using burst recovery concept to obtain global stability and performance of discrete time adaptive controller for time varying systems in this note a new technique is proposed for the global stability analysis of adaptive control of time varying systems the proposed method is based on the evaluation of possible burstings in the adaptive loop its simplicity and effectiveness is demonstrated by analyzing global stability and performance of the discrete time direct adaptive controller the developed technique reflects physical phenomena inside the adaptive loop i e possible occurrence of instabilities and burstings precise upper bounds on the admissible speed of the parameter variations and on all the signals are established in terms of clearly defined physical quantities

strict lyapunov functions for time varying systems with persistency of excitation we study the stability of the origin for a class of linear time varying systems with a drift that may be divided in two parts under the action of the first a function of the trajectories is guaranteed to converge to zero under the action of the second the solutions are restricted to a periodic orbit hence by assumption the systems trajectories are bounded our main results focus on two generic case studies that are motivated by common nonlinear control problems model reference adaptive control control of nonholonomic systems tracking control problems to name a few then based on the standing assumption that the systems dynamics is persistently excited we construct a time dependent lyapunov function that has a negative definite derivative our main statements may be regarded as off the shelf tools of analysis for linear and nonlinear time varying systems

model reference adaptive control of time varying and stochastic systems the adaptive control of general delay linear time varying systems is addressed a simple model reference adaptive control law is devised it does not require a priori knowledge of the sign of the high frequency gain this control law coupled with the parameter estimation equations allows a simple representation of the closed loop system this greatly eases the stability and performance analysis and has potential for generalization to adaptive pole placement and other control laws suitable for nonminimum phase systems for the kalman filter parameter estimator coupled with this control law stability is obtained without persistence of excitation or knowledge of the sign of the high frequency gain performance results for the extended least squares algorithm are described

integral action in robust adaptive control conditions are studied under which integral action in robust adaptive control is soundly based the method of analysis amounts to verifying that the key conditions needed for convergence are satisfied a simple strategy is described for choosing the integral constant and global convergence is established for the resultant algorithm this illustrates a proof paradigm which could be similarly applied to other problems the principal assumptions used are that the plant when augmented by an integrator has a known degree of controllability and that an overbounding function is known for the unmodeled system response the continuous time case is treated but the corresponding discrete time results follow mutatis mutandis by simply replacing p d dt by delta q 1 delta l sub 2 by l sub 2 integral by sigma and so on

higher order direct model reference adaptive control with generic uniform ultimate boundedness this paper proposes a new higher order model reference adaptive control ho mrac approach following direct adaptive control philosophy which estimates unknown time varying parameters this approach leads to a lyapunov based conventional mrac update law augmented by an observer type parameter predictor dynamics the predictor dynamics are composed of a stable known part a feedback of the parameter error and unknown higher order parameters which are updated using a lyapunov based adaptive design so this ho mrac can cope with rapidly changing parameters due to estimation of their time derivatives moreover for stability analysis a lyapunov based generic ultimate boundedness theorem is presented which allows for a computation of separate bounds for each state vector partition furthermore this theorem formulates the explicit specification of transient and ultimate bounds reaching time on the ultimate bounds and a set of admissible initial conditions two challenging illustrative examples demonstr

a parameter adaptive controller which provides exponential stability the first order case abstract classical discrete time adaptive controllers provide asymptotic stabilization while the original adaptive controllers did not handle noise or unmodelled dynamics well redesigned versions were proven to have some tolerance however neither exponential stabilization nor a bounded noise gain is typically proven here we consider the first order case and prove that if the original ideal projection algorithm is used in the estimation process subject to the common assumption that the plant parameters lie in a convex compact set and that the parameter estimates are restricted to that set then it guarantees linear like convolution bounds on the closed loop behaviour which implies exponential stability and a bounded noise gain as well an easily proven tolerance to unmodelled dynamics and plant parameter variation

an adaptive control algorithm for linear systems having unknown time delay abstract this paper presents an algorithm for adaptive control of linear systems having unknown time delay a rational approximation is used for the delay and it is argued that within this framework the analysis of the properties of the corresponding adaptive control algorithm essentially reduces to the issue of robustness to unmodelled dynamics a global convergence theory is presented using recent methods for analyzing robustness properties of adaptive control algorithms the analysis is supported by simulation results

a globally stable apcs in the presence of bounded noises and disturbances this paper presents a globally stable adaptive predictive control system apcs for discrete linear processes with pure time delays in the presence of bounded measurement and process noise plus unmeasured disturbances the main contribution is the proof of stability in the context of discrete adaptive control schemes this proof is based on the minimization of the a posteriori estimation error and the convergence of the estimated parameters

adaptive linear control of nonlinear systems the theory of stable parameter adaptive control has advanced to allow linear time varying plants however a more honest view of such systems is that they are often derived from inexact linearization about a trajectory of a nonlinear system standard adaptive control based on a linear model can then be interpreted as one way to realize a nonlinear controller for a nonlinear plant the implications of this view are studied analytically the stability problem is seen to be equivalent to showing robustness to time varying parameters and a locally bounded model uncertainty it is shown that if the trajectory is known to be within a bound a parameter estimator with projection can ensure boundedness of departures from the trajectory

