paper nonlinear adaptive model following control the use of discontinuous control in adaptive model following continuous control systems with nonlinear time varying plant is described the first approach is based on the theory of variable structure systems hyperstability theory is the basis of the second scheme the third one results by combining the previous approaches the link among the three approaches is explored by studying the error dynamics practical implementation and applications are discussed

on simple scheme of finite fixed time control design control laws are designed for stabilisation of a chain of integrators of arbitrary degree in finite and fixed time presented control laws are obtained with use of lyapunov function method and homo

design of variable structure controllers with continuous switching control a modified variable structure controller is proposed to deal with the conirol chattering problem which is one of the major difficulties for implementing the variable structure control vsc the new control strategy is effective for a class of uncertain nonlinear dynamical systems based on a suitably designed sliding sector a continuous switching controller whose control structure is switched whereas the control signal at switching remains continuous is constructed the complete attractiveness and the stability properties of the sliding sector in the sense of lyapunov stability ensure the retention of benefits achieved with the conventional vsc some typical examples are also investigated which show the improvement of system performance

brief paper output feedback variable structure control design with an h2 performance bound constraint in this paper we give an lmi based method for designing an output feedback variable structure control vsc system with an h 2 constraint the uncertain system model under consideration may have nonmatching disturbance input signals nonmatching disturbance input signal reduction is performed via h 2 norm minimization in terms of a constrained riccati inequality we give a sufficient condition for the existence of a linear sliding surface and a compensator guaranteeing an h 2 constraint and we show that the control parameters can be characterized by using the solution to the given inequality condition we also give a simple lmi based design algorithm of an output feedback vsc law guaranteeing an h 2 constraint finally by using a design example we show that our method can supplement the existing results

moving switching surfaces for robust control of second order variable structure systems abstract most of the switching surfaces proposed so far for a variable structure control system vscs have been determined independently of initial conditions the vscs with these typical switching surfaces may be sensitive to parameter variations and extraneous disturbances during the reaching phase to overcome this drawback we propose a new switching surface which is initially designed to pass arbitrary initial conditions and subsequently move towards a predetermined switching surface by rotating or and shifting we call it a moving switching surface mss using the mss a low sensitivity system is obtained through shortening the reaching phase furthermore the system robustness is guaranteed during whole intervals of control action by eliminating the reaching phase to illustrate the advantages of the proposed method a simple second order linear system subjected to external disturbance is considered as a preliminary example followed by a two link manipulator

on the stability of discrete time sliding mode control systems the stability of discrete time sliding mode control systems is investigated and a new sliding mode condition is suggested it is shown that the control must have upper and lower bounds a numerical example is discussed as an illustration

pullbacks of saito kurokawa lifts pullbacks of siegel eisenstein series have been studied by garrett 17 18 bocherer 6 7 heim 26 and play a key role in the proof of the algebraicity of critical values of certain automorphic l functions more generally one might consider pullbacks of siegel cusp forms for example ikeda 30 gave a conjectural formula for pullbacks of ikeda lifts 29 in terms of critical values of l functions for spn gl2 also the gross prasad conjecture 22 23 8 27 8 would relate pullbacks of siegel cusp forms of degree 2 to central critical values of l functions for gsp2 gl2 gl2 indeed bocherer furusawa and schulze pillot 8 gave an explicit formula for pullbacks of yoshida lifts 57 in this paper we give an explicit formula for pullbacks of saito kurokawa lifts and prove the algebraicity of central critical values of certain l functions for sp1 gl2 to be precise let be an odd positive integer let f s2 sl2 z be a normalized hecke eigenform and h s 1 2 0 4 a hecke eigenform associated to f by the shimura correspondence let f s 1 sp2 z be the saito kurokawa lift of h for each normalized hecke eigenform g s 1 sl2 z we consider the period integral f h h g g given by f h h g g

on the gamma factor of the triple l function i introduction the study of the triple l function began with garrett 2 from a representation theoretic point of view piatetski shapiro and rallis 9 and the author 6 defined the archimedean or nonarchimedean l factor as the greatest common divisor gcd of local integrals the purpose of this paper is to prove that the archimedean gcd l factor agrees with the expected l factor up to invertible functions if the local representation comes from a cuspidal automorphic representation this theorem follows from the local functional equation by formal argument except when the representation is unramified to treat the unramified case we carry out the explicit calculation of the unramified local integral stimulated by stade 12 we make use of a hypergeometric function 3f2 and its two term relations and three term relation we also need a theorem on some infinite integral involving bessel functions proved by bailey 1 in 1936 the key lemma is the following see lemma 2 4

