further results on least squares based adaptive minimum variance control based on the recently established results on self tuning regulators originally proposed by astrom and wittenmark this paper presents various novel and extended results on least squares based adaptive minimum variance control for linear stochastic systems these results establish self optimality self tuning property and the best possible convergence rate of the control law in a variety of situations of interest

on the convergence of least squares estimates in white noise the problem of convergence of least squares ls estimates in a stochastic linear regression model with white noise is considered it is well known that if the parameter estimates are known to converge the convergence analysis for many adaptive systems can be rendered considerably less arduous for an important case where the regression vector is a measurable function of the observations and the noise is gaussian it has been shown by using a bayesian embedding argument that the ls estimates converge almost surely for almost all true parameters in the parameter space except for a zero measure set however nothing can be said about a particular given system which is usually the objective it has long been conjectured that such a bad zero measure set in the parameter space does not actually exist a conclusive answer to this important question is provided and it is shown that the set can indeed exist this then shows that to provide conclusive convergence results for stochastic adaptive systems it is necessary to resort to a sample pathwise analysis instead of the bayesian embedding approach

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

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

a spinor like representation of the contact superconformal algebra k 4 in this work we construct an embedding of a nontrivial central extension of the contact superconformal algebra k 4 into the lie superalgebra of pseudodifferential symbols on the supercircle s1 2 associated with this embedding is a one parameter family of spinor like tiny irreducible representations of k 4 realized just on 4 fields instead of the usual 16

adaptive control of parametric nonlinear autoregressive models via a new martingale approach the purpose of this note is to investigate the stability and the optimality of the adaptive tracking for a wide class of parametric nonlinear autoregressive models via a new martingale approach several asymptotic results for the standard least squares estimator of the unknown model parameter such as a central limit theorem a law of iterated logarithm and strong laws of large numbers are also provided

poisson lie group of pseudodifferential symbols we introduce a lie bialgebra structure on the central extension of the lie algebra of differential operators with scalar or matrix coefficients on the line and on the circle this defines a poisson lie structure on the dual group of pseudodifferential symbols of an arbitrary real or complex order we show that the usual second benney gl n kdv or gl n adler gelfand dickey and kp poisson structures are naturally realized as restrictions of this poisson structure to submanifolds of this universal poisson lie group moreover the reduced sl n versions of these manifolds orw n algebras in physical terminology can be viewed as certain subspaces of the quotient of this poisson lie group by the dressing action of the group of functions on the circle or as a result of a poisson reduction finally we define an infinite set of commuting functions on the poisson lie group that give the standard families of hamiltonians when restricted to the submanifolds mentioned above the poisson structure and hamiltonians on the whole group interpolate between the poisson structures and hamiltonians of benney kp and kdv flows we also discuss the geometrical meaning ofw as a limit of poisson algebraswe as e 0

embedding of the lie superalgebra d 2 1 α into the lie superalgebra of pseudodifferential symbols on s1 2 we obtain an embedding of the one parameter family of exceptional simple lie superalgebras d 2 1 into the lie superalgebra of pseudodifferential symbols on the supercircle s1 2 correspondingly there is an embedding of d 2 1 into a nontrivial central extension of the derived contact superconformal algebra k 4 realized in terms of 4 4 matrices over a weyl algebra

adaptive control of a class of discrete time affine nonlinear systems the adaptive control problem is addressed in the paper for a class of discrete time affine nonlinear input output stochastic models with linear unknown parameters the controller is a certainty equivalence weighted one step ahead control and is constructed by using the weighted least squares and random regularization methods global stability of the closed loop systems is established which shows that arbitrarily large growth rate is allowed for the multiplicative nonlinear part of the systems

stabilization of discrete time nonlinear uncertain systems by feedback based on ls algorithm this paper is concerned with the use of the least squares ls algorithm to design a feedback control law to stabilize a basic class of discrete time nonlinear uncertain systems the result shows that if a certain polynomial criterion is satisfied the system can be stabilized by feedback based on the ls algorithm for gaussian distributed noise and unknown parameters this result thus provides an answer to the question of what are the fundamental limitations of the discrete time adaptive nonlinear control this issue of feedback capability has been an open problem for more than ten years since it was put forward

adaptive regulator for discrete time nonlinear nonparametric systems a direct adaptive regulator for nonlinear nonparametric systems with measurement corrupted by noise is proposed under reasonable conditions the state of the closed loop system is adaptively regulated so that it converges to zero as time tends to infinity an illustrative example being an affine nonlinear system with all imposed conditions satisfied is given the method of proof is based on stochastic approximation techniques

further results on stabilizability of discrete time nonlinearly parameterized systems with scalar parameters this note advances the work simultaneous identification and stabilization of nonlinearly parameterized discrete time systems by nonlinear least squares algorithm by li and chen by allowing the sensitivity functions of discrete time nonlinearly parameterized systems with scalar parameters admitting arbitrarily many zeros for large outputs stabilizability theorems and impossible theorems have been provided both for time invariant parameter and time varying parameter cases a practical estimation algorithm is also proposed to facilitate the implementation in computations