supervisory control of uncertain linear time varying systems we consider the problem of adaptively stabilizing linear plants with unknown time varying parameters in the presence of noise disturbances and unmodeled dynamics using the supervisory control framework which employs multiple candidate controllers and an estimator based switching logic to select the active controller at every instant of time time varying uncertain linear plants can be stabilized by supervisory control provided that the plant s parameter varies slowly enough in terms of mixed dwell time switching and average dwell time switching the noise and disturbances are bounded and small enough in terms of l infinity norms and the unmodeled dynamics are small enough in the input to state stability sense this work extends previously reported works on supervisory control of linear time invariant systems with constant unknown parameters to the case of linear time varying uncertain systems a numerical example is included and limitations of the approach are discussed

testing one hypothesis twice in observational studies in a matched observational study of treatment effects a sensitivity analysis asks about the magnitude of the departure from random assignment that would need to be present to alter the conclusions of an analysis that assumes that matching for measured covariates removes all bias the reported degree of sensitivity to unmeasured biases depends on both the process that generated the data and the chosen methods of analysis so a poor choice of method may lead to an exaggerated report of sensitivity to bias this suggests the possibility of performing more than one analysis with a correction for multiple inference say testing one null hypothesis using two or three different tests in theory and in an example it is shown that in large samples the gains from testing twice will often be large because testing twice has the larger of the two design sensitivities of the component tests and the losses due to correcting for two tests will often be small because two tests of one hypothesis will typically be highly correlated so a correction for multiple testing that takes this into account will be small an illustration uses data from the u s national health and nutrition examination survey concerning lead in the blood of cigarette smokers copyright 2012 oxford university press

bahadur efficiency of sensitivity analyses in observational studies an observational study draws inferences about treatment effects when treatments are not randomly assigned as they would be in a randomized experiment the naive analysis of an observational study assumes that adjustments for measured covariates suffice to remove bias from nonrandom treatment assignment a sensitivity analysis in an observational study determines the magnitude of bias from nonrandom treatment assignment that would need to be present to alter the qualitative conclusions of the naive analysis say leading to the acceptance of a null hypothesis rejected in the naive analysis observational studies vary greatly in their sensitivity to unmeasured biases but a poor choice of test statistic can lead to an exaggerated report of sensitivity to bias the bahadur efficiency of a sensitivity analysis is introduced calculated and connected to established concepts such as the power of a sensitivity analysis and the design sensitivity the bahadur slope equals zero when the sensitivity parameter equ

sensitivity analysis for equivalence and difference in an observational study of neonatal intensive care units in randomized experiments it is sometimes important to demonstrate that two treatments do not differ greatly in their effects or to demonstrate that the treatments have very different effects on one outcome but similar effects on another outcome these demonstrations may take the form of rejecting a null hypothesis of inequivalence in an equivalence test or rejecting a null hypothesis of equal and inequivalent effects on two outcomes the procedures often express a complex hypothesis in terms of component hypotheses and combine the component significance levels to test the complex hypothesis if used in a randomized trial randomization provides valid significance levels for each component test and hence also for the combined procedure in an observational study that is in a study of treatments that were not randomly assigned there is typically concern that significance levels for testing hypotheses about treatment effects may be distorted by failure to control for some unobserved pretreatment cov

combining phase i and phase ii in a potential reduction algorithm for linear programming this paper describes an affine potential reduction algorithm for linear programming that simultaneously seeks feasibility and optimality the algorithm is closely related to a similar method of anstreicher the new features are that we use a two dimensional programming problem to derive better lower bounds than anstreicher that our direction finding subproblem treats phase i and phase ii more symmetrically and that we do not need an initial lower bound our method also allows for the generation of a feasible solution so that phase i is terminated during the course of the iterations and we describe two ways to encourage this behavior

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

theoretical efficiency of a shifted barrier function algorithm for linear programming abstract this paper examines the theoretical efficiency of solving a standard form linear program by solving a sequence of shifted barrier problems of the form minimize x c t x e j 1 n ln x j eh j s t a x b x eh 0 for a given and fixed shift vector h 0 and for a sequence of values of 0 that converges to zero the resulting sequence of solutions to the shifted barrier problems will converge to a solution to the standard form linear program the advantage of using the shifted barrier approach is that a starting feasible solution is unnecessary and there is no need for a phase i phase ii approach to solving the linear program either directly or through the addition of an artificial variable furthermore the algorithm can be initiated with a warm start i e an initial guess of a primal solution x that need not be feasible the number of iterations needed to solve the linear program to a desired level of accuracy will depend on a measure of how close the initial solution x is to being feasible and optimal the number of iterations will also depend on the judicious choice of the shift vector h if an approximate center of the dual feasible region is known in advance then h can be chosen so that the guaranteed fractional decrease in at each iteration is 1 1 6 n which contributes afactor of 6 n to the number of iterations needed to solve the problem

polynomial affine algorithms for linear programming the method of steepest descent with scaling affine scaling applied to the potential functionq logc x i 1n logxi solves the linear programming problem in polynomial time forq n ifq n then the algorithm terminates in no more than o n2l iterations if q n sqrt n withq o n then it takes no more than o nl iterations a modified algorithm using rank 1 updates for matrix inversions achieves respectively o n4l and o n3 5l arithmetic computions

