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

a lanczos type method for multiple starting vectors given a square matrix and single right and left starting vectors the classical nonsymmetric lanczos process generates two sequences of bior thogonal basis vectors for the right and left krylov subspaces induced by the given matrix and vectors in this paper we propose a lanczos type algorithm that extends the classical lanczos process for single starting vectors to mul tiple starting vectors given a square matrix and two blocks of right and left starting vectors the algorithm generates two sequences of biorthogonal basis vectors for the right and left block krylov subspaces induced by the given data the algorithm can handle the most general case of right and left start ing blocks of arbitrary sizes while all previously proposed extensions of the lanczos process are restricted to right and left starting blocks of identical sizes other features of our algorithm include a built in deation procedure to detect and delete linearly dependent vectors in the block krylov sequences and the option to employ look ahead to remedy the potential breakdowns that may occur in nonsymmetric lanczos type methods

a new indirect adaptive control scheme for time varying plants structures are developed for the control and estimation parts of the indirect adaptive scheme which are more appropriate for time varying plants in contrast to the usual pointwise schemes the new controller structure can meet the control objective exactly for a wide class of plants with smooth but otherwise unrestricted parameter variations on the other hand the possibly available knowledge of the form or frequency of variation of the fast parameters is included in the new estimator structure so that for successful estimation the overall plant is not restricted to varying slowly with time the new estimator and control law are combined using the certainty equivalence principle to develop an indirect adaptive control scheme meeting the control objective for plants with time varying parameters whose fast varying parts are of known form and unknown parts are slow in the mean

behavior of plane waves propagating through a temperature inhomogeneous region abstract description and analysis of acoustic waves in ducts with a region containing temperature inhomogeneous fluid represent a significant problem of scientific and practical interest this interest is induced by the need of understanding how temperature fields affect acoustic processes which would lead to a more efficient design and control of systems involving thermoacoustic interactions most of the works addressing these problems limit themselves to the assumption of weak temperature profile gradients or to temperature profiles which do not connect neighboring temperature homogeneous regions smoothly in our work we investigate the behavior of plane acoustic waves that enter a region with an arbitrary temperature gradient a polynomial character of the used temperature profile ensures smooth connection with constant temperature regions the one dimensional wave equation for ducts with an axial mean temperature gradient is solved analytically the derived solutions based on heun functions extend the class of published exact analytical solutions of model wave equations taking into account the medium temperature gradient due to the property that our proposed polynomial temperature function has derivatives equal to zero at points which are connected with the surrounding temperature homogeneous regions we can form more complex smooth temperature profiles for which it is possible to use the transfer matrix method

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

computing the kalman decomposition an optimal method in this paper we describe a method for computing the complete kalman decomposition of a linear dynamical system and we show that this method is optimal in a certain sense specifically we describe an algorithm to compute a mapping that when applied to the original system yields a complete kalman decomposition we show that of all transformations that yield a kalman decomposition the one we construct here has the lowest condition number

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

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

adaptive control of linear time varying plants abstract in this paper the model reference adaptive control mrac problem of a class of linear time varying ltv plants is considered the plant parameters are assumed to be smooth bounded functions of time which satisfy the usual assumptions of mrac for time invariant plants at each frozen time instant it is first shown that if the plant parameters are sufficiently slowly varying with time a control parameter vector with smooth elements exists such that the closed loop plant behaves almost like a linear time invariant reference model the robust adaptive law proposed in ioannou and tsakalis 1986 ieee trans aut control ac 31 1033 is then used to adjust the controller parameters and establish boundedness of all signals in the adaptive loop for any bounded initial conditions it is shown that the bound for the residual tracking error depends on the speed of the plant parameter variations in such a way that as these parameters become constant the bound reduces to zero

