note on the generalized h optimal control problem it is shown that by a suitable embedding in the standard h control problem the generalized h optimal control problem may be recast as a one block nehari problem since an explicit solution exists for the latter there seems little need for the iterative polynomial based solution procedures recently presented in the literature

an h minimax approach to the design of robust control systems abstract a realistic feedback design problem is posed based on the minimization of a weighted combination of the sensitivity and complementary sensitivity matrices a solution is obtained which makes use of the recently proposed methods for minimizing the sensitivity function alone

solution of the h sub infinity optimal linear filtering problem for discrete time systems the solution of l sub 2 minimum variance and h sub infinity estimation problems is considered using a polynomial systems approach the results for the l sub 2 filtering problem which corresponds with wiener or kalman filtering prediction are first presented in polynomial matrix form attention then turns to the solution of the h sub infinity estimation problem for scalar systems numerous examples are presented to illustrate the computational procedures the two types of estimator are appropriate to very different estimation problems and the new h sub infinity devices should be valuable in certain application areas

existence of bubbling solutions for chern simons model on a torus we study the existence of bubbling solutions for the the following chern simons higgs equation delta u frac1 varepsilon 2 rm e u 1 rm e u 4 pi sum i 1 2k delta p i quad text in omega where is a torus if k 1 for any critical point q of the associated sum of the green functions we introduce a quantity d q see 1 11 below we show that for any non degenerate critical point q with d q 0 the above problem has a solution ue satisfying that e 0 ue blows up at q the calculations in this paper also show that if a sequence of solutions ue blows up at q as e 0 then q must be a critical point of the associated sum of the green functions and d q leqq 0 so the condition d q 0 is almost necessary to obtain our result we also construct solutions with k bubbles for k geqq 2

the relativistic non abelian chern simons equations we study ther xr system of nonlinear elliptic equations delta u a lambda sum limits b 1 r k ab e u b lambda sum limits b 1 r sum limits c 1 r e u b k ab e u c k bc 4 pi sum limits j 1 n a delta p aj a 1 2 r x r 2 where 0 is a constant parameter k kab is the cartan matrix of a semi simple lie algebra and p is the dirac measure concentrated atp r 2 this system of equations arises in the relativistic non abelian chern simons theory and may be viewed as a nonintegrable deformation of the integrable toda system we establish the existence of a class of solutions known as topological multivortices the crucial step in our method is the use of the decomposition theorem of cholesky for positive definite matrices so that a variational principle can be formulated

the robust h sub 2 control problem a worst case design the worst case effect of a disturbance system on the h sub 2 norm of the system is analyzed an explicit expression is given for the worst case h sub 2 norm when the disturbance system is allowed to vary over all nonlinear time varying and possibly noncausal systems with bounded l sub 2 induced operator norm an upper bound for this measure which is equal to the worst case h sub 2 norm if the exogeneous input is scalar is defined some further analysis of this upper bound is done and a method to design controllers which minimize this upper bound over all robustly stabilizing controllers is given the latter is done by relating this upper bound to a parameterized version of the auxiliary cost function studied in the literature

optimal h robustness and the relationship to lqg design problems a solution to the hx optimal control problem is obtained by employing a standard lqg polynomial based solution procedure the derivation is straightforward and avoids many of the more abstract mathematical results usually employed the relationship between the lqg and hm design methods becomes transparent and the similarities and differences can be identified

a nash game approach to mixed h sub 2 h sub spl infin control the established theory of nonzero sum games is used to solve a mixed h sub 2 h sub spl infin control problem our idea is to use the two pay off functions associated with a two player nash game to represent the h sub 2 and h sub spl infin criteria separately we treat the state feedback problem and we find necessary and sufficient conditions for the existence of a solution both the finite and infinite time problems are considered in the infinite horizon case we present a full stability analysis the resulting controller is a constant state feedback law characterized by the solution to a pair of cross coupled riccati equations which may be solved using a standard numerical integration procedure we begin our development by considering strategy sets containing linear controllers only at the end of the paper we broaden the strategy sets to include a class of nonlinear controls it turns out that this extension has no effect on the necessary and sufficient conditions for the existence of a solution or on the nature of the controllers

a behavioral approach to the h optimal control problem this paper considers the general h optimal control problem from a behavioral perspective a formalization of this problem is given that departs from the usual h control paradigm in the sense that system variables of the plant are treated in a symmetric way without distinguishing control inputs measurements exogenous inputs and to be controlled variables interconnection variables are introduced and controllers are allowed to constrain the interconnection variables of the plant necessary and sufficient conditions are given for the existence of controllers that achieve an h control objective for a given linear time invariant plant the set of all such controllers is parametrized by means of j spectral factorizations

l sup 1 optimal estimation for discrete time linear systems a linear multichannel estimation problem with discrete time linear shift invariant models is formulated in the time domain as a minimum l sup 1 norm approximation problem it is shown using some key results from optimization theory that solving the approximation problem is equivalent to solving a sequence of linear programming problems which terminates when an optimal or near optimal solution is reached the motivation for considering an l sup 1 optimal design versus l sup 2 or h sup infinity optimal designs is presented a sample problem is solved to illustrate the computational procedure as well as to compare the relative performances of the l sup 1 l sup 2 and h sup infinity optimal estimators in a practical situation

