adaptive pole positioning in mimo linear systems by periodic multirate input controllers abstract in this paper the certainty equivalence principle is used to combine the identification method with a control structure derived from the pole placement problem which rely on periodic multirate input controllers the proposed adaptive pole placers contain a sampling mechanism with different sampling period to each system input and rely on a periodically varying controller which suitably modulates the sampled outputs and reference signals of the plant under control such a control strategy allows us to arbitrarily assign the poles of the sampled closed loop system in desired locations and does not make assumptions on the plant other than controllability and observability of the continuous and the sampled system and the knowledge of a set of structural indices namely the locally minimum controllability indices of the continuous time plant an indirect adaptive control scheme is derived which estimates the unknown plant parameters and consequently the controller parameters on line from sequential data of the input and outputs of the plant which are recursively updated within the time limit imposed by a fundamental sampling period t0 using the proposed algorithm the controller determination is based on the transformation of the discrete analogous of the system under control to a phase variable canonical form prior to the application of the control design procedure the solution of the problem can then be obtained by a quite simple utilization of the concept of state similarity transformation known indirect adaptive pole placement schemes usually resort to the computation of dynamic controllers through the solution of a polynomial diophantine equation thus introducing high order exogenous dynamics in the control loop moreover in many cases the solution of the diophantine equation for a desired set of closed loop eigenvalues might yield an unstable controller and the overall adaptive pole placement scheme is unstable with unstable compensators because their outputs are unbounded the proposed control strategy avoids these problems since here gain controllers are essentially needed to be designed moreover persistency of excitation and therefore parameter convergence of the continuous time plant is provided without making any assumption either the richness of the reference signals or on the existence of specific convex sets in which the estimated parameters belong or finally on the coprimeness of the polynomials describing the arma model as in known adaptive pole placement schemes

frequency domain adaptive control band wise compensation abstract the idea of band wise compensation is extended to the design of parametric model based controllers given an lti unknown plant and a frequency domain specification one first choses a frequency set where the open loop compensation is required then for each frequency band one represents the plant by a lower first or second order transfer function and designs a band compensator this procedure allows the reduction of a high dimensional problem pole placement lqg etc to a set of lower dimensional problems avoiding the problem of singularity arising in most adaptive control by using the certainty equivalence a numerical example is included to illustrate this idea

convergence and stability properties of an adaptive regulator with variable forgetting factor abstract a modified version of fortescue s adaptive regulator is described based on a minimum variance estimator with variable forgetting factor and a d step ahead control law as in the fortescue algorithm the forgetting factor is chosen at each step to keep a measure of the information content constant but the formula obtained is slightly different and avoids the need for an arbitrary lower bound it also makes possible a proof of convergence for a deterministic linear system without additional assumptions a similar analysis is given for an incremental version of the regulator

bounded disturbance adaptive control with exponential and selective data weightings a method of combination of selective and exponential data weighting algorithms for parameter identification is proposed bounded disturbances in systems with unknown statistical properties are considered the proposed method ensures a stable control system in addition it does not need the condition of persistent excitation when the predicted output error is small

improved least squares identification an improved recursive least squares algorithm for parameter estimation is presented which includes on off criteria to prevent parameter drift during periods of low excitation a variable forgetting factor which maintains the trace of the covariance matrix at a user specified value data preprocessing and normalization to improve numerical accuracy scaling of the regressor vector to minimize the condition number of the covariance matrix plus independent estimation of the mean values of the input output data which can be used to eliminate errors due to d c bias or slowly drifting elements in the regressor vector the algorithm can also include parameter projection to constrain the estimates to a priori specified regions and retains the formal properties such as convergence of a true weighted least squares algorithm the proposed algorithm is compared with other modifications suggested in the literature and its advantages are demonstrated by a simulated example

finding houses and holes in graphs a house is the complement of an induced path on five vertices a hole is an induced cycle on five or more vertices a domino is the cycle on six vertices with a long chord a graph is hh free if it does not contain a house or a hole a graph is hhd free if it does not contain a house or a hole or a domino we present o n3 algorithms to recognize hh free graphs and hhd free graphs the previous best algorithms for the problems run in o n4 time

