a new recursive identification algorithm for singularity free adaptive control reportedly guaranteeing the controllability of the estimated system is a crucial problem in adaptive control in this paper we introduce a least squares based identification algorithm for stochastic siso systems which secures the uniform controllability of the estimated system and presents closed loop identification properties similar to those of the least squares algorithm the proposed algorithm is recursive and therefore easily implementable its use however is confined to cases in which the parameter uncertainly is highly structured

uniform stability of switched linear systems extensions of lasalle s invariance principle this paper addresses the uniform stability of switched linear systems where uniformity refers to the convergence rate of the multiple solutions that one obtains as the switching signal ranges over a given set we provide a collection of results that can be viewed as extensions of lasalle s invariance principle to certain classes of switched linear systems using these results one can deduce asymptotic stability using multiple lyapunov functions whose lie derivatives are only negative semidefinite depending on the regularity assumptions placed on the switching signals one may be able to conclude just asymptotic stability or uniform exponential stability we show by counter example that the results obtained are tight

global tunability of one dimensional siso systems it is shown by example that with a suitably defined certainty equivalence controller sigma sub r it is possible to make a closed loop parameterized system sigma tunable on its entire parameter space p even though p may contain points at which the parameterized sigma sub d upon which sigma sub r s definition is based is not stabilizable the implications of this discovery are briefly discussed

stabilization of switched linear systems in this note we study the stabilization problem of systems that switch among a finite set of controllable linear systems with arbitrary switching frequency for both cases of known and unknown switching functions feedback laws are designed to achieve exponential stability for the later case a method combining on line adaptive estimation and feedback stabilization is developed in the controller design

dynamic stability of stiffened laminated composite plates and shells subjected to in plane pulsating forces the dynamic stability of laminated composite stiffened or non stiffened plates and shells due to periodic in plane forces at boundaries is investigated in this paper a three dimensional 3 d degenerated shell element and a 3 d degenerated curved beam element are used to model plates shells and stiffeners respectively the characteristic equations to find the natural frequencies buckling loads and their corresponding mode shapes are obtained from the finite element equation of motion then the method of hill s infinite determinants or the method of multiple scales is applied to analyse the dynamic instability regions numerical results are presented to demonstrate the effects of various parameters such as skew angle lamination scheme stiffened scheme in plane force type and curvature of cylindrical shell on the dynamic stability of stiffened and non stiffened plates and shells subjected to in plane pulsating forces at boundaries

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

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

a gain matrix decomposition and some of its applications abstract any real square matrix m can be written as m u i l s where u is a matrix of 0 s 1 s and 1 s having exactly one nonzero element in each row and column l is a strictly lower triangular matrix and s is a symmetric positive semidefinite matrix the aim of this paper is to demonstrate the utility of this easily derived fact this is done in two ways first the decomposition is used to develop an identifier based solution to a simplified multivariable adaptive stabilization problem solved previously using nonidentifier based methods second it is briefly explained how to use the decomposition together with hysteresis switching and a certain lifted discrete time system representation to obtain an excitation free identifier based adaptive stabilizer for the entire class of n dimensional siso controllable observable discrete time linear process models this is accomplished by exploiting a new method of discrete time parameter adjustment called pseudo continuous tuning

global adaptive pole positioning adaptive pole positioning for linear time invariant discrete time systems is considered under the constraint that the controller consists of an identifier the gains in which do not go to zero an observer and a state feedback law the latter two elements being viewed in transfer function form a globally convergent algorithm is presented for achieving a prescribed set of closed loop poles persistency of excitation of an external input is required together with an underbound on the magnitude of the sylvester resultant of the plant numerator and denominator polynomials this in effect being an underbound on the product of a measure of pole zero separation and a generalized gain

the role of convexity in the adaptive control of rapidly time varying systems abstract in classical adaptive control the parameters are assumed to be fixed or slowly time varying in order to facilitate parameter estimation tuning it is desirable to have the set of admissible parameters lie in a convex set if this set is not convex a common trick is to replace it with its convex hull but the adaptive control problem is challenging if stabilizability of the set of admissible parameters is lost however such a convexity assumption is an artifact of the approach to the problem rather than an inherent constraint since most logic based and supervisory approaches to the problem make no such requirement on the other hand here we show that losing stabilizability on the convex hull of the set of admissible parameters plays an important role in the adaptive control of rapidly time varying systems

online removable knapsack problem under convex function abstract in this paper we address an online knapsack problem under a convex size profit function we first give a greedy online algorithm with a competitive ratio 2 then we propose an improved online algorithm with a competitive ratio 5 3 we also prove that when the convex function has a specific property our improved online algorithm is 1 5 2 competitive which is optimal finally we prove that the lower bound of this problem is 1 5 2