on tracking control for affine nonlinear systems by sliding mode abstract the stability problem of output tracking of a bounded time varying reference by decouplable affine nonlinear systems using sliding mode control is investigated it is shown that when the error dynamics on the sliding surface is chosen to be linear time invariant closed loop stability of systems under the presented sliding mode control can be guaranteed only if the systems are minimum phase

analysis and design of variable structure systems using a geometric approach multivariable variable structure systems in the sliding mode are studies using a geometric approach the properties of system order reduction and disturbance rejection are proved using projector theory new design methods for the choice of switching hyperplanes are derived for the closed loop eigenvalue eigenvector assignment problem

sliding order and sliding accuracy in sliding mode control the synthesis of a control algorithm that stirs a nonlinear system to a given manifold and keeps it within this constraint is considered usually what is called sliding mode is employed in such synthesis this sliding mode is characterized in practice by a high frequency switching of the control it turns out that the deviation of the system from its prescribed constraints sliding accuracy is proportional to the switching time delay a new class of sliding modes and algorithms is presented and the concept of sliding mode order is introduced these algorithms feature a bounded control continuously depending on time with discontinuities only in the control derivative it is also shown that the sliding accuracy is proportional to the square of the switching time delay

variable structure robust control of uncertain time delay systems abstract this paper introduces a variable structure output feedback robust control for uncertain time delay systems new types of switching manifolds with integral terms are implemented to consider larger class of linear systems by overcoming both the observability constraints of the reduced order system and the kimura davison condition two types of control laws are introduced by which an estimate of a region of asymptotic stability to the origin and a region of attraction to the switching manifold are defined

reconstructing sliding surfaces for siso variable structure output feedback control systems using inverse method there exists a dynamic mapping relationship between the sliding variable and the output variable in a linear time invariant lti single input single output siso system this relationship is invariant of the matched disturbances which lies in the control space in this note a continuous time dynamic inverse compensator is proposed to reconstruct the sliding variable from the system output this inverse compensator is stable and causal provided that the original siso system is minimum phase and that the input output relative degree is less than or equal to one in case the system relative degree is greater than one a digital approximation for the inverse compensator is introduced to track the sliding variable in discrete time to the accuracy of o t where t is the sampling period thus the discrete time variable structure control vsc law can be implemented without full state accessibility

continuous state feedback guaranteeing uniform ultimate boundedness for uncertain dynamic systems we consider a dynamic system containing uncertain elements only the set of possible values of these uncertainties is known based on this information a class of state feedback controls is proposed in order to guarantee uniform ultimate boundedness of every system response within an arbitrarily small neighborhood of the zero state these feedback controls are continuous functions of the state

a new method of switching surface design for multivariable variable structure systems in this paper we discuss the problem of the switching surface for a multivariable variable structure system we first propose a new switching surface by which robustness of the controlled system to disturbances is provided based on the switching surface we develop control input to drive the system to track the desired trajectory this control input does not produce the chattering that normally occurs when a conventional control input is used we apply the proposed method to a multivariable linear system and discuss the simulation results to show the computational procedure and its effectiveness

on maass lifts and the central critical values of triple product l functions we express certain period integrals of maass lifts which appear in the gross prasad conjecture in terms of the central critical values of triple product l functions in the imbalanced case

dynamic output integral sliding mode control with disturbance attenuation this technical note proposes a dynamic output feedback sliding mode control algorithm for linear mimo systems with mismatched norm bounded uncertainties along with disturbances and matched nonlinear perturbations a control law is first designed to ensure that the system behavior can satisfy the reaching and sliding condition a scheme designed to combine the output dependent integral sliding surface with a full order compensator is then proposed through utilizing h infin control analytical technique once the system is in the sliding mode the proposed algorithm can guarantee robust stabilization and sustain the nature of performing disturbance attenuation when the solutions to two algebraic riccati inequalities can be found finally the feasibility of our proposed algorithm is illustrated using a numerical example