uniqueness of topological solutions and the structure of solutions for the chern simons system with two higgs particles the existence of topological solutions for the chern simons equation with two higgs particles has been proved by lin ponce and yang 16 however both the uniqueness problem and the existence of non topological solutions have been left open in this paper we consider the case of one vortex at origin among others we prove the uniqueness of topological solutions and give a complete study of the radial solutions in particular the existence of some non topological solutions

cubulating random groups at density less than 1 6 we prove that random groups at density less than 1 6 act freely and cocompactly on cat 0 cube complexes and that random groups at density less than 1 5 have codimension 1 subgroups in particular property t fails to hold at density less than 1 5

comments on ripple free deadbeat control of siso discrete systems by h r sirisena the commenter argues that the necessary and sufficient conditions given by m r sirisena ibid vol ac 30 p 168 170 feb 1985 for solving the ripple free deadbeat problem are incorrect

on the mean field type bubbling solutions for chern simons higgs equation abstract this paper is the second part of our comprehensive study on the structure of the solutions for the following chern simons higgs equation 0 1 u 1 e 2 e u 1 e u 4 j 1 n p j in u is doubly periodic on where is a parallelogram in r 2 and e 0 is a small parameter in part 1 29 we proved the non coexistence of different bubbles in the bubbling solutions and obtained an existence result for the chern simons type bubbling solutions under some nearly necessary conditions mean field type bubbling solutions for 0 1 have been constructed in 27 in this paper we shall study two other important issues for the mean field type bubbling solutions the necessary conditions for the existence and the local uniqueness the results in this paper lay the foundation to find the exact number of solutions for 0 1

a system of elliptic equations arising in chern simons field theory we prove the existence of topological vortices in a relativistic self dual abelian chem simons theory with two higgs particles and two gauge fields through a study of a coupled system of two nonlinear elliptic equations over r 2 we present two approaches to prove existence of solutions on bounded domains via minimization of an indefinite functional and via a fixed point argument we then show that we may pass to the full r 2 limit from the bounded domain solutions to obtain a topological solution in r 2

elliptic functions green functions and the mean field equations on tori we show that the green functions on flat tori can have either 3 or 5 critical points only there does not seem to be any direct method to attack this problem instead we have to employ sophisticated non linear partial differential equations to study it we also study the distribution of number of critical points over the moduli space of flat tori through deformations the functional equations of special theta values provide important inequalities which lead to a solution for all rhombus tori the general picture is also emerged though some of the necessary technicality is still to de developed 1 introduction and statement of results the study of geometric or analytic problems on two dimensional tori is the same as the study of problems on r 2 with doubly periodic data such situations occur naturally in sciences and mathematics since early days the mathematical foundation of elliptic functions was subsequently devel oped in the 19th century it turns out that these special functions are rather deep objects by themselves tori of different shape may result in very dif ferent behavior of the elliptic functions and their associated objects arith metic on elliptic curves is perhaps the eldest and the most vivid example in this paper we show that this is also the case for certain non linear par tial differential equations indeed researches on doubly periodic problems in mathematical physics or differential equations often restrict the study to rectangular tori for simplicity this leaves the impression that the theory for general tori may resemble much the same way as for the rectangular case however this turns out to be false we will show that the solvability of themean field equation dependson the shape of the green function which in turn depends on the geometry of the tori in an essential way recall that the green function g z w on a flat torus t c z 1 z 2 is the unique function on t t which satisfies zg z w w z 1 t

on polynomial matrix spectral factorization by symmetric extraction we revise the 1963 davis algorithm 2 for the spectral factorization of a para hermitian nonnegative polynomial matrix phi by symmetric factor extraction this algorithm is careless about zeros at infinity by introducing the notion of diagonal reducedness of phi we obtain an easy sufficient test for the absence of zeros at infinity we show then how to get phi diagonally reduced by diagonal excess reduction steps similar to the oono and yasuura steps removing all zeros at infinity and then how to remove synunetrically finite zeros while keeping el diagonally reduced hence free of zeros at infinity this results in a revised symmetric extraction spectral factorization algorithm with monotone degree control an example shows the didactical conceptual simplicity of the method appropriate symmetric extraction is discovered by revising and discovering important particular one sided factor extraction properties of polynomial matrices

on the entire radial solutions of the chern simons su 3 system in this paper we study the entire radial solutions of the self dual equations arising from the relativistic su 3 chern simons model proposed by kao and lee phys rev d 50 6626 6632 1994 and dunne phys lett b 345 452 457 1995 nuclear phys b 433 333 348 1995 understanding the structure of entire radial solutions is one of the fundamental issues for the system of nonlinear equations in this paper we prove that any entire radial solutions must be one of topological non topological and mixed type solutions and completely classify the asymptotic behaviors at infinity of these solutions even for radial solutions this classification has remained an open problem for many years as an application of this classification we prove that the two components u and v have intersection at most finite times