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

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

adaptive systems and time varying plants abstract the behaviour of four adaptive algorithms lms equation error output error identification and the goodwin ramadge caines adaptive control algorithm are examined in the face of plant parameter variations the key point to note is that persistency of excitation conditions in the time invariant parameter case guarantees exponential convergence then standard and newly developed lyapunov stability results allow us to guarantee tracking error and parameter error boundedness when the plant parameters are actually time varying

a new approach to model reference control for a class of arbitrarily fast time varying unknown plants abstract in this note a new standard model reference control nsmrc to arbitrarily fast linear single input single output time varying plants with relative degree one is presented a modified version of standard model reference control smrc structure is developed which incorporates the concept of variable structure design and null adaptation process for fast time varying plants it is shown that the output error will converge to zero in finite time without any restriction on the time varying rate of the plant parameters while all signals inside the closed loop system remain uniformly bounded so long as some design parameters are chosen properly large superior transient responses as well as convergence properties can be observed from the simulation results provided

adaptive control of mimo time varying systems with indicator function based parametrization abstract this paper studies a new solution framework for adaptive control of a class of mimo time varying systems with indicator function based parametrization motivated by a general discrete time mimo takagi sugeno t s fuzzy system model in an input output form with unknown parameters an indicator membership function based parametrization has some favorable capacity to deal with certain large parameter variations a new discrete time mimo system prediction model is derived for approximating a nonlinear dynamic system and its system properties are clarified an adaptive control scheme is developed with desired controller parametrization and stable parameter estimation for control of such uncertain mimo time varying systems a control singularity problem is addressed and the closed loop stability and output tracking properties are analyzed this work provides a new method for multivariable t s fuzzy system modeling and adaptive control an illustrative example and simulation results are presented to demonstrate the proposed novel concepts and to verify the desired adaptive control system performance

stability analysis of an adaptive system with unmodelled dynamics stability bounds for fast and slow adaptation are derived for a simple adaptive system with one unmodelled parasitic pole which is approximated by a right half plane zero in fast adaptation the product of the adaptive gain and power of the reference input must be smaller than the parasitic pole in slow adaptation most of the input signal energy must be in the frequency range lower than the square root of the parasitic pole it is shown that a plant bypass ensures a global stability property by making the linear time invariant part of the adaptive loop strictly positive real spr the price paid is an increase of the tracking error at very low frequencies and with slow adaptation when the equilibrium of the system without bypass is exponentially stable

adaptive control for time variant processes abstract this paper establishes conditions of global stability for adaptive predictive control systems apcs when applied to a general class of multivariate stochastic time variant stable inverse processes with time delays these conditions rely on assumed convergence properties of the apcs estimation scheme therefore the design of stable apcs or research into apcs stability proofs for time variant processes proceeds from this perspective with the design and analysis of estimation schemes which may satisfy the required convergence properties using this approach an asymptotically stable apcs is derived for a class of time variant processes with a finite number of bounded changes in their parameter values and a perturbation vector with a finite l2 norm the methodology used to derive the convergent estimation scheme has a general scope and is conceptually simple

weighted m statistics with superior design sensitivity in matched observational studies with multiple controls in a nonrandomized or observational study a weak association between receipt of the treatment and an outcome may be explained not as effects caused by the treatment but rather by a small bias in the assignment of individuals to treatment or control however a strong association may be explained as noncausal only by a large bias the strength of the association between treatment and outcome is not uniform across the data from a study and this motivates giving greater weight where the association is stronger in an observational study with treated control matched pairs it is known that results are less sensitive to unmeasured biases if pairs with small absolute differences in outcomes are given little weight in the analysis more precisely such a test statistic has superior design sensitivity how should outcomes be weighted if an observational study is matched in sets with one treated subject and several controls an m statistic is the quantity equated to zero in defining huber s m estimates includin

a potential function reduction algorithm for solving a linear program directly from an infeasible warm start this paper develops an algorithm for solving a standard form linear program directly from an infeasible warm start i e directly from a given infeasible solution hat x that satisfies a hat x b but hat x ngeqslant 0 the algorithm is a potential function reduction algorithm but the potential function is somewhat different than other interior point method potential functions and is given by f x b q ln c t x b sum limits j 1 n ln x j h j c t x b where q n sqrt n is a given constant h is a given strictly positive shift vector used to shift the nonnegativity constaints andb is a lower bound on the optimal value of the linear program the duality gapc t x b is used both in the leading term as well as in the barrier term to help shift the nonnegativity constraints the algorithm is shown under suitable conditions to achieve a constant decrease in the potential function and so achieves a constant decrease in the duality gap and hence also in the infeasibility in o n iterations under more restrictive assumptions regarding the dual feasible region this algorithm is modified by the addition of a dual barrier term and will achieve a constant decrease in the duality gap and in the infeasibility in o sqrt n iterations

on the value of information in system identification bounded noise case assuming instantaneous bounds on the noise system parameter identification is formulated as membership set estimation problem sequential algorithms are constructed to estimate the membership sets of the parameters which are consistent with the measurements and the noise constraints the important new feature of the proposed algorithms is their ability to ignore redundant data the efficient data extraction property of the new algorithms is achieved with small computational effort and with improved performance when compared to the least square algorithm the convergence properties and the notion of identifiability in the set theoretic context are also studied

a method for the parametric center problem with a strictly monotone polynomial time algorithm for linear programming given a system of linear inequalities ax b dt and equalities mx g ht where the right hand sides are parametrically deformed over the scalar t the parametric center problem is to trace the parametric family of approximate solutions x t to the center problems p t where p t is the problem maximize i 1m ln bi dit aix subject to ax b dt and mx g ht we present an algorithm for tracing the parametric family of solutions x t over some given range at the kth iterate of the algorithm the point x tk is an approximate solution to the center problem p tk in an appropriate measure of approximation the value of tk is increased to tk 1 and a newton step is used to generate x tk 1 which is an approximate solution to the center problem p tk 1 the sequence of values of t exhibit at least one of the following geometric rates of change tmax tk 1 tmax tk 1 1 128m tk 1 tmin tk tmin 1 1 128m where tmin tmax is the maximum minimum number t such t