extended discrete time multivariable adaptive control using long term predictor an extended method for the design of discrete time multivariable adaptive control is presented unlike most adaptive control algorithms future control inputs are in this method predetermined by using the long term predictor with this concept applications of discrete time multivariable adaptive controls which have been applied to only a limited class of practical problems owing to the unboundedness of the control inputs can be extended to some types of non minimum phase process in addition it is shown that a more generalized control objective such as minimizing a sum of quadratic errors plus a penalty on control action can be easily adopted in the design of adaptive controllers by using the concept of a long term predictor

ridge regression biased estimation for nonorthogonal problems in multiple regression it is shown that parameter estimates based on minimum residual sum of squares have a high probability of being unsatisfactory if not incorrect if the prediction vectors are not orthogonal proposed is an estimation procedure based on adding small positive quantities to the diagonal of x x introduced is the ridge trace a method for showing in two dimensions the effects of nonorthogonality it is then shown how to augment x x to obtain biased estimates with smaller mean square error

model reference adaptive control with unknown high frequency gain sign abstract this paper presents an indirect model reference adaptive control for minimum phase linear systems of arbitrary order with unknown high frequency gain sign it is proved that the modified estimate of the high frequency gain has a uniform positive lower bound the problem has been solved by using the least squares covariance matrix properties to define an appropriate modification of the parameters estimates

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

brief papers independent tracking and regulation adaptive control with forgetting factor this paper considers a discrete time adaptive control algorithm with a forgetting factor applicable to minimum phase plants the tracking and regulation objectives are independently specified the relevance of the eigenvalues of the gain matrix f k used in the updating equation for the adaptive parameters gq k is shown it is proved that if the maximum eigenvalue of the inverse of the gain matrix f k has an upper bound and a non zero lower bound then the global convergence of the control algorithm is insured the result of the design is a simple control scheme using a linear constant feedforward controller and a nonlinear feedback controller the performance of the control structure in tracking and regulation are evaluated by simulations

paper zeros of sampled systems the zeros of the discrete time system obtained when sampling a continuous time system are explored theorems for the limiting zeros for large and small sampling periods are given conditions which guarantee that the sampled system has stable zeros are also presented

maximum set estimators with bounded estimation error we consider the linear regression problem of estimating a deterministic parameter vector x from observations y hx w where h is known and w is additive noise we seek an estimator whose estimation error does not exceed a given maximum error for as wide a range of conditions as possible the maximum error is a design choice and is generally lower than the error provided by the well known least squares ls estimator we develop estimators guaranteeing the required error for as large a parameter set as possible and for as large a noise level as possible we discuss methods for finding these estimators and demonstrate that in many cases the proposed estimators outperform the ls estimator

cram acute text e r rao bound for constrained parameter estimation using lehmann unbiasedness the constrained cram acute text e r rao bound ccrb is a lower bound on the mean squared error mse of estimators that satisfy some unbiasedness conditions although the ccrb unbiasedness conditions are satisfied asymptotically by the constrained maximum likelihood cml estimator in the non asymptotic region these conditions are usually too strict and the commonly used estimators such as the cml estimator do not satisfy them therefore the ccrb may not be a lower bound on the mse matrix of such estimators in this paper we propose a new definition for unbiasedness under constraints denoted by c unbiasedness which is based on using lehmann unbiasedness with a weighted mse wmse risk and taking into account the parametric constraints in addition to c unbiasedness a cram acute text e r rao type bound on the wmse of c unbiased estimators denoted as lehmann unbiased ccrb lu ccrb is derived this bound is a scalar bound that depends on the chosen weighted combination of estimation errors it is shown that c unbiasedness is less restrictive than the ccrb unbiasedness conditions thus the set of estimators that satisfy the ccrb unbiasedness conditions is a subset of the set of c unbiased estimators and the proposed lu ccrb may be an informative lower bound in cases where the corresponding ccrb is not in the simulations we examine linear and nonlinear estimation problems under nonlinear constraints in which the cml estimator is shown to be c unbiased and the lu ccrb is an informative lower bound on the wmse while the corresponding ccrb on the wmse is not a lower bound and is not informative in the non asymptotic region