adaptive tracking and recursive identification for hammerstein systems a weighted least squares wls based adaptive tracker is designed for a class of hammerstein systems it is proved that the tracking error is asymptotically minimized incorporating with the diminishing excitation technique the minimality of the tracking error and strong consistency of the estimates for parameters of the system are simultaneously achieved numerical examples are given and the simulation results are consistent with the theoretical analysis

the inverse problem in classical statistical mechanics we address the problem of whether there exists an external potential corresponding to a given equilibrium single particle density of a classical system results are established for both the canonical and grand canonical distributions it is shown that for essentially all systems without hard core interactions there is a unique external potential which produces any given density the external potential is shown to be a continuous function of the density and in certain cases it is shown to be differentiable as a consequence of the differentiability of the inverse map which is established without reference to the hard core structure in the grand canonical ensemble we prove the existence of the ornstein zernike direct correlation function a set of necessary but not sufficient conditions for the solution of the inverse problem in systems with hard core interactions is derived

on adaptive control of stochastic bilinear systems the minimum variance control law for bilinear systems with known parameters is shown to yield in most cases controls with infinite variance this calls into question the use of the so called bilinear self tuning regulators an adaptive weighted minimum variance controller based upon the cost with weighted control efforts is suggested for first order bilinear systems and is shown to yield boundedness of the closed loop system variables under a certain condition on the parameter estimate

central limit theorem and law of iterated logarithm for least squares algorithms in adaptive tracking in autoregressive adaptive tracking we prove that the least squares and the weighted least squares algorithms possess the same asymptotic properties sharing the same central limit theorem and the same law of iterated logarithm we also obtain the same asymptotic behavior and show the limitations of these results in the autoregressive with moving average framework

equivalence between chain categories of representations of affine sl 2 and n 2 superconformal algebras highest weight type representation theories of the affine sl 2 and n 2 superconformal algebras are shown to be equivalent modulo the respective spectral flows

prediction based discrete time stochastic adaptive control a new step towards non linear growth rate in this paper we will study adaptive control of a class of discrete time parametric strict feedback non linear stochastic systems almost all the existing results for such systems need lipschitz condition the main purpose of this paper is to remove this restriction and to get some positive result under non linear growth condition the control law is designed based on weighted least squares wls algorithms and on recursive adaptive predictors global stability and tracking performance are established for the closed loop systems

brief paper on using least squares updates without regressor filtering in identification and adaptive control of nonlinear systems in continuous time system identification and adaptive control the least squares parameter estimation algorithm has always been used with regressor filtering which adds to the dynamic order of the identifier and affects its performance we present an approach for designing a least squares estimator that uses an unfiltered regressor we also consider a problem of adaptive nonlinear control and present the first least squares based adaptive nonlinear control design that yields a complete lyapunov function the design is presented for linearly parametrized nonlinear control systems in normal form a scalar linear example is included which adds insight into the key ideas of our approach and allows showing that for linear systems our lyapunov ls design with unfiltered regressor presented in the note for unnormalized least squares can also be extended to normalized least squares

on the thermodynamic v representability of one particle density matrices we consider thermodynamicallyv representable one matrices i e one particle density matrices that are obtained by reducing the gibbs grand canonical density matrix of a quantum mechanical many particle system subject to a suitable external potential and show them to obey an inequality lower bounding their eigenvalues in terms of those of the one particle kinetic energy operator the result imposes a severe constraint on the asymptotic behavior of the eigenvalues of any one matrix to bev representable for noninteracting particles the corresponding upper bound is also proven implying that a one matrix can be interactionlesslyv representable for at most one temperature we expect the upper bound to be valid more generally as is illustrated by a model of coupled harmonic oscillators where thev representable one matrices can be explicitly calculated and discuss its implications for certain aspects of density matrix functional theory

stochastic adaptive prediction and model reference control guo and chen 1991 have recently shown how to establish the self optimality and mean square stability of a self tuning regulator the idea allows us to proceed with the development of a more comprehensive theory of stochastic adaptive filtering control and identification in adaptive filtering we examine both indirect and noninterlaced direct schemes for prediction using both least squares and gradient parameter estimation algorithms in addition to analyzing similar direct adaptive control algorithms we propose new generalized certainty equivalence adaptive model reference control laws with simultaneous disturbance rejection we also establish that the parameters converge to the null space of a certain matrix from this one may deduce the convergence of several adaptive controllers

robust estimation without positive real condition the strictly positive real spr condition on the noise model is necessary for a discrete time linear stochastic control system with unmodeled dynamics even so for a time invariant armax system in the past robust analysis of parameter estimation however this condition is hardly satisfied for a high order and or multidimensional system with correlated noise the main work in this paper is to show that for robust parameter estimation and adaptive tracking as well as closed loop system stabilization the spr condition is replaced by a stable matrix polynomial the main method is to design a two step recursive least squares algorithm with or without a weighted factor and with a fixed lag regressive vector and to define an adaptive control with bounded external excitation and with randomly varying truncation

