on stabilization for discrete linear time varying systems abstract in this paper we consider the stabilization problem for discrete linear time varying systems in an operator theoretic framework by using the complete finiteness of a certain discrete nest algebra we show that a system is stabilizable if and only if it has one kind of strong representation and we also give a parametrization for all the stabilizing controllers in terms of this strong representation this result extends the youla parametrization theorem by only requiring a strong left or a strong right representation but not both the strong stabilization problem is also discussed

discovering multi label temporal patterns in sequence databases sequential pattern mining is one of the most important data mining techniques previous research on mining sequential patterns discovered patterns from point based event data interval based event data and hybrid event data in many real life applications however an event may involve many statuses it might not occur only at one certain point in time or over a period of time in this work we propose a generalized representation of temporal events we treat events as multi label events with many statuses and introduce an algorithm called mltpm to discover multi label temporal patterns from temporal databases the experimental results show that the efficiency and scalability of the mltpm algorithm are satisfactory we also discuss interesting multi label temporal patterns discovered when mltpm was applied to historical nasdaq data

stabilization of navier stokes equations by oblique boundary feedback controllers one designs a linear stabilizing boundary feedback controller u for the equilibrium solutions to navier stokes system on a bounded and open domain mathcal o subset mathbb r d d 2 u eta mbox 1 mathrml gamma displaystyle sum nolimits n j 1 mu j left phi j x alpha x vec n x where gamma is a connected component of the boundary partial mathcal o and mbox 1 mathrml gamma is the characteristic function of gamma here phi j are related to the eigenfunction system varphi j for the adjoint stokes oseen system vec n is the normal to partial mathcal o left is the scalar product in l 2 mathcal o d and alpha is an arbitrary c 2 function with circulation zero on partial mathcal o for d 2 3 this controller stabilizes the corresponding linearized oseen stokes system

internal exponential stabilization to a nonstationary solution for 3d navier stokes equations we consider the navier stokes system in a bounded domain with a smooth boundary given a sufficiently regular time dependent global solution we construct a finite dimensional feedback control that is supported by a given open set and stabilizes the linearized equation the proof of this fact is based on a truncated observability inequality the regularizing property for the linearized equation and some standard techniques of the optimal control theory we then show that the control constructed for the linear problem stabilizes locally also the full navier stokes system

simultaneous controller design for time varying linear systems abstract in this paper we establish the parametrization of all simultaneously stabilizing controllers for two time varying linear systems a new approach to the simultaneous stabilization of three time varying linear systems is also provided

pod based feedback control of the burgers equation by solving the evolutionary hjb equation a new approach for solving finite time horizon feedback control problems for distributed parameter systems is proposed it is based on model reduction by proper orthogonal decomposition combined with efficient numerical methods for solving the resulting low order evolutionary hamilton jacobi bellman hjb equation the feasibility of the proposed methodology is demonstrated by means of optimal feedback control for the burgers equation the method for solving the hjb equation is first tested on several 1 d problems and then successfully applied to the control of the reduced order burgers equation the effect of noise is investigated and parallelism is used for computational speedup

on a general structure of the stabilizing controllers based on stable range in this paper we prove that some stabilizing controllers of a plant which admits a left right coprime factorization have a special form where their stable and unstable parts are separated the dimension of the unstable part depends on the algebraic concept of stable range of the ring a of siso stable plants moreover we prove that if the stable range of a is equal to 1 then every plant defined by a transfer matrix with entries in the quotient field of a and admitting a left right coprime factorization can be stabilized by a stable controller strong stabilization in particular using a result of treil proving that the stable range of h infty mathbb d is equal to 1 we show that every stabilizable plant defined by a transfer matrix with entries in the quotient field of h infty mathbb d or h infty mathbb c is strongly stabilizable and equivalently every couple of stabilizable plants can be simultaneously stabilized by a controller simultaneous stabilization finally using the fact that the topological stable range of h infty mathbb d is equal to 2 a result due to suarez we show that every unstabilizable siso plant defined by a transfer function with entries in the quotient field of h infty mathbb d is as close as we want to a stabilizable plant in the product topology

galerkin proper orthogonal decomposition methods for a general equation in fluid dynamics error estimates for galerkin proper orthogonal decomposition pod methods for nonlinear parabolic systems arising in fluid dynamics are proved for the time integration the backward euler scheme is considered the asymptotic estimates involve the singular values of the pod snapshot set and the grid structure of the time discretization as well as the snapshot locations