higher accuracy output feedback sliding mode control of sampled data systems the problem of output feedback sliding mode control for sampled data systems in the presence of external disturbances is considered the proposed output feedback control strategy helps obtain a quasi sliding mode with an o t 3 boundary layer where t is the sampling period this outperforms the o t 2 result induced by the one step delayed disturbance approximation method the proposed scheme is applicable to linear systems which are relative degree one and minimum phase an example is given to illustrate the efficacy of the new method

estimation of sliding mode domains of uncertain variable structure systems with bounded controllers the problem of estimating regions of asymptotic stability ras of uncertain dynamical systems with bounded controllers and the sliding model requirement is discussed the notion of combining different lyapunov functions is utilized different lyapunov functions are found and for each lyapunov function an estimate of the ras is found different regions are combined in order to find an improved ras the combined region is not in general a convex region and cannot be found analytically by using just a single lyapunov function a class of uncertain linear time invariant multivariable control systems is considered and a transformation for decoupling the system into two subsystems is used the transformation simplifies the ras estimation problem stability domains are estimated for a linear variable structure control system with sliding mode performance in the case of a discontinuous bounded controller

decentralized variable structure control for tracking in non linear systems the problem of tracking time varying trajectories in non linear systems is considered these trajectories could be generated on line by a reference model the problem is tackled by considering the overall system as a set of decentralized linear sub systems which can be modelled as a set of double integrators and treating the non linearities as uncertainties with known bounds on their magnitudes a variable structure controller is designed based on the theory of uncertain dynamical systems the system is shown to track a class of trajectories generated by the reference mode a set of double integrators to within a specified tolerance some analysis is presented to explain the dynamic behaviour of the closed loop system and bounds are derived linking the rate of convergence and the tracking ability to system parameters such as available control and magnitude of the uncertainty simulation results are presented to validate the conclusions

the sparse matrix transform for covariance estimation and analysis of high dimensional signals covariance estimation for high dimensional signals is a classically difficult problem in statistical signal analysis and machine learning in this paper we propose a maximum likelihood ml approach to covariance estimation which employs a novel non linear sparsity constraint more specifically the covariance is constrained to have an eigen decomposition which can be represented as a sparse matrix transform smt the smt is formed by a product of pairwise coordinate rotations known as givens rotations using this framework the covariance can be efficiently estimated using greedy optimization of the log likelihood function and the number of givens rotations can be efficiently computed using a cross validation procedure the resulting estimator is generally positive definite and well conditioned even when the sample size is limited experiments on a combination of simulated data standard hyperspectral data and face image sets show that the smt based covariance estimates are consistently more accurate than both traditional shrinkage estimates and recently proposed graphical lasso estimates for a variety of different classes and sample sizes an important property of the new covariance estimate is that it naturally yields a fast implementation of the estimated eigen transformation using the smt representation in fact the smt can be viewed as a generalization of the classical fast fourier transform fft in that it uses butterflies to represent an orthonormal transform however unlike the fft the smt can be used for fast eigen signal analysis of general non stationary signals

bayesian estimation of karhunen loeve expansions a random subspace approach one of the most widely used procedures for dimensionality reduction of high dimensional data is principal component analysis pca more broadly low dimensional stochastic representation of random fields with finite variance is provided via the well known karhunen loeve expansion kle the kle is analogous to a fourier series expansion for a random process where the goal is to find an orthogonal transformation for the data such that the projection of the data onto this orthogonal subspace is optimal in the l 2 sense i e which minimizes the mean square error in practice this orthogonal transformation is determined by performing an svd singular value decomposition on the sample covariance matrix or on the data matrix itself sampling error is typically ignored when quantifying the principal components or equivalently basis functions of the kle furthermore it is exacerbated when the sample size is much smaller than the dimension of the random field in this paper we introduce a bayesian kle procedure allowing one to obtain a probabilistic model on the principal components which can account for inaccuracies due to limited sample size the probabilistic model is built via bayesian inference from which the posterior becomes the matrix bingham density over the space of orthonormal matrices we use a modified gibbs sampling procedure to sample on this space and then build probabilistic karhunen loeve expansions over random subspaces to obtain a set of low dimensional surrogates of the stochastic process we illustrate this probabilistic procedure with a finite dimensional stochastic process inspired by brownian motion

