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

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

arbitrary adaptive pole placement for linear multivariable systems this paper presents a methodology for adaptively assigning the closed loop poles of either continuous or discrete time linear mnltivariable systems the scheme is direct in nature in that no parametrized model of the unknown plant needs to be explicitely identified rather the control parameters and an equivalent plant parameterization are simultaneously estimated from input output data using linear parameter estimation procedures implementation of the scheme requires only knowledge of the system controllability indexes and an upper bound on the observabilily index

scale space view of curve estimation scale space theory from computer vision leads to an interesting and novel approach to nonparametric curve estimation the family of smooth curve estimates indexed by the smoothing parameter can be represented as a surface called the scale space surface the smoothing parameter here plays the same role as that played by the scale of resolution in a visual system in this paper we study in detail various features of that surface from a statistical viewpoint weak convergence of the empirical scale space surface to its theoretical counterpart and some related asymptotic results have been established under appropriate regularity conditions our theoretical analysis provides new insights into nonparametric smoothing procedures and yields useful techniques for statistical exploration of features in the data in particular we have used the scale space approach for the development of an effective exploratory data analytic tool called sizer

remarks on persistency of excitation for nonminimal models of systems having purely deterministic disturbances a persistency of excitation result for nonminimal models of systems having purely deterministic disturbances has been given recently in 1 in this note we give a direct and simple proof for the case of bounded signals of the result of 1 and show via a counterexample that an assumption on system signals boundedness which does not appear in 1 is necessary when arbitrary unbounded signals are allowable finally we give a proper persistency of excitation result which does not require signal boundedness for the case when the system input consists of a bounded external signal and of a constant coefficient feedback component

stable hybrid adaptive control this paper examines the asymptotic properties of a hybrid adaptive control scheme while there are many different meanings of the word hybrid control in the literature we are referring to a scheme where the on line parameter estimation and underlying control design are carried out in a discrete time using digital electronics and do not require any analog multiplications or divisions this is of critical importance in practice since analog multipliers dividers are subject to serious drift and offset errors for such hybrid schemes we establish stability and an output tracking property without recourse to persistence of exitation the proof of stability requires a sufficiently fast sampling rate for the discrete time parameter estimation and the underlying control design

mdpe a very robust estimator for model fitting and range image segmentation in this paper we propose a novel and highly robust estimator called mdpe1 maximum density power estimator this estimator applies nonparametric density estimation and density gradient estimation techniques in parametric estimation model fitting mdpe optimizes an objective function that measures more than just the size of the residuals both the density distribution of data points in residual space and the size of the residual corresponding to the local maximum of the density distribution are considered as important characteristics in our objective function mdpe can tolerate more than 85 outliers compared with several other recently proposed similar estimators mdpe has a higher robustness to outliers and less error variance we also present a new range image segmentation algorithm based on a modified version of the mdpe quick mdpe and its performance is compared to several other segmentation methods segmentation requires more than a simple minded application of an estimator no matter how good that estimator is our segmentation algorithm overcomes several difficulties faced with applying a statistical estimator to this task

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

adaptive regulation of mimo linear discrete time systems without requiring a persistent excitation an adaptive regulator which does not require a persistent excitation is developed for multiinput multioutput mimo linear discrete time systems the assumptions on the plant are 1 an upper bound on the system dimension is known 2 the unknown system parameters belong to known bounded intervals 3 the plant is stabilizable for all possible values of the unknown system parameters the stabilizability condition can be tested before the system is put into operation a recursive parameter estimation scheme is given which forces the parameter estimates to converge to the known intervals using this estimator an adaptive regulator is derived which results in a globally stable closed loop system

robustness of an adaptive pole placement algorithm in the presence of bounded disturbances and slow time variation of parameters the robustness properties of a specific adaptive pole placement scheme in the presence of bounded disturbances and slow time variation of parameters are studied it is shown that the least squares algorithm used in this scheme retains the global stability of the overall system in the presence of bounded disturbances of small magnitude and slow time variation of system parameters within a compact set