fast discovery of sequential patterns in large databases using effective time indexing sequential pattern mining algorithms can often produce more accurate results if they work with specific constraints in addition to the support threshold many systems implement time independent constraints by selecting qualified patterns this selection cannot implement time dependent constraints because the support computation process must validate the time attributes of every data sequence during mining therefore we propose a memory time indexing approach called metisp to discover sequential patterns with time constraints including minimum gap maximum gap exact gap sliding window and duration constraints metisp scans the database into memory and constructs time index sets for effective processing metisp uses index sets and a pattern growth strategy to mine patterns without generating any candidates or sub databases the index sets narrow down the search space to the sets of designated in memory data sequences and speed up the counting of potential items within the indicated ranges our comprehensive experiments show that metisp has better efficiency even with low support and large databases than the well known gsp and delisp algorithms metisp scales up linearly with respect to database size

local exact boundary controllability of 3d navier stokes equations abstract given a time dependent solution of the navier stokes equations and an arbitrary open subset of the boundary the existence of a boundary control supported in the given subset that drives the system to the given solution in finite time is proven null controllability of the oseen system is investigated as well and continuity results of the driving control on the initial data are derived

on the controllability of parabolic systems with a nonlinear term involving the state and the gradient we present some results concerning the controllability of a quasi linear parabolic equation with linear principal part in a bounded domain of mathbb r n with dirichlet boundary conditions we analyze the controllability problem with distributed controls supported on a small open subset and boundary controls supported on a small part of the boundary we prove that the system is null and approximately controllable at any time if the nonlinear term f y nabla y grows slower than y log 3 2 1 y nabla y nabla y log 1 2 1 y nabla y at infinity generally in this case in the absence of control blow up occurs the proofs use global carleman estimates parabolic regularity and the fixed point method

stabilizability and existence of system representations for discrete time time varying systems in this paper right and left representations as an alternate but equivalent framework to coprime factorizations of operators are developed the main theorem of the paper establishes that a linear time varying discrete time plant is stabilizable if and only if its graph can be represented as the range respectively kernel of a causal bounded operator which is left respectively right invertible the proof relies on certain factorization theorems of arveson for nest algebras the paper extends the youla parametrization of all stabilizing compensators to this framework also it is proven that a time invariant plant that is not stabilizable by a time invariant compensator is not stabilizable with a time varying compensator an example of a time varying plant of feintuch is considered and shown to be not stabilizable finally the continuous time case is examined and the problems encountered in extending the proof are discussed however it is shown that a stabilizable plant must have a closed graph

the linear regulator problem for parabolic systems we present an approximation framework for computation in finite dimensional spaces of riccati operators that can be guaranteed to converge to the riccati operator in feedback controls for abstract evolution systems in a hilbert space it is shown how these results may be used in the linear optimal regulator problem for a large class of parabolic systems

oblique projection local feedback stabilization of nonautonomous semilinear damped wave like equations abstract the stabilization of a class of nonlinear weakly damped wave equations by means of a finite dimensional feedback control is investigated the stabilizing control is constructed based on an appropriate oblique projection and it enters as a time dependent linear combination of a finite number of suitable indicator functions supported in small regions firstly it is shown that an oblique projection feedback is able to globally exponentially stabilize linear nonautonomous weakly damped wave equations then relying on this result the local stabilization for semilinear equations is proven for a suitable class of nonlinearities finally numerical experiments are given which validate the theoretical results

the stable rank of the algebra h equals 1 abstract it is proved that if the functions f g h f 1 g 1 satisfy the carleson corona condition z inf f z g z def o then there exists a function g h such that the fucntion f gg is invertible in h and moreover g c 1 c where the constant c depends only on

remarks on the internal exponential stabilization to a nonstationary solution for 1d burgers equations the feedback stabilization of the burgers system to a nonstationary solution using finite dimensional internal controls is considered estimates for the dimension of the controller are derived in the particular case of no constraint on the support of the control a better estimate is derived and the possibility of getting an analogous estimate for the general case is discussed some numerical examples are presented illustrating the stabilizing effect of the feedback control and suggesting that the existence of an estimate in the general case analogous to that in the particular one is plausible