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

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

analysis of a general recursive prediction error identification algorithm a general class of algorithms for recursive identification of stochastic dynamical systems is studied in this class the discrepancy between the measured output and the output predicted from previous data according to a candidate model the prediction error is minimized over the model set using a stochastic approximation approach it is proved that this class of methods has the same convergence properties as its off line counterparts under mild and general assumptions these assumptions do not for example include stationary conditions or conditions that the true system can be exactly represented within the model set the considered class of methods contains as special cases several well known algorithms other common recursive identification methods like the extended least squares method and the extended kalman filter can be interpreted as approximate prediction error methods with simplified gradient calculations therefore the approach taken here may also serve as a basis for unified description of many recursive identification methods

linear minimax regret estimation of deterministic parameters with bounded data uncertainties we develop a new linear estimator for estimating an unknown parameter vector x in a linear model in the presence of bounded data uncertainties the estimator is designed to minimize the worst case regret over all bounded data vectors namely the worst case difference between the mean squared error mse attainable using a linear estimator that does not know the true parameters x and the optimal mse attained using a linear estimator that knows x we demonstrate through several examples that the minimax regret estimator can significantly increase the performance over the conventional least squares estimator as well as several other least squares alternatives

technical communique convergence analysis of recursive identification algorithms with forgetting factor a convergence analysis of a modified version of the least squares recursive identification algorithm with forgetting factor is given it is shown that the parametric distance converges to a zero mean random variable it is also shown that under persistent excitation condition on both system input and output the condition number of the adaptation gain matrix is bounded the variance of the parametric distance is bounded by the product of the noise variance times the upper bound of the condition number of the gain matrix this is done by normalizing the measurement vector entering in the identification algorithm and by using a forgetting factor verifying l t 0

semi global stabilization of discrete time systems with bounded inputs using a periodic controller we show that semi global stabilization is achieved for linear discrete time systems with bounded controls the proposed scheme is a linear periodic controller and is applicable to systems having open loop eigenvalues in the closed unit disc

robustness of discrete time direct adaptive controllers the problem of preserving stability of discrete time adaptive controllers in spite of reduced order modeling and output disturbances is addressed in this paper conditions for global stability convergence of the tracking error with bounded signals are derived for a discrete time pole zero placement adaptive controller where the parameter estimator is modified in terms of normalized signals following an input output perpective the overall system is decomposed into two subsystems reflecting the parameter estimation and modeling errors respectively and its stability is studied using the sector stability and passivity theorems first the analysis is carried for the class of disturbances and reference inputs that are either decaying or can be exactly hulled by a linear controller of the chosen structure in this l 2 framework it is shown that the only substantive assumption to assure stability is the existence of a linear controller such that the closed loop transfer function verifies certain conicity conditions the convergence speed and alertness properties of various parameter adaptation algorithms regarding this condition are discussed the results are further extended to a broader class of l infty disturbances and reference inputs

robust stabilization of lti systems via indirect adaptive controllers this paper presents a robust indirect adaptive stabilization controller for systems with linear time invariant lti nominal parts uncertain dynamic errors and bounded disturbances the a priori knowledge required for designing the adaptive controller is that the nominal part of the system is of known order and is stabilizable

direct adaptive control with integral action for nonminimum phase systems this note presents a direct adaptive control scheme for nonminimum phase systems where controller parameters are estimated from the recursive least squares algorithm some additional auxiliary parameters are obtained from the proposed polynomial identity and a local convergence is guaranteed without any extra conditions integral action is incorporated into the adaptive controller to eliminate the steady state error and to satisfy a condition of the unique solution for the polynomial identity as well

adaptive stabilization of unstable and nonminimum phase stochastic systems abstract the system under consideration is the discrete time stochastic system a z yn zb z un wn driven by a martingale difference sequence wn where a z are polynomilas in backward shift operator z with unknown coefficients and both a z and b z may be unstable with the purpose of demonstrating theoretical possibility rather than designing a practically applicable control law this paper constructs an adaptive control that stabilizes the system and simultaneously guarantees strong consistency of the least squares estimates for unknown coefficients

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

extended horizon liftings for stable inversion of nonminimum phase systems the lifting of lozano 1989 is generalized and shown to be one in a large class of liftings which enjoy the same zero annihilation properties i e placement of transmission zeros to the origin the new class of liftings allows for longer horizons and leads to plant inverse controllers for nonminimum phase systems having significantly reduced control gains and peak torque requirements

on some generalizations of landau s theorem applicable to analysis of adaptive systems a generalization of landau s theorem concerning the properties of a class of adaptive algorithms is given this generalization enables us firstly to establish an exponential convergence result for some special algorithms and secondly to establish the properties used in the stability analysis of adaptive control schemes for a broader class of algorithms than has been done before

a pre post feedforward compensator design for zero placement we demonstrate the design of a pre post feedforward compensator that places the transmission zeros of a stabilisable and detectable multi input multi output linear time invariant plant at arbitrary locations