invariant prime ideals in quantizations of nilpotent lie algebras de concini kac and procesi defined a family of subalgebras u of a quantized universal enveloping algebra uq g associated to the elements of the corresponding weyl group w they are deformations of the universal enveloping algebras u n adw n where n are the nilradicals of a pair of dual borel subalgebras based on results of gorelik and joseph and an interpretation of u as quantized algebras of functions on schubert cells we construct explicitly the h invariant prime ideals of each u and show that the corresponding poset is isomorphic to w where h is the group of group like elements of uq g moreover for each h prime of u w we construct a generating set in terms of demazure modules related to fundamental representations using results of ramanathan and kempf we prove similar theorems for vanishing ideals of closures of torus orbits of symplectic leaves of related poisson structures on schubert cells in flag varieties

indirect adaptive control for interconnected systems an indirect adaptive controller for interconnected systems is introduced each subsystem is subject to bounded disturbances and to possibly unbounded interconnections with other subsystems a variable dead zone is incorporated into a gradient estimation scheme to limit the effects of the interconnections and disturbances an adaptive state feedback control law is described which stabilizes the interconnected system forcing the input and output signals of each subsystem to remain bounded

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

mean shift mode seeking and clustering mean shift a simple interactive procedure that shifts each data point to the average of data points in its neighborhood is generalized and analyzed in the paper this generalization makes some k means like clustering algorithms its special cases it is shown that mean shift is a mode seeking process on the surface constructed with a shadow kernal for gaussian kernels mean shift is a gradient mapping convergence is studied for mean shift iterations cluster analysis if treated as a deterministic problem of finding a fixed point of mean shift that characterizes the data applications in clustering and hough transform are demonstrated mean shift is also considered as an evolutionary strategy that performs multistart global optimization

brief interval excitation through impulse sequences a technical lemma we present a technical lemma that establishes in a general framework an interval excitation property using a specific class of impulse sequences according to such an interval excitation property an impulse applied within a time interval generates excitation within the same interval this property does not hold for arbitrary exciting sequences the lemma is a unified statement of previous results corresponding to particular choices of the exciting sequence

an algorithm for data driven bandwidth selection the analysis of a feature space that exhibits multiscale patterns often requires kernel estimation techniques with locally adaptive bandwidths such as the variable bandwidth mean shift proper selection of the kernel bandwidth is however a critical step for superior space analysis and partitioning this paper presents a mean shift based approach for local bandwidth selection in the multimodal multivariate case the method is based on a fundamental property of normal distributions regarding the bias of the normalized density gradient this paper demonstrates that within the large sample approximation the local covariance is estimated by the matrix that maximizes the magnitude of the normalized mean shift vector using this property the paper develops a reliable algorithm which takes into account the stability of local bandwidth estimates across scales the validity of the theoretical results is proven in various space partitioning experiments involving the variable bandwidth mean shift

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

modeling spatial extremes via ensemble of trees of pairwise copulas assessing the risk of extreme events in a spatial domain such as hurricanes floods and droughts presents a unique significance in practice unfortunately the existing extreme value statistical models are typically not feasible for practical large scale problems graphical models on the other hand are capable of handling sizable number of variables but have yet to be explored in the realm of extreme value analysis to bridge the gap an extreme value graphical model is introduced in this paper i e an ensemble of trees of pairwise copulas etpc in the proposed graphical model extreme value marginal distributions are stitched together by means of a pairwise copulas which in turn are the building blocks of the ensemble of trees novel linear complexity stochastic gradient based algorithms are then developed for learning the etpc model and inferring missing data as a result the etpc model is applicable to extreme value problems with thousands of variables it can be proven that under mild conditions the etpc model exhibits the favorable property of tail dependence between an arbitrary pair of sites variables consequently the model is able to reliably capture statistical dependence between extreme values at different sites experimental results for both synthetic and real data demonstrate the advantages of the etpc model in modeling fitting imputation and computational efficiency

