finite dimensional controllers for linear distributed parameter systems exponential stability using residual mode filters abstract modal control has often been proposed as a way to design stabilizing low order controllers for distributed parameter systems dps however it is well known that such controllers designed from a reduced order modal model do not necessarily stabilize the actual dps in this paper we prove that exponential closed loop stability can always be achieved by the addition of a residual mode filter of sufficiently large dimension

minimum cost spanning tree games we consider the problem of cost allocation among users of a minimum cost spanning tree network it is formulated as a cooperative game in characteristic function form referred to as a minimum cost spanning tree m c s t game we show that the core of a m c s t game is never empty in fact a point in the core can be read directly from any minimum cost spanning tree graph associated with the problem for m c s t games with efficient coalition structures we define and construct m c s t games on the components of the structure we show that the core and the nucleolus of the original game are the cartesian products of the cores and the nucleoli respectively of the induced games on the components of the efficient coalition structure

structure of intermediate wakimoto modules abstract we show that our construction of boson type realizations of affine sl n 1 in terms of intermediate wakimoto modules gives representations that are generically isomorphic to certain verma type modules we then use this identification to obtain information about the submodule structure of intermediate wakimoto modules

mobile point controls versus locally distributed ones for the controllability of the semilinear parabolic equation it is well known now that a rather general semilinear parabolic equation with globally lipschitz nonlinear term is both approximately and exactly null controllable in l2 omega when governed in a bounded domain by the locally distributed controls in this paper we intend to show that in fact in one space dimension omega 0 1 the very same results can be achieved by employing em at most two mobile point controls with support on the curves properly selected within an arbitrary subdomain of qt 0 1 0 t we will show that such curves can be described by a certain differential inequality and the explicit examples are provided we also discuss some extensions of our main results to the superlinear terms and to the case of several dimensions

on the concavity of delivery games abstract delivery games introduced by hamers borm van de leensel and tijs in 1994 are combinatorial optimization games that arise from delivery problems closely related to the chinese postman problem cpp they showed that delivery games are not necessarily balanced for delivery problems corresponding to the class of bridge connected euler graphs they showed that the related games are balanced this paper focuses on the concavity property for delivery games a delivery game arising from a delivery model corresponding to a bridge connected euler graph need not be concave the main result will be that for delivery problems corresponding to the class of bridge connected cyclic graphs which is a subclass of the class of bridge connected euler graphs the related delivery games are concave further we discuss some extreme points of the core and the value for this class of concave delivery games

a galerkin neural network based design of guaranteed cost control for nonlinear distributed parameter systems this paper presents a galerkin neural network based guaranteed cost control gcc design for a class of parabolic partial differential equation pde systems with unknown nonlinearities a parabolic pde system typically involves a spatial differential operator with eigenspectrum that can be partitioned into a finite dimensional slow one and an infinite dimensional stable fast complement motivated by this in the proposed control scheme galerkin method is initially applied to the pde system to derive an ordinary differential equation ode system with unknown nonlinearities which accurately describes the dynamics of the dominant slow modes of the pde system the resulting nonlinear ode system is subsequently parameterized by a multilayer neural network mnn with one hidden layer and zero bias terms then based on the neural model and a lure type lyapunov function a linear modal feedback controller is developed to stabilize the closed loop pde system and provide an upper bound for the quadratic cost function associated with the finite dimensional slow system for all admissible approximation errors of the network the outcome of the gcc problem is formulated as a linear matrix inequality lmi problem moreover by using the existing lmi optimization technique a suboptimal guaranteed cost controller in the sense of minimizing the cost bound is obtained finally the proposed design method is applied to the control of the temperature profile of a catalytic rod