boundary stabilisation to non stationary solutions for deterministic and stochastic parabolic type equations abstractin this work we design explicit finite dimensional boundary feedback laws for stabilisation to trajectories for parabolic type equations the simple form of the feedback allows to write the solution of the corresponding closed loop equation in a mild formulation via a kernel then taking advantage of this the stability is shown as an application null stabilisation for stochastic parabolic type equations is deduced as well as far as we know the present work is the first result on boundary feedback stabilisation to trajectories and for stochastic parabolic type equations with stability guaranteed independent of how large the level of the noise is

on a generalization of the youla kucera parametrization part i the fractional ideal approach to siso systems abstract in this paper we show how to use the theory of fractional ideals in order to study the fractional representation approach to analysis and synthesis problems for siso systems within this mathematical framework we give necessary and sufficient conditions so that a plant is internally strongly bistably stabilizable or admits a weak coprime factorization moreover we show how to generalize the youla kucera parametrization of the stabilizing controllers to any stabilizable plant which does not necessarily admit a coprime factorization this parametrization is generally affine in two free parameters

the stabilization problem for discrete time varying linear systems in this paper we consider the strong stabilization problem for a time varying linear system which admits a coprime factorization we also study the simultaneous and robust stabilization problems for this class of systems

simultaneously stabilising controllers for time varying linear systems within the framework of nest algebras abstractfrom the perspective of strong transitivity a controller design method is provided to simultaneously stabilise a collection of time varying linear systems within the framework of nest algebras in particular all simultaneously stabilising controllers for a class of linear plants are characterised based on the doubly coprime factorisations these results hold as well in the time invariant case an illustrative example is given to demonstrate the validity of the method

on the number of determining nodes for the 2d navier stokes equations abstract it is known that the solutions of the 2d navier stokes equations in bounded domains are determined by a finite discrete set of nodal values that is if the large time behavior of the solutions to the navier stokes equations is known on an appropriate finite discrete set then the large time behavior of the solution itself is totally determined here an upper bound is rigorously established for the number of nodes needed to determine the solutions of the navier stokes equations in two dimensions with periodic boundary conditions

transitivity in simultaneous stabilization for a family of time varying systems abstract this paper develops necessary and sufficient conditions for the so called transitivity and strong transitivity precise definitions later for a family of discrete time varying linear systems which when satisfied lead to characterizations for simultaneous stabilizability and simultaneously stabilizing feedback controllers some criteria for the strong transitivity are established in terms of single coprime factorizations of only one plant and one controller the resulting characterization involves coprime factorizations of fewer systems compared to previous work

stabilization of parabolic nonlinear systems with finite dimensional feedback or dynamical controllers application to the navier stokes system let a mathcal d a to mathcal x be the generator of an analytic semigroup and b mathcal v to mathcal d a a relatively bounded control operator in this paper we consider the stabilization of the system y ay bu where u is the linear combination of a family v 1 ldots v k our main result shows that if a b satisfies a unique continuation property and if k is greater than or equal to the maximum of the geometric multiplicities of the unstable modes of a then the system is generically stabilizable with respect to the family v 1 ldots v k with the same functional framework we also prove the stabilizability of a class of nonlinear systems when using feedback or dynamical controllers we apply these results to stabilize the navier stokes equations in two and three dimensions by using boundary controls

polynomial approximation of high dimensional hamilton jacobi bellman equations and applications to feedback control of semilinear parabolic pdes a procedure for the numerical approximation of high dimensional hamilton jacobi bellman hjb equations associated to optimal feedback control problems for semilinear parabolic equations is proposed its main ingredients are a pseudospectral collocation approximation of the pde dynamics and an iterative method for the nonlinear hjb equation associated to the feedback synthesis the latter is known as the successive galerkin approximation it can also be interpreted as newton iteration for the hjb equation at every step the associated linear generalized hjb equation is approximated via a separable polynomial approximation ansatz stabilizing feedback controls are obtained from solutions to the hjb equations for systems of dimension up to fourteen