incremental learning of 3d dct compact representations for robust visual tracking visual tracking usually requires an object appearance model that is robust to changing illumination pose and other factors encountered in video many recent trackers utilize appearance samples in previous frames to form the bases upon which the object appearance model is built this approach has the following limitations 1 the bases are data driven so they can be easily corrupted and 2 it is difficult to robustly update the bases in challenging situations in this paper we construct an appearance model using the 3d discrete cosine transform 3d dct the 3d dct is based on a set of cosine basis functions which are determined by the dimensions of the 3d signal and thus independent of the input video data in addition the 3d dct can generate a compact energy spectrum whose high frequency coefficients are sparse if the appearance samples are similar by discarding these high frequency coefficients we simultaneously obtain a compact 3d dct based object representation and a signal reconstruction based similarity measure reflecting the information loss from signal reconstruction to efficiently update the object representation we propose an incremental 3d dct algorithm which decomposes the 3d dct into successive operations of the 2d discrete cosine transform 2d dct and 1d discrete cosine transform 1d dct on the input video data as a result the incremental 3d dct algorithm only needs to compute the 2d dct for newly added frames as well as the 1d dct along the third dimension which significantly reduces the computational complexity based on this incremental 3d dct algorithm we design a discriminative criterion to evaluate the likelihood of a test sample belonging to the foreground object we then embed the discriminative criterion into a particle filtering framework for object state inference over time experimental results demonstrate the effectiveness and robustness of the proposed tracker

effacement des derivations et spectres premiers des algebres quantiques abstract given any commutative field k and any iterated ore extension r k x1 x2 2 2 xn n n satisfying some suitable assumptions we construct the so called derivative elimination algorithm it consists of a sequence of changes of variables inside the division ring f fract r starting with the indeterminates x1 xn and terminating with new variables t1 tn these new variables generate some quantum affine space r such that f fract r this algorithm induces a natural embedding spec r spec r which satisfies the following property if p is in spec r then fract r p fract r p we study both the derivative elimination algorithm and natural embedding and use them to produce for the general case a common proof of the quantum gelfand kirillov property for the prime homomorphic images of the following quantum algebras u q w g b q w g w w r q g where g denotes any complex semi simple connected simply connected lie group with associated lie algebra g and weyl group w quantum matrices algebras quantum weyl algebras and quantum euclidean respectively symplectic spaces another application will be given in g cauchon j algebra to appear in the general case the prime spectrum of any quantum matrices algebra satisfies the normal separation property

discrete time model following adaptive control for multivariable non minimum phase systems in this paper a control system design that is applicable to both minimum and non minimum phase plants is discussed the output of this system can follow an arbitrary reference output with a bounded input in the first part of this paper we propose a new concept which is a bounded input calculation method of following a reference output it is then used to design a model following control system mfcs for multivariable non minimum phase plants corresponding to the right and left coprime factorizations of the plant two mfcs designs are given an extension of the mfcs to adaptive control is discussed and numerical examples are given to illustrate the effectiveness of the proposed adaptive system design

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

stabilizability of linear systems over a commutative normed algebra with applications to spatially distributed and parameter dependent systems the problem of achieving stabilization by using state feedback is considered for linear systems given by a pair of matrices whose entries belong to a real or complex commutative normed algebra this framework is applicable to various types of linear systems including spatially distributed systems systems depending on parameters and infinite dimensional systems necessary and sufficient conditions for stabilizability are derived in terms of solutions to an associated riccati equation defined in the gelfand transform domain necessary and sufficient conditions for stabilizability are also given in terms of a local rank criterion involving the gelfand transform of the system coefficients the results are applied to the problem of positioning a long seismic cable