asymptotic behavior of condensate solutions in the chern simons higgs theory we study the asymptotic behavior of condensate solutions in the chern simons higgs model as the chern simons coupling parameter tends to zero using the variational method we prove that there exist condensate solutions which show concentration phenomena

cubulating graphs of free groups with cyclic edge groups we prove that if g is a group that splits as a finite graph of finitely generated free groups with cyclic edge groups and g has no non euclidean baumslag solitar subgroups then g is the fundamental group of a compact nonpositively curved cube complex in addition if g is also word hyperbolic i e if g contains no baumslag solitar subgroups of any type we show that g is linear in fact is a subgroup of sl n z

improved formulae for the 2 block h super optimal solution abstract improved formulae are presented for the algorithm given in gu et al automatica25 215 221 1989 for finding 2 block h super optimal solutions

feedback minimax sensitivity and optimal robustness in this paper we look for feedbacks that minimize the sensitivity function of a linear single variable feedback system represented by its frequency responses sensitivity to disturbances and robustness under plant perturbations are measured in a weighted h infty norm in an earlier paper zames proposed an approach to feedback design involving the measurement of sensitivity by multiplicative seminorms which have certain advantages over the widely used quadratic norm in problems where there is plant uncertainty or where signal power spectra are not fixed but belong to sets the problem was studied in a general setting and some h infty examples were solved here a detailed study of the single variable case is undertaken the results are extended to unstable plants and explicit formulas for the general situation of a finite number of right half plane rhp plant zeros or poles are provided the q or approximate inverse parametrization of feedbacks that maintain closed loop stability is extended to the ease of unstable plants the h infty and wiener hopf approaches are compared

the finite horizon singular h control problem with dynamic measurement feedback this paper is concerned with the finite horizon version of the h problem with measurement feedback given a finite dimensional linear time varying system together with a positive real number we obtain necessary and sufficient conditions for the existence of a possibly time varying dynamic compensator such that the l2 0 t1 induced norm of the closed loop operator is smaller than these conditions are expressed in terms of a pair of quadratic differential inequalities generalizing the well known riccati differential equations introduced recently in the context of finite horizon h control

improper cal l _ infty optimal suboptimal controllers we consider l control of mimo systems and address solvability of the problem over all finite dimensional lti controllers i e controllers whose transfer functions can be proper or improper we show that improper controllers are easily dealt with using the behavioral approach unlike the standard state space transfer matrix methods and argue that there are cases where an improper controller can outperform a proper controller in this setting we next formulate and prove necessary and sufficient conditions for suboptimal l control problem solvability and relate this to existing results about system invariant zeros further we infer that in our formulation assuming suboptimal solvability conditions on the system an optimal controller always exists possibly with an improper transfer function in other words the infimum l norm of the closed loop system is achievable when dealing with both proper and improper controller transfer functions we illustrate these results through an example for which the optimal l controller has an improper transfer function

strengthened h sup spl infin control via state feedback a majorization approach using algebraic riccati inequalities we extend the algebraic riccati equation approach to h sup spl infin h sup 2 state feedback design to incorporate additional constraints on the other nonmaximum singular values it is shown that a state feedback control law that satisfies a singular values singular vectors constraint exists if and only if a corresponding algebraic riccati inequality admits a stabilizing and positive definite solution the results are applied to devise a majorization approach for constructing state feedback controllers that strive to optimize some obvious design objectives

minimax lq stochastic tracking and servo problems it is proved that the separation between feedback and feedforward of the two degree of freedom linear quadratic lq stochastic controller reported by e mosca and g zappa ibid vol 34 p 240 2 1989 can be suitably extended when a linear controller is postulated to the minimax lq stochastic tracking and servo problems besides the relevance of the results the authors show that in some problems the wiener and the h sub infinity approaches can play a fruitful complementary role

all optimal hankel norm approximations of linear multivariable systems and their l error bounds the problem of approximating a multivariable transfer function g s of mcmillan degree n by s of mcmillan degree k is considered a complete characterization of all approximations that minimize the hankel norm is derived the solution involves a characterization of all rational functions s f s that minimize where s has mcmillan degree k and f s is anticavisal the solution to the latter problem is via results on balanced realizations all pass functions and the inertia of matrices all in terms of the solutions to lyapunov equations it is then shown that where k 1 g s is the k l st hankel singular value of g s and for one class of optimal hankel norm approximations the method is not computationally demanding and is applied to a 12 state model

