equivariant cohomology fock space and loop groups equivariant de rham cohomology is extended to the infinite dimensional setting of a loop subgroup acting on a loop group using hida supersymmetric fock space for the weil algebra and malliavin test forms on the loop group the mathai quillen isomorphism in the brst formalism of kalkman is defined so that the equivalence of various models of the equivariant de rham cohomology can be established

almost invariant subspaces an approach to high gain feedback design part ii almost conditionally invariant subspaces in part i of this paper almost controlled invariant subspaces were studied in this part we will consider their duals the almost conditionally invariant subspaces these concepts give immediately by dualization of the almost disturbance decoupling control by state feedback the solution of the almost disturbance decoupled estimation problem finally we consider the problem of approximate disturbance decoupling by measurement feedback and it is shown that this problem is solvable to any arbitrary degree of accuracy if and only if 1 almost disturbance decoupling by state feedback and 2 almost disturbance decoupled estimation of the to be controlled output are both possible

controllability and stabilizability of a class of continuous piecewise affine dynamical systems this paper studies controllability and stabilizability of continuous piecewise affine dynamical systems which can be considered as a collection of ordinary finite dimensional linear input state output systems together with a partition of the product of the state space and input space into full dimensional polyhedral regions each of these regions is associated with one particular linear system from the collection the main results of the paper are popov belevitch hautus type necessary and sufficient conditions for both controllability and stabilizability of such systems

de rham hodge kodaira operator on loop groups we consider a based loop group le g over a compact lie groupg endowed with its pinned wiener measure the law of the brownian bridge ong and we shall calculate the ricci curvature for differentialn forms over le g a type of bochner weitzenbock formula for general differentialn forms or shigekawa identity will be established

a fast chebyshev s method for quadratic equations a multiresolution transform corresponding to interpolatory technique is used for fast application of chebyshev s method in designing this algorithm we apply data compression to the linear and the bilinear forms that appear on the method a convergence theorem is performed finally some numerical results are presented

brief paper a full characterization of stabilizability of bimodal piecewise linear systems with scalar inputs this paper studies open loop stabilization problem for bimodal systems with continuous vector field it is based on the earlier work of the authors on the controllability problem for the same class of systems a full characterization of stabilizability is established by presenting algebraic necessary and sufficient conditions it is also shown that controllability implies stabilizability for these systems in a very similar fashion to the linear case

a subspace approach to linear dynamical systems abstract in this paper we present an approach to linear dynamical systems which combines the positive features of two well known formulations namely standard state space theory see for e g wonham 1978 9 and behavioural systems theory see polderman and willems 1997 4 our development is also geometric in the tradition of wonham and others but instead of using explicit linear maps we work with linear relations implicitly which amounts to working with subspaces one of our primary motivations is computational efficiency all our computations can be performed on the system as it is without elimination of variables and further unlike the behaviourists who manipulate matrices with polynomial entries we work only with real matrices using our formulation we derive the standard vector space results on controlled and conditioned invariant subspaces of linear dynamical systems duality which is a distinctive feature of state space theory but not of the behavioural view point comes out naturally in our approach too through the use of the adjoint we illustrate our ideas for an important class of dynamical systems viz electrical networks the theory proposed in this paper gives a unified description of both the standard linear dynamical systems and the linear singular systems or the linear descriptor systems see for e g f gantmacher 1959 1 and lewis 1986 2 therefore the algorithms described for the invariant spaces in this paper are also applicable to linear singular systems

supersymmetry and morse theory it is shown that the morse inequalities can be obtained by consideration of a certain supersymmetric quantum mechanics hamiltonian some of the implications of modern ideas in mathematics for supersymmetric theories are discussed

secant like methods for solving nonlinear integral equations of the hammerstein type we consider a one parametric family of secant type iterations for solving nonlinear equations in banach spaces we establish a semilocal convergence result for these iterations by means of a technique based on a new system of recurrence relations this result is then applied to obtain existence and uniqueness results for nonlinear integral equations of the hammerstein type we also present a numerical example where the solution of a particular hammerstein integral equation is approximated by different secant type methods

on observability subspaces the paper presents an in depth study of topics in geometric control pertaining to observer theory from a functional point of view we give characterizations of several classes of subspaces including observability almost observability and reconstructibility subspaces we solve completely the problem of spectral assignability for observer dynamics by generalizing rosenbrock s pole placement theorem these results are then applied to observer theory

on the fixed poles for disturbance rejection we propose a geometric characterization of the fixed poles for the disturbance rejection problem by static state feedback and in the particular case when the system is controllable a structural characterization in terms of finite invariant zeros of certain open loop subsystems we propose solutions through which all the other poles can be freely assigned

squaring down lti systems a geometric approach in this paper the problem of reducing a given lti system into a left or right invertible one is addressed and solved with the standard tools of the geometric control theory first it will be shown how an lti system can be turned into a left invertible system thus preserving key system properties like stabilizability phase minimality right invertibility relative degree and infinite zero structure moreover the additional invariant zeros introduced in the left invertible system thus obtained can be arbitrarily assigned in the complex plane by duality the scheme of a right inverter will be derived straightforwardly moreover the squaring down problem will be addressed in fact when the left and right reduction procedures are applied together a system with an unequal number of inputs and outputs is turned into a square and invertible system furthermore as an example it will be shown how these techniques may be employed to weaken the standard assumption of left invertibility of the plant in many optimization problems

on the well posedness in the solution of the disturbance decoupling by dynamic output feedback with self bounded and self hidden subspaces abstract this paper studies the disturbance decoupling problem by dynamic output feedback with required closed loop stability in the general case of nonstrictly proper systems we will show that the extension of the geometric solution based on the ideas of self boundedness and self hiddenness presents structural differences with respect to the strictly proper case the most crucial aspect that emerges in the general case is the issue of the well posedness of the feedback interconnection which obviously has no counterpart in the strictly proper case a fundamental property of the feedback interconnection that has so far remained unnoticed in the literature is investigated in this paper the well posedness condition is decoupled from the remaining solvability conditions an important consequence of this fact is that the well posedness condition written with respect to the supremal output nulling and infimal input containing subspaces does not need to be modified when we consider the solvability conditions of the problem with internal stability where one would expect the well posedness condition to be expressed in terms of supremal stabilizability and infimal detectability subspaces and also when we consider the solution which uses the dual lattice structures of basile and marro

robust eigenstructure assignment in geometric control theory in this paper we employ the rosenbrock system matrix pencil for the computation of output nulling subspaces of linear time invariant systems which appear in the solution of a large number of control and estimation problems we also consider the problem of finding friends of these output nulling subspaces i e the feedback matrices that render such subspaces invariant with respect to the closed loop map and output nulling with respect to the output map and which at the same time deliver a robust closed loop eigenstructure we show that the methods presented in this paper offer considerably more robust eigenstructure assignment than the other commonly used methods and algorithms

a modified chebyshev s iterative method with at least sixth order of convergence this paper is devoted to the construction and analysis of a high order variant of the classical chebyshev method the method has order of convergence at least six for simple roots the extension to system of equations and its semilocal convergence for nonlinear equations are presented finally an application to well known algebraic riccati equation is considered

disturbance decoupling problems by measurements feedback a characterization of all solutions and fixed modes this paper presents a new approach to disturbance decoupling problems by measurement feedback ddpm the novelty in this approach is that it yields a characterization of the sets of all solutions to ddpm and ddpm with internal stability and that the set of fixed modes of ddpm with respect to dynamic output feedback is easily identified the central object used in deriving these results is a minimal polynomial basis of a rational vector space which conveniently represents the problem data

algebraic necessary and sufficient conditions for the controllability of conewise linear systems the problem of checking certain controllability properties of even very simple piecewise linear systems is known to be undecidable this paper focuses on conewise linear systems i e systems for which the state space is partitioned into conical regions and a linear dynamics is active on each of these regions for this class of systems we present algebraic necessary and sufficient conditions for controllability we also show that the classical results of controllability of linear systems and input constrained linear systems can be recovered from our main result our treatment employs tools both from geometric control theory and mathematical programming

a family of halley chebyshev iterative schemes for non frechet differentiable operators a modification of some classical third order methods is studied the main advantage of these methods is that they do not need evaluate any frechet derivative a convergence theorem in banach spaces just assuming that the second divided difference is bounded by a nondecreasing function and a punctual condition is presented frechet differentiability is not required finally a particular example is analyzed where our conditions are fulfilled and the classical ones fail

the application of an inverse free jarratt type approximation to nonlinear integral equations of hammerstein type abstract we consider an inverse free jarratt type approximation whose order of convergence is four for solving nonlinear equations the convergence of this method is analysed under two different types of conditions we use a new technique based on constructing a system of real sequences finally this method is applied to the study of hammerstein s integral equations

the generic number of invariant zeros of a structured linear system in this paper we consider a structured linear system represented by means of a directed graph we present a graph theoretic method to compute the generic number of invariant zeros of the corresponding rosenbrock matrix the method is based on a fundamental decomposition of the directed graph representing the structured system the generic number of invariant zeros is important in generic versions of problems involving controllability and pole placement

brst model for equivariant cohomology and representatives for the equivariant thom class in this paper the brst formalism for topological field theories is studied in a mathematical setting the brst operator is obtained as a member of a one parameter family of operators connecting the weil model and the cartan model for equivariant cohomology furthermore the brst operator is identified as the sum of an equivariant derivation and its fourier transform using this the mathai quillen representative for the thom class of associated vector bundles is obtained as the fourier transform of a simple brst closed element

index theorem and equivariant cohomology on the loop space in this paper extending ideas of witten and atiyah we describe some relations of equivariant cohomology on the loop space of a manifold to the path integral representation of the index of the dirac operator on a twisted spin complex in particular the natural extension of the chern character to the whole loop space is described also it is shown that the non zero free homotopy classes of the loop space have 0 measure for the index measures associated to the index problem

some variants of cauchy s method with accelerated fourth order convergence in this paper we present some variants of cauchy s method for solving non linear equations analysis of convergence shows that the methods have fourth order convergence per iteration the new methods cost almost the same as cauchy s method numerical results show that the methods can compete with cauchy s method

brief fixed poles of disturbance rejection by dynamic measurement feedback a geometric approach this paper deals with the problem of disturbance rejection by dynamic measurement feedback it aims at proposing new geometric characterizations for the fixed poles of this problem we also propose solutions to the problem for which all the poles except the fixed poles of the problem are freely placed these fixed poles are also characterized as some particular invariant zeros as a corollary we propose a necessary and sufficient condition for the existence of internally stable solutions which generalizes the sufficient condition proposed by basile and marro

the generalised discrete algebraic riccati equation in linear quadratic optimal control this paper investigates the properties of the solutions of the generalised discrete algebraic riccati equation arising from the classic infinite horizon linear quadratic lq control problem in particular a geometric analysis is used to study the relationship existing between the solutions of the generalised riccati equation and the output nulling subspaces of the underlying system and the corresponding reachability subspaces this analysis reveals the presence of a subspace that plays an important role in the solution of the related optimal control problem which is reflected in the generalised eigenstructure of the corresponding extended symplectic pencil in establishing the main results of this paper several ancillary problems on the discrete lyapunov equation and spectral factorisation are also addressed and solved

disturbance localization and pole shifting by dynamic compensation this paper concerns the problem of disturbance localization and pole shifting by dynamic compensation in multivariable linear systems with inaccessible state vector a necessary and sufficient condition for the solvability of the problem is given two synthesis procedures of the compensator are presented one is based on an observer and the other is based on a dual observer the observer designed by the proposed procedure acts as as unknown input observer for a linear function an improved procedure of designing a reduced order unknown input observer is also given the result may be applicable to reducing the compensator order

an adaptive version of a fourth order iterative method for quadratic equations a fourth order iterative method for quadratic equations is presented a semilocal convergence theorem is performed a multiresolution transform corresponding to interpolatory technique is used for fast application of the method in designing this algorithm we apply data compression to the linear and the bilinear forms that appear on the method finally some numerical results are studied

quadratic stability and stabilization of bimodal piecewise linear systems abstract this paper deals with quadratic stability and feedback stabilization problems for continuous bimodal piecewise linear systems first we provide necessary and sufficient conditions in terms of linear matrix inequalities for quadratic stability and stabilization of this class of systems later these conditions are investigated from a geometric control point of view and a set of sufficient conditions in terms of the zero dynamics of one of the two linear subsystems for feedback stabilization are obtained

newton like methods for the computation of fixed points abstract the celebrated banach fixed point theorem provides conditions which assure that the method of successive substitution is convergent the convergence however may take place very slowly so that it may be desirable to use a newton like method for the computation of the fixed point if newton s method itself is applied one ignores the additional information that the problem arises from a frixed point problem with a contraction mapping in the present note some variants of newton s method are discussed which make use of this contraction information it turns out that the convergence of newton s method can be accelerated without any relevant additional computational labour

existence uniqueness and cohomology of the classical brst charge with ghosts of ghosts a complete canonical formulation of the brst theory of systems with redundant gauge symmetries is presented these systems includep form gauge fields the superparticle and the superstring we first define the koszul tate differential and explicitly show how the introduction of the momenta conjugate to the ghosts of ghosts makes it acyclic the global existence of the brst generator is then demonstrated and the brst charge is proved to be unique up to canonical transformations in the extended phase space which includes the ghosts finally the brst cohomology in classical mechanics is investigated and shown to be equal to the cohomology of the exterior derivative along the gauge orbits as in the irreducible case this is done by re expressing the exterior algebra along the gauge orbits as a free differential algebra containing generators of higher degree which are identified with the ghosts of ghosts the quantum cohomology is not dealt with

regulator synthesis using c a b pairs the concept of a c a b pair of subspaces was introduced in an earlier paper by the author to study problems of compensator design here it is shown that the same concept plays a basic role in the theory of tracking and regulation from a few fundamental properties the main results of regulator theory are derived in a relatively simple and straightforward manner another new feature is that we are able to allow the presence of an unknown input thereby unifying the fields of tracking and regulation and disturbance decoupling all results are fully constructive and an example is given to illustrate the theory

a two step steffensen s method under modified convergence conditions a simplification of a third order iterative method is proposed the main advantage of this method is that it does not need to evaluate neither any frechet derivative nor any bilinear operator a semilocal convergence theorem in banach spaces under modified kantorovich conditions is analyzed a local convergence analysis is also performed finally some numerical results are presented

a general approach to the eigenstructure assignment for reachability and stabilizability subspaces abstract this paper is concerned with the problem of determining basis matrices for the supremal output nulling reachability and stabilizability subspaces and the simultaneous computation of the associated friends that place the assignable closed loop eigenvalues at desired locations our aim is to show that the moore laub algorithm in moore and laub 1978 for the computation of these subspaces was stated under unnecessary restrictive assumptions we prove the same result under virtually no system theoretic hypotheses this provides a theoretical foundation to a range of recent geometric techniques that are more efficient and robust and as general as the standard ones based on the computation of sequences of subspaces

brief paper almost disturbance decoupling and pole placement we revisit here the almost disturbance decoupling problem addp willems 1981 by state feedback with the objective to solve addp and simultaneously place the maximal number of poles in the closed loop solution indeed when addp is solvable we show that whatever be the choice of a particular feedback solution the obtained closed loop system always has a set of fixed poles we characterize these fixed poles of addp the other non fixed poles can be placed freely and we characterize the optimal solutions in terms of ad hoc subspaces and feedbacks which allow us to solve addp with maximal pole placement from our contribution which treats the most general case for studying addp with maximal usually partial pole placement directly follow the solutions of addp with complete pole placement when there are no addp fixed poles and addp with internal stability when all the fixed poles of addp are stable without requiring the use of stabilizability subspaces as in willems 1981 we extend the concept of self bounded controlled invariant subspaces basile marro 1992 to almost ones an example is proposed that illustrates our contributions

brst cohomology for certain reducible topological symmetries in this paper two different definitions of the brst complex are connected we obtain the brst complex of topological quantum field theories leading to equivariant cohomology from the standard definition of the classical brst complex leading to lie algebra cohomology provided that we include ghosts for ghosts hereby we use a finite dimensional model with a semi direct product action ofh diffm on a configuration spacem whereh is a compact lie group representing the gauge symmetry in this model

a canonical parameterization of the kronecker form of a matrix pencil abstract the kronecker form is the classical canonical form for matrix pencils under strict equivalence transformation consider a matrix pencil whose entries are smooth functions of a parameter vector the kronecker form of the parameterized pencil will in general be a discontinuous function of the parameters for a linear time invariant control system these discontinuities correspond to a change in the finite and infinite invariant zero structure since many control strategies require knowledge of or place restrictions on the zero structure these points of discontinuity are of considerable interest in this paper a general approach to the study of such points is developed in the framework of singularity theory we derive a miniversal parameterization of a given pencil that is a parameterized family of pencils that i includes the given pencil ii is locally equivalent to any other family up to a change of parameters and iii uses the fewest number of parameters to achieve this property all nearby zero structures can be obtained by varying parameter values in the miniversal parameterization from all miniversal parameterizations one having a particularly uncluttered representation is selected as canonical however some restrictions on the finite elementary divisors are then required

a new solution to the regulator problem with output stability a new solution to the regulator problem with output stability external disturbance is also considered is achieved by straightforward application of self hidden conditioned invariants the proposed solution also has an interesting feature in the corresponding induced synthesis it is always possible to avoid hard eigenspace computations a possible order reduction in the compensator synthesis is discussed

structural invariants of two dimensional systems in this paper some fundamental structural properties of two dimensional 2 d systems which remain invariant under feedback and output injection transformation groups are identified and investigated for the first time as is well known structural invariants that follow from the definition of controlled and conditioned invariance output nulling input containing self bounded and self hidden subspaces play pivotal roles in many theoretical studies of systems theory and in the solution of several control estimation problems these concepts are developed and studied within a 2 d context in this paper

almost invariance and noninteracting control a frequency domain analysis abstract we solve a number of feedback synthesis problems in the context of noninteracting control or block diagonal decoupling for finite dimensional linear time invariant systems we consider a plant that apart from a control input and a measurement output has a given number of exogenous input vectors and the same number of exogenous output vectors the decoupling problem studied is to find dynamic compensators from the plant measurement output which in this paper will be assumed to be the full plant state to the plant control input in such a way that the following requirements are met 1 the closed loop transfer matrix is block diagonal 2 the remaining diagonal blocks are stable with respect to an a priori given first stability set and 3 the clossed loop system is internaly stable with respect to an a priori given second in general larger stability set in addition we study the almost version of the above problem in the latter the requirement of exact decoupling is replaced by a requirement of approximate decoupling in the sense that the compensators to be designed should yield off diagonal blocks in the closed loop transfer matrix that are arbitrarily small in h norm necessary and sufficient conditions for the existence of such dynamic compensators are formulated in terms of controlled invariant and almost controlled invariant subspaces

geometric constructions of iterative functions to solve nonlinear equations in this paper we present the geometrical interpretation of several iterative methods to solve a nonlinear scalar equation in addition we also review the extension to general banach spaces and some computational aspects of these methods

a nine fold canonical decomposition for linear systems the zero structure for non minimal proper systems in state space form is investigated the approach is geometric and a complete characterization in geometric terms is given of the invariant decoupling system and transmission zeros as defined by rosenbrock the first main result is a formula for the transmission zeros second a canonical lattice diagram is presented of a decomposition of the state space which can be viewed as the product of the kalman canonical decomposition and the morse canonical decomposition this decomposition gives a straightforward characterization of all zeros just mentioned in terms of spectral properties of subspaces under a certain class of feedback and injection mappings via this diagram a number of equivalent formulae for the transmission zeros are derived the freedom in pole assignment leads to new characterizations for the invariant and system zeros in terms of greatest common divisors of characteristic polynomials finally the relation is demonstrated be

stochastic equivariant cohomologies and cyclic cohomology we give two stochastic diffeologies on the free loop space which allow us to define stochastic equivariant cohomology theories in the chen souriau sense and to establish a link with cyclic cohomology with the second one we can establish a stochastic fixed point theorem

smith mcmillan factorizations at infinity of rational matrix functions and their control interpretation in this paper the smith mcmillan factorizations at infinity of a transfer function are studied the non uniqueness of these factorizations is characterized via a multiplicative group of bicausal isomorphisms control interpretations are given in terms of system equivalence under some groups of transformations a characterization of the stabilizer of morse group at a b c is given for irreducible systems

on the lyapunov equation coinvariant subspaces and some problems related to spectral factorizations a geometric approach to stochastic realization theory and hence to spectral factorization problems has been developed by lindquist and picci 1985 1991 and lindquist et al 1995 most of this work was done abstractly fuhrmann and gombani 1998 adopted an entirely hardy space approach to this set of problems studying the set of rectangular spectral factors of given size for a weakly coercive spectral function the parametrization of spectral factors in terms of factorizations of related inner functions as developed in fuhrmann 1995 had to be generalized this led to a further understanding of the partial order introduced by lindquist and picci in the set of stable spectral factors in the present paper we study the geometry of finite dimensional coinvariant subspaces of a vectorial hardy space h 2 via realization theory emphasizing the role of the lyapunov equation in lifting the hardy space metric to the statespace domain we follow this by deriving state space formulas for rectangular spect

self bounded subspaces for nonstrictly proper systems and their application to the disturbance decoupling with direct feedthrough matrices in this paper the concept of self bounded controlled invariance is extended to nonstrictly proper systems moreover its use in connection with the disturbance decoupling problem with internal stability is investigated in the case where the feedthrough matrices from the control input and from the disturbance to the output to be decoupled are possibly nonzero

disturbance decoupling by measurement feedback with stability or pole placement in this paper we solve the disturbance decoupling problem by measurement feedback and requiring stability or pole placement on the closed loop system the problem is attacked using the geometric approach through the concepts of a bmod mathcal b invariant and controllability subspaces and their duals a mid k invariant and complementary observability subspaces the solution of this problem has an interesting structure consisting of a feedback processor which decomposes into i a disturbance decoupling loop ii a disturbance input stabilization or pole placement loop and iii a controlled output stabilization or pole placement loop

feedback invariants of restrictions a polynomial approach the possible feedback invariants of a linear time invariant dynamical system represented by a pair of matrices a b are studied when the only information about the system is that it has an a b invariant subspace s whose restriction is an autonomous system and the quotient is controllable this problem is shown to be related to the problem of designing a control matrix b 1 for a series connected system to have prescribed feedback invariants

a third order method for fixed points in banach spaces this paper deals with a third order stirling like method used for finding fixed points of nonlinear operator equations in banach spaces the semilocal convergence of the method is established by using recurrence relations under the assumption that the first frechet derivative of the involved operator satisfies the holder continuity condition a theorem is given to establish the error bounds and the existence and uniqueness regions for fixed points the r order of the method is also shown to be equal to at least 2p 1 for p 0 1 the efficacy of our approach is shown by solving three nonlinear elementary scalar functions and two nonlinear integral equations by using both stirling like method and newton like method it is observed that our convergence analysis is more effective and give better results

some supplementary results on the 1 sqrt 2 order method for the solution of nonlinear equations recently an iterative method for the solution of systems of nonlinear equations having at leastr order 1 sqrt 2 for simple roots has been investigated by the author 7 this method uses as many function evaluations per step as the classical newton method in the present note we deal with several properties of the method such as monotone convergence asymptotic inclusion of the solution and convergence in the case of multiple roots

quotient of a loop group and witten genus we define a dirac ramond operator over the quotient lg h of a loop group by a subgroup h of the compact lie group g we state the conjecture that its equivariant index with respect of the natural circle action over the quotient of the loop group is equal to the witten genus of the homogeneous manifold g h we motivate the conjecture by a short time argument which allows to come back to a dirac ramond operator at the manner of taubes on a limit model where all the computations can be done by hand

convergence and numerical analysis of a family of two step steffensen s methods we provide sufficient conditions for the semilocal convergence of a family of two step steffensen s iterative methods on a banach space the main advantage of this family is that it does not need to evaluate neither any frechet derivative nor any bilinear operator but having a high speed of convergence some numerical experiments are also presented

some geometric considerations about the kronecker normal form abstract in the first part of this paper we develop general algorithms from the kronecker normal form of any matrix pencil and give some of their properties in the second part these results are applied to the so called restricted matrix pencil associated with a given c a b system and introduced by jaffe and karcanias 1981 this allows us to make a link with well known algorithms of the geometric approach particularly the a b invariant subspace algorithm and the almost a b controllability subspace algorithm finally relationships between morse s invariants morse 1973 and the invariants of the restricted matrix pencil are exhibited

the model following problem for linear constant a b c d quadruples the aim of this note is to deal with the model following problem mfp for linear constant a b c d quadruples in the first part we tackle the mfp with state feedback and we extend the results previously given by morse 7 for a b c triples the main result of this paper is given in the second part where we give necessary and sufficient conditions under which solutions using regular output feedback may exist such conditions were lacking up until now

equivariant brst quantization and reducible symmetries working from first principles quantization of a class of hamiltonian systems with reducible symmetry is carried out by constructing first the appropriate reduced phase space and then the brst cohomology the constraints of this system correspond to a first class set for a group g and a second class set for a subgroup h the brst operator constructed is equivariant with respect to h using algebraic techniques analogous to those of equivariant de rham theory the brst operator is shown to correspond to that obtained by bv quantization of a class of systems with reducible symmetry the ghosts for ghosts correspond to the even degree two generators in the cartan model of equivariant cohomology as an example of the methods developed a topological model is described whose brst quantization relates to the equivariant cohomology of a manifold under a circle action

the state feedback h problem at optimality abstract we discuss the infinite horizon h control problem by state feedback for a linear time invariant plant which is not restricted with respect to its finite or infinite zero structure we provide an algebraic characterization for the optimal value to be attained in terms of the solvability of a nonstrict riccati inequality and propose possibilities for verifying these criteria if the optimum is not achieved we give a complete test for the need of high gain feedback in order to approach the optimal value

continuous time singular linear quadratic control necessary and sufficient conditions for the existence of regular solutions abstract the purpose of this paper is to provide a full understanding of the role that the constrained generalized continuous algebraic riccati equation plays in singular linear quadratic lq optimal control indeed in spite of the vast literature on lq problems only recently a sufficient condition for the existence of a non impulsive optimal control has for the first time connected this equation with the singular lq optimal control problem in this paper we establish four equivalent conditions providing a complete picture that connects the singular lq problem with the constrained generalized continuous algebraic riccati equation and with the geometric properties of the underlying system

families of linear quadratic problems continuity properties in this paper we investigate for given one parameter families of linear time invariant finite dimensional systems the parameter dependence of the linear quadratic optimal cost optimal control inputs optimal state trajectories and optimal outputs it is shown that results that have been obtained in the past in the context of the problem of cheap control can in fact be generalized to a much broader class of parameter dependent cost functionals including cost functionals in which for every parameter value the weighting matrix of the control inputs is singular essentially only two assumptions on the parameter dependence of the cost functionals are required in order to have continuity of the optimal cost and optimal control inputs with respect to the underlying parameter one assumption is concerned with the continuity of the weighting matrices with respect to this parameter the other with the monotonicy of the weighting matrices with respect to the parameter instrumental in our development is a characterization of the linear quadratic optimal cost in terms of the so called dissipation inequality the results obtained are applied to the problem of cheap control and to a problem of priority control the latter provides an example of a family of quadratic cosl functionals with a polynomial parameter dependence

third order iterative methods under kantorovich conditions we study a class of third order iterative methods for nonlinear equations on banach spaces a characterization of the convergence under kantorovich type conditions and optimal estimates of the error are found though in general these methods are not very extended due to their computational costs we will show some examples in which they are competitive and even cheaper than other simpler methods we center our analysis in both analytic and computational aspects

all optimal controls for the singular linear quadratic problem without stability a new interpretation of the optimal cost abstract the singular linear quadratic control problem without stability is solved by means of a generalized dual structure algorithm in order to generate all optimal inputs furthermore it is shown that the optimal cost can be interpreted as the smallest nonnegative rank minimizing solution of a certain matrix inequality the so called dissipation inequality

uniqueness of ground states for schrodinger operators over loop groups abstract over the space l of based loops in a compact connected lie group g there is a natural gradient operator induced by the left action on l of the hilbert lie group k 0 which consists of finite energy elements of l denote by pinned brownian motion measure on l the schrodinger operator v acting in l 2 l is shown to have a unique ground state over each homotopy class in l the proof of uniqueness is reduced to the proof of ergodicity of the left action of k 0 on l for a simply connected group g of compact type ergodicity in turn is proved by first characterizing the ito expansion coefficients of k 0 invariant functions and then regularizing such functions via a smooth approximation of multiple stratonovich integrals as a byproduct of this method one obtains an isometric isomorphism of l 2 g heat kernel measure at time one with a natural completion of the universal enveloping algebra of g thus extending to the noncommutative case the well known isometry between l 2 r d gauss measure and the space of symmetric tensors over r d

realizations in generalized state space form for polynomial system matrices and the definitions of poles zeros and decoupling zeros at infinity this paper contains three main results firstly a realization procedure is presented that brings a polynomial system matrix of a non proper multivariable system to generalized state space form such that all relevant properties including phenomena of redundancy associated with finite and infinite decoupling zeros are retained secondly new definitions are proposed for poles zeros and decoupling zeros at infinity of a general polynomial system matrix as a third result a theorem of rosenbrock 1974 e on the redundancy of lcr multiports is generalized to include the decoupling zeros at infinity

third order iterative methods without using any frechet derivative a modification of classical third order methods is proposed the main advantage of these methods is they do not need to evaluate any frechet derivative a convergence theorem in banach spaces just assuming the second divided difference is bounded and a punctual condition is analyzed finally some numerical results are presented

a stirling like method with holder continuous first derivative in banach spaces in this paper the convergence of a stirling like method used for finding a solution for a nonlinear operator in a banach space is examined under the relaxed assumption that the first frechet derivative of the involved operator satisfies the holder continuity condition many results exist already in the literature to cover the stronger case when the second frechet derivative of the involved operator satisfies the lipschitz holder continuity condition our convergence analysis is done by using recurrence relations the error bounds and the existence and uniqueness regions for the solution are obtained finally two numerical examples are worked out to show that our convergence analysis leads to better error bounds and existence and uniqueness regions for the fixed points