a recursive local linear estimator for identification of nonlinear arx systems asymptotical convergence and applications in this paper we propose a recursive local linear estimator rlle for nonparametric identification of nonlinear autoregressive systems with exogenous inputs narx first the rlle is introduced next the strong consistency as well as the asymptotical mean square error properties of the rlle are established and then an application of the rlle to an additive nonlinear system is discussed the rlle provides recursive estimates not only for the function values but also their gradients at fixed points a simulation example is provided to confirm the theoretical analysis

on feedback capability in a class of nonlinearly parameterized uncertain systems in this technical note we will investigate the maximum capability and limitations of the feedback mechanism in globally stabilizing a basic class of discrete time nonlinearly parameterized dynamical systems with multiple unknown parameters both possibility and impossibility theorems together with a fairly complete characterization on the capability of feedback will be presented it will be seen that to characterize the feedback capability the growth rates of the sensitivity functions of the nonlinear dynamics with respect to the uncertain parameters play a crucial role and a suitable decomposition of the family of the nonlinearly parameterized functions in question turns out to be necessary

adaptive linear quadratic gaussian control the cost biased approach revisited in adaptive control a standard approach is to resort to the so called certainty equivalence principle which consists of generating some standard parameter estimate and then using it in the control law as if it were the true parameter as a consequence of this philosophy the estimation problem is decoupled from the control problem and this substantially simplifies the corresponding adaptive control scheme on the other hand the complete absence of dual properties makes certainty equivalent controllers run into an identifiability problem which generally leads to a strictly suboptimal performance in this paper we introduce a cost biased parameter estimator to overcome this difficulty this estimator is applied to a linear quadratic gaussian controller the corresponding adaptive scheme is proven to be stable and optimal when the unknown system parameter lies in an infinite yet compact parameter set

self convergence of weighted least squares with applications to stochastic adaptive control a recursive least squares algorithm with slowly decreasing weights for linear stochastic systems is found to have self convergence property i e it converges to a certain random vector almost surely irrespective of the control law design such algorithms enjoy almost the same nice asymptotic properties as the standard least squares this universal convergence result combined with a method of random regularization then easily can be applied to construct a self convergent and uniformly controllable estimated model and thus may enable us to form a general framework for adaptive control of possibly nonminimum phase autoregressive moving average with exogenous input armax systems as an application we give a simple solution to the well known stochastic adaptive pole placement and linear quadratic gaussian lqg control problems in the paper

on robust stability of discrete time adaptive nonlinear control abstract we consider adaptive control of discrete time nonlinear systems with a single unknown parameter in this paper we demonstrate that the necessary and sufficient condition for the existence of a feedback stabilizer that is robust to bounded noise is that the nonlinear growth rate of the system dynamics is less than 4 this result further confirms the conclusion of guo on critical stability of discrete time adaptive nonlinear control ieee trans automat control 42 1997 1488 1499 which addresses unbounded noise in a stochastic setting also in our worst case approach we find that much simpler adaptive stabilizers can be constructed when the nonlinear growth rate is less than 4

exceptional n 6 superconformal algebra we realize the exceptional n 6 superconformal algebra spanned by 32 fields inside the lie superalgebra of pseudodifferential symbols on the supercircle s1 3 correspondingly we obtain two nonisomorphic one parameter families of irreducible representations of this superconformal algebra in a superspace spanned by 8 fields

an impossibility theorem on a class of high order discrete time nonlinear control systems a high order discrete time nonlinear system with unknown parameters and gaussian noise is studied in this paper and it is shown that under a simple algebraic condition concerning the nonlinearity of the system there does not exist any feedback controller that globally stabilizes the uncertain system this impossibility result attempts to understand the capability and limitation of feedback mechanism of a high order discrete time nonlinear system and continues a series of previous research on similar first order systems this result shows that for the high order discrete time nonlinear system studied here a polynomial corresponding to the first order principle part of the system determines the limit of the feedback mechanism

how much uncertainty can be dealt with by feedback feedback is used primarily for reducing the effects of the plant uncertainty on the performance of control systems and as such understanding the following questions is of fundamental importance how much uncertainty can be dealt with by feedback what are the limitations of feedback how does the feedback performance depend quantitatively on the system uncertainty how can the capability of feedback be enhanced if a priori information about the system structure is available as a starting point toward answering these questions a typical class of first order discrete time dynamical control systems with both unknown nonlinear structure and unknown disturbances is selected for our investigation and some concrete answers are obtained in the paper in particular we find that in the space of unknown nonlinear functions the generalized lipschitz norm is a suitable measure for characterizing the size of the structure uncertainty and that the maximum uncertainty that can be dealt with by the feedback mechanism is described by a ball with radius 3 2 spl radic 2 in this normed function space

the aastrom wittenmark self tuning regulator revisited and els based adaptive trackers although considerable progress has been made in stochastic adaptive control the problem concerning the convergence of the original self tuning regulator proposed by k j aastrom and b wittenmark 1973 is still open since it is attractive in theory and important in applications this problem is examined and a rigorous proof of its stability and optimality is given related problems such as convergence of the extended least squares els based adaptive tracker are also considered

adaptive stabilization of bilinear systems for a class of deterministic and stochastic bilinear systems modified self tuning regulators are given by using recursive least squares and modified recursive least squares respectively the closed loop systems are shown globally stable and asymptotically optimal in some sense without any restriction on location of poles or zeros of nominal linear part of the open loop system considered simulations show that the methods used here work very well