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

asymptotic controllability and observability imply semiglobal practical asymptotic stabilizability by sampled data output feedback it is shown for general nonlinear systems that asymptotic controllability and observability are sufficient for semiglobal practical asymptotic stabilization by output feedback indeed as previously shown in the literature asymptotic controllability implies the existence of a discontinuous in general state feedback that when implemented by sample and hold is semiglobally practically stabilizing and robust to measurement disturbance moreover a weak form of observability allows reconstruction of the state with arbitrary precision in an arbitrarily short amount of time so we can build an output feedback that operates periodically in two modes an initial small fraction of a sampling period is used to estimate the state and the remainder of the sampling period is used to implement the state feedback control using the state estimate our stabilization results are presented not only for compact target sets e g the origin but also for noncompact target sets

parameter adaptive control a solution to the overmodeling problem this paper presents a parameter adaptive controller that will stabilize and asymptotically regulate any single input single output linear time invariant controllable and observable discrete time plant given only that an upper bound on its order is known

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

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

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

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

a globally convergent adaptive pole placement algorithm without a persistency of excitation requirement this paper presents an indirect adaptive control scheme for deterministic plants which are not necessarily minimum phase global convergence is established for the scheme in the sense that the closed loop poles are asymptotically assigned for the given data sequence and the system input and output remain bounded for all time a key feature of the scheme is that no persistency of excitation condition is required the algorithm uses recursive least squares with variable forgetting factor normalized regression vectors and a matrix gain with constant trace

stochastic adaptive pole zero assignment with convergence analysis abstract the adaptive control u n is designed for the stochastic system a z y n 1 b z u n c z w n 1 with unknown constant matrix coefficients in the polynomials a z b z and c z in the shift back operator with the purposes that 1 the unknown matrices are strongly consistently estimated and 2 the poles and zeros are replaced in such a way that the system itself is transferred to a 0 z y n 1 b 0 z u n 0 e n 1 with given a 0 z b 0 z and u n 0 so that the pole zero assignment error e n 1 is minimized the problem of adaptive pole zero assignment combined with tracking is also considered in this paper conditions used are imposed only on a z b z and c z

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

on extended p 4 reducible and extended p 4 sparse graphs abstract a graph g was defined in 16 as p 4 reducible if no vertex in g belongs to more than one chordless path on four vertices or p 4 a graph g is defined in 15 as p 4 sparse if no set of five vertices induces more than one p 4 in g p 4 sparse graphs generalize both p 4 reducible and the well known class of p 4 free graphs or cographs in an extended abstract in 11 the first author introduced a method using the modular decomposition tree of a graph as the framework for the resolution of algorithmic problems this method was applied to the study of p 4 sparse and extended p 4 sparse graphs in this paper we begin by presenting the complete information about the method used in 11 we propose a unique tree representation of p 4 sparse and a unique tree representation of p 4 reducible graphs leading to a simple linear recognition algorithm for both classes of graphs in this way we simplify and unify the solutions for these problems presented in 16 19 the tree representation of an n vertex p 4 sparse or a p 4 reducible graph is the key for obtaining o n time algorithms for the weighted version of classical optimization problems solved in 20 these problems are np complete on general graphs finally by relaxing the restriction concerning the exclusion of the c 5 cycles from p 4 sparse and p 4 reducible graphs we introduce the class of the extended p 4 sparse and the class of the extended p 4 reducible graphs we then show that a minimal amount of additional work suffices for extending most of our algorithms to these new classes of graphs

towards a globally stable direct adaptive control scheme for not necessarily minimum phase systems a direct adaptive control scheme for not necessarily minimum phase systems is presented the algorithm is based on simultaneous identification of input and output prediction models this leads to a bilinear parameter estimation problem for which a least squares criterion minimization is proposed this framework makes it possible to establish global convergence without any extra condition we give an example to illustrate the practical features