fuzzy model based control stability robustness and performance issues a nonlinear controller based on a fuzzy model of mimo dynamical systems is described and analyzed the fuzzy model is based on a set of arx models that are combined using a fuzzy inference mechanism the controller is a discrete time nonlinear decoupler which is analyzed both for the adaptive and the fixed parameter cases a detailed stability analysis is carried out and the main result is that the closed loop is globally stable and robust with respect to unstructured uncertainty which may include modeling error and disturbances in addition bounds on the asymptotic and transient performance are given the main assumptions on the system and model are that they must not have strong nonminimum phase effects except time delay and the unstructured uncertainty must not be too large a simulation example illustrates some of the properties of the modeling method and model based control structure

on plane wave propagation in a uniform pipe in the presence of a mean flow and a temperature gradient a theoretical study on the propagation of plane waves in the presence of a hot mean flow in a uniform pipe is presented the temperature variation in the pipe is taken to be a linear temperature gradient along the axis the theoretical studies include the formulation of a wave equation based on continuity momentum and state equation and derivation of a general four pole matrix which is shown to yield the well known transfer matrices for several other simpler cases

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

on uniqueness transfer and combination of acoustic sources in one dimensional systems the use of electroacoustic analogies suggests that a source of acoustical energy such as an engine compressor blower turbine loudspeaker etc can be characterized by an acoustic source pressure ps and internal source impedance zs analogous to the open circuit voltage and internal impedance of an electrical source the present paper shows analytically that the source characteristics evaluated by means of the indirect methods are independent of the loads selected that is the evaluated values of ps and zs are unique and that the results of the different methods including the direct method are identical in addition general relations have been derived here for the transfer of source characteristics from one station to another station across one or more acoustical elements and also for combining several sources into a single equivalent source finally all the conclusions are extended to the case of a uniformly moving medium incorporating the convective as well as dissipative effects of the mean flow

direct block tridiagonalization of single input single output systems abstract in this paper we derive a direct method for block tridiagonalizing a single input single output system triple a b c the method is connected to the nonsymmetric lanczos procedure developed in 10 2 1 and also leads to canonical representations of such triples

brief paper lyapunov exponential stability of 1 d linear hyperbolic systems of balance laws explicit boundary dissipative conditions are given for the exponential stability in l 2 norm of one dimensional linear hyperbolic systems of balance laws email protected email protected email protected x 0 over a finite interval when the matrix m is marginally diagonally stable the result is illustrated with an application to boundary feedback stabilisation of open channels represented by linearised saint venant exner equations

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

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

a krylov subspace projection method for simultaneous solution of helmholtz problems at multiple frequencies abstract a krylov subspace projection method which provides simultaneous solutions of the helmholtz equation at multiple frequencies in one solution step is presented the projector is obtained with an unsymmetric block lanczos algorithm applied to a transfer function derived from a finite element discretization this approach is equivalent to a matrix valued pade approximation of the transfer function the proposed method is an extension of the formulation presented in j comput acoust 8 2000 223 to unsymmetric systems and allows the treatment of a much wider range of practical problems including near field and fluid structure interaction computations

exact solutions to one dimensional acoustic fields with temperature gradient and mean flow an exact solution for one dimensional acoustic fields in ducts in the presence of an axial mean temperature gradient and mean flow is presented in this paper the analysis is valid for mean mach numbers such that the square of the mean mach number is much less than one the one dimensional wave equation for ducts with axial mean temperature gradient and mean flow is derived by appropriate transformations the wave equation is reduced to an analytically solvable hypergeometric differential equation for the case of a linear mean temperature profile the developed solution is applied to investigate the dependence of sound propagation in a duct on factors such as temperature gradient and mean flow the results obtained using the analytical solution compare very well with the numerical results the developed solution is also compared with an existing analytical solution