grey box modelling and identification using physical knowledge and bayesian techniques abstract advanced control design requires a model that describes process behaviour adequately such a model can be constructed using physical modelling or statistical identification techniques both have their disadvantages physical models are rigorous and thus often expensive to construct while black box model structures are not necessarily compatible with physical reality since both approaches have undeniable merits as well their combination seems to be attractive and rewarding this paper discusses an approach to statistical estimation where a best linearly parametrized dynamic regression model is identified which is also consistent with specified knowledge about process responses such characteristics are forced upon the black box models yielding a grey box model set it will be shown that crucial physical knowledge such as process stability and sign of stationary gains can be translated into linear inequality constraints on the black box model parameters in order to select best estimators in the grey box class a bayesian approach is adopted given a prior distribution associated with the physical knowledge and given the data likelihood a posterior distribution is constructed maximum and average a posteriori estimators are analysed explicit solutions are given for special cases of gaussian likelihood and a prior which is uniformly or piece wise linearly distributed on a linearly constrained grey box model class finally simulation results and an application to a distillation process show the advantage of the contrained estimates under realistic experiment conditions considerable variance reductions at the cost of a somewhat larger bias can be achieved indicating the potential for e g adaptive control applications

uniformly optimal control of linear time varying systems abstract an optimal control problem is formulated in the context of linear discrete time time varying systems the cost is the supremum over all exogenous inputs in a weighted ball of the sum of the weighted energies of the plant s input and output the controller is required to be causal and to achieve internal stability existence of an optical controller is proved and a formula for the minimum cost is derived

l sub 2 gain analysis of nonlinear systems and nonlinear state feedback h sub infinity control previously obtained results on l2 gain analysis of smooth nonlinear systems are unified and extended using an approach based on hamilton jacobi equations and inequalities and their relation to invariant manifolds of an associated hamiltonian vector field on the basis of these results a nonlinear analog is obtained of the simplest part of a state space approach to linear h sub infinity control namely the state feedback h sub infinity optimal control problem furthermore the relation with h sub infinity control of the linearized system is dealt with

robust nonlinear h filtering this paper investigates the robust nonlinear h filtering problem for nonlinear systems with uncertainties which are described by integral functional constraints the objective is to design a dynamic filter such that the l 2 gain from an exogenous input to an estimation error is minimized or guaranteed to be less or equal to a prescribed value for all admissable uncertainties we establish the interconnection between the robust nonlinear h filtering problem and the nonlinear h filtering problem for known systems i e systems without uncertainties using the existing nonlinear h filtering results for known systems we solve the robust nonlinear h filtering problem in terms of hamilton jacobi inequalities

frequency response algorithms for h sub infinity optimization with time domain constraints a very broad framework for control system design is considered that encompasses frequency response methodologies for h sub infinity optimization that solve various aspects of the control design problem and that are less well known that state space methods the focus is on linear programming lawson s algorithm and trefethen s algorithm a modified lawson s algorithm is proposed and related to trefethan s method the modified algorithm is shown to be significantly faster than linear programming and lawson s algorithm it is also shown how to extend the modified lawson s algorithm so as to handle time domain constraints in addition to frequency domain specifications which distinguishes it from other h sub infinity optimization methods some steps are taken toward dealing with time domain constraints within an h sub infinity optimization framework

paper efficient algorithm for matrix spectral factorization an algorithm is presented for the spectral factorization of polynomial or rational matrices arising in optimal control and filtering theory as well as in network theory there are two versions of the algorithm one applicable to continuous time problems the other to discrete time ones both versions are based on newton s method feature quadratic convergence and provide a significant improvement in efficiency over the existing methods

h sub infinity minimum error state estimation of linear stationary processes a state estimator is derived which minimizes the h sub infinity norm of the estimation error power spectrum matrix two approaches are presented the first achieves the optimal estimator in the frequency domain by finding the filter transfer function matrix that leads to an equalizing solution the second approach establishes a duality between the problem of h sub infinity filtering and the problem of unconstrained input h sub infinity optimal regulation using this duality previously published results for the latter regulation problem are applied which lead to an optimal filter that possess the structure of the corresponding kalman filter the two approaches usually lead to different results they are compared by a simple example which also demonstrates a clear advantage of the h sub infinity estimate over the conventional l sub 2 estimate

h sup spl infin optimality of the lms algorithm we show that the celebrated least mean squares lms adaptive algorithm is h sup spl infin optimal the lms algorithm has been long regarded as an approximate solution to either a stochastic or a deterministic least squares problem and it essentially amounts to updating the weight vector estimates along the direction of the instantaneous gradient of a quadratic cost function we show that the lms can be regarded as the exact solution to a minimization problem in its own right namely we establish that it is a minimax filter it minimizes the maximum energy gain from the disturbances to the predicted errors whereas the closely related so called normalized lms algorithm minimizes the maximum energy gain from the disturbances to the filtered errors moreover since these algorithms are central h sup spl infin filters they minimize a certain exponential cost function and are thus also risk sensitive optimal we discuss the various implications of these results and show how they provide theoretical justification for the widely observed excellent robustness properties of the lms filter

dissipative systems synthesis a linear algebraic approach abstract in this paper we consider the problem of synthesis of dissipative systems for the case that first and higher order derivatives of the concerned variables also appear in the weighting function the problem is formulated and solved using the behavioral approach to systems and control we relate the problem of weighted h control as a special case of this synthesis problem the synthesis problem and its solution can be systematically understood when one notices that it is similar to finding a non negative subspace non negative with respect to a given constant matrix within a finite dimensional vector space satisfying certain inclusion and dimension constraints