eigenvalue placement in a specified sector for variable structure control systems the design of the sliding hyperplanes of a variable structure control system is an important part of the controller design process and will be considered in this paper the method outlined here results in the eigenvalues of the closed loop system during sliding lying in a specified sector in the left hand half plane numerical examples are given and the effect of an arbitrary positive definite matrix in a complex riccati equation on the positioning of the eigenvalues within the sector is investigated

stable robust tracking by sliding mode control sliding mode control is examined from the perspective of obtaining stable and robust tracking of an arbitrary time varying reference by a multi input output linear time invariant system driven by a certain class of bounded errors nonlinearities and disturbances most existing schemes for such systems are subsumed by the one presented here the results are developed via the use of inverse models and make clear the constraints imposed by the finite and infinite zero structure of the system in particular stable and robust tracking is shown to be obtained by the scheme in this paper if and only if the system is minimum phase

computation of the zeros and zero directions of linear multivariable systems a new geometric method of calculating multivariable system zeros and zero directions is presented by considering a particular choice of state feedback control law this control law has been motivated by the study of variable structure systems in the sliding mode the cases of singular and non singular cb have been treated separately

an ilmi approach to robust static output feedback sliding mode control this paper proposes a systematic methodology for designing robust static output feedback sliding mode control sofsmc for a class of systems with mismatched uncertainties this methodology consists of two parts one is a new sufficient and necessary condition for the existence problem in terms of two matrix inequalities the other is a direct solving method using the iterative linear matrix inequality ilmi technique the main advantages of this method are that only original system parameters are involved without any extra coordinate changes and that appealing to solving the static output feedback stabilization sofs problem is no longer required in addition the ilmi algorithm includes an optimal part to avoid high control efforts a numerical example also demonstrates the efficacy of the proposed approach

a variable structure approach to feedback regulation of uncertain dynamical systems feedback control of uncertain dynamical systems is considered adopting a deterministic approach based on the theory of variable structure systems a feedback regulator is developed which guarantees global asymptotic stability or global ultimate boundedness under certain hypotheses on the bounded system uncertainties and disturbances

a modified variable structure controller abstract it has long been known that one of the difficulties with the conventional variable structure systems vss design is the chattering problem in this paper a modified variable structure controller vsc is proposed to alleviate this problem at the same time retaining the benefits achieved in conventional vss design namely fast response good robustness and disturbance rejection

a stabilized pod model for turbulent flows over a range of reynolds numbers optimal parameter sampling and constrained projection abstract we present a reduced basis technique for long time integration of parametrized incompressible turbulent flows the new contributions are threefold first we propose a constrained galerkin formulation that corrects the standard galerkin statement by incorporating prior information about the long time attractor for explicit and semi implicit time discretizations our statement reads as a constrained quadratic programming problem where the objective function is the euclidean norm of the error in the reduced galerkin algebraic formulation while the constraints correspond to bounds for the maximum and minimum value of the coefficients of the n term expansion second we propose an a posteriori error indicator which corresponds to the dual norm of the residual associated with the time averaged momentum equation we demonstrate that the error indicator is highly correlated with the error in mean flow prediction and can be efficiently computed through an offline online strategy third we propose a greedy algorithm for the construction of an approximation space procedure valid over a range of parameters the greedy is informed by the a posteriori error indicator developed in this paper we illustrate our approach and we demonstrate its effectiveness by studying the dependence of a two dimensional turbulent lid driven cavity flow on the reynolds number

output feedback sliding mode control for sampled data systems we address the output feedback sliding mode control problem for a sampled data linear system with external disturbances of the matching type by taking into account the disturbance compensation a deadbeat high gain output feedback control strategy with additional dynamics is able to attenuate the disturbances in the framework of singular perturbation analysis it is shown that the closed loop system exhibits good robustness against exogenous disturbances

sliding surface design for discrete vss using lqr technique with a preset real eigenvalue abstract this paper presents an lqr based sliding surface design procedure that allows one to specify a desired weighting matrix and a desired real eigenvalue which is important in discrete vss the procedure computes a weighting matrix that simultaneously stays closest to the desired one and yields the desired eigenvalue sliding surface is then determined from the lqr gain matrix and the desired eigenvalue it is shown that feasible weighting matrices almost always exist and are not unique moreover the underlying constrained optimization problem is convex and least squares method may be used to simplify or solve the problem the paper ends with two numerical examples that illustrate the design procedure