adaptive control with a forgetting factor with multiple samples between parameter adjustments a discrete time adaptive control algorithm with a forgetting factor that permits multiple samples between parameter adjustments is presented a free integer value may be chosen in the design in order to reduce the minimum sampling period imposed by the computational requirements of the parameter adjustment laws this fact makes the algorithm particularly suitable for inexpensive microcomputer implementation a proof of global convergence of the algorithm is presented and the performance of the control structure is evaluated by simulations

indirect adaptive periodic control a indirect adaptive control method is presented the method is based on a lifted representation of the plant that can be stabilized using a simple performant periodic control scheme the controller parameters computation involves the inverse of the controllability observability matrix potential singularities of this matrix are avoided by means of an appropriate estimates modification this estimates transformation is linked to the covariance matrix properties and hence it preserves the convergence properties of the original estimates this modification involves the singular value decomposition of the controllability observability matrix s estimate as compared with previous studies on the subject the controller proposed here does not require the frequent introduction of periodic n length sequences of zero inputs therefore the new controller is such that the system is almost always operating in closed loop which should lead to better performance characteristics

paper unification of discrete time explicit model reference adaptive control designs various discrete time explicit mrac designs based on stability considerations are presented from a unified point of view a general structure and a design procedure are given which contain as particular cases various possible designs some of these designs have been already given in the literature but some are new the general structure considered removes some of the restrictions encountered in previous designs and solves the important problem of independent specification of tracking and regulation objectives the proof of boundedness of the control variables is also given simulations are included in order to evaluate the various designs in a deterministic environment

an o nm time certifying algorithm for recognizing hhd free graphs in this paper we consider the recognition problem on a class of perfectly orderable graphs namely the hhd free graphs such graphs do not contain any induced subgraph isomorphic to a house a hole or a domino we prove properties of the hhd free graphs which enable us to present an o nm time and o n m space algorithm for determining whether a graph on n vertices and m edges is hhd free currently this is the fastest algorithm for this problem we also describe how the algorithm can be augmented to provide a certificate an induced house hole or domino whenever it decides that the input graph is not hhd free thus answering an open question posed by hoang and sritharan theoretical computer science 259 2001 233 244 the certificate computation requires o n m additional time and o n space

adaptive stabilization of nonminimum phase first order continuous time systems presents an adaptive control scheme for first order systems of the form y spl dot a y b sub 0 u spl dot b sub 1 u which may possibly be a nonminimum phase the control scheme achieves asymptotical stabilization without any a priori knowledge on the plant parameters the adaptive scheme is free from singularities in the sense that the plant estimated model is always controllable the singularity has been overcome through a suitable modification of the parameter estimates which is based on standard least squares covariance matrix properties and the use of a hysteresis switching function

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

covariance shaping least squares estimation a new linear estimator is proposed which we refer to as the covariance shaping least squares csls estimator for estimating a set of unknown deterministic parameters x observed through a known linear transformation h and corrupted by additive noise the csls estimator is a biased estimator directed at improving the performance of the traditional least squares ls estimator by choosing the estimate of x to minimize the weighted total error variance in the observations subject to a constraint on the covariance of the estimation error so that we control the dynamic range and spectral shape of the covariance of the estimation error the presented csls estimator is shown to achieve the cramer rao lower bound for biased estimators furthermore analysis of the mean squared error mse of both the csls estimator and the ls estimator demonstrates that the covariance of the estimation error can be chosen such that there is a threshold snr below which the csls estimator yields a lower mse than the ls estimator for all values of x as we show some of the well known modifications of the ls estimator can be formulated as csls estimators this allows us to interpret these estimators as the estimators that minimize the total error variance in the observations among all linear estimators with the same covariance

stability result with application to adaptive control we prove a relatively simple stability result for a particular system of time varying difference equations we then display its usefulness in analysing the stability and convergence of discrete time adaptive control systems in particular we apply our result to demonstrate the stability and convergence of two disparate adaptive control schemes

exponential convergence of adaptive identification and control algorithms output and equation error adaptive identification algorithms are shown to be exponentially convergent under a deterministic or stochastic persistently exciting or spanning condition on the system inputs together with several other standard conditions an adaptive control algorithm is shown to be exponentially convergent under a deterministic or stochastic persistently exciting condition on the reference trajectory together with some standard conditions

