and disturbances a new adaptive law is proposed which guarantees the existence of a large region of attraction from which all signals are bounded and the tracking error converges to a small residual set in contrast to the adaptive law used in 1 2 the new adaptive law guarantees a smaller residual set for the tracking error which reduces to zero when the parasitics and disturbances disappear

harmonic generation in adaptive feedforward cancellation schemes the paper investigates the generation of harmonics in adaptive feedforward cancellation schemes specifically it is shown that an algorithm designed to reject a certain number of frequency components may in fact be capable of reducing higher order harmonics as well this effect originates in the time variation of the adaptive parameters a consequence is that the adaptive system may perform better than the algorithm with the fixed ideal parameters surprisingly the response to higher order harmonics can be calculated precisely using a laplace transform analysis the origin of the numerical procedure is in the equivalence between the adaptive feedforward cancellation scheme and a control scheme based on the internal model principle the implication of the results on design and implementation issues is discussed

new approach to robust model reference adaptive control for a class of plants motivated by recent advances in designing robust adaptive controllers and in dealing with uncertain dynamical systems a new model reference adaptive control which is robust to a class of unmodelled dynamics and bounded output disturbances in the case of relative degree one is presented the implementation of the controllers includes a switching mechanism which plays a crucially important role in functions of stabilizing as well as tracking it is shown that global stability of the overall system is achieved under no assumption of persistency of excitation and tracking errors will converge to a residual set whose size can be directly related to the size of unmodelled dynamics and of output disturbances explicitly in the ideal case the residual set degenerates to a single null point and convergence can be achieved in finite time without any requirement of persistency of excitation

precoded integer forcing universally achieves the mimo capacity to within a constant gap an open loop single user multiple input multiple output mimo communication scheme is considered where a transmitter equipped with multiple antennas encodes the data into independent streams all taken from the same linear code the coded streams are then linearly precoded using the encoding matrix of a perfect linear dispersion space time code at the receiver side integer forcing equalization is applied followed by standard single stream decoding it is shown that this communication architecture achieves the capacity of any gaussian mimo channel up to a gap that depends only on the number of transmit antennas

disturbance instabilities in an adaptive system two types of disturbance instability of simple adaptive schemes are analyzed a drift equation shows how stable equilibria are forced to infinity by infrequent but persistent switches of a constant disturbance the modification proposed by p ioannou counteracts these instabilities

a faster strongly polynomial time algorithm for submodular function minimization we consider the problem of minimizing a submodular function f defined on a set v with n elements we give a combinatorial algorithm that runs in o n 5eo n 6 time where eo is the time to evaluate f s for some s subseteq v this improves the previous best strongly polynomial running time by more than a factor of n we also extend our result to ring families

necessary and sufficient conditions for parameter convergence in adaptive control a complete description of parameter convergence in model reference adaptive control may be given in terms of the spectrum of the exogenous reference input signal abstract using generalized harmonic analysis a complete description of parameter convergence in model reference adaptive control mrac is given in terms of the spectrum of the exogenous reference input signal roughly speaking if the reference signal contains enough frequencies then the parameter vector converges to its correct value if not it converges to an easily characterizable subspace in parameter space

gaussian half duplex relay networks improved constant gap and connections with the assignment problem this paper considers a gaussian relay network where a source transmits a message to a destination with the help of n half duplex relays the information theoretic cut set upper bound to the capacity is shown to be achieved to within 1 96 n 2 bits by noisy network coding thereby reducing the previously known gap this gap is obtained as a special case of a more general constant gap result for gaussian half duplex multicast networks it is then shown that the generalized degrees of freedom of this network is the solution of a linear program where the coefficients of the linear inequality constraints are proved to be the solution of several linear programs referred as the assignment problem in graph theory for which efficient numerical algorithms exist the optimal schedule that is the optimal value of the 2 n possible transmit receive configuration states for the relays is investigated and known results for diamond networks are extended to general relay networks it is shown for the case of n 2 relays that only n 1 3 out of the 2 n 4 possible states have a strictly positive probability and suffice to characterize the capacity to within a constant gap extensive experimental results show that for a general n relay network with n leq 8 the optimal schedule has at most n 1 states with a strictly positive probability as an extension of a conjecture presented for diamond networks it is conjectured that this result holds for any half duplex relay network and any number of relays finally a network with n 2 relays is studied in detail to illustrate the channel conditions under which selecting the best relay is not optimal and to highlight the nature of the rate gain due to multiple relays

approximately achieving gaussian relay network capacity with lattice based qmf codes recently a new relaying strategy quantize map and forward qmf scheme has been demonstrated to approximately achieve within an additive constant number of bits the gaussian relay network capacity universally i e for arbitrary topologies channel gains and snrs this was established using gaussian codebooks for transmission and random mappings at the relays in this paper we develop structured lattice codes that implement the qmf strategy the main result of this paper is that such structured lattice codes can approximately achieve the gaussian relay network capacity universally again within an additive constant in addition we establish a similar result for half duplex networks where we demonstrate that one can approximately achieve the capacity using fixed transmit receive tx rx schedules for the relays with no transmit power optimization across the different tx rx states of the network

an energy amplification condition for decentralized adaptive stabilization the author is interested here in the problem of global decentralized adaptive regulation of the plant output to zero of square multivariable linear time invariant systems without any restrictions on relative degrees or matching assumptions the first solution to this problem was recently reported by the author using morse s new dynamic certainty equivalent adaptive controller to prove that global stabilization is possible if the unmodeled interconnections do not induce amplification of the energy of the signals in all channels in this paper the author shows that to preserve global convergence it is actually enough to have only one nonamplifying channel instrumental for the establishment of the authors result is the fundamental s procedure losslessness theorem of megretsky and treil together with some basic loop transformations and d scalings

a new robust mrac using variable structure design for relative degree two plants abstract variable structure design concept has been shown not only useful in dealing with uncertain systems but also useful in establishing controllers in the adaptive context continuing the work this research proposed a new robust model reference adaptive control for single input single output linear plants with relative degree two a class which encompasses a large number of linearized mechanical systems when compared with the conventional mrac schemes the current approach drastically improves the transient behavior and the tracking performance of the closed loop system from several numerical simulations furthermore if the reference input satisfies the persistently exciting condition or if the prior knowledge about the interval in which the true parameter vector lies is available the magnitude of the input force can be considerably reduced into a more realistic level in the presence of mild unmodelled dynamics and bounded output disturbances the proposed scheme possesses similar well behaved properties it can be shown that the tracking error will in fact fall into a residual set whose size can be directly related to the size of unmodelled dynamics and of output disturbances

averaging bounds for lattices and linear codes general random coding theorems for lattices are derived from the minkowski hlawka theorem and their close relation to standard averaging arguments for linear codes over finite fields is pointed out a new version of the minkowski hlawka theorem itself is obtained as the limit for p spl rarr spl infin of a simple lemma for linear codes over gf p used with p level amplitude modulation the relation between the combinatorial packing of solid bodies and the information theoretic soft packing with arbitrarily small but positive overlap is illuminated the soft packing results are new when specialized to the additive white gaussian noise channel they reduce to a version of the de buda poltyrev result that spherically shaped lattice codes and a decoder that is unaware of the shaping can achieve the rate 1 2 log sub 2 p n