h _ infty fuzzy observer based control for a class of nonlinear distributed parameter systems with control constraints an hinfin fuzzy observer based control design is proposed for a class of nonlinear parabolic partial differential equation pde systems with control constraints for which the eigenspectrum of the spatial differential operator can be partitioned into a finite dimensional slow one and an infinite dimensional stable fast complement in the proposed control scheme galerkin s method is initially applied to the pde system to derive a nonlinear ordinary differential equation ode system that accurately describes the dynamics of the dominant slow modes of the pde system the resulting nonlinear ode system is subsequently represented by the takagi sugeno t s fuzzy model then based on the t s fuzzy model a fuzzy observer based controller is developed to stabilize the nonlinear pde system and achieve an optimized hinfin disturbance attenuation performance for the finite dimensional slow system while control constraints are respected the outcome of the hinfin fuzzy observer based control problem is formulated as a bilinear matrix inequality bmi optimization problem a local optimization algorithm that treats the bmi as a double linear matrix inequality is presented to solve this bmi optimization problem finally the proposed design method is applied to the control of the temperature profile of a catalytic rod to illustrate its effectiveness

non linear feedback control of parabolic partial differential difference equation systems this paper proposes a general method for the synthesis of non linear output feedback controllers for single input singleoutput quasi linear parabolic partial differential difference equation pdde systems for which the eigenspectrum of the spatial differential operator can be partitioned into a finite dimensional slow one and an infinite dimensional stable fast complement initially a non linear model reduction scheme which is based on combination of galerkin s method with the concept of approximate inertial manifold is employed for the derivation of differential difference equation dde systems that describe the dominant dynamics of the pdde system then these dde systems are used as the basis for the explicit construction of non linear output feedback controllers through combination of geometric and lyapunov techniques the controllers guarantee stability and enforce output tracking in the closed loop parabolic pdde system independently of the size of the state delay provided that the separation o

generalized network problems yielding totally balanced games a class of multiperson mathematical optimization problems is considered and is shown to generate cooperative games with nonempty cores the class includes but is not restricted to numerous versions of network flow problems it was shown by owen that for games generated by linear programming optimization problems optimal dual solutions correspond to points in the core we identify a special class of network flow problems for which the converse is true i e every point in the core corresponds to an optimal dual solution

on some balanced totally balanced and submodular delivery games this paper studies a class of delivery problems associated with the chinese postman problem and a corresponding class of delivery games a delivery problem in this class is determined by a connected graph a cost function defined on its edges and a special chosen vertex in that graph which will be referred to as the post office it is assumed that the edges in the graph are owned by different individuals and the delivery game is concerned with the allocation of the traveling costs incurred by the server who starts at the post office and is expected to traverse all edges in the graph before returning to the post office a graph g is called chinese postman submodular or for short cp submodular cp totally balanced cp balanced respectively if for each delivery problem in which g is the underlying graph the associated delivery game is submodular totally balanced balanced respectively for undirected graphs we prove that cp submodular graphs and cp totally balanced graphs are weakly cyclic graphs and conversely an undirected graph is shown to be cp balanced if and only if it is a weakly euler graph for directed graphs cp submodular graphs can be characterized by directed weakly cyclic graphs further it is proven that any strongly connected directed graph is cp balanced for mixed graphs it is shown that a graph is cp submodular if and only if it is a mixed weakly cyclic graph finally we note that undirected directed and mixed weakly cyclic graphs can be recognized in linear time

fuzzy boundary control design for a class of nonlinear parabolic distributed parameter systems this paper deals with the problem of fuzzy boundary control design for a class of nonlinear distributed parameter systems which are described by semilinear parabolic partial differential equations pdes both distributed measurement form and collocated boundary measurement form are considered a takagi sugeno t s fuzzy pde model is first applied to accurately represent the semilinear parabolic pde system based on the t s fuzzy pde model two types of fuzzy boundary controllers which are easily implemented since only boundary actuators are used are proposed to ensure the exponential stability of the resulting closed loop system sufficient conditions of exponential stabilization are established by employing the lyapunov direct method and the vector valued wirtinger s inequality and presented in terms of standard linear matrix inequalities finally the advantages and effectiveness of the proposed control methodology are demonstrated by the simulation results of two examples

borel subalgebras and categories of highest weight modules for toroidal lie algebras abstract in this article we begin an investigation of the conjugacy classes of borel subalgebras together with verma modules induced from standard borel subalgebras of a toroidal lie algebra t in two variables we define for each highest weight a category o of representations of t that contain these verma modules and show that when a certain central element acts nontrivially this category is equivalent to the category o m for an extension of a suitable affine kac moody algebra m t from this equivalence we obtain a bgg type resolution and bgg duality theorem in the setting of o