the zero divisor problem of multivariable stochastic adaptive control abstract stochastic adaptive minimum variance control algorithms require a division by a function of a recursively computed parameter estimate at each instant of time in order that the analysis of these algorithms is valid zero divisions must be events of probability zero this property is established for the stochastic gradient adaptive control algorithm under the condition that the initial state of the system and all finite segments of its random disturbance process have a joint distribution which is absolutely continuous with respect to lebesgue measure this result is deduced from the following general result established in this paper a non constant rational function of a finite set of random variables x 1 x n is absolutely continuous with respect to lebesgue measure if the joint distribution function of x 1 x n has this property

on the usefulness of persistent excitation in arx adaptive tracking the usefulness of persistent excitation is well known in the control community thanks to a persistently excited adaptive tracking control we show that it is possible to avoid the strong controllability assumption recently proposed in the multidimensional arx framework we establish the almost sure convergence for both least squares and weighted least squares estimators of the unknown parameters a central limit theorem and a law of iterated logarithm are also provided all this asymptotical analysis is related to the schur complement of a suitable limiting matrix

a new n 6 superconformal algebra in this paper we construct a newn 6 superconformal algebra which extends the virasoro algebra by theso 6 current algebra by 6 odd primary fields of conformal weight 3 2 and by 10 odd primary fields of conformal weight 1 2 the commutation relations of this algebra which we will refer to asck 6 are represented by short distance operator product expansions ope we constructck 6 as a subalgebra of theso 6 superconformal algebra k6 thus giving it a natural representation as first order differential operators on the circle withn 6 extended symmetry we show thatck 6 has no nontrivial central extensions

singularity free adaptive pole placement without resorting to persistency of excitation detailed analysis for first order systems abstract this paper presents a novel approach to avoid singularities in adaptive pole placement control algorithms the control scheme is applicable to either minimum or nonminimum phase plants and the closed loop stability is guaranteed in spite of bounded disturbances the algorithm uses a least squares identification algorithm with a particular dead zone that allows the definition of modified estimate that retain the convergence properties of the original estimates explicit modification to the parameters estimates is given that secures well conditioned matrices in the adaptive control law detailed analysis is given for one pole one zero systems

indirect adaptive pole placement control of mimo stochastic systems self tuning results in this paper we consider indirect adaptive pole placement control appc of linear multivariable stochastic systems instead of the canonical representation often used in the literature we propose using a non minimal but otherwise uniquely identifiable pseudo canonical parameterization that is more suitable for multivariable armax model identification to identify the plant we use the weighted extended least squares wels algorithm a least squares method with slowly decreasing weights which was introduced in bercu 1995 the pole placement controller parameters are then calculated by using a certain perturbation of the parameter estimates such that the linear models corresponding to the perturbed estimates are uniformly controllable and observable we prove that with a reasonable amount of prior information the resulting appc scheme is globally stabilizing and asymptotically self tuning regardless of the degree of persistency of external excitation these results represent the most complete study of stochastic multivariable appc systems to this date

on stabilizability of nonlinearly parameterized discrete time systems most existing works on adaptive control of discrete time systems focus on the case of linear parametrization for nonlinearly parameterized systems the stabilizability turns out to be an intractable issue this technical note is devoted to seeking the essential factors that determine the stabilizability of nonlinearly parameterized discrete time systems a sufficient condition imposed on the structures of the system functions is established analysis shows that the sensitivity function of unknown parameters plays a crucial role in characterizing the uncertainties of parameterized systems one of the implications of this result is that arbitrarily growing nonlinearities in the uncertain model may be allowed for global stabilization

experimental studies in nonlinear discrete time adaptive prediction and control this paper presents implementation results using recently introduced discrete time adaptive prediction and control techniques using online function approximators we consider a process control experiment as our test bed and develop a discrete time adaptive predictor for liquid volume and a discrete time adaptive controller for reference volume tracking we use takagi sugeno ts fuzzy systems as our function approximators and for both prediction and control we investigate the use of a least squares update of the fuzzy system s parameters

is measurement based feedback still better for quantum control systems in this paper we put forward a fundamental question concerning feedback control of quantum systems is measurement based feedback control still better than open loop control in contrast to the classical control theory the answer is far from obvious this is because measurement based feedback needs measurement to reduce the system uncertainty whereas the measurement on a quantum system will inevitably increase the system uncertainty in turn in fact there is a complicated tradeoff between the uncertainty introduced and the information gained by the measurement on a quantum system to investigate this fundamental problem we will only focus on a typical model of coherent control mode with and without the decoherence term in the paper by establishing some fundamental limits on the performances of both the open loop and measurement based feedback controls we will demonstrate via simulation that the measurement based feedback control of quantum systems is still superior to the open loop control in some sense for the typical model under consideration