an algorithm for super optimal h design the two block case abstract in this paper we consider the strengthened h optimization problem in the two block case an algorithm for the super optimal solution is proposed it is based on results by the authors ieee trans aut control ac 33 833 1988 for the less practical one block case it uses state space models and is numerically implementable a feature of the procedure is an optimality criterion which is a natural generalization of that used in the iterative scheme of doyle lecture notes in advances in multivariable control onr honeywell workshop minneapolis u s a 1984 for the unstrengthened problem

uniqueness and solution structure of nonlinear equations arising from the chern simons gauged o 3 sigma models abstract in this paper we study radially symmetric solutions of nonlinear equations arising from the chern simons gauged o 3 sigma models there are three types of solutions according to the boundary conditions topological solutions nontopological solutions of type i and ii we classify radially symmetric nontopological solutions of type i and ii by the decay rates at infinity in particular we provide a complete picture of the graph of which gives uniqueness and structure of solutions

h sub infinity control by state feedback and fast algorithms for the computation of optimal h sub infinity norms the suboptimality of some parameter for h sub infinity optimization by dynamic state feedback is characterized in terms of the solvability of riccati inequalities this is done without restricting the finite zero structure of the plant if there are no system zeros on the imaginary axis the h sub infinity problem can be treated in a complete and satisfactory way explicit characterizations optimum to be achieved are provided and a closed formula for the optimal value is derived in terms of the h sub infinity norm of some fixed transfer matrix if the optimum is not attained any sequence of controllers of bounded size which is constructed to approach the infimal norm must necessarily be high gain a globally and quadratically convergent algorithm to compute the optimal value is proposed this algorithm is generalized to the h sub infinity optimization problem by measurement feedback

extensions to h multivariable robust controllers and the relationship to lqg design problems an alternative set of equations for generating h multivariable controllers is derived which are of quadratic form these can be solved by newton raphson procedures as in the work by kwakernaak 1986 it is shown that the h controller may be put in the form of a youla parameterization the particular parameterization employed provides a link with the equivalent lqg robust optimal controller since when the youla gain falls to zero the controller becomes identical it is also shown that for canonical multivariable industrial system models the equations to be solved have a very simple structure this enables the multivariable problem to be solved using algorithms which are almost as simple as for the scalar case that the results have a practical application is illustrated in a strip flatness cold rolling problem

property a and cat 0 cube complexes property a is a non equivariant analogue of amenability defined for metric spaces euclidean spaces and trees are examples of spaces with property a simultaneously generalising these facts we show that finite dimensional cat 0 cube complexes have property a we do not assume that the complex is locally finite we also prove that given a discrete group acting properly on a finite dimensional cat 0 cube complex the stabilisers of vertices at infinity are amenable

a state space approach to super optimal h sup infinity control problems a numerically stable algorithm is presented for solving the strengthened or super optimal model matching problem the steps of the algorithm follows closely those given by n j young 1986 except that for each step a reliable implementation using state space models is provided

classification of the entire radial self dual solutions to non abelian chern simons systems abstract we consider the entire radial solutions to the non abelian chern simons systems of rank 2 u v k e u e v k e u 0 0 e v k e u e v 4 n 1 0 4 n 2 0 0 1 in r 2 where n i 0 i 1 2 and k a i j is a 2 2 matrix satisfying a 11 a 22 0 a 12 a 21 0 and a 11 a 22 a 12 a 21 0 this system is motivated by the relativistic non abelian chern simons model lozano marques moreno schaposnik model of bosonic sector of n 2 supersymmetric chern simons higgs theory and gudnason model of n 2 supersymmetric yang mills chern simons higgs theory understanding the structure of entire radial solutions is one of fundamental issues for the system of nonlinear equations we prove that any entire radial solutions of 0 1 must be one of topological non topological and mixed type solutions and completely classify the asymptotic behaviors at infinity of these solutions as an application of this classification we prove that the two components u and v have intersection at most finite times

cubulating malnormal amalgams let g be a group splitting as a graph of groups where each vertex group acts properly on a cat 0 cube complex when g is hyperbolic relative to virtually abelian subgroups we examine conditions producing a proper action of g on a cat 0 cube complex when g is hyperbolic this action is also cocompact

closed form solutions to a class of h optimization problems a closed form solution is presented to the h sub optimal control problem via state or output feedback the problem formulation is general and does not impose any restrictions on feedthrough terms between the control input and the controlled output or between the disturbance input and the measurement output variables it is however required that both the transfer function from the disturbance input to the measurement output and the transfer function from the control input to the controlled output have no invariant zeros on the jw axis and that they satisfy certain geometric conditions for the same class of systems the conditions under which the h optimal control problem via state feedback has a solution are given moreover explicit expressions for the optimal solutions are provided finally the pole zero cancellations in the closed loop system resulting from the h optimal or sub optimal state or output feedback are examined