deterministic adaptive control with slowly varying parameters an averaging analysis in this work averaging methods are used to analyse the behaviour of an adaptive controller with slowly varying parameters the incorporation of time varying parameters into a stability analysis of an adaptive controller leads to certain perturbation terms in the error system the type of averaging results so far applied to adaptive control cannot deal with these perturbations thus some new averaging theorems are needed these results are known in the averaging literature however here a very simple proof technique has been found which gives finite and infinite interval averaging results under weaker conditions the averaging analysis shows that with regard to parameter tracking the adaptive algorithm behaves like a first order filter it is also clear that successful tracking then requires knowledge of the true speed of parameter change

an improved and simplified full newton step o n infeasible interior point method for linear optimization we present an improved version of an infeasible interior point method for linear optimization published in 2006 in the earlier version each iteration consisted of one so called feasibility step and a few at most three centering steps in this paper each iteration consists of only a feasibility step whereas the iteration bound improves the earlier bound by a factor 2 sqrt 2 the improvements are due to a new lemma that gives a much tighter upper bound for the proximity after the feasibility step

adaptive control of time varying linear systems the authors present a global bounded input bounded state stability theory for a class of continuously adapting controllers applied to time varying linear systems this gives theoretical support to the application of many of the algorithms used in practice a key feature of the analysis is that no persistence of excitation requirement is needed

an infeasible interior point predictor corrector algorithm for linear programming a predictor corrector method is proposed for solving standard form linear programming problems starting from initial points that strictly satisfy the positivity constraints but do not necessarily satisfy the equality constraints the algorithm is globally convergent under the assumption that the linear program has an optimal solution under some additional assumptions on the starting point we prove that epsilon feasibility and epsilon complementarily can be obtained in o n ln frac 1 epsilon iterations

a new u statistic with superior design sensitivity in matched observational studies summary in an observational or nonrandomized study of treatment effects a sensitivity analysis indicates the magnitude of bias from unmeasured covariates that would need to be present to alter the conclusions of a naive analysis that presumes adjustments for observed covariates suffice to remove all bias the power of sensitivity analysis is the probability that it will reject a false hypothesis about treatment effects allowing for a departure from random assignment of a specified magnitude in particular if this specified magnitude is no departure then this is the same as the power of a randomization test in a randomized experiment a new family of u statistics is proposed that includes wilcoxon s signed rank statistic but also includes other statistics with substantially higher power when a sensitivity analysis is performed in an observational study wilcoxon s statistic has high power to detect small effects in large randomized experiments that is it often has good pitman efficiency but small effects are invariably sensitive to small unobserved biases members of this family of u statistics that emphasize medium to large effects can have substantially higher power in a sensitivity analysis for example in one situation with 250 pair differences that are normal with expectation 1 2 and variance 1 the power of a sensitivity analysis that uses wilcoxon s statistic is 0 08 while the power of another member of the family of u statistics is 0 66 the topic is examined by performing a sensitivity analysis in three observational studies using an asymptotic measure called the design sensitivity and by simulating power in finite samples the three examples are drawn from epidemiology clinical medicine and genetic toxicology

a general class of one sample nonparametric test statistics based on subsamples abstract a general class of nonparametric test statistics is constructed by considering the sign of the most extreme value in subsamples of size m taken from n independent observations the test statistics can be expressed as linear rank statistics and reduce to the sign test statistic for m 1 and a modified wilcoxon signed rank test statistic for m 2 asymptotic normality of properly standardized versions of our statistics is established under general conditions small sample power simulations as well as pitman and bahadur efficiencies indicate that members of our class do well in comparison with already existing test statistics

an ol n 3 potential reduction algorithm for linear programming we describe a primal dual potential function for linear programming phi x s rho ln x t s sum limits j 1 n ln x j s j where n x is the primal variable ands is the dual slack variable as a result we develop an interior point algorithm seeking reductions in the potential function with rho n sqrt n neither tracing the central path nor using the projective transformation the algorithm converges to the optimal solution set in o sqrt n l iterations and uses o n3l total arithmetic operations we also suggest a practical approach to implementing the algorithm

adaptive control of a class of slowly time varying systems with modeling uncertainties in a recent work a new linear adaptive controller based on certainty equivalence and backstepping design which promises a level of transient and asymptotic performance comparable to that of the tuning functions adaptive backstepping controller without using high order nonlinearities was proposed for linear time invariant systems the proposal was supplemented with robustness and performance analysis in the presence of modeling uncertainties in this note the same idea is used to develop a new linear adaptive controller for slowly time varying systems with modeling uncertainties the new adaptive control scheme guarantees robustness with respect to modeling errors via normalizing damping parameter projection and static normalization use of normalizing damping is essential in protecting the linearity of the system which plays a key role in reaching the stability and robustness results

average case complexity results for a centering algorithm for linear programming problems under gaussian distributions abstract to solve linear programming problems by interior point methods an approximately centered interior point has to be known such a point can be found by an algorithmic approach a so called phase 1 algorithm or centering algorithm for random linear programming problems distributed according to the rotation symmetry model especially with normal distribution we present probabilistic results on the quality of the origin as starting point and the average number of steps of a centering algorithm