online knapsack problem under concave functions in this paper we address an online knapsack problem under concave function f x i e an item with size x has its profit f x we first obtain a simple lower bound max q frac f 0 f 1 where q approx 1 618 then show that this bound is not tight and give an improved lower bound finally we find the online algorithm for linear function 8 can be employed to the concave case and prove its competitive ratio is frac f 0 f 1 q then we give a refined online algorithm with a competitive ratio frac f 0 f 1 1 and we also give optimal algorithms for some piecewise linear functions

online minimization knapsack problem in this paper we address the online minimization knapsack problem i e the items are given one by one over time and the goal is to minimize the total cost of items that covers a knapsack we study the removable model where it is allowed to remove old items from the knapsack in order to accept a new item we obtain the following results i we propose a 8 competitive deterministic and memoryless algorithm for the problem which contrasts with the result for the online maximization knapsack problem that no online algorithm has a bounded competitive ratio 14 ii we propose a 2e competitive randomized algorithm for the problem iii we derive a lower bound of 2 for deterministic algorithms for the problem iv we propose a 1 618 competitive deterministic algorithm for the case in which each item has size equal to its cost and show that this is best possible

applications of hysteresis switching in parameter adaptive control the hysteresis switching algorithm of r h middleton et al ibid vol 33 no 1 p 50 8 jan 1988 is reexamined in a broader context to demonstrate its utility the algorithm is applied to various families of identifier based parameterized controllers of both the direct and indirect control types application to the direct control type results in a model reference adaptive controller capable of stabilizing without excitation any siso process which can be modeled by a minimum phase linear system whose transfer function has relative and mcmillan degrees not exceeding prescribing integers m and n respectively it is shown that such processes can also be adaptively stabilized with indirect adaptive controllers and hysteresis switching a simple numerical example involving a non minimum phase process model is used to illustrate how hysteresis switching might be applied to implicitly tuned parameterized controllers to realize an adaptive controller with capabilities which might prove very difficult if not impossible to achieve without hysteresis switching or some other form of discontinuous control

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

randomized algorithms for online knapsack problems in this paper we study online knapsack problems the input is a sequence of items e 1 e 2 e n each of which has a size and a value given the ith item e i we either put e i into the knapsack or reject it in the removable setting when e i is put into the knapsack some items in the knapsack are removed with no cost if the sum of the size of e i and the total size in the current knapsack exceeds the capacity of the knapsack our goal is to maximize the profit i e the sum of the values of items in the last knapsack we present a simple randomized 2 competitive algorithm for the unweighted non removable case and show that it is the best possible where knapsack problem is called unweighted if the value of each item is equal to its size for the removable case we propose a randomized 2 competitive algorithm despite there is no constant competitive deterministic algorithm we also provide a lower bound 1 1 e 1 368 for the competitive ratio for the unweighted removable case we propose a 10 7 competitive algorithm and provide a lower bound 1 25 for the competitive ratio

robust adaptive regulation without persistent excitation a globally convergent adaptive regulator for minimum or nonminimum phase systems subject to bounded disturbances is presented the control strategy is designed for a particular input output representation obtained from the state space representation of the system the leading coefficient of the novel representation is the product of the observability and controllability matrices of the system the controller scheme uses a least squares identification algorithm with a dead zone the dead zone is chosen to obtain convergence properties on the estimates and on the covariance matrix as well this allows the definition of modified estimates which secure well conditioned matrices in the adaptive control law explicit bounds on the plant output are given

online knapsack of unknown capacity how to optimize energy consumption in smartphones abstract we propose a new variant of the standard online knapsack problem where the only information missing to the provided instances is the capacity b of the knapsack we refer to this problem as the online knapsack of unknown capacity kuc problem any algorithm solving the kuc problem must provide a strategy for filling online the knapsack until its capacity is revealed when the knapsack capacity is revealed no other item can be inserted and also the last inserted item is discarded if it does not completely fit in the knapsack apart for the interest in a new version of the fundamental knapsack problem the motivations that lead to define this new variant come from energy consumption constraints in smartphones communications we provide lower and upper bounds to the problem for various cases in general we design an optimal algorithm admitting a 1 2 competitive ratio when all items admit uniform ratio of profit over size our algorithm provides a 49 86 569 competitive ratio that leaves some gap with the provided bound of 1 618 the inverse of the golden number we then conduct experimental analysis for the competitive ratio guaranteed algorithms compared to the optimum and to various heuristics