assessment of stability robustness for adaptive controllers the problem of improving the stability characteristics of discrete time siso reduced order adaptive controllers is addressed in this note a method is proposed to adjust the observer poles of an indirect adaptive scheme in order to ensure stability of the closed loop system in spite of possible unstructured uncertainties e g process model order mismatch assuming that the identified model transfer function module converges within a previously defined uncertainty range the frequency response like compensation method is shown to lead to a stable design provided that the reduced order estimated model is stable and stably invertible and the system is open loop stable

singularity free multivariable model reference adaptive control in this paper we propose a way to solve the problem of singularities in model reference adaptive control of linear multi input multi output mimo systems using a parameter modification procedure based on the least squares covariance matrix inverse the scheme does not require any explicit prior knowledge about the leading coefficient matrix associated with the control input and secures a uniform lower bound for the determinant of the estimate of this matrix a global convergence analysis is presented

direct model reference adaptive pole placement control with exponential weighting properties a parameterization for a linear system is presented to design a direct model reference adaptive pole placement controller this parameterized model is one of the structured nonminimal models the exponentially weighted least squares algorithm is employed to estimate the control parameters the direct adaptive controller has the exponential weighting properties by the proposed method of selecting the characteristic polynomials of the sensitivity function filters in connection with the reference model

block form control of linear time invariant discrete time systems defined over commutative rings abstract a new approach based on a block input block output state model is developed for the study of linear time invariant discrete time systems whose coefficients belong to a commutative ring with 1 it is well known that such systems arise in the study of various classes of complex linear systems including systems depending on parameters and multidimentional systems by time compressing the block input state representation new results are obtained on the construction of a memoryless block form state feedback control law that yields a type of assignability and or deadbeat control these results are then dualized to yield results on a new type of state observer based on a block of output measurements the observer and state feedback controller are then combined to yield new results on input output regulation and set point tracking for systems defined over an arbitrary commutative ring in the last part of the paper the block input form is utilized to study the stabilization of systems defined over a normed algebra

reformulation of the parameter identification problem for systems with bounded disturbances abstract the problem of deriving parameter identification algorithms that incorporate prior knowledge of a bound on the disturbance is studied particular emphasis is given to the following aspects firstly to motivate from geometrical and optimization considerations the modifications dead zones required to cope with the disturbances secondly to guarantee the convergence properties which are essential in the establishment of stability of identification based adaptive control systems projection and least squares algorithms are studied in both cases an interpretation is given to the new dead zone that has proven to be a key ingredient in recent robustness studies e g goodwin et al 1986 automatica 22 199 207 kreisselmeier and anderson 1985 ieee trans aut control 31 127 133 and lozano leal and ortega 1986 2nd ifac workshop on adapt syst in control and signal proc lund sweden

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

persistency of excitation in the presence of possibly unbounded signals this note develops an explicit characterization of the concept of persistency of excitation for time invariant linear systems in the presence of possibly unbounded signals this result can be used to establish exponential convergence for a range of adaptive control algorithms a feature of our proof is a particular technique for dealing with the initial condition response

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

brief paper combining model reference adaptive controllers and stochastic self tuning regulators the similarities between model reference adaptive controllers mrac for minimum phase plants where the control objectives are specified by reference models and stochastic self tuning regulators s sture for minimum phase plants where the control objectives are specified by autoregressive moving average arma stochastic models are investigated these similarities permit the extension for these two classes of adaptive systems of the duality existing in the linear case with known parameters between modal control and minimum variance control the convergence analysis of these schemes in a combined deterministic and stochastic environment allows one finally to define schemes which behave as a desired mrac in a deterministic environment and as a desired s sture in a stochastic environment the problem of removing the positive real conditions for convergence in deterministic and stochastic environment is also discussed

global stability proofs for continuous time indirect adaptive control schemes this note presents a general stability proof for continuous time adaptive control with very general assumptions on the identifier and controller we show that if the exogenous input signal is rich enough then both the identifier and the controller converge to their true values applications of the proof to pole placement design and design based on the factorization approach are discussed

adaptive control of continuous time overmodeled plants this paper presents an adaptive controller that will stabilize and asymptotically regulate any continuous time linear time invariant plant which has one input and one output the only assumptions on the plant are observability controllability and the a priori knowledge of an upper bound on the plant order the adaptive control concept combines continuous time state observation and sampled data control with a generalized plant dependent hold function the feedback gains and the hold function are adaptively tuned