model reference adaptive control system for discrete linear time varying systems with periodically varying parameters and time delay this paper presents a new method for designing a model reference adaptive control system for a class of discrete linear time varying systems with periodically varying parameters and time delay based on lyapunov s stability theorem adaptive control algorithms guarantee the asymptotic stability of the error between the plant output and the reference sequence using no anticipative value of the plant output the validity of the theoretical result is illustrated by numerical examples

effect modification and design sensitivity in observational studies in an observational study of treatment effects subjects are not randomly assigned to treatment or control so differing outcomes in treated and control groups may reflect a bias from nonrandom assignment rather than a treatment effect after adjusting for measured pretreatment covariates perhaps by matching a sensitivity analysis determines the magnitude of bias from an unmeasured covariate that would need to be present to alter the conclusions of the naive analysis that presumes adjustments eliminated all bias other things being equal larger effects tend to be less sensitive to bias than smaller effects effect modification is an interaction between a treatment and a pretreatment covariate controlled by matching so that the treatment effect is larger at some values of the covariate than at others in the presence of effect modification it is possible that results are less sensitive to bias in subgroups experiencing larger effects two cases are considered i an a priori grouping into a few categ

probabilistic models for linear programming we propose and investigate new probabilistic models for linear programming in contrast to previous models ours guarantee the existence of optimal solutions and are symmetric under duality while in some respects our distributions are very special there is sufficient flexibility to permit an arbitrary degree of primal and or dual degeneracy either just at the optimal solution or throughout the feasible region using null variables moreover the precision of the distributions allows us to compute the probability that the feasible region is bounded as well as the distribution of the distance to a constraint hyperplane and that of the components of a vertex interest in these measures stems from karmarkar s algorithm and we also introduce a model for generating random linear programming problems on a simplex

a combined phase i phase ii scaled potential algorithm for linear programming we develop an extension of the affinely scaled potential reduction algorithm which simultaneously obtains feasibility and optimality in a standard form linear program without the addition of any m terms the method and its lower bounding procedure are particularly simple compared with previous interior algorithms not requiring feasibility

performance limitations of adaptive parameter estimation and system identification algorithms in the absence of excitation we address the problem of fundamental performance limitations in adaptive parameter estimation and system identification occurring in environments where perturbations are present but there is lack of sufficient excitation we construct a simple yet general bursting scenario to derive an analytical lower bound on the worst case peak steady state error for a wide class of parameter estimation and system identification algorithms our results show that in the absence of any input constraints arbitrarily small perturbations impose a serious performance limitation in the sense that the worst case performance deteriorates proportionally with the size of the parametric uncertainty set

unconditional stabilization of linear discrete systems via adaptive control this paper deals with the conditions of overall deterministic stability of the adaptive control schemes which may be obtained by associating any usual identification and control methods e g recursive minimum square stochastic approximation extended kalman filter for identification model reference pole placement quadratic optimization for control the deterministic and time invariance hypotheses are introduced here only for the analysis of the above schemes but not for their synthesis there are no assumptions of sufficiently exciting input or any requirement for parameter convergence nor an hypothesis of bounded input and output signals

brief identification of linear time varying systems using a modified least squares algorithm in this paper a modified version of the standard least squares algorithm is presented the aim is to use the proposed modified ls algorithm in linear time varying systems the proposed modification involves the addition of extra terms to both the parameter estimates and the covariance s update laws we establish a series of properties on the identification error the parameter estimates and the covariance matrix these properties are important in an adaptive control context because ls algorithms provide an easy way of modifying the parameter estimates in order to avoid singular points in the control scheme

modified barrier functions theory and methods the nonlinear rescaling principle employs monotone and sufficiently smooth functions to transform the constraints and or the objective function into an equivalent problem the classical lagrangian which has important properties on the primal and the dual spaces the application of the nonlinear rescaling principle to constrained optimization problems leads to a class of modified barrier functions mbf s and mbf methods mbfm s being classical lagrangians cl s for an equivalent problem the mbf s combine the best properties of the cl s and classical barrier functions cbf s but at the same time are free of their most essential deficiencies due to the excellent mbf properties new characteristics of the dual pair convex programming problems have been found and the duality theory for nonconvex constrained optimization has been developed the mbfm have up to a superlinear rate of convergence and are to the classical barrier functions cbf s method as the multipliers method for augmented lagrangians is to the classical penalty function method based on the dual theory associated with mbf the method for the simultaneous solution of the dual pair convex programming problems with up to quadratic rates of convergence have been developed the application of the mbf to linear lp and quadratic qp programming leads to a new type of multipliers methods which have a much better rate of convergence under lower computational complexity at each step as compared to the cbf methods the numerical realization of the mbfm leads to the newton modified barrier method nmbm the excellent mbf properties allow us to discover that for any nondegenerate constrained optimization problem there exists a hot start from which the nmbm has a better rate of convergence a better complexity bound and is more stable than the interior point methods which are based on the classical barrier functions

stochastic optimal control of unknown linear networked control system in the presence of random delays and packet losses in this paper the stochastic optimal control of linear networked control system ncs with uncertain system dynamics and in the presence of network imperfections such as random delays and packet losses is derived the proposed stochastic optimal control method uses an adaptive estimator ae and ideas from q learning to solve the infinite horizon optimal regulation of unknown ncs with time varying system matrices next a stochastic suboptimal control scheme which uses ae and q learning is introduced for the regulation of unknown linear time invariant ncs that is derived using certainty equivalence property update laws for online tuning the unknown parameters of the ae to obtain the q function are derived lyapunov theory is used to show that all signals are asymptotically stable as and that the estimated control signals converge to optimal or suboptimal control inputs simulation results are included to show the effectiveness of the proposed schemes the result is an optimal control scheme that operates forward in time manner for unknown linear systems in contrast with standard riccati equation based schemes which function backward in time