weighted estimation and tracking for branching processes with immigration for branching processes with immigration we propose an approach which allows us to consistently estimate the means m spl lambda and the variances spl sigma sup 2 b sup 2 of the offspring and immigration distributions respectively generally statistical results for branching processes are established under the well known trichotomy m 1 for example no parameters of the immigration distribution can be consistently estimated if m 1 the purpose of the paper is to obtain through the introduction of a suitable adaptive control strongly consistent estimators for all the parameters m spl lambda spl sigma sup 2 and b sup 2 without any restriction on the range of m central limit theorems and laws of iterated logarithm are also provided

convergence and logarithm laws of self tuning regulators abstract this paper starts with a survey of some recent results on least squares ls and ls based self tuning regulators str several long standing problems concerning the basic properties of ls based str such as stability optimality consistency and the best convergence rate are solved within a unified framework some previously related results are also subsumed and extended various new techniques for analysing ls based adaptive tracking systems are presented which may also be useful for analysing other adaptive control problems

on the stability and convergence of self tuning control virtual equivalent system approach this article presents a unified understanding and judgement of the stability and convergence of a general self tuning control stc system which consists of arbitrary control strategy arbitrary parameter estimation algorithm and a deterministic stochastic linear time invariant lti plant the necessary conditions required for the global stability and convergence of a general stc system are relaxed i e the convergence of parameter estimates is removed for both deterministic and stochastic stc schemes to reach this goal virtual equivalent system ves concept and methodology is adopted with the help of ves the original nonlinear dominant nonlinear in structure problem is converted to a linear dominant linear in structure problem the results developed in this article show that stc systems are stable and convergent for the abundance of control strategies and parameter estimation algorithms which will provide great flexibility in the applications of stc

on critical stability of discrete time adaptive nonlinear control in this paper we examine the global stability and instability problems for a class of discrete time adaptive nonlinear stochastic control the systems to be controlled may exhibit chaotic behavior and are assumed to be linear in unknown parameters but nonlinear in output dynamics which are characterized by a nonlinear function say f x it is found and proved that in the scalar parameter case there is a critical stability phenomenon for least squares ls based adaptive control systems to be specific let the growth rate of f x be f x o spl par x spl par sup 6 with b spl ges 0 then it is found that b 4 is a critical value for global stability i e the closed loop adaptive system is globally stable if b 4 and is unstable in general if b spl ges 4 as a consequence we find an interesting phenomenon that the linear case does not have for some ls based certainty equivalence adaptive controls even if the ls parameter estimates are strongly consistent the closed loop systems may still be unstable this paper also indicates that adaptive nonlinear stochastic control that is designed based on e g taylor expansion or weierstrass approximation for nonlinear models may not be feasible in general

prediction based discrete time adaptive nonlinear stochastic control adaptive control of a class of discrete time parametric strict feedback nonlinear systems with additive white noises is considered in this paper the control law is designed based on weighted least squares wls algorithms and on recursive adaptive predictors global stability and tracking error bounds are established for the closed loop systems

a limit to the capability of feedback feedback is ubiquitous and is a basic concept in the area of control where it is used primarily for reducing internal or external uncertainties or both in this note we will study the capability of feedback in dealing with both internal and external uncertainties for a class of pth order nonlinear autoregressive control systems the size of the uncertainty is described by the lipschitz constant say l of the uncertain nonlinear function in consideration it is shown that if p and l satisfy a certain inequality then there exists no globally stabilizing feedback for the corresponding class of uncertain systems and thus finding a quantitative limit to the capability of the feedback mechanism in dealing with structural uncertainties

active identification for discrete time nonlinear control ii strict feedback systems the problem of controlling nonlinear systems with unknown parameters has received a great deal of attention in the continuous time case in contrast its discrete time counterpart remains largely unexplored primarily due to the difficulties associated with utilizing lyapunov design techniques in a discrete time framework existing results impose restrictive growth conditions on the nonlinearities to yield global stability in this paper we propose a novel approach which removes this obstacle and yields global stability and tracking for systems that can be transformed into an output feedback canonical form in which the nonlinearities depend only on the measured output but are otherwise arbitrary the main novelties of our design are i the temporal and algorithmic separation of the parameter estimation task from the control task and ii the development of an active identification procedure which uses the control input to actively drive the system state to points in the state space that allow the orthogonalized projection estimator to acquire all the necessary information about the unknown parameters we prove that our algorithm guarantees complete for control purposes identification in a finite time interval whose maximum length we compute thus the traditional structure of concurrent online estimation and control is replaced by a two phase control strategy first use active identification and then utilize the acquired parameter information to implement any control strategy as if the parameters were known

superconformal algebras and transitive group actions on quadrics a classification of physical superconformal algebras is given the list consists of seven algebras the virasoro algebra the neveu schwarz algebra then 2 3 and 4 algebras the superalgebra of all vector fields on then 2 supercircle and a new algebrack6 constructed in 3 the proof relies heavily on the classification of all connected subgroups ofson c which act transitively on the quadric v v 1