guaranteed cost fuzzy state observer design for semilinear parabolic pde systems under pointwise measurements abstract this paper studies the guaranteed cost fuzzy state observer gcfso design via pointwise measurement sensors for a class of distributed parameter systems described by semilinear parabolic partial differential equations pdes initially a takagi sugeno t s fuzzy model is employed to accurately represent the original pde system in a local region then based on the t s fuzzy model a fuzzy state observer is constructed for the state estimation by augmenting the state estimation error system with the fuzzy pde system and utilizing lyapunov technique and wirtinger s inequality a fuzzy state observer design with a guaranteed cost is developed in terms of linear matrix inequalities lmis the resulting fuzzy observer can exponentially stabilize the augmented system while providing an upper bound on the cost function of state estimation error moreover a suboptimal gcfso design problem is also addressed to make the upper bound as small as possible finally the numerical simulation results on two examples demonstrate the effectiveness of the proposed method

cost allocation in the chinese postman problem this paper considers a cost allocation problem that arises from a delivery problem associated with the chinese postman problem cpp a delivery problem is described by a connected undirected graph in which each edge belongs to a different player a cost function on the edges of this graph and a fixed vertex which is referred to as the post office assume that the post office is providing some service to the players the nature of this service which can be thought of as mail delivery requires that a server will travel along the edges of the graph and returns to the post office the cost allocation problem is concerned with the cost of providing the service to all players a specific cost allocation rule is introduced and characterized further the class of delivery problems gives rise to a new class of cooperative combinatorial optimization games called delivery games it is shown that the outcome of the allocation rule with respect to a bridge connected euler graph is a core element of the corresponding delivery game

control of 1d parabolic pdes with volterra nonlinearities part ii analysis for a class of stabilizing boundary controllers for nonlinear 1d parabolic pdes introduced in a companion paper we derive bounds for the gain kernels of our nonlinear volterra controllers prove the convergence of the series in the feedback laws and establish the stability properties of the closed loop system we show that the state transformation is at least locally invertible and include an explicit construction for computing the inverse of the transformation using the inverse we show l 2 and h 1 exponential stability and explicitly construct the exponentially decaying closed loop solutions we then illustrate the theoretical results on an analytically tractable example

exponential pointwise stabilization of semilinear parabolic distributed parameter systems via the takagi sugeno fuzzy pde model this paper deals with the problem of exponential stabilization for nonlinear parabolic distributed parameter systems using the takagi sugeno t s fuzzy partial differential equation pde model where a finite number of actuators are active only at some specified points of the spatial domain these actuators are referred to as pointwise actuators three cases of state feedback are respectively considered in this study as follows full state feedback piecewise state feedback and collocated pointwise state feedback it is initially assumed that a t s fuzzy pde model obtained via the sector nonlinearity approach is employed to accurately represent the semilinear parabolic pde system based on the obtained t s fuzzy pde model lyapunov based design methodologies of fuzzy feedback control laws are subsequently derived for the above three state feedback cases by using the vector valued wirtinger s inequality to guarantee locally exponential pointwise stabilization of the semilinear pde system and presented in terms of standard linear matrix inequalities lmis moreover the favorable property offered by sharing all the same premises in the t s fuzzy pde models and fuzzy controllers is not applicable for the case of collocated pointwise state feedback a parameterized lmi is introduced for this case to enhance the stabilization ability of the fuzzy controller finally the merit and effectiveness of the proposed design methods are demonstrated by numerical simulation results of two examples