bubbling solutions for relativistic abelian chern simons model on a torus we prove the existence of bubbling solutions for the following chern simons higgs equation delta u frac 1 varepsilon 2 e u 1 e u 4 pi sum j 1 n delta p j quad rm in omega where is a torus we show that if n 4 and p 1 p j j 2 n then for small e 0 the above problem has a solution u e and as e 0 u e blows up at the vertex point p 1 and satisfies frac 1 varepsilon 2 e u 1 e u to 4 pi n delta p 1 this is the first result for the existence of a solution which blows up at a vertex point

feedback and optimal sensitivity model reference transformations multiplicative seminorms and approximate inverses in this paper the problem of sensitivity reduction by feedback is formulated as an optimization problem and separated from the problem of stabilization stable feedback schemes obtainable from a given plant are parameterized salient properties of sensitivity reducing schemes are derived and it is shown that plant uncertainty reduces the ability of feedback to reduce sensitivity the theory is developed for input output systems in a general setting of banach algebras and then specialized to a class of multivariable time invariant systems characterized by n times n matrices of h infty frequency response functions either with or without zeros in the right half plane the approach is based on the use of a weighted seminorm on the algebra of operators to measure sensitivity and on the concept of an approximate inverse approximate invertibility of the plant is shown to be a necessary and sufficient condition for sensitivity reduction an indicator of approximate invertibility called a measure of singularity is introduced the measure of singularity of a linear time invariant plant is shown to be determined by the location of its right half plane zeros in the absence of plant uncertainty the sensitivity to output disturbances can be reduced to an optimal value approaching the singularity measure in particular if there are no right half plane zeros sensitivity can be made arbitrarily small the feedback schemes used in the optimization of sensitivity resemble the lead lag networks of classical control design some of their properties and methods of constructing them in special cases are presented

minimax lq exact and inexact model matching problems abstract a mixed h 2 h optimal problem is presented for both disturbance attenuation and model mismatching minimization its solution is in the form of a two degrees of freedom controller whose feedback and feedforward paths can be independently designed if the conditions for exact model matching are not met an inexact model matching problem is addressed this solution provides an effective model matching design methodology for non minimum phase plants

the general distance problem in h optimal control theory abstract the general distance problem that arises in h optimal control theory is considered transformations that reduce the general h problem to the general distance problem are reviewed and an iterative scheme called iteration is considered in which the general distance problem is reduced to a standard best approximation problem the iteration is viewed as a problem of finding the zero crossing of a function this function is shown to be continuous monotonically decreasing convex and bounded by some very simple functions these properties make it possible to obtain very rapid convergence of the iterative process the issues of model reduction and approximation in h synthesis will also be addressed

periodic maxwell chern simons vortices with concentrating property in order to study electrically and magnetically charged vortices in fractional quantum hall effect and anyonic superconductivity the maxwell chern simons mcs model was introduced by lee et al phys lett b 252 79 83 1990 as a unified system of the classical abelian higgs model ah and the chern simons cs model in this article the first goal is to obtain the uniform cs limit result of mcs model with respect to the chern simons parameter without any restriction on either a particular class of solutions or the number of vortex points as the chern simons mass scale tends to infinity the most important step for this purpose is to derive the relation between the higgs field and the neutral scalar field our cs limit result also provides the critical clue to answer the open problems raised by ricciardi and tarantello comm pure appl math 53 811 851 2000 and tarantello milan j math 72 29 80 2004 and we succeed to establish the existence of periodic maxwell chern simons vortices satisfying the concentrating property of the density of superconductive electron pairs furthermore we expect that the cs limit analysis in this paper would help to study the stability multiplicity and bubbling phenomena for solutions of the mcs model

non topological multivortex solutions to the self dual maxwell chern simons higgs systems in this paper we construct non topological multivortex solutions to the non relativistic self dual maxwell chern simons higgs system in r2 which make the energy functional finite moreover our proof of the existence of solutions reveals precise asymptotic behavior of solutions near spatial infinity using exactly the same method we also establish the existence of non topological multivortex solutions to the relativistic self dual maxwell chern simons higgs system

on a sharp sobolev type inequality on two dimensional compact manifolds motivated by the asymptotic analysis of double vortex condensates in the chern simons higgs theory we construct a suitable minimizing sequence for a sharp sobolev inequality a la moser for two dimensional compact manifolds as a consequence we first obtain a direct proof of the sharp character of such an inequality secondly and more interestingly we use such minimizing sequence to show that for the flat torus the corresponding extremal problem attains its infimum

bubbling solutions for the su 3 chern simons model on a torus we consider the following nonlinear system derived from the su 3 chern simons models on a torus where denotes the dirac measure at when if we look for a solution with then 0 1 is reduced to the chern simons higgs equation the existence of bubbling solutions to 0 1 has been a longstanding problem in this paper we prove the existence of such solutions such that even if 2012 wiley periodicals inc