brief adaptive control of linear time varying systems single input single output uncertain linear time varying systems are considered which are affected by unknown bounded additive disturbances the uncertain time varying parameters are required to be smooth and bounded but are neither required to be sufficiently slow nor to have known bounds the output which is the only measured variable is required to track a given smooth bounded reference trajectory the undisturbed system is assumed to be minimum phase and to have known and constant relative degree known sign of the high frequency gain known upper bound on the system order an adaptive output feedback control algorithm is designed which assures i boundedness of all closed loop signals ii arbitrarily improved transient performance of the tracking error iii asymptotically vanishing tracking error when parameter time derivatives are l 1 signals and disturbances are l 2 signals

paper an input output view of robustness in adaptive control the stability and robustness properties of adaptive control systems are examined using input output stability theory i e passivity and small gain theory a generic adaptive error system is developed based on the concept of a tuned system an ideal converged nonadaptive closed loop system using this error system with passivity theory gives conditions for global stability where only boundedness in norm is required on the external inputs e g disturbance reference and initial conditions small gain theory is used to develop local stability results where the magnitudes of the external inputs are restricted in the global case a particular system operator not the plant is required to be strictly passive a condition which is unlikely to hold in actual use due to unmodeled dynamics the local results however are not so restricted and allow for unmodeled dynamics in this latter case an estimate of the stability margin is given under a persistent excitation condition

model reference adaptive control of linear time varying plants the case of jump parameter variations in this paper we consider the model reference adaptive control problem of single input single output linear time varying plants we assume that the plant parameters are uniformly bounded and piecewise lipschitz continuous inside the intervals of continuity we assume that the plant satisfies certain controllability observability relative degree and zero dynamics assumptions but the speed of parameter variations is not restricted to be small under these general conditions we design a control law of the model reference type which guarantees the boundedness of the closed loop plant and small tracking error in the mean square sense provided that the number of discontinuities of the plant parameters is small on average furthermore in the case of partially unknown plant parameters we show that the adaptive controller obtained by combining this control law with a suitable estimation algorithm guarantees closed loop boundedness and small tracking error in the mean square sense provided that in additi

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

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

general lemmas for stability analysis of linear continuous time systems with slowly time varying parameters this note investigates stability conditions for some dynamic systems with slowly time varying parameters or with unknown internal or external disturbances the models and conditions are motivated by adaptive control problems the results presented here provide some sufficient conditions for the exponential convergence of the state sequence of systems without system disturbance and for the uniform boundedness of the state sequence of such systems when they are subject to uniformly bounded system disturbances

brief further results on localization based switching adaptive control we investigate a switching adaptive control scheme based on falsification which is conceptually different from existing switching adaptive control schemes a feature of the proposed localization method is its fast model falsification capability in the lti case this is manifested as the rapid convergence of the switching controller by analysing the geometry of localization we give a complete solution to the problem of optimal localization

brief adaptive control of input constrained type 1 plants stabilization and tracking we consider the problem of controlling non minimum phase type 1 plants in presence of model uncertainty and a saturation constraint imposed on the control input the control objectives are the following i robust global asymptotic stabilization of the controlled plant with respect to a multiplicative modeling error ii output regulation in presence of external perturbations and iii tracking of output reference trajectories the problem is dealt with using a saturated indirect adaptive regulator based on a specific pole placement of the closed loop poles the slower the reference trajectory and the perturbation sequence the better the tracking and regulation quality

a new periodic adaptive control approach for time varying parameters with known periodicity a new adaptive control approach is proposed to deal with nonlinear systems with a class of time varying parametric uncertainties which are in an unknown compact set periodic nonvanishing rapid time varying and the only prior knowledge is the periodicity unlike most continuous time adaptation laws which are of differential types in this work a periodic type adaptation law is introduced for continuous time systems the new adaptive controller updates the parameters and the control signal periodically in a pointwise manner over one entire period in the sequel achieves the asymptotic tracking convergence

general lemma for the stability analysis of discrete time adaptive control we present a general lemma to investigate the uniform b undedness of the solutions of a class of discrete time dynamic systems in practical terms this lemma allows a demonstration of the bounded input bounded output bibo robust stability of all the available discrete time adaptive linear control systems

robust adaptive regulation with minimal prior knowledge a robust adaptive regulator is designed under minimal prior knowledge namely the order of a nominal plant model in a well defined sense the involved robustness means that the closed loop stability is guaranteed in the presence of some class of time varying parameters and unmodeled dynamics the main design feature of the proposed adaptive regulator consists in its self excitation capability together with an appropriate identification stabilization time splitting unlike in the available literature concerning robust adaptive control the involved self excitation is established independently of the parameter estimator properties the use of the robustness oriented modifications as deadzone and parameter projection or contraction which are aimed at achieving the parameter estimates boundedness is no longer required beforehand thereby reducing the underlying prior knowledge

dealing with time varying parameter problem of robot manipulators performing path tracking tasks using the properties of the element by element or hadamard product of matrices the authors obtain the robot dynamics in parameter isolated form from which a new control scheme is developed the controller proposed yields zero asymptotic tracking errors when applied to robotic systems with time varying parameters by using a switching type control law the results obtained are global in the initial state of the robot and can be applied to rapidly varying systems