convergence analysis for reduced order adaptive controller design of uncertain siso linear systems with noisy output measurements we consider in this article a class of uncertain siso linear systems that are subject to system and measurement noises reduced order adaptive controller designs have been proposed before for such systems by the authors and stability analysis of the closed loop systems has been established here we analyse further the robustness properties for these reduced order adaptive control systems by providing detailed convergence analysis results for the key closed loop signals and parameter estimates we rigorously prove that whenever the exogenous disturbance input is of finite energy and bounded and the reference trajectory and its derivatives up to rth order are bounded r being the relative degree of the transfer function of the true system a set of signals including the tracking error the estimation error between the system output and its estimate the projection signal are of finite energy and converge to zero and the system states and their estimates exhibit asymptotic behaviours with certain form

weighted estimation and tracking for armax models for complex multivariate armax models the author studies the weighted least squares algorithm which offers by the choice of suitable weightings the advantages of both the extended least squares and the stochastic gradient algorithms concerning adaptive tracking problems the strong consistency of the estimator and control optimality are both ensured almost sure rates of convergence are also provided

stability of adaptively stabilized stochastic systems stochastic adaptive stabilization usually leads to the boundedness of the average of squared output of the stabilized system but gives no conclusion on stability of the resulting system this paper proves that adaptively stabilized stochastic system in its steady state is truly stable in the conventional sense

density functional approach to quantum lattice systems for quantum lattice systems we consider the problem of characterizing the set of single particle densities which come from the ground state eigenspace of somen particle hamiltonian of the form h 0 sum nolimits i 1 n v x i whereh0 is a fixed bounded operator representing the kinetic and interaction energies we show that the conditions on are that it be strictly positive properly normalized and consistent with the pauli principle our results are valid for both finite and infinite lattices and for either bosons or fermions the coulomb interaction may be included inh0 if the lattice dimension is 2 we also characterize those single particle densities which come from the gibbs states of such hamiltonians at finite temperature in addition to the conditions stated above must satisfy a finite entropy condition

deforming the lie algebra of vector fields on s 1 inside the poisson algebra on t s 1 we study deformations of the standard embedding of the lie algebra vect s1 of smooth vector fields on the circle into the lie algebra of functions on the cotangent bundle t s1 with respect to the poisson bracket we consider two analogous but different problems a formal deformations of the standard embedding of vect s1 into the lie algebra of functions on t s1 s1 which are laurent polynomials on fibers and b polynomial deformations of the vect s1 subalgebra inside the lie algebra of formal laurent series on t s1

input output parametric models for non linear systems part ii stochastic non linear systems recursive input output models for non linear multivariate discrete time systems are derived and sufficient conditions for their existence are defined the paper is divided into two parts the first part introduces and defines concepts such as nerode realization multistructural forms and results from differential geometry which are then used to derive a recursive input output model for multivariable deterministic non linear systems the second part introduces several examples compares the derived model with other representations and extends the results to create prediction error or innovation input output models for non linear stochastic systems these latter models are the generalization of the multivariable arm ax models for linear systems and are referred to as narmax or non linear autoregressive moving average models with exogenous inputs

a new critical theorem for adaptive nonlinear stabilization it is fairly well known that there are fundamental differences between adaptive control of continuous time and discrete time nonlinear systems in fact even for the seemingly simple single input single output control system y t email protected 1f y t u t w t 1 with a scalar unknown parameter q 1 and noise disturbance w t and with a known function f having possible nonlinear growth rate characterized by f x email protected x b with b 1 the necessary and sufficient condition for the system to be globally stabilizable by adaptive feedback is b 4 this was first found and proved by guo 1997 for the gaussian white noise case and then proved by li and xie 2006 for the bounded noise case subsequently a number of other types of critical values and impossibility theorems on the maximum capability of adaptive feedback were also found mainly for systems with known control parameter as in the above model in this paper we will study the above basic model again but with additional unknown control parameter q 2 i e u t is replaced by q 2u t in the above model interestingly it turns out that the system is globally stabilizable if and only ifb 3 this is a new critical theorem for adaptive nonlinear stabilization which has meaningful implications for the control of more general uncertain nonlinear systems

convergence of adaptive minimum variance algorithms via weighting coefficient selection weighted least squares and related stochastic approximation algorithms are studied for parameter estimation adaptive state estimation adaptive n step ahead prediction and adaptive control in both white and colored noise environments for the fundamental algorithm which is the basis for the various applications the step size in the stochastic approximation versions and the weighting coefficient in the weighted least squares schemes are selected according to a readily calculated stability measure associated with the estimator the selection is guided by the convergence theory in this way strong global convergence of the parameter estimates state estimates and prediction or tracking errors is not only guaranteed under the appropriate noise passivity and stability or minimum phase conditions but the convergence is also as fast as it appears reasonable to achieve given the simplicity of the adaptive scheme

brief paper a new concept of strong controllability via the schur complement for arx models in adaptive tracking we propose a new concept of strong controllability related to the schur complement of a suitable limiting matrix this new notion allows us to extend the previous convergence results associated with multidimensional arx models in stochastic adaptive tracking on the one hand we carry out a sharp analysis of the almost sure convergence for both least squares and weighted least squares algorithms on the other hand we also provide a central limit theorem and a law of iterated logarithm for these two algorithms