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

generalised relaxed radon transform gr2t for robust inference this paper introduces the generalised relaxed radon transform gr 2t as an extension to the generalised radon transform grt 1 this new modelling allows us to define a new framework for robust inference the resulting objective functions are probability density functions that can be chosen differentiable and that can be optimised using gradient methods one of this cost function is already widely used in the forms of the hough transform and generalised projection based m estimator and it is interpreted as a conditional density function on the latent variables of interest in addition the joint density function of the latent variables is also proposed as a cost function and it has the advantage of including a prior about the latent variable several applications including lines detection in images and volume reconstruction from silhouettes captured from multiple views are presented to underline the versatility of this framework

towards a link between the factorization approach and mimo robust adaptive control based on a doubly coprime factorization theorem nett et al 1984 an adaptive controller for discrete time mimo systems consisting of a not necessarily minimum phase modelled part and fraction type unmodelled dynamics which are not necessarily stable non linear and time varying is developed then by virtue of a stability result which is itself of interest it is shown that the adaptive closed loop system is bibo stable even in the presence of small but not necessarily stable unmodelled dynamics and arbitrarily bounded initial conditions consequently an initial but important step for applying the factorization approach to mimo robust adaptive control is completely established

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

bump hunting with non gaussian kernels it is well known that the number of modes of a kernel density estimator is monotone nonincreasing in the bandwidth if the kernel is a gaussian density there is numerical evidence of nonmonotonicity in the case of some non gaussian kernels but little additional information is available the present paper provides theoretical and numerical descriptions of the extent to which the number of modes is a nonmonotone function of bandwidth in the case of general compactly supported densities our results address popular kernels used in practice for example the epanechnikov biweight and triweight kernels and show that in such cases nonmonotonicity is present with strictly positive probability for all sample sizes n 3 in the epanechnikov and biweight cases the probability of nonmonotonicity equals 1 for all n 2 nevertheless in spite of the prevalence of lack of monotonicity revealed by these results it is shown that the notion of a critical bandwidth the smallest bandwidth above which the number of modes is guaranteed to be monotone is still well defined moreover just as in the gaussian case the critical bandwidth is of the same size as the bandwidth that minimises mean squared error of the density estimator these theoretical results and new numerical evidence show that the main effects of nonmonotonicity occur for relatively small bandwidths and have negligible impact on many aspects of bump hunting jj

on adaptive state regulation an indirect adaptive state regulator consisting of an adaptive observer and an asymptotic feedback matrix synthesis is discussed in a rigorous analysis lyapunov stability of the resulting closed loop system without the need for external excitation possible global instabilities as well as global convergence subject to sufficient excitation are shown moreover the behavior of the closed loop system is analyzed for cases in which the true plant differs from the assumed linear time invariant model in that it is of higher order contains slight nonlinearities and time variation effects and is subject to plant and measurement disturbances

on the limited memory bfgs method for large scale optimization we study the numerical performance of a limited memory quasi newton method for large scale optimization which we call the l bfgs method we compare its performance with that of the method developed by buckley and lenir 1985 which combines cycles of bfgs steps and conjugate direction steps our numerical tests indicate that the l bfgs method is faster than the method of buckley and lenir and is better able to use additional storage to accelerate convergence we show that the l bfgs method can be greatly accelerated by means of a simple scaling we then compare the l bfgs method with the partitioned quasi newton method of griewank and toint 1982a the results show that for some problems the partitioned quasi newton method is clearly superior to the l bfgs method however we find that for other problems the l bfgs method is very competitive due to its low iteration cost we also study the convergence properties of the l bfgs method and prove global convergence on uniformly convex problems

adaptive control with finite time persistency of excitation an adaptive control algorithm for discrete time siso systems is presented the main feature is the fact that it requires an external persistently exciting signal for a finite interval of time in this way tracking of a class of signals such as set points can be achieved within an arbitrarily small error