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

towards understanding the capability of adaptation for time varying systems the information uncertainty coupled with the structural complexity is more pertinent than the rate of parameter changes in characterizing the capability of adaptation for time varying systems

amplification of sensitivity analysis in matched observational studies a sensitivity analysis displays the increase in uncertainty that attends an inference when a key assumption is relaxed in matched observational studies of treatment effects a key assumption in some analyses is that subjects matched for observed covariates are comparable and this assumption is relaxed by positing a relevant covariate that was not observed and not controlled by matching what properties would such an unobserved covariate need to have to materially alter the inference about treatment effects for ease of calculation and reporting it is convenient that the sensitivity analysis be of low dimension perhaps indexed by a scalar sensitivity parameter but for interpretation in specific contexts a higher dimensional analysis may be of greater relevance an amplification of a sensitivity analysis is defined as a map from each point in a low dimensional sensitivity analysis to a set of points perhaps a curve in a higher dimensional sensitivity analysis such that the possible inferences are

robust adaptive pole placement for linear time varying systems this paper studies the robustness properties of a basic adaptive control algorithm with respect to plant parameter variation as well as modeling errors and bounded disturbances the algorithm consists of a projected gradient estimator and a pole assignment controller a unified method of proof is presented for robust stability of both discrete and continuous time adaptively controlled time varying systems the robust performance of an adaptive pole assignment controller is also discussed

polynomial time algorithms for linear programming based only on primal scaling and projected gradients of a potential function this paper presents extensions and further analytical properties of algorithms for linear programming based only on primal scaling and projected gradients of a potential function the paper contains extensions and analysis of two polynomial time algorithms for linear programming we first present an extension of gonzaga s o nl iteration algorithm that computes dual variables and does not assume a known optimal objective function value this algorithm uses only affine scaling and is based on computing the projected gradient of the potential function q ln x t s sum limits j 1 n ln x j wherex is the vector of primal variables ands is the vector of dual slack variables and q n sqrt n the algorithm takes either a primal step or recomputes dual variables at each iteration we next present an alternate form of ye s o sqrt n l iteration algorithm that is an extension of the first algorithm of the paper but uses the potential function q ln x t s sum limits j 1 n ln x j sum limits j 1 n ln s j where q n sqrt n we use this alternate form of ye s algorithm to show that ye s algorithm is optimal with respect to the choice of the parameterq in the following sense suppose thatq n n t wheret 0 then the algorithm will solve the linear program in o n r l iterations wherer max t 1 t thus the value oft that minimizes the complexity bound ist 1 2 yielding ye s o sqrt n l iteration bound

cross screening in observational studies that test many hypotheses abstractwe discuss observational studies that test many causal hypotheses either hypotheses about many outcomes or many treatments to be credible an observational study that tests many causal hypotheses must demonstrate that its conclusions are neither artifacts of multiple testing nor of small biases from nonrandom treatment assignment in a sense that needs to be defined carefully hidden within a sensitivity analysis for nonrandom assignment is an enormous correction for multiple testing in the absence of bias it is extremely improbable that multiple testing alone would create an association insensitive to moderate biases we propose a new strategy called cross screening different from but motivated by recent work of bogomolov and heller on replicability cross screening splits the data in half at random uses the first half to plan a study carried out on the second half then uses the second half to plan a study carried out on the first half and reports the more favorable conclusions of the tw

projective transformations for interior point algorithms and a superlinearly convergent algorithm for the w center problem the purpose of this study is to broaden the scope of projective transformation methods in mathematical programming both in terms of theory and algorithms we start by generalizing the concept of the analytic center of a polyhedral system of constraints to the w center of a polyhedral system which stands for weighted center where there is a positive weight on the logarithmic barrier term for each inequality constraint defining the polyhedronx we prove basic results regarding contained and containing ellipsoids centered at the w center of the systemx we next shift attention to projective transformations and we exhibit an elementary projective transformation that transforms the polyhedronx to another polyhedronz and that transforms the current interior point to the w center of the transformed polyhedronz we work throughout with a polyhedral system of the most general form namely both inequality and equality costraints

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

confidence intervals for uncommon but dramatic responses to treatment a small literature discusses locally most powerful rank tests when only a fraction of treated subjects respond to treatment the ranks used in these tests are very different from conventional ranks being relatively flat for low responses and then rising steeply and the associated tests are much more powerful than conventional rank tests when indeed only a small fraction of treated subjects exhibit dramatic responses because the tests are derived from considerations of local power they do not yield a plausible family of models for effect and therefore they do not yield confidence intervals for the magnitude of effect formed by inverting the tests there is a similarity between these tests and another family of tests originally motivated by different considerations involving peak performance in small subsets exploiting this similarity a method for obtaining confidence statements is proposed in the case of observational studies sensitivity to unobserved bias from nonrandom assignment of treatments is also examined two examples are used as illustrations i a study of smoking during pregnancy and its effects on birth weight in which smokers are matched to six controls and ii a matched pair study of damage to dna among workers at aluminum production plants

brief adaptive control for linear slowly time varying systems using direct least squares estimation in this paper we propose a least squares based non recursive identification algorithm capable of dealing with slowly time varying parameters the minimized criterion is an l 2 norm of the identification error with forgetting factor the proposed estimation algorithm does not require explicit knowledge on the noise bound or the region where the true parameters lie finally a pole placement hybrid controller is designed and the system s state is shown to be bounded