petri net representation of switched fuzzy systems switched fuzzy systems can be used to describe the hybrid systems with fuzziness however the languages to describe the switching logic and the fuzzy subsystems are in general different and this difference makes the system analysis and implementation hard in this paper we use differential petri net dpn as a unified model to represent both the discrete logic and fuzzy dynamic processes to exam the rationality of the representation we prove the correctness of the representation for the discrete part and estimate the approximation accuracy of the representation for the dynamic part our work provides a way to analyze the switched fuzzy systems by checking the pn and to use the pn model for further system implementation we demonstrate the benefits of our work via a case study

extensions and contractions of the lie algebra ofq pseudodifferential symbols on the circle abstract we construct cocycles on the lie algebra of pseudo and q pseudodifferential symbols of one variable and on their close relatives the sine algebra and the poisson algebra on two torus a quantum godbillon vey cocycle on pseudo differential operators appears in this construction as a natural generalization of the gelfand fuchs 3 cocycle on periodic vector fields a nontrivial embedding of the virasoro algebra into a completion of q pseudodifferential symbols is proposed we describe q analogs of the kp and kdv hierarchies admitting an infinite number of conserved charges as well as q deformed gelfand dickey structures

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

convergence rate of least squares identification and adaptive control for stochastic systems the strong consistency and the convergence rate of least squares identification for the multidimensional armax model are established under some decaying excitation conditions which are satisfied if both input and output do not grow too fast and the attenuating excitation technique is applied the parameter identification results are applied to adaptive control systems with a quadratic loss function the rate of convergence of the loss function to its minimum is also obtained

simultaneous identification and stabilization of nonlinearly parameterized discrete time systems by nonlinear least squares algorithm this paper addresses the challenging problem of designing an adaptive feedback strategy for simultaneous identification and stabilization for a class of nonlinearly parameterized uncertain systems in discrete time the nonlinear least squares nls algorithm is applied to estimate the unknown parameters and it turns out to be the standard least squares ls algorithm whenever the model is linearly parameterized based on this algorithm both the strong consistency of the estimator and the global stability of the system are achieved with the output feedback design for the scalar parameter case

coarse grained spin density functional theory infinite volume limit via the hyperfinite coarse grained spin density functional theory sdft is a version of sdft which works with number spin densities specified to a limited resolution averages over cells of a regular spatial partition and external potentials constant on the cells this coarse grained setting facilitates a rigorous investigation of the mathematical foundations which goes well beyond what is currently possible in the conventional formulation problems of existence uniqueness and regularity of representing potentials in the coarse grained sdft setting are here studied using techniques of robinsonian nonstandard analysis every density which is nowhere spin saturated is v representable and the set of representing potentials is the functional derivative in an appropriate generalized sense of the lieb internal energy functional quasi continuity and closure properties of the set valued representing potentials map are also established the extent of possible non uniqueness is similar to that found in non rigorous studies

application of stochastic control techniques to chaotic nonlinear systems a control algorithm based on stochastic control techniques is devised for chaotic nonlinear systems the algorithm uses a state estimator based on the kalman filter and yields performance improvements in at least some regions of state space with respect to that obtainable by use of a controller utilizing only the conditional mean of the system state vector the method is applied to two typical chaotic nonlinear systems the henon heiles system and the lorenz system and their behavior with control is explored numerically

adaptive pole placement without excitation probing signals this paper presents an indirect adaptive control scheme for linear systems which may possibly be a nonminimum phase the control scheme achieves asymptotical pole placement without either introducing persistent excitation probing signals into the systems or assuming any a priori knowledge on the plant parameters the system order is the only a priori knowledge required on the plant the adaptive control law is free from singularities in the sense that the estimated plant model is always controllable the singularities are overcome by a suitable parameter estimates modification which is based upon standard least squares covariance matrix properties the analysis of the stability and the global convergence of a closed loop system is given in detail for both discrete time and continuous time systems

hohenberg kohn theorem and non v representable densities abstract in the density functional formalism of hohenberg and kohn1 the variation is only allowed over the one particle densities which are pure state v representable ps v representable levy2 and lieb3 proved that not every ensemble v representable e v representable density is ps v representable since we show that the hohenberg kohn formalism can be extended to a variation over e v representable densities for degenerated ground states levy s and lieb s result is not a counterexample to the universality of the hohenberg kohn theorem the question whether every n representable density is e v representable has remained open so far presenting examples of non e v representable densities we answer this question in the negative thus the value of levy s functional4 for the calculation of ground state energies is obvious since this functional only requires the n representability of the densities therefore we transfer two approaches for the calculation of excited state energies into the framework of levy s formalism

beyond v representability local one body hamiltonians for arbitrary densities the v representability problem arising in density functional theory is this for an particle system of interacting identical particles can every one particle density of finite intrinsic energy be realized as a ground state density upon modifying the hamiltonian by addition of an appropriate external one body potential v the answer is known to be no we show that the answer is yes if the inter particle interaction is bounded and allowed modifications are broadened from one body potentials to local one body operators the required operator is obtained from a non standard potential in the sense of non standard analysis which is a simple function defined on a regular grid of infinitesimal finesse at a vague conceptual level therefore the result is not far from universal v representability