a breakdown free variation of the nonsymmetric lanczos algorithms the nonsymmetric lanczos tridiagonalization algorithm is essentially the gram schmidt biorthogonalization method for generating biorthogonal bases of a pair of krylov subspaces it suffers from breakdown and instability when a pivot at some step is zero or nearly zero which is often the result of mismatch of the two krylov subspaces in this paper we propose to modify one of the two krylov subspaces by introducing a new start vector when a pivot is small this new start vector generates another krylov subspace which we add to the old one in an appropriate way so that the gram schmidt method for the modified subspaces yields a recurrence similar to the lanczos algorithm our method enforces the pivots to be above a certain threshold and can handle both exact breakdown and near breakdown in particular we recover lookahead lanczos algorithms and arnoldi s algorithm as two special cases we also discuss theoretical and practical issues concerning the new start procedure and present a convergence analysis as well as some numerical examples

robust adaptive control of discrete nominally stabilizable plants this paper presents an indirect pole placement based adaptive control scheme for discrete linear time invariant non necessarily inversely stable and stabilizable systems the scheme is a pole placement type without requiring the plant inverse stability assumption the control objective is that the plant output should asymptotically track in the absence of unmodeled dynamics and bounded disturbances a reference signal given by an arbitrary stable filter under a bounded tracking error while ensuring robust closed loop stability the adaptive stabilizability and the robustness of this system under the presence of unmodeled dynamics and possibly bounded disturbances are proved without assuming the controllability of the modeled plant a normalized least squares algorithm with a relative adaptation dead zone and a posteriori modification of the parameter estimates is used to ensure the controllability of the modified estimation plant model at all sampling instants and at the limit such a property is crucial to solve the stable pole placement problem on the other hand the relative adaptation dead zone is included for robustness purposes under unmodeled dynamics and possibly bounded disturbances

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

an implementation of the look ahead lanczos algorithm for non hermitian matrices the nonsymmetric lanczos method can be used to compute eigenvalues of large sparse non hermitian matrices or to solve large sparse non hermitian linear systems however the original lanczos algorithm is susceptible to possible breakdowns and potential instabilities an implementation of a look ahead version of the lanczos algorithm is presented that except for the very special situation of an incurable breakdown overcomes these problems by skipping over those steps in which a breakdown or near breakdown would occur in the standard process the proposed algorithm can handle look ahead steps of any length and requires the same number of matrix vector products and inner products as the standard lanczos process without look ahead

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

singular perturbation approximation by means of a h 2 lyapunov function for linear hyperbolic systems abstract a linear hyperbolic system of two conservation laws with two time scales is considered in this paper the fast time scale is modeled by a small perturbation parameter by formally setting the perturbation parameter to zero the full system is decomposed into two subsystems the reduced subsystem representing the slow dynamics and the boundary layer subsystem standing for the fast dynamics the solution of the full system can be approximated by the solution of the reduced subsystem this result is obtained by using a h 2 lyapunov function the estimate of the errors is the order of the perturbation parameter for all initial conditions belonging to h 2 and satisfying suitable compatibility conditions moreover for a particular subset of initial conditions more precise estimates are obtained the main result is illustrated by means of numerical simulations

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

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

tikhonov theorem for linear hyperbolic systems abstract a class of linear hyperbolic systems of conservation laws with multiple time scales which are modeled by a perturbation parameter is considered in this paper by setting the perturbation parameter to zero two subsystems the reduced subsystem standing for the slow dynamics and the boundary layer subsystem representing the fast dynamics are computed it is first proved that the exponential stability of the full system implies the stability of both subsystems secondly a counterexample is given to indicate that the stability of the two subsystems does not ensure the full system s stability moreover a new tikhonov theorem for this class of infinite dimensional systems is stated the solution of the full system can be approximated by that of the reduced subsystem and this is proved by lyapunov techniques an application to boundary feedback stabilization of gas transport model is used to illustrate the results

exact solution for one dimensional acoustic fields in ducts with a quadratic mean temperature profile the purpose of this letter is to present an exact analytical solution for sound propagation in ducts with a quadratic mean temperature profile using appropriate transformations the one dimensional wave equation for ducts with an axial mean temperature gradient was reduced to the hypergeometric differential equation whose solution can be expressed in terms of hypergeometric functions the analysis neglects the effects of mean flow and is therefore valid only for small mean mach numbers