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

global stability of adaptive pole placement algorithms this paper presents direct and indirect adaptive control schemes for assigning the closed loop poles of a single input single output system in both the continuous and discrete time cases the resulting closed loop system is shown to be globally stable when driven by an external reference signal consisting of a sum of sinusoids in particular persistent excitation of the potentially unbounded closed loop input output data and hence convergence of a sequential least squares identification algorithm is proved the results are applicable to standard sequential least squares and least squares with covariance reset

adaptive control of linear time varying plants a new model reference controller structure the problem of developing a control law which can force the output of a linear time varying plant to track the output of a stable linear time invariant reference model is discussed it is shown that the standard model reference controller used for linear time invariant plants cannot guarantee zero tracking error in general when the plant is time varying a new model reference controller is proposed which guarantees stability and zero tracking error for a general class of linear time varying plants with known parameters when the time varying plant parameters are unknown but vary slowly with time it is shown that the new controller can be combined with a suitable adaptive law so that all the signals in the closed loop remain bounded for any bounded initial conditions and the tracking error is small in the mean the assumption of slow parameter variations in the adaptive case can be relaxed if some information about the frequency or the form of the fast varying parameters is available a priori such information can be incorporated in an appropriately designed adaptive law so that stability and improved tracking performance is guaranteed for a class of plants with fast varying parameters

robustness of adaptive control without deadzones data normalization or persistence of excitation abstract robustness properties have been established for modified adaptive control algorithms the major modifications involve various combinations of normalization relative deadzones persistence of excitation parameter projection and or so called modification results showing global boundedness have used some form of data normalization many results on local properties have depended on persistence of excitation however use of these modifications involve some a priori knowledge of the plant for good performance this may lead to complications in practice here it is shown that some useful local robustness properties hold if only parameter projection is used as a modification of the basic gradient estimator

self tuning pid controllers algorithms and implementation a class of controllers with integral action is shown to arise directly from appropriate system models via the zero gain predictor approach a corresponding class of hybrid self tuning controllers is shown to have both integral action in the controller and offset removal in the tuning algorithm implementation details and some experimental results are given

following a balanced trajectory from an infeasible point to an optimal linear programming solution with a polynomial time algorithm this paper is concerned with the problem of following a trajectory from an infeasible starting point directly to an optimal solution of the linear programming problem a class of trajectories for the problem is defined based on the notion of a balanced solution to the problem given a prespecified positive balancing constant an infeasible solution x is said to be balanced if the optimal value gap is less than or equal to times the infeasibility gap mathematically this can be written as ctx z tx where the linear form tx is the phase i objective function and z is the optimal objective value of the linear program the concept of a balanced solution is used to define a class of trajectories from an infeasible point to an optimal solution of a given linear program each trajectory has the property that all points on or near the trajectory in a suitable metric are balanced the main thrust of the paper is the development of an algorithm that traces a given balanced trajectory from a starting point near the trajectory to an optimal solution to the given linear programming problem in polynomial time more specifically the algorithm allows for fixed improvement in the bound on the phase i and the phase ii objectives in on newton steps

a polynomial method of approximate centers for linear programming we present a path following algorithm for the linear programming problem with a surprisingly simple and elegant proof of its polynomial behaviour this is done both for the problem in standard form and for its dual problem we also discuss some implementation strategies

a robust adaptive controller with minimal modifications for discrete time varying systems the goal of this paper is to show that an indirect adaptive controller with parameter projection as the only modification on the basis of conventional adaptive control algorithms can globally stabilize systems having fast parasitics bounded external disturbances and time varying parameters without any restriction on signals in the closed loop system such as persistence of excitation further the controller can still retain the properties of earlier unmodified conventional adaptive controllers when the controlled plant satisfies so called ideal assumptions or the rates at which the plant parameters change belong to the l sub 1 or l sub 2 space

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

a potential reduction algorithm with user specified phase i phase ii balance for solving a linear program from an infeasible warm start this paper develops a potential reduction algorithm for solving a linear programming problem directly from a warm start initial point that is neither feasible nor optimal the algorithm is an interior point variety that seeks to reduce a single potential function which simultaneously coerces feasibility improvement phase i and objective value improvement phase ii the key feature of the algorithm is the ability to specify beforehand the desired balance between infeasibility and nonoptimality in the following sense given a prespecified balancing parameter beta 0 the algorithm maintains the following phase i phase ii beta balancing constraint throughout left c t x z right beta xi t x where c t x is the objective function z is the unknown optimal objective value of the linear program and xi t x measures the infeasibility of the current iterate x this balancing constraint can be used to either emphasize rapid attainment of feasibility set beta large

global boundedness of discrete time adaptive control just using estimator projection in this paper we study a discrete time indirect adaptive control algorithm which contains a constrained gradient parameter estimator and a pole assignment control law synthesis module this adaptive control algorithm does not involve modifications like data normalization use of deadzones or injection of persistently excited signals also it requires no a priori knowledge of system modelling errors it is shown that global robustness properties still hold when this simple algorithm is applied to systems with bounded disturbances and arbitrarily small fast parasitic dynamics the problem of indirect decentralized adaptive control of interconnected systems is also considered we use the above adaptive algorithm to design completely decentralized local adaptive controllers for each isolated subsystem by ignoring interactions between subsystems we show that the local controllers designed in this way are robust in the sense that all signals in the closed loop adaptive system are bounded for bounded initial conditions reference inputs disturbances and an arbitrarily small amount of interaction between subsystems and unmodelled dynamics of each subsystem