on convergence properties of the em algorithm for gaussian mixtures we build up the mathematical connection between the expectation maximization em algorithm and gradient based approaches for maximum likelihood learning of finite gaussian mixtures we show that the em step in parameter space is obtained from the gradient via a projection matrix p and we provide an explicit expression for the matrix we then analyze the convergence of em in terms of special properties of p and provide new results analyzing the effect that p has on the likelihood surface based on these mathematical results we present a comparative discussion of the advantages and disadvantages of em and other algorithms for the learning of gaussian mixture models

stability analysis of elliott s direct adaptive pole placement abstract the stability of elliott s direct adaptive pole placement algorithm is examined without the persistency of excitation assumption the conditions for the sequence of estimated parameters that are sufficient for the plant input and the plant output to be bounded are given it is also shown that the modifications proposed in many papers for ensuring the global stability of the indirect adaptive pole placement algorithm can be also applied to the direct one if an auxiliary estimation algorithm for identifying the plant parameters is applied

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 global stability of adaptive systems using an estimator with parameter freezing the results of r kosut and b friedlander 1985 on robust global stability of direct adaptive controllers using an integral adaptation law are extended to the case where the adaptation algorithm includes a parameter freezing mechanism i e the control parameters are held constant at certain time intervals the authors main concern is to propose an estimator with freezing capabilities which preserve the property needed for the global stability analysis namely that it defines a passive operator in an adaptive control context the additional degree of freedom provided by the freezing imposes no further assumptions for global stability a crucial requirement for the analysis is that the number of freezing intervals is finite

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

kernel based object tracking a new approach toward target representation and localization the central component in visual tracking of nonrigid objects is proposed the feature histogram based target representations are regularized by spatial masking with an isotropic kernel the masking induces spatially smooth similarity functions suitable for gradient based optimization hence the target localization problem can be formulated using the basin of attraction of the local maxima we employ a metric derived from the bhattacharyya coefficient as similarity measure and use the mean shift procedure to perform the optimization in the presented tracking examples the new method successfully coped with camera motion partial occlusions clutter and target scale variations integration with motion filters and data association techniques is also discussed we describe only a few of the potential applications exploitation of background information kalman tracking using motion models and face tracking

on the parameter convergence properties of a combined vs adaptive control scheme during sliding motion the effects of the use of a variable structure control component within an adaptive control scheme previously proposed by the authors 1992 1995 are investigated in this paper the discontinuous control action does not allow the explicit identification of the coefficients of the filters but only the identification of the so called equivalent control coinciding with the ideal control by coupling the variable structure control strategy with a continuous parameter adjustment mechanism it is instead possible to obtain an equivalent control which during the sliding motion turns out to be equal to a suitably constructed prediction error as long as the parameter adaptation is driven by both the tracking error which vanishes in finite time and the prediction error then the controller parameters prove to be exponentially convergent to the ideal values provided that the reference signal is sufficiently persistently exciting

mean shift is a bound optimization we build on the current understanding of mean shift as an optimization procedure we demonstrate that in the case of piecewise constant kernels mean shift is equivalent to newton s method further we prove that for all kernels the mean shift procedure is a quadratic bound maximization

paper an approach to stable indirect adaptive control stable indirect adaptive control of minimum and nonminimum phase plants is established for cases where a priori bounds on the unknown plant parameters are known and where for each set of parameter values within these bounds the plant has no unstable pole zero cancellation by incorporating this partial parameter knowledge in the adaptive law and using a nonminimal representation of the plant it is shown that the adaptive closed loop control system can be written as an exponentially stable system driven by the identification error the stability of the adaptive control system is then shown using techniques similar to those known from the model reference adaptive control approach