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

adaptive control of a class of slowly time varying plants abstract an adaptive control system of the type considered earlier by the author which is designed to be stable under the assumption that the unknown plant parameters are constant is shown to maintain stability when the plant parameters are slowly time varying

paper discrete time adaptive control for deterministic time varying systems there is currently considerable interest in the application of recently developed self tuning control algorithms to real control problems however there exist few algorithms which will work for other than slow time varying systems a new algorithm which is able to successfully control unknown systems with quite rapidly varying parameters is presented several simulation results are also presented a convergence proof in the linearly time varying parameter case is given

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

a look ahead lanczos algorithm for unsymmetric matrices abstract the two sided lanczos algorithm is known to suffer from serious breakdowns these occur when the associated moment matrix does not permit triangular factorization we modify the algorithm slightly so that it corresponds to using a 2 x 2 pivot in triangular factorization whenever a 1 x 1 pivot would be dangerous the incidence of breakdown is greatly reduced the price paid is that the tridiagonal matrix produced by the algorithm now has bumps whenever a 2 x 2 pivot is used author

the lanczos algorithm and hankel matrix factorization abstract we explore the connections between the lanczos algorithm for matrix tridiagonalization and two fast algorithms for hankel matrix factorization we show how the asymmetric lanczos process is related to the berlekamp massey algorithm and how the symmetrized lanczos process is related to the phillips algorithm we also discuss conditions under which the analysis of phillips applies

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

the lanczos arnoldi algorithm and controllability we present methods for computing the controllable space of a linear dynamic system the methods are based on orthogonalizing krylov sequences and can use much less storage than other methods with little or no loss of numerical stability

a sufficient condition on the exponential stability of two dimensional 2 d shift variant systems in this paper we consider a class of two dimensional 2 d shift variant systems based on the bound on the deviation of parameters a sufficient condition is derived which ensures exponential stability with different decaying rates along the two directions an example is presented to illustrate the result

a general minimal residual krylov subspace method for large scale model reduction this paper considers approximating a given nth order stable transfer matrix g s by an rth order stable transfer matrix g sub r s in which n spl gt r and where n is large the arnoldi process is used to generate a basis to a part of the controllability subspace associated with the realization of g s and a residual error is defined for any approximation in this subspace we establish that minimizing the l sub spl infin norm of this residual error over the set of stable approximations leads to a 2 block distance problem finally the solution of this distance problem is used to construct reduced order approximate models the behavior of the algorithms is illustrated with a simple example

generalized biorthogonal bases and tridiagonalisation of matrices in connection with the breakdown problem of the lanczos algorithm a theory of generalized biorthogonal bases is developed the connection between the generalized biorthogonal bases of krylov chains and look ahead lanczos recursions is worked out in detail it is shown how generalized biorthogonal bases with antidiagonal blocks can be constructed with small computational effort finally a special look ahead lanczos algorithm is derived which requires minimal computational effort and storage

the one dimensional acoustic field in a duct with arbitrary mean axial temperature gradient and mean flow abstract this paper presents an analytical solution for the one dimensional acoustic field in a duct with arbitrary mean temperature gradient and mean flow a wave equation for the pressure perturbation is derived which relies on very few assumptions an analytical solution for this is derived using an adapted wkb approximation the solution is a superposition of waves travelling in either direction and thus provides physical insight it is also very easy to calculate the proposed solution is applied to ducts with a mean temperature profile which varies axially with i a linear and ii a partial sine wave profile predictions are compared to those obtained by numerically solving the linearised euler equations lees the analytical solution reproduces the acoustic field very accurately across a wide range of flow conditions which span both low and moderate to high subsonic mach numbers it always performs well when the frequency exceeds a certain value when the mean temperature profile is linear it also performs well to very low frequencies this increased frequency range for linear mean temperature profiles leads to its application to more complicated profiles in a piecewise linear manner axially segmenting the temperature profile into regions that can be approximated as linear the acoustic field is predicted very accurately as long as enough segmentation points are used and the condition for the linear mean temperature profile is satisfied k 0 where k0 is the local wave number when there is no mean flow and is the normalised mean density gradient the proposed solution is extensively compared to previous analytical solutions and is found to be more accurate and reliable especially at higher mach numbers the entropy wave generated by communication between the acoustic waves and the distributed mean temperature zone is calculated using the lees it is found to remain very small across all operating conditions such that both the entropy wave and its impact on the acoustic field can be neglected