knowledge gathering of fuzzy multi time interval sequential patterns mining sequential patterns to find ordered events or subsequence patterns is essential in many applications such as analysis of consumer shopping data web clickstreams and biological sequences traditional patterns reveal which items are frequently purchased together and in what order however information about the time intervals between purchases is missing therefore yang proposed using multi time interval sequential patterns to consider the time intervals between each pair of items in a pattern for example means that bread is bought before milk within an interval of ti 1 and jam is bought after bread and milk within intervals of ti 2 and ti 1 respectively where ti 1 and ti 2 are predefined time intervals although this new type of pattern considers the intervals between all pairs of items it contains a sharp boundary problem that is when the time interval between two purchases is near the boundary of two predetermined time ranges we either ignore or overemphasize it in this study we applied the concept of fuzzy sets to solve the sharp boundary problem the discovered patterns called fuzzy multi time interval sequential patterns describe time intervals in linguistic terms for better understanding two algorithms fuzzmi apriori and fuzzmi prefixspan were developed for mining fuzzy multi time interval patterns experiments using synthetic and real datasets showed the algorithms computational efficiency scalability and effectiveness

the fractional representation approach to synthesis problems an algebraic analysis viewpoint part ii internal stabilization in this second part of the paper a quadrat siam j control optim 40 2003 pp 266 299 we show how to reformulate the fractional representation approach to synthesis problems within an algebraic analysis framework in terms of modules we give necessary and sufficient conditions for internal stabilizability moreover we characterize all the integral domains a of siso stable plants such that every mimo plant defined by means of a transfer matrix whose entries belong to the quotient field k q a of a is internally stabilizable finally we show that this algebraic analysis approach allows us to recover on the one hand the approach developed in m c smith ieee trans automat control 34 1989 pp 1005 1007 and on the other hand the ones developed in k mori and k abe siam j control optim 39 2001 pp 1952 1973 s shankar and v r sule siam j control optim 30 1992 pp 11 30 v r sule siam j control optim 32 1994 pp 1675 1695 m vidyasagar h schneider and b a francis ieee trans automat control 27 1982 pp 880 894 m vidyasagar control system synthesis a factorization approach mit press cambridge ma 1985

abstract settings for tangential boundary stabilization of navier stokes equations by high and low gain feedback controllers abstract the present paper seeks to continue the analysis in barbu et al tangential boundary stabilization of navier stokes equations memoir ams to appear on tangential boundary stabilization of navier stokes equations d 2 3 as deduced from well posedness and stability properties of the corresponding linearized equations it intends to complement v barbu i lasiecka r triggiani tangential boundary stabilization of navier stokes equations memoir ams to appear on two levels i by casting the riccati based results of barbu et al tangential boundary stabilization of navier stokes equations memoir ams to appear for d 2 3 in an abstract setting thus extracting the key relevant features so that the resulting framework may be applicable also to other stabilizing boundary feedback operators as well as to other parabolic like equations of fluid dynamics ii by including in the case d 2 this time also the low level gain counterpart of the results in barbu et al tangential boundary stabilization of navier stokes equations memoir ams to appear with both riccati based and spectral based tangential feedback controllers this way new local boundary stabilization results of navier stokes equations are obtained over v barbu i lasiecka r triggiani tangential boundary stabilization of navier stokes equations memoir ams to appear

on strong stabilization for linear time varying systems abstract this paper deals with the strong stabilization problem for linear time varying systems and gives a sufficient condition in terms of the coprime factors for the existence of strong stabilizers for such a system

the transitivity in simultaneous stabilization this paper deals with the transmission problem in simultaneous stabilization of time varying linear systems we establish two criteria for the transitivity in simultaneous stabilization in particular we give a necessary and sufficient condition for certain linear systems to satisfy a strengthened version of transitivity

the fractional representation approach to synthesis problems an algebraic analysis viewpoint part i weakly doubly coprime factorizations in this paper we show how to reformulate the fractional representation approach to analysis and synthesis problems within an algebraic analysis framework in terms of modules we give necessary and sufficient conditions so that a system admits weakly left right doubly coprime factorizations moreover we explicitly characterize the integral domains a such that every plant defined by means of a transfer matrix whose entries belong to the quotient field of a admits weakly doubly coprime factorizations finally we show that this algebraic analysis approach allows us to recover on the one hand the approach developed in m c smith ieee trans automat control 34 1989 pp 1005 1007 and on the other hand the ones developed in k mori and k abe siam j control optim 39 2001 pp 1952 1973 v r sule siam j control optim 32 1994 pp 1675 1695 and 36 1998 pp 2194 2195 m vidyasagar h schneider and b a francis ieee trans automat control 27 1982 pp 880 894 m vidyasagar control system synthesis a factorization approach mit press cambridge ma 1985