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

bayesian constrained local models revisited this paper presents a novel bayesian formulation for aligning faces in unseen images our approach revisits the constrained local models clm formulation where an ensemble of local feature detectors are constrained to lie within the subspace spanned by a point distribution model pdm fitting such a model to an image typically involves two main steps a local search using a detector obtaining response maps for each landmark likelihood term and a global optimization that finds the pdm parameters that jointly maximize all the detections at once the so called global optimization can be posed as a bayesian inference problem where the posterior distribution of the shape and pose parameters can be inferred in a maximum a posteriori map sense this work introduces an extended bayesian global optimization strategy that includes two novel additions 1 to perform second order updates of the pdm parameters accounting for their covariance and 2 to model the underlying dynamics of the shape variations encoded in the prior term by using recursive bayesian estimation extensive evaluations were performed against state of the art methods on several standard datasets imm bioid xm2vts lfw and fgnet talking face results show that the proposed approach significantly increases the fitting performance

combinatorics of h primes in quantum matrices abstract for q c transcendental over q we give an algorithmic construction of an order isomorphism between the set of h primes of o q m n c and the sub poset s of the reverse bruhat order of the symmetric group s 2 n consisting of those permutations that move any integer by no more than n positions further we describe the permutations that correspond via this bijection to rank t h primes more precisely we establish the following result imagine that there is a barrier between positions n and n 1 then a 2n permutation s corresponds to a rank t h invariant prime ideal of o q m n c if and only if the number of integers that are moved by from the right to the left of this barrier is exactly n t the existence of such an order isomorphism was conjectured by goodearl and lenagan

winding invariant prime ideals in quantum 3 3 matrices abstract a complete determination of the prime ideals invariant under winding automorphisms in the generic 3 3 quantum matrix algebra o q m 3 k is obtained explicit generating sets consisting of quantum minors are given for all of these primes thus verifying a general conjecture in the 3 3 case the result relies heavily on certain tensor product decompositions for winding invariant prime ideals developed in an accompanying paper in addition new methods are developed here which show that certain sets of quantum minors not previously manageable generate prime ideals in o q m n k

the frt construction via quantum affine algebras and smash products abstract for every element w in the weyl group of a simple lie algebra g de concini kac and procesi defined a subalgebra u q w of the quantized universal enveloping algebra u q g the algebra u q w is a deformation of the universal enveloping algebra u n w n we construct smash products of certain finite type de concini kac procesi algebras to obtain ones of affine type we have analogous constructions in types a n and d n we show that the multiplication in the affine type de concini kac procesi algebras arising from this smash product construction can be twisted by a cocycle to produce certain subalgebras related to the corresponding faddeev reshetikhin takhtajan bialgebras

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

paper a perspective on convergence of adaptive control algorithms this paper presents an overview of the current status of convergence theory for adaptive control algorithms rather than giving a comprehensive survey the paper aims to emphasize the conceptual common ground between different approaches possible areas for future research are also discussed

simulated annealing for convex optimization we apply the method known as simulated annealing to the following problem in convex optimization minimize a linear function over an arbitrary convex set where the convex set is specified only by a membership oracle using distributions from the boltzmann gibbs family leads to an algorithm that needs only o n phases for instances in rn this gives an optimization algorithm that makes o n4 5 calls to the membership oracle in the worst case compared to the previous best guarantee of o n5 the benefits of using annealing here are surprising because such problems have no local minima that are not also global minima hence we conclude that one of the advantages of simulated annealing in addition to avoiding poor local minima is that in these problems it converges faster to the minima that it finds we also give a proof that under certain general conditions the boltzmann gibbs distributions are optimal for annealing on these convex problems

on the control of linear systems whose coefficients are functions of parameters the stabilization and regulation of linear discrete time systems whose coefficients depend on one or more parameters is studied for linear systems whose coefficients are continuous functions of real or complex parameters respectively analytic or rational functions of real parameters it is shown that reachability of the system for all values of the parameters implies that the system can be stabilized using gains that are also continuous analytic rational functions of the parameters closed form expressions for a collection of stabilizing gains are given in terms of the reachability gramian for systems which are stabilizable for all values of the parameters it is shown that continuous analytic rational stabilizing gains can be computed from a finite time solution to a riccati difference equation whose coefficients are functions of the parameters these results are then applied to the problem of tracking and disturbance rejection in the case when both the plant and the exogenous signals contain parameters