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

mimo design models and internal regulators for cyclicly switched parameter adaptive control systems in pait and morse 1994 the concept of cyclic switching was proposed as a means of dealing with the well known stabilizability problem which arises in adaptive controller synthesis because of the existence of points in parameter space where the design model upon which certainty equivalence control is based loses stabilizability while the procedure outlined in the above paper is specific enough to enable one to construct cyclicly switched adaptive controllers for siso process models for the mimo case two key issues are left unresolved the objective of this paper is to address both of these issues thereby extending excitation free identifier based adaptive control methods to minimum and nonminimum phase mimo linear systems

determinability and state estimation for switched differential algebraic equations the problem of state reconstruction and estimation is considered for a class of switched dynamical systems whose subsystems are modeled using linear differential algebraic equations daes since this system class imposes time varying dynamic and static in the form of algebraic constraints relations on the evolution of state trajectories an appropriate notion of observability is presented which accommodates these phenomena based on this notion we first derive a formula for the reconstruction of the state of the system where we explicitly obtain an injective mapping from the output to the state in practice such a mapping may be difficult to realize numerically and hence a class of estimators is proposed which ensures that the state estimate converges asymptotically to the real state of the system

stochastic on line knapsack problems different classes of on line algorithms are developed and analyzed for the solution of 0 1 and relaxed stochastic knapsack problems in which both profit and size coefficients are random variables in particular a linear time on line algorithm is proposed for which the expected difference between the optimum and the approximate solution value iso log3 2n an 1 lower bound on the expected difference between the optimum and the solution found by any on line algorithm is also shown to hold

boundedness properties of simple indirect adaptive control systems examining adaptive controllers for a class of first order linear continuous time plants with different estimators and control laws the authors obtain explicit solutions completely describing the nonlinear behavior of the resultant adaptive systems some of these adaptive systems exhibit either finite time escapes or other forms of unbounded behavior due to a loss of stabilizability of the estimated model some fixes for the loss of stabilizability problem are analyzed implications of these results for the general indirect adaptive control case are discussed

bibo stability of linear switching systems in this paper we show that for linear switching systems of the form x sub n 1 a sub n x sub n u sub n 1 where the matrices a sub n are chosen arbitrarily from a given set of matrices bounded input bounded output stability implies uniform exponential stability

a cyclic switching strategy for parameter adaptive control this paper introduces a new strategy called cyclic switching to deal with the well known certainty equivalence control synthesis problem which arises in the design of identifier based adaptive controllers because of the existence of points in parameter space where the design model spl sigma sub d upon which certainty equivalence synthesis is based loses stabilizability unlike most previously suggested methods for handling this problem the technique proposed here can be employed with or without process excitation for the technique to work it is not necessary for there to be a mechanism for moving tuned parameters away from values at which spl sigma sub d loses stabilizability and no such mechanism is used

towards a unified theory of parameter adaptive control ii certainty equivalence and implicit tuning for pt i see ibid vol 35 p 1002 12 1990 it is shown that for a large class of linear multivariable process models a properly designed certainty equivalence controller results in a tunable closed loop parameterized system the importance of this result to both the analysis and synthesis of parameter adaptive control systems is discussed it is demonstrated by means of examples how the connection between certainty equivalence and tunability together with the concept of tunability itself can be used to markedly simplify the stability analysis of adaptive control systems a new family of indirect parameterized controllers is introduced which has capabilities comparable to those of the well known direct parameterized controllers which have served as basic building blocks for adaptive control systems of all types the concept of implicit tuning is formalized and its potential importance to adaptive control is briefly discussed it is explained how the idea of tunability can be used to analyze an implicitly tuned system

the dynamic and stochastic knapsack problem the dynamic and stochastic knapsack problem dskp is defined as follows items arrive according to a poisson process in time each item has a demand size for a limited resource the knapsack and an associated reward the resource requirements and rewards are jointly distributed according to a known probability distribution and become known at the time of the item s arrival items can be either accepted or rejected if an item is accepted the item s reward is received and if an item is rejected a penalty is paid the problem can be stopped at any time at which time a terminal value is received which may depend on the amount of resource remaining given the waiting cost and the time horizon of the problem the objective is to determine the optim al policy that maximizes the expected value rewards minus costs accumulated assuming that all items have equal sizes but random rewards optimal solutions are derived for a variety of cost structures and time horizons and recursive algorithms for computing them are developed optimal closed form solutions are obtained for special cases the dskp has applications in freight transportation in scheduling of batch processors in selling of assets and in selection of investment projects

the dynamic and stochastic knapsack problem with deadlines in this paper a dynamic and stochastic model of the well known knapsack problem is developed and analyzed the problem is motivated by a wide variety of real world applications objects of random weight and reward arrive according to a stochastic process in time the weights and rewards associated with the objects are distributed according to a known probability distribution each object can either be accepted to be loaded into the knapsack of known weight capacity or be rejected the objective is to determine the optimal policy for loading the knapsack within a fixed time horizon so as to maximize the expected accumulated reward the optimal decision rules are derived and are shown to exhibit surprising behavior in some cases it is also shown that if the distribution of the weights is concave then the decision rules behave according to intuition