control of 1 d parabolic pdes with volterra nonlinearities part i design boundary control of nonlinear parabolic pdes is an open problem with applications that include fluids thermal chemically reacting and plasma systems in this paper we present stabilizing control designs for a broad class of nonlinear parabolic pdes in 1 d our approach is a direct infinite dimensional extension of the finite dimensional feedback linearization backstepping approaches and employs spatial volterra series nonlinear operators both in the transformation to a stable linear pde and in the feedback law the control law design consists of solving a recursive sequence of linear hyperbolic pdes for the gain kernels of the spatial volterra nonlinear control operator these pdes evolve on domains t n of increasing dimensions n 1 and with a domain shape in the form of a hyper pyramid 0 x n x n 1 x 1 x 1 we illustrate our design method with several examples one of the examples is analytical while in the remaining two examples the controller is numerically approximated for all the examples we include simulations showing blow up in open loop and stabilization for large initial conditions in closed loop in a companion paper we give a theoretical study of the properties of the transformation showing global convergence of the transformation and of the control law nonlinear volterra operators and explicitly constructing the inverse of the feedback linearizing volterra transformation this in turn allows us to prove l 2 and h 1 local exponential stability with an estimate of the region of attraction where possible and explicitly construct the exponentially decaying closed loop solutions

guaranteed cost design for controlling semilinear parabolic pde systems with mobile collocated actuators and sensors this paper investigates the guaranteed cost design problem for controlling a class of semilinear parabolic partial differential equation pde systems using mobile collocated actuators and sensors

brief paper an lmi approach to h boundary control of semilinear parabolic and hyperbolic systems exponential stability analysis and l 2 gain analysis are developed for scalar uncertain distributed parameter systems governed by semilinear partial differential equations of parabolic and hyperbolic types sufficient exponential stability conditions with a given decay rate are derived in the form of linear matrix inequalities lmis for both systems these conditions are then utilized to synthesize h static output feedback boundary controllers of the systems in question

semi infinite induction and wakimoto modules the purpose of this paper is to suggest the construction and study properties of semi infinite induction which relates to semi infinite cohomology the same way induction relates to homology and coinduction to cohomology we prove a version of the shapiro lemma showing that the semi infinite cohomology of a module is isomorphic to that of the semi infinitely induced module a practical outcome of our construction is a simple construction of the wakimoto modules highest weight modules used in double sided bgg resolutions of irreducible modules

totally balanced games and games of flow a class of characteristic function games arising from maximum flow problems is introduced and is shown to coincide with the class of totally balanced games the proof relies on the max flow min cut theorem of ford and fulkerson and on the observation that the class of totally balanced games is the span of the additive games with the minimum operation

traveling salesman games in this paper we discuss the problem of how to divide the total cost of a round trip along several institutes among the institutes visited we introduce two types of cooperative games fixed route traveling salesman games and traveling salesman games as a tool to attack this problem under very mild conditions we prove that fixed route traveling salesman games have non empty cores if the fixed route is a solution of the classical traveling salesman problem core elements provide us with fair cost allocations a traveling salesman game may have an empty core even if the cost matrix satisfies the triangle inequality in this paper we introduce a class of matrices defining ts games with non empty cores

a new class of unitarizable highest weight representations of infinite dimensional lie algebras ii on donne les details rigoureux pour le probleme de classification on redemontre l unitarite de la representation exceptionnelle on considere les produits tensoriels et les problemes d integrabilite

the galerkin method and feedback control of linear distributed parameter systems abstract in the development of feedback control theory for distributed parameter systems dps i e systems described by partial differential equations it is important to maintain the finite dimensionality of the controller even though the dps is infinite dimensional since this dimension is directly related to the available on line computer capacity it must be finite and not very large in order to make the controller implementable from an engineering standpoint in previous work it has been our intention to investigate what can be accomplished by finite dimensional control of infinite dimensional systems in particular we have concentrated on controller design and closed loop stability the starting point for all of this is some means for producing a finite dimensional approximation a reduced order model of the actual dps when the modes of the dps are known the natural candidate for model reduction is projection onto the modal subspace spanned by a finite number of critical modes unfortunately in real engineering systems these modes are never known exactly and some other reasonable approximation must be used in this paper the model reduction is based on the well known galerkin procedure we generate the galerkin reduced order model and develop a finite dimensional controller from it then we analyze the stability of this controller in closed loop with the actual dps our results indicate conditions under which model reduction based on consistent galerkin approximations will lead to stable finite dimensional control