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

adaptive control for systems with bounded disturbances the authors present an identification algorithm that can be used to design globally stable indirect adaptive controllers for minimum and nonminimum phase systems subject to bounded disturbances the parameter estimation scheme is a least squares algorithm with dead zone the dead zone is such that the estimates converge and make it possible to define projected estimates having the same convergence properties as the original estimates in the minimum phase case the projection facility can be used to ensure that the leading coefficient projected estimate is greater than or equal to the true leading coefficient in absolute value the projection procedure can also be used to avoid pole zero cancellations in an adaptive pole placement algorithm

a brief survey of bandwidth selection for density estimation abstract there has been major progress in recent years in data based bandwidth selection for kernel density estimation some second generation methods including plug in and smoothed bootstrap techniques have been developed that are far superior to well known first generation methods such as rules of thumb least squares cross validation and biased cross validation we recommend a solve the equation plug in bandwidth selector as being most reliable in terms of overall performance this article is intended to provide easy accessibility to the main ideas for nonexperts

an adaptive lq controller for non minimum phase systems abstract the paper studied the problem of the adaptive tracking of a reference signal by the output of any deterministic discrete siso linear system with unknown parameters an adaptive control scheme based on the lq control solution is proposed the stability of the resulting adaptively controlled system and conditions for a good tracking are studied several simulations illustrate the proposal

poisson structures on affine spaces and flag varieties ii the standard poisson structures on the flag varieties g p of a complex reductive algebraic group g are investigated it is shown that the orbits of symplectic leaves in g p under a fixed maximal torus of g are smooth irreducible locally closed subvarieties of g p isomorphic to intersections of dual schubert cells in the full flag variety g b of g and their zariski closures are explicitly computed two different proofs of the former result are presented the first is in the framework of poisson homogeneous spaces and the second one uses an idea of weak splittings of surjective poisson submersions based on the notion of poisson dirac submanifolds for a parabolic subgroup p with abelian unipotent radical in which case g p is a hermitian symmetric space of compact type it is shown that all orbits of the standard levi factor l of p on g p are complete poisson subvarieties which are quotients of l equipped with the standard poisson structure moreover it is proved that the poisson structure on g p vanishes at all special base points for the l orbits on g p constructed by richardson rohrle and steinberg

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

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

global adaptive pole placement detailed analysis of a first order system this paper studies a deterministic adaptive pole positioning problem for a linear first order system the principal contribution is to specify an adaptive control law which secures global convergence the key conditions required are that an externally available plant input be persistently exciting and that an underbound not necessarily tight be known on the magnitude of the input coupling gain the pattern of the solution to the problem can carry over to high order systems

conditional filters for image sequence based tracking application to point tracking a new conditional formulation of classical filtering methods is proposed this formulation is dedicated to image sequence based tracking these conditional filters allow solving systems whose measurements and state equation are estimated from the image data in particular the model that is considered for point tracking combines a state equation relying on the optical flow constraint and measurements provided by a matching technique based on this two point trackers are derived the first one is a linear tracker well suited to image sequences exhibiting global dominant motion this filter is determined through the use of a new estimator called the conditional linear minimum variance estimator the second one is a nonlinear tracker implemented from a conditional particle filter it allows tracking of points whose motion may be only locally described these conditional trackers significantly improve results in some general situations in particular they allow for dealing with noisy sequences abrupt changes of trajectories occlusions and cluttered background