dynamic output feedback variable structure control for system stabilization simplex type dynamic output feedback variable structure control for stabilizing multivariable linear time invariant plants is analysed two types of controllers are considered a compensator type and an observer type it is shown that while the compensator type controller stabilizes the plant only if the plant is minimum phase the observer type controller does not face the same restriction the design of low order less than the order of the plant observer type controllers is also considered

output feedback variable structure control design this paper describes a procedure for variable structure output feedback control vsofc for a class of multivariable linear time invariant systems the equivalent control method of utkin in the output feedback mode yields a reduced order system exhibiting output feedback equivalent dynamics using the kimura davison sufficient conditions for pole placement using output feedback a sufficient condition is derived to assign the eigenvalues of the reduced order system the observability and controllability of the reduced system is discussed two switching surface design algorithms are introduced based on both a static output feedback and on an eigenstructure assignment techniques a control design is discussed as well

spectral representation and reduced order modeling of the dynamics of stochastic reaction networks via adaptive data partitioning dynamical analysis tools are well established for deterministic models however for many biochemical phenomena in cells the molecule count is low leading to stochastic behavior that causes deterministic macroscale reaction models to fail the main mathematical framework representing these phenomena is based on jump markov processes that model the underlying stochastic reaction network conventional dynamical analysis tools do not readily generalize to the stochastic setting due to nondifferentiability and absence of explicit state evolution equations we developed a reduced order methodology for dynamical analysis that relies on the karhunen loeve decomposition and polynomial chaos expansions the methodology relies on adaptive data partitioning to obtain an accurate representation of the stochastic process especially in the case of multimodal behavior as a result a mixture model is obtained that represents the reduced order dynamics of the system the schlogl model is used as a prototype bistable process that exhibits time scale separation and leads to multimodality in the reduced order model

robust hyperplane design in multivariable variable structure control systems the problem of designing a stable sliding mode giving robust performance of a variable structure control system is studied a set of specified eigenvalues is assigned to the closed loop feedback system during the sliding mode the design philosophy seeks to build on the known robustness and invariance properties associated with the use of discontinuous or continuous non linear controls by assigning the eigenvectors associated with the sliding mode eigenvalues in a manner that leads to a robust control scheme a previously developed canonical form for the hyperplane design problem is again employed the design technique centres on a recently published eigenvalue assignment algorithm and is illustrated by the inclusion of an example

doubling constructions and tensor product l functions the linear case we present an integral representation for the tensor product l function of a pair of automorphic cuspidal representations one of a classical group the other of a general linear group our construction is uniform over all classical groups and is applicable to all cuspidal representations it does not require genericity the main new ideas of the construction are the use of generalized speh representations as inducing data for the eisenstein series and the introduction of a new global and local model which generalizes the whittaker model here we consider linear groups but our construction also extends to arbitrary degree metaplectic coverings this will be the topic of an upcoming work

an lmi based switching surface design method for a class of mismatched uncertain systems in this note we consider the problem of designing linear sliding surfaces for multivariable uncertain systems with mismatched uncertainties in the state matrix in terms of linear matrix inequalities we give a new invariance condition guaranteeing the existence of a linear switching surface such that the reduced order equivalent sliding mode dynamics restricted to the switching surface is not only stable but completely invariant to mismatched uncertainties we also give an explicit formula of such linear switching surfaces together with a design example

robust control of linear discrete time systems abstract given a linear discrete time system with additive disturbances a general methodology for designing a stable control algorithm is shown the approach is lyapunov based with certain liberty of tailoring the candidate function for a given problem comparison to the existing solutions based on a variable structure approach is given

new methods to design an integral variable structure controller this paper presents two methods to design a single input single output integral variable structure system once an overall transfer function is selected two simple ways are presented to determine the required switching surface and the control function the proposed methods not only avoid transforming the original plant into a companion form but also enable the resulting control system to achieve the asymptotic tracking for a step reference signal and disturbance rejection for a bounded disturbance signal simultaneously two examples are given to illustrate the effectiveness of the proposed methods

