design of robust static output feedback for large scale systems the design of static output feedback is of fundamental importance in control theory in this note we propose a new approach to this problem based on linear matrix inequalities a distinguishing feature of the method is its ability to handle large scale problems with additive nonlinearities the resulting control is robust with respect to uncertainties and can incorporate several types of information structure constraints the effectiveness of the proposed strategy is demonstrated by application to a practical large scale system

regular implementation in the space of compactly supported functions abstract this article extends results on regular implementability in p rocha canonical controllers and regular implementation of nd behaviors in proceedings of the 16th ifac world congress 2005 and h l trentelman d napp avelli on the regular implementability of nd systems systems control lett 56 4 2007 265 271 to the case when the signal space is not an injective cogenerator for instance the space d of compactly supported smooth functions on r n in this case the bijective correspondence between behaviors and modules fails to hold also projections and sums of behaviors need not in general be behaviors a more general version of implementability is introduced and necessary and sufficient conditions are established for the implementation and regular implementation of a given desired behavior

control design for large scale lur e systems with arbitrary information structure constraints abstract in this paper an lmi based approach is proposed for the design of static output feedback for multi nonlinear lur e postnikov systems the resulting control laws ensure absolute stability and at the same time maximize the size of the nonlinear sectors the proposed method is computationally efficient and can accommodate feedback laws with arbitrary information structure constraints the effectiveness of this approach is demonstrated on a large scale example with 100 state variables

computing the state difference equations for discrete overdetermined linear m d systems we derive an algorithm that computes the state difference equations for a given set of poles of linear discrete overdetermined autonomous m d systems these difference equations allow the realization of the dynamical system by means of delay multiplication and addition elements in simulation diagrams in doing so we generalize the classical cayley hamilton theorem to multivariate polynomial ideals and provide a system theoretic interpretation to the notion of polynomial ideals leading monomials and grobner bases furthermore we extend the problem to include poles at infinity and so arrive at a description of overdetermined descriptor systems this results in a new state space description of autonomous m d descriptor systems in addition we discuss the separation of the state variables of singular m d systems into a regular and singular part a sufficient condition under which these two state vector parts can be interpreted as a forward evolving regular part and a backward evolving singular part is given the robustness and efficiency of the developed algorithms are demonstrated via numerical experiments

brief parametric absolute stability of multivariable lur e systems the objective of this paper is to consider parametric absolute stability of multivariable lur e systems with uncertain parameters and constant reference inputs both state space and frequency domain conditions are formulated to guarantee that the system remains stable despite the shift of the equilibrium location caused by changes of uncertain parameters and reference inputs the state space condition can be tested using existing software tools for solving linear matrix inequalities for testing the popov type frequency domain condition the value set software tool for the interval arithmetic can be used

on the transport diffusion algorithm and its applications to the navier stokes equations this paper deals with an algorithm for the solution of diffusion and or convection equations where we mixed the method of characteristics and the finite element method globally it looks like one does one step of transport plus one step of diffusion or projection but the mathematics show that it is also an implicit time discretization of thepde in lagrangian form we give an error bound h t h h t in the interesting case that holds also for the navier stokes equations even when the reynolds number is infinite euler equation

parametric quadratic stabilizability of uncertain nonlinear systems abstract the objective of this paper is to introduce the notion of parametric quadratic stabilizability pq stabilizability of nonlinear control systems x a a p x b p u when we consider nonlinear systems reference inputs and disturbances may alter dynamics in an essential way by moving the equilibrium to a new location or destroying it altogether for this reason when we consider quadratic stabilizability q stabilizability of nonlinear systems we need to combine the two concepts of parametric stability and q stabilizability and consider pq stabilizability when nonlinear function belongs to a subclass of passive functions it is shown that the necessary and sufficient condition for quadratic stabilizability q stabilizability of linear systems via dynamic state feedback which was derived by zhou and khargonekar is also a necessary and sufficient condition for that of nonlinear systems considered in this paper moreover when nonlinear function belongs to a subclass of incresing functions and when b 0 it shown that the necessary and sufficient condition for q stabilizability of linear systems via static state feedback which was derrived by petersen is also a necessary and sufficient condition for that of nonlinear systems considered in this paper

paradigms and puzzles in the theory of dynamical systems a self contained exposition is given of an approach to mathematical models in particular to the theory of dynamical systems the basic ingredients form a triptych with the behavior of a system in the center and behavioral equations with latent variables as side panels the author discusses a variety of representation and parametrization problems in particular questions related to input output and state models the proposed concept of a dynamical system leads to a new view of the notions of controllability and observability and of the interconnection of systems in particular to what constitutes a feedback control law the final issue addressed is that of system identification it is argued that exact system identification leads to the question of computing the most powerful unfalsified model

causal input output representation of 2d systems in the behavioral approach in this paper the concept of causal input output representation of two dimensional 2d systems in the behavioral approach is introduced these representations provide an interesting connection between classical 2d systems theory and 2d systems theory in the behavioral approach some characterizations of such representations are presented finally a technique that allows us to obtain causal input output representations is proposed

numerical methods for convection dominated diffusion problems based on combining the method of characteristics with finite element or finite difference procedures finite element and finite difference methods are combined with the method of characteristics to treat a parabolic problem of the form cu t bu x au x x f optimal order error estimates in l 2 and w 1 2 are derived for the finite element procedure various error estimates are presented for a variety of finite difference methods the estimates show that for convection dominated problems b gg a these schemes have much smaller time truncation errors than those of standard methods extensions to n space variables and time dependent or nonlinear coefficients are indicated along with applications of the concepts to certain problems described by systems of differential equations

on the reduction of high order linear pdes to first order abstract different first order representations of high order linear pdes depending on which notion of the degree of a polynomial is chosen are possible two notions of degree namely the total degree and multi degree are standard and the most natural in our recent article a straightforward way was provided to convert a system of high order constant coefficient linear pdes into a system of first order pdes based on the notion of total degree in the present article an analogous development is carried out in the multi degree setting

time relevant stability of 2d systems for many 2d systems one of the independent variables plays a distinct role in the evolution of the trajectories since often this special independent variable is time we call such systems time relevant in this paper we introduce a stability notion for time relevant systems described by higher order difference equations we give algebraic tests in terms of the location of the zeros of the determinant of a polynomial matrix describing the system we also give an lmi characterization of time relevant stability involving only constant matrices

a finite element semi lagrangian method with l2 interpolation summary high order accurate methods for convection dominated problems have the potential to reduce the computational effort required for a given order of solution accuracy the state of the art in this field is more advanced for eulerian methods than for semi lagrangian slag methods in this paper we introduce a new slag method that is based on combining the modified method of characteristics with a high order interpolating procedure the method employs the finite element method on triangular meshes for the spatial discretization an l