fast and stable algorithms for computing the principal square root of a complex matrix this note presents recursive algorithms that are rapidly convergent and more stable for finding the principal square root of a complex matrix also the developed algorithms are utilized to derive the fast and stable matrix sign algorithms which are useful in developing applications to control system problems

parameter drift instability in disturbance free adaptive systems adaptive identification and control algorithms can exhibit local instability when certain ideal assumptions such as satisfaction of strictly positive real spr conditions are violated however conjectures suggest that due to a self stabilization mechanism global boundedness may still hold despite local instabilities counterexamples to these are presented showing that self stabilization is bypassed via hidden unbounded parameter drift although parameter drift instability is known to occur in adaptive systems with disturbances concrete examples are given to show that unbounded drift can also occur in the disturbance free case when spr conditions are violated

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

blind minimax estimation we consider the linear regression problem of estimating an unknown deterministic parameter vector based on measurements corrupted by colored gaussian noise we present and analyze blind minimax estimators bmes which consist of a bounded parameter set minimax estimator whose parameter set is itself estimated from measurements thus our approach does not require any prior assumption or knowledge and the proposed estimator can be applied to any linear regression problem we demonstrate analytically that the bmes strictly dominate the least squares ls estimator i e they achieve lower mean squared error mse for any value of the parameter vector both stein s estimator and its positive part correction can be derived within the blind minimax framework furthermore our approach can be readily extended to a wider class of estimation problems than stein s estimator which is defined only for white noise and nontransformed measurements we show through simulations that the bmes generally outperform previous extensions of stein s technique

comparing between estimation approaches admissible and dominating linear estimators we treat the problem of evaluating the performance of linear estimators for estimating a deterministic parameter vector x in a linear regression model with the mean squared error mse as the performance measure since the mse depends on the unknown vector x a direct comparison between estimators is a difficult problem here we consider a framework for examining the mse of different linear estimation approaches based on the concepts of admissible and dominating estimators we develop a general procedure for determining whether or not a linear estimator is mse admissible and for constructing an estimator strictly dominating a given inadmissible method so that its mse is smaller for all x in particular we show that both problems can be addressed in a unified manner for arbitrary constraint sets on x by considering a certain convex optimization problem we then demonstrate the details of our method for the case in which x is constrained to an ellipsoidal set and for unrestricted choices of x as a by product of our results we derive a closed form solution for the minimax mse estimator on an ellipsoid which is valid for arbitrary model parameters as long as the signal to noise ratio exceeds a certain threshold

singularity free adaptive pole placement for second order systems abstract this paper proposes a new adaptive pole placement control scheme which overcomes the crucial singularity problem in indirect adaptive control that is it guarantees the controllability of the estimated plant model allowing the calculation of the controller parameters without introducing persistency of excitation into the system the control scheme is applicable to either minimum or non minimum phase systems and guarantees the closed loop stability of the controlled system detailed analysis is given for second order systems

redesign of explicit and implicit discrete time model reference adaptive control schemes the design of mrac for achieving independent tracking and regulation objectives with a unique equilibrium point in the controller parameter space is presented the corresponding schemes can use either an explicit reference model or an implicit reference model the design is done from a stability point of view by extending an appropriate control configuration used for the case of known plant parameters the result of the design is a simple control scheme using a linear constant feedforward controller and a non linear feedback controller the stability of the system and boundness of various variables do not require any positivity condition the performances of the control structure in tracking and regulation are evaluated by simulations

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

semiglobal stabilization of continuous time systems with bounded inputs presents a simple linear periodic controller that achieves semi global stabilization of linear systems with amplitude constrained inputs the central scheme is applicable to continuous time null controllable systems i e systems having open loop poles in the closed left half plane