constructing discontinuity surfaces for variable structure systems a lyapunov approach the problem of constructing discontinuity surfaces in variable structure systems is studied from a lyapunov point of view a switching surface determined by the control coefficient matrix and the associated lyapunov function is able to ensure asymptotic stability for the system in sliding mode the proposed method may also be used for systems with nonlinear dynamics and for linear systems with delays

sliding mode design via quadratic performance optimization with pole clustering constraint we consider a novel method for designing the sliding mode that minimizes the quadratic performance while keeping a pole clustering constraint our approach is based on the manipulations of linear matrix inequalities lmis imposed by the design objectives for this purpose we newly propose lmi conditions for the quadratic performance optimization and the pole clustering problem respectively in a full order state then they are combined in the lmi framework that is typically devised for the sliding mode design in the convex form an effort is made to reduce the generic conservatism by allowing different lyapunov matrices in addition a class of polytope uncertain systems is addressed to illustrate the advantages of the proposed method

choice of discontinuous control component for robust sliding mode performance the robustness properties of sliding mode behaviour are considered in terms of the choice of non linear control structure the performance of two classes of variable structure controllers in the presence of unmatched uncertainty is discussed criteria for suitable choice of a non linear control structure are presented and the concept of a performance sliding mode is introduced a numerical example is given to illustrate the phenomenon described

h sub 2 guaranteed cost switching surface design for sliding modes with nonmatching disturbances this paper presents an extension of utkin and yang s method 1978 for sliding surface design via the minimization of a quadratic performance criterion the method proposed takes into account nonmatching disturbance signals and nonmatching system model uncertainties an upper bound for the h sub 2 norm of the disturbance to output transfer function is minimized leading to a guaranteed cost h sub 2 controller

min max sliding mode control for multimodel linear time varying systems an original linear time varying system with unmatched disturbances and uncertainties is replaced by a finite set of dynamic models such that each one describes a particular uncertain case including exact realizations of possible dynamic equations as well as external bounded disturbances such a tradeoff between an original uncertain linear time varying dynamic system and a corresponding higher order multimodel system with a complete knowledge leads to a linear multi model system with known bounded disturbances each model from a given finite set is characterized by a quadratic performance index the developed min max sliding mode control strategy gives an optimal robust sliding surface design algorithm which is reduced to a solution of an equivalent linear quadratic problem that corresponds to the weighted performance indices with weights from a finite dimensional simplex an illustrative numerical example is presented

probabilistic principal component analysis principal component analysis pca is a ubiquitous technique for data analysis and processing but one which is not based upon a probability model in this paper we demonstrate how the principal axes of a set of observed data vectors may be determined through maximum likelihood estimation of parameters in a latent variable model closely related to factor analysis we consider the properties of the associated likelihood function giving an em algorithm for estimating the principal subspace iteratively and discuss the advantages conveyed by the definition of a probability density function for pca

a variable structure control with simple adaptation laws for upper bounds on the norm of the uncertainties in deterministic design of feedback controllers for uncertain dynamical systems upper bounds on the norm of the uncertainties are an important clue to guarantee the stability of the closed loop system sometimes however these upper bounds may not be easily obtained because of the complexity of structure of the uncertainties simple adaptation laws for upper bounds on the norm of the uncertainties are proposed and these adaptive upper bounds are used to design a variable structure control system that guarantees the asymptotic stability of uncertain dynamical systems

on ultimate boundedness control of uncertain systems in the absence of matching assumptions this paper describes an approach to ultimate boundedness control under hypotheses less stringent than heretofore required instead of imposing the so called matching conditions of previous authors a certain decomposition of the dynamics is performed the resulting decomposed system has two parts a matched portion and a mismatched portion a certain measure of mismatch m is defined and it is shown that effective control is possible as long as m does not exceed some critical mismatch threshold m it is seen that this threshold depends on the choice of feedback hence it becomes possible to investigate the tradeoffs between the size of the mismatch threshold and the sizes of the feedback gains which achieve the desired ultimate boundedness of solutions

singular perturbations and time scale methods in control theory survey 1976 1983 recent progress in the use of singular perturbation and two time scale methods of modeling and design for control systems is reviewed over 350 references are organized into major problem areas representative issues and results are discussed with a view to outlining research directions and indicating potential areas of application the survey is aimed at engineers and applied mathematicians interested in model order reduction separation of time scales and allied simplified methods of control system analysis and design the exposition does not assume prior knowledge of singular perturbation methods