singularly perturbed problems in partial differential equations a survey this survey paper contains a surprisingly large amount of material on singularly perturbed partial differential equations and indeed can serve as an introduction to some of the ideas and methods of the singular perturbation theory starting from prandtl s work a large amount of work has been done in the area of singular perturbations this paper limits its coverage to some standard singular perturbation models considered by various workers and the methods developed by numerous researchers after 1980 2000 in this review we have covered singularly perturbed partial differential equations about odes the survey has already been done by us see m k kadalbajoo k c patidar appl math comput 130 2002 457 510

stable adaptive control for not necessarily stable discrete linear plants with bounded non linear inputs abstract this paper deals with the design of stable adaptive control schemes for discrete plants under non linear bounded inputs two algorithms are studied one of them being a generalization of the d step ahead standard algorithm while the second one involves the use of a time decreasing adaptation gain the class of inputs for which the algorithms perform in a stable fashion include saturations relays and saturated dead zones the plant stability assumption is not requested to prove standard non asymptotic stability results the mechanism to achieve scheme s stability is the use of an extra weighted additive term in the adaptation error which takes into account the output deviation with respect to that associated with linear inputs

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

the influence of a liquid flow on sound fields confined by conical walls abstract sound propagation in conical waveguides is analyzed for the case where a background flow is maintained through the cone and points along the radial co ordinate r only a general expression for the acoustic pressure is derived and the perturbations of the acoustic field accommodated by the presence of a background flow are found by use of the green function method in the second part of this paper flow measurement properties are discussed the designation of propagation constants such as the wave number and phase speed lose much of their intuitive meaning in a conical waveguide instead the so called pseudo guide wave number and pseudo phase speed are introduced as they are well defined in the cone case and simplifies to the wave number and phase speed in the cylinder case respectively it is shown that changes due to a background flow in pseudo guide wave number pseudo phase speed and zero point crossing times all exhibit an oscillatory behavior as a function of the r co ordinate this is in contrast to the case of a cylinder where such changes become a linear function of the distance from the transmitter the oscillatory behavior in the changes in zero point crossing times as a function of r does not hamper flow measurement in the cone case since the only requirement to be fulfilled is in principle that a one to one correspondence between measured output changes in zero point crossing times and actual flow determined by v 0 at a specific receiver location exists it is shown that this requirement is fulfilled as changes in zero point crossing times depend linearly on the flow coefficient v 0 at a given r co ordinate there are however certain discrete r co ordinate values where this is not the case namely those where changes in zero point crossing times become zero for any value of v 0 in other words if the receiver is positioned near r co ordinates where zero point crossing times are at a maximum or a minimum for a given value of v 0 the truncated cone flow meter sensor is able to measure flow unambiguiosly by detection of changes in zero point crossing times induced by a background flow

controlling nonlinear time varying systems via euler approximations abstract a discrete time model reference control algorithm for continuous time systems represented by essentially unknown nonlinear time varying ordinary differential equations is presented and analysed provided the reference model and the inverse dynamics of the plant are bounded input bounded output stable it is shown that a discrete control using state measurements based on euler approximations for the systems response can achieve arbitrary tracking accuracy the effect of unmodelled dynamics and disturbances is analysed