robust mean squared error estimation in the presence of model uncertainties we consider the problem of estimating an unknown parameter vector x in a linear model that may be subject to uncertainties where the vector x is known to satisfy a weighted norm constraint we first assume that the model is known exactly and seek the linear estimator that minimizes the worst case mean squared error mse across all possible values of x we show that for an arbitrary choice of weighting the optimal minimax mse estimator can be formulated as a solution to a semidefinite programming problem sdp which can be solved very efficiently we then develop a closed form expression for the minimax mse estimator for a broad class of weighting matrices and show that it coincides with the shrunken estimator of mayer and willke with a specific choice of shrinkage factor that explicitly takes the prior information into account next we consider the case in which the model matrix is subject to uncertainties and seek the robust linear estimator that minimizes the worst case mse across all possible values of x and all possible values of the model matrix as we show the robust minimax mse estimator can also be formulated as a solution to an sdp finally we demonstrate through several examples that the minimax mse estimator can significantly increase the performance over the conventional least squares estimator and when the model matrix is subject to uncertainties the robust minimax mse estimator can lead to a considerable improvement in performance over the minimax mse estimator

a globally convergent adaptive predictor this paper establishes global convergence for an adaptive prediction algorithm key features of the algorithm are i a priori residuals are used in the regression vector ii the input signal need not be persistently exciting iii only an upper bound is required on the system order iv no monitoring or projection procedure is required to guarantee stability and v arbitrary feedback is allowed between output and input

universal weighted mse improvement of the least squares estimator since the seminal work of stein in the 1950s there has been continuing research devoted to improving the total mean squared error mse of the least squares ls estimator in the linear regression model however a drawback of these methods is that although they improve the total mse they do so at the expense of increasing the mse of some of the individual signal components here we consider a framework for developing linear estimators that outperform the ls strategy over bounded norm signals under all weighted mse measures this guarantees for example that both the total mse and the mse of each of the elements will be smaller than that resulting from the ls approach we begin by deriving an easily verifiable condition on a linear method that ensures ls domination for every weighted mse we then suggest a minimax estimator that minimizes the worst case mse over all weighting matrices and bounded norm signals subject to the universal weighted mse domination constraint

adaptive control of nonminimum phase systems recent papers have established global convergence for a class of adaptive control algorithms for discrete time linear dynamic systems however in most cases studied to date it has been assumed that the system is stably invertible this assumption plays a major role in the proofs of convergence in this paper we consider the more general case in which it is not assumed that the system is either stable or stably invertible we establish local convergence for a class of adaptive control algorithms applied to general discrete deterministic linear time invariant systems by convergence in this context we mean that the system inputs and outputs remain bounded for all time and the closed loop poles are effectively assigned in the limit for a given desired trajectory

bias compensating least squares method for identification of continuous time systems from sampled data abstract least squares ls techniques are applied to the identification problem of continuous time systems from sampled data of input output measurements the linear integral filter which solves the intial condition problem is employed for handling time derivatives the asymptotic bias in the ls estimator is derived and is compensated in a modified ls algorithm called a bias compensating ls method to obtain consistent estimates of the unknown parameters when it is unknown the variance of the noise can be estimated recursively together with the system parameters the bias compensating ls method not only has all merits of the ls method but also possesses good consistency properties it is applicable to both time invariant and time varying continuous time systems in the time varying case an adaptive ls algorithm with a variable forgetting factor is chosen to make the estimates track the changing parameters quickly and the bias is compensated as is done in the time invariant case representative nu

uniformly improving the cramer rao bound and maximum likelihood estimation an important aspect of estimation theory is characterizing the best achievable performance in a given estimation problem as well as determining estimators that achieve the optimal performance the traditional cramer rao type bounds provide benchmarks on the variance of any estimator of a deterministic parameter vector under suitable regularity conditions while requiring a priori specification of a desired bias gradient in applications it is often not clear how to choose the required bias a direct measure of the estimation error that takes both the variance and the bias into account is the mean squared error mse which is the sum of the variance and the squared norm of the bias here we develop bounds on the mse in estimating a deterministic parameter vector x0 over all bias vectors that are linear in x0 which includes the traditional unbiased estimation as a special case in some settings it is possible to minimize the mse over all linear bias vectors more generally direct minimization is not possible since the optimal solution depends on the unknown x0 nonetheless we show that in many cases we can find bias vectors that result in an mse bound that is smaller than the cramer rao lower bound crlb for all values of x0 furthermore we explicitly construct estimators that achieve these bounds in cases where an efficient estimator exists by performing a simple linear transformation on the standard maximum likelihood ml estimator this leads to estimators that result in a smaller mse than the ml approach for all possible values of x0