existence of mixed type solutions in the chern simons gauge theory of rank two in r2 abstract we consider the self dual equations arising from the chern simons gauge theory of rank 2 such as the s u 3 s o 5 and g 2 chern simons model in r 2 there are three possible types of solutions in these theories namely topological nontopological and mixed type solutions the existence of a mixed type solution for an arbitrary configuration of vortex points has been a long standing open problem we construct here a family of mixed type solutions u 1 e u 2 e e 0 for an arbitrary configuration of vortex points under a mild non degeneracy condition the main new idea of our construction of an approximate solution is to use different scalings for different components in the process of the finite dimensional reduction all estimates for this particular construction become rather delicate

h sub infinity fixed lag smoothing filter for scalar systems the solution of the h sub infinity optimal linear fixed lag smoothing problem is considered using a polynomial matrix description for the discrete system the smoother is obtained from the solution of a linear equation and a spectral factorization calculation the pole zero properties of the optimal smoother are obvious in the polynomial representation and insights into the measurement noise rejection properties of the smoother are obtained allowance is made for both dynamic cost weighting and colored measurement noise the polynomial form of the smoothing filter may be incorporated into a self tuning algorithm and a simple adaptive smoother is discussed

h sub infinity optimal control as a weighted wiener hopf problem it is shown that h sub infinity optimization is equivalent to weighted h sub 2 optimization in the sense that the solution of the latter problem also solves the former the weighting rational matrix that achieves this equivalence is explicitly computed in terms of a state space realization the authors do not suggest transforming h sub infinity optimization problems to h sub 2 optimization problems as a computational approach rather their results reveal an interesting connection between h sub infinity and h sub 2 optimization problems which is expected to offer additional insight for example h sub 2 optimal controllers are known to have an optimal observer full state feedback structure the result obtained shows that the minimum entropy solution of h sub infinity optimal control problems can be obtained as an h sub 2 optimal solution therefore it can be expected that the corresponding h sub infinity optimal controller has an optimal observer full state feedback structure

self dual symmetric nontopological solutions in the su 3 model in mathbb r 2 in this paper we study non topological solutions u 1 u 2 to the su 3 chern simons system satisfying the asymptotic behavior u k x 2 alpha k ln x o 1 for some alpha k 1 k 1 2 we show that solutions remain uniformly bounded as long as 1 2 lies in s n see sect 1 and then we prove the existence of non topological solutions for any alpha 1 alpha 2 in s n for this purpose we have to study the phenomena of partial blowup at infinity and show that s n is the optimal range of 1 2 such that the partial blowup could occur if 1 2 is on some part of partial s n

relative ends l 2 invariants and property t we establish a splitting theorem for one ended groups h g such that e g h 2 and the almost malnormal closure of h is a proper subgroup of g this yields splitting theorems for groups g with non trivial first l2 betti number 12 g we verify the kropholler conjecture for pairs h g satisfying 12 g 12 h we also prove that every n dimensional poincare duality pdn group containing a pdn 1 group h with property t splits over a subgroup commensurable with h

degree counting and shadow system for toda system of rank two one bubbling abstract we initiate the program for computing the leray schauder topological degree for toda systems of rank two this program still contains a lot of challenging problems for analysts as the first step we prove that if a sequence of solutions u 1 k u 2 k blows up then one of h j e u j k m h j e u j k d v g j 1 2 tends to a sum of dirac measures this is so called the phenomena of weak concentration our purposes in this article are i to introduce the shadow system due to the bubbling phenomena when one of parameters i crosses 4 and j 4 n where 1 i j 2 ii to show how to calculate the topological degree of toda systems by computing the topological degree of the general shadow systems iii to calculate the topological degree of the shadow system for one point blow up we believe that the degree counting formula for the shadow system would be useful in other problems

two degree of freedom h sub infinity optimization of multivariable feedback systems a solution to the two degree of freedom h sub infinity minimization problem that arises in the design of multivariable optimal continuous time stochastic control systems is derived a decoupling approach that enables a partially independent design of the prefilter and the feedback controller and yields a simple solution to the optimization problem is applied this solution is obtained by transforming the optimization problem into two standard form four block problems

blow up at infinity in the su 3 chern simons model part i abstract we consider non topological solutions of a nonlinear elliptic system problem see 1 4 below derived from the s u 3 chern simons models in r 2 the existence of non topological solutions even for radial symmetric case has been a long standing open problem recently choe kim and lin in 7 8 showed the existence of radial symmetric non topological solution when the vortex points collapse however the arguments in 7 8 cannot work for an arbitrary configuration of vortex points in this paper we develop a new approach by using different scalings for different components of the system to construct a family of non topological solutions which blows up at infinity

linear estimation in krein spaces ii applications we have shown that several interesting problems in h sup spl infin filtering quadratic game theory and risk sensitive control and estimation follow as special cases of the krein space linear estimation theory developed in part i we show that all these problems can be cast into the problem of calculating the stationary point of certain second order forms and that by considering the appropriate state space models and error gramians we can use the krein space estimation theory to calculate the stationary points and study their properties the approach discussed here allows for interesting generalizations such as finite memory adaptive filtering with varying sliding patterns