further results on limitations to the capability of feedback in this paper we study the limitations of the capability of the feedback mechanism in dealing with structural uncertainty for a class of pth order non linear autoregressive control systems the size of the structural uncertainty is characterized by multiple lipschitz constants say l 1 l 2 lp of the uncertain non linear function it is shown that if l 1 l 2 lp satisfy certain algebraic conditions then there exists no globally stabilizing feedback control law for the corresponding uncertain systems the result here is an extension of the previous result obtained by zhang and guo 2002

adaptive lqg control of input output systems a cost biased approach in this paper we consider linear systems in input output form and introduce a new adaptive linear quadratic gaussian lqg control scheme which is shown to be self optimizing the identification algorithm incorporates a cost biasing term which favors the parameters with smaller lqg optimal cost and a second term that aims at moderating the time variability of the estimate the corresponding closed loop scheme is proven to be stable and to achieve an asymptotic lqg cost equal to the one obtained under complete knowledge of the true system self optimization the results of this paper extend in a nontrivial way previous results established along the cost biased approach in other settings

on bilinear estimation and control discrete single input single output bilinear systems with constant parameters are considered first the minimum variance regulator for known parameters is determined then the least squares parameter estimation method is applied and is seen to have certain desirable properties finally the least squares parameter estimator is combined with the minimum variance regulator for the estimated model to produce a bilinear self tuning regulator blstr it is found that though the estimation may be biased under certain assumptions the blstr will converge to the minimum variance control law

convergence of adaptive control schemes using least squares parameter estimates the stability convergence asymptotic optimality and self tuning properties of stochastic adaptive control schemes based on least squares estimates of the unknown parameters are examined it is assumed that the additive noise is i i d and gaussian and that the true system is of minimum phase the bayesian embedding technique is used to show that the recursive least squares parameter estimates converge in general the normal equations of least squares are used to establish that all stable control law designs used in a certainty equivalent i e indirect procedure generally yield a stable adaptive control system four results are given to characterize the limiting behavior precisely a certainty equivalent self tuning regulator is shown to yield strongly consistent parameter estimates when the delay is strictly greater than one even without any excitation in the reference trajectory

technical communique robust adaptive regulation of discrete time nonlinear systems with arbitrary nonlinearities this note develops a new recursive estimator with a dead zone by using the estimator a robust adaptive regulator for a class of simple discrete time nonlinear systems with bounded disturbance is presented a global stability result of the closed loop system is obtained through lyapunov analysis without assuming any growth conditions on the nonlinearities the regulation performance is also presented through a simulation example

adaptive continuous time linear quadratic gaussian control the adaptive linear quadratic gaussian control problem where the linear transformation of the state a and the linear transformation of the control b are unknown is solved assuming only that a b is controllable and a q sub 1 sup 1 2 is observable where q sub 1 determines the quadratic form for the state in the integrand of the cost functional a weighted least squares algorithm is modified by using a random regularization to ensure that the family of estimated models is uniformly controllable and observable a diminishing excitation is used with the adaptive control to ensure that the family of estimates is strongly consistent a lagged certainty equivalence control using this family of estimates is shown to be self optimizing for an ergodic quadratic cost functional

fundamental limitations of discrete time adaptive nonlinear control a particular polynomial is introduced which can be used to determine under what conditions a typical class of discrete time nonlinear systems with uncertainties in both parameters and noises is not stabilizable by feedback thus demonstrating the fundamental limitations of discrete time adaptive nonlinear control as a consequence it is shown that for nonlinear systems with unknown parameters and noises the systems may indeed be nonstabilizable in general whenever the usual linear growth condition is relaxed and the number of unknown parameters is large even though the corresponding noise free systems are globally stabilizable

detectability and stabilizability of time varying discrete time linear systems the concepts of detectability and stabilizability are explored for time varying systems we study duality invariance under feedback an extended version of the lemma of lyapunov existence of stabilizing feedback laws linear quadratic filtering and control and the existence of approximate canonical forms

nonlinear black box modeling in system identification a unified overview a nonlinear black box structure for a dynamical system is a model structure that is prepared to describe virtually any nonlinear dynamics there has been considerable recent interest in this area with structures based on neural networks radial basis networks wavelet networks and hinging hyperplanes as well as wavelet transform based methods and models based on fuzzy sets and fuzzy rules this paper describes all these approaches in a common framework from a user s perspective it focuses on what are the common features in the different approaches the choices that have to be made and what considerations are relevant for a successful system identification application of these techniques it is pointed out that the nonlinear structures can be seen as a concatenation of a mapping form observed data to a regression vector and a nonlinear mapping from the regressor space to the output space these mappings are discussed separately the latter mapping is usually formed as a basis function expansion the basis functions are typically formed from one simple scalar function which is modified in terms of scale and location the expansion from the scalar argument to the regressor space is achieved by a radial or a ridge type approach basic techniques for estimating the parameters in the structures are criterion minimization as well as two step procedures where first the relevant basis functions are determined using data and then a linear least squares step to determine the coordinates of the function approximation a particular problem is to deal with the large number of potentially necessary parameters this is handled by making the number of used parameters considerably less than the number of offered parameters by regularization shrinking pruning or regressor selection