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

on the necessity of block invariance for the convergence of adaptive pole placement algorithm with persistently exciting input global convergence of a number of discrete time adaptive control algorithms with persistently exciting inputs has been established in the literature a key element of the convergence proof is the block invariance feature of the algorithm while the parameters are estimated at every sample the controller parameters remain invariant throughout a block of samples and are updated only at the end of each such block the necessity of this block invariance feature for guaranteeing convergence is established here by a counterexample

robust adaptive control of discrete time systems using persistent excitation abstract an important result in the robust adaptive control of continuous time systems using the persistent excitation of the reference input was recently given by narendra and annaswamy 1986 ieee trans aut control ac 31 306 315 according to this result the global boundedness of all the signals in the adaptive system can be assured if the degree of persistent excitation of the reference input is larger than an appropriate bound on the external disturbance the main theorem in narendra and annaswamy 1986 is proved for a class of plants characterized by the property that the reference model used in the adaptive controller could be chosen to be strictly positive real a condition which involves constraints on the relative degree of the plant this paper presents a generalization of the above result to plants of arbitrary relative degree together with the work reported in the earlier paper it demonstrates that the boundedness of all the signals in an adaptive system in the presence of bounded disturbances and arbitrary initial conditions can be assured by increasing the degree of persistent excitation of the reference input

fast global kernel density mode seeking applications to localization and tracking tracking objects in video using the mean shift ms technique has been the subject of considerable attention in this work we aim to remedy one of its shortcomings ms like other gradient ascent optimization methods is designed to find local modes in many situations however we seek the global mode of a density function the standard ms tracker assumes that the initialization point falls within the basin of attraction of the desired mode when tracking objects in video this assumption may not hold particularly when the target s displacement between successive frames is large in this case the local and global modes do not correspond and the tracker is likely to fail a novel multibandwidth ms procedure is proposed which converges to the global mode of the density function regardless of the initialization point we term the procedure annealed ms as it shares similarities with the annealed importance sampling procedure the bandwidth of the procedure plays the same role as the temperature in conventional annealing we observe that an over smoothed density function with a sufficiently large bandwidth is unimodal using a continuation principle the influence of the global peak in the density function is introduced gradually in this way the global maximum is more reliably located since it is imperative that the computational complexity is minimal for real time applications such as visual tracking we also propose an accelerated version of the algorithm this significantly decreases the number of iterations required to achieve convergence we show on various data sets that the proposed algorithm offers considerable promise in reliably and rapidly finding the true object location when initialized from a distant point

a semi infinite horizon lq self tuning regulator for armax plants based on rls so far no extension of the celebrated self tuning property of the rls gmv adaptive controller is available for the steady state lq stochastic control the above extension is addressed in the paper namely we pose the question is it possible to adaptively get the semi infinite horizon lq stochastic control for any armax plant by using a finite number of predictors whose parameters are estimated by standard rls an adaptive control algorithm solving an underlying control problem that coincides with the semi infinite lq stochastic feedback is developed it embodies a standard rls separate identification of the parameters of t n 1 predictors of the joint i o process n being the order of the armax plant together with an appropriate control synthesis rule the proposed algorithm turns out to be a slightly modified version of musmar with the capability of turning itself to the semi infinite horizon lq stochastic regulator

adaptive control of a class of discrete time mimo nonlinear systems with uncertain couplings in this article adaptive control is investigated for a class of discrete time multi input multi output nonlinear systems in block triangular form with uncertain couplings of delayed states among subsystems future states prediction is carried out to facilitate adaptive control design and auxiliary outputs are introduced to develop a novel compensation mechanism for the uncertain nonlinear couplings by using lyapunov method and ordering signals growth rate it is rigorously proved that all the signals in the whole closed loop systems are globally bounded and the output tracking errors asymptotically converge to zeros the effectiveness of the proposed control is demonstrated in the simulation study

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

robust stable pole placement adaptive control of linear systems with multiestimation this paper is concerned with a robust pole placement based adaptive control of continuous linear systems in the presence of bounded noise and a common class of unmodeled dynamics with the use of multiple estimation schemes working in parallel the multiestimation scheme consists of the above set of various single estimation schemes while being a tool used to minimize the plant identification error by building an estimate which is a convex combination of the estimates at all time the weighting functions of the individual estimates are provided at each time by a suboptimization scheme for a quadratic loss function the robust stability of the overall adaptive scheme is ensured by an adaptation relative dead zone which takes into account the contribution of the unmodeled dynamics and bounded noise

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