degree counting for toda system with simple singularity one point blow up abstract in this paper we study the degree counting formula of the rank two toda system with simple singular source when 1 0 4 4 8 and 2 4 n the key step is to derive the degree formula of the shadow system which arises from the bubbling solutions as 1 tends to 4 in order to compute the topological degree of the shadow system we need to find some suitable deformation during this deformation we shall deal with new difficulty arising from the phenomenon blow up does not necessarily imply concentration of mass this phenomenon occurs due to the collapsing of singularities this is a continuation of the previous work 25

a polynomial approach to minimax frequency domain optimization of multivariable feedback systems the properties of a feedback system where the plant has rational transfer matrix h and the compensator has transfer matrix g can be characterized through the system functions s i hg and t g i hg 1 good disturbance attenuation robustness limited bandwidth and compensator roll off may be obtained by minimizing a criterion of the form z where z v s t w1 wls t w2 w2t v with respect to the compensator transfer matrix g here v w1 and w2 are suitable rational weighting matrices the solution of the problem can be reduced to a pair of matrix polynomial equations since the optimal solution is highly non unique special solutions with additional optimality properties are considered as well the paper includes a discussion of the numerical solution of the polynomial equations and of the question how to choose the weighting matrices to ensure required feedback system properties an example illustrates the results

a transfer function approach to the problems of discrete time systems h sub infinity optimal linear control and filtering a solution is derived to the problems of h sub infinity optimal linear state regulation and filtering the solution method for both problems is based on a transfer function approach which applies standard spectral factorization return difference relations are given which are extensions of the relations associated with the linear quadratic problem

codimension 1 subgroups and splittings of groups abstract we show that under certain circumstances a codimension 1 subgroup h of a finitely generated group g either provides a splitting of g as an amalgam or provides a codimension 1 subgroup of h in particular if g is hyperbolic and h is quasiconvex one gets a descending sequence of codimension 1 subgroups terminating at a splitting in the process we settle a conjecture of kropholler and roller for the case of quasiconvex subgroups of hyperbolic groups

nondefinite least squares and its relation to h sub infinity minimum error state estimation the problem of recursive nondefinite least squares state estimation of continuous time stationary processes is solved by applying pontryagin s maximum principle a comparison of the derived solution to the result that is obtained for the h sub infinity minimum error estimation suggests a new interpretation for the h sub infinity optimal estimation mechanism according to this interpretation the estimator tries to optimally estimate the required combination of the states in the l sub 2 norm sense against the worst disturbance signal that stems from a fictitious measurement of this combination

state space solutions to standard h sub 2 and h sub infinity control problems simple state space formulas are derived for all controllers solving the following standard h sub infinity problem for a given number gamma 0 find all controllers such that the h sub infinity norm of the closed loop transfer function is strictly less than gamma it is known that a controller exists if and only if the unique stabilizing solutions to two algebraic riccati equations are positive definite and the spectral radius of their product is less than gamma sup 2 under these conditions a parameterization of all controllers solving the problem is given as a linear fractional transformation lft on a contractive stable free parameter the state dimension of the coefficient matrix for the lft constructed using the two riccati solutions equals that of the plant and has a separation structure reminiscent of classical lqg i e h sub 2 theory this paper is intended to be of tutorial value so a standard h sub 2 solution is developed in parallel

comments on stein s postulated high frequency behavior of h sub infinity optimal controllers g stein 26th ieee conf decision control los angeles ca dec 1987 showed that h sub infinity controller designs often give very unrealistic high frequency behavior the polynomial systems approach to h sub infinity is used by the commenter to demonstrate that the high frequency gain of h sub infinity controllers can be made to fall off at any desired rate provided improper noise and weighting models are chosen

a two sided interpolation approach to h sub infinity optimization problems a solution to the two sided interpolation problem which arises in h sub infinity optimization theory is obtained this solution is found in closed form explicitly in terms of the required interpolation directions it is simple to obtain and it does not require the application of the relatively complicated matrix pick nevanlinna theory the solution obtained is of minimum order due to its simplicity the order reduction which occurs at the minimum value of the h sub infinity norm is clearly explained

norm preserving dilations and their applications to optimal error bounds the problem is given a b c to find d such that left begin array 20 c a c b d end array right leqq mu here we deal with hilbert space operators a b and c ar

a boundary criterion for cubulation we give a criterion in terms of the boundary for the existence of a proper cocompact action of a word hyperbolic group on a rm cat 0 cube complex we describe applications towards lattices and hyperbolic 3 manifold groups in particular by combining the theory of special cube complexes the surface subgroup result of kahn markovic and agol s criterion we find that every subgroup separable closed hyperbolic 3 manifold is virtually fibered

a simple method for deriving j spectral factors a simple method is presented for deriving the j spectral factor of a transfer function matrix explicitly in terms of the parameters of this matrix this method provides closed form expressions for the j spectral factor and its inverse which only require a solution of a single linear sylvester equation this method can be easily applied in the solution of the h sub infinity optimal regulation problem and it provides useful geometric insight into the structure of the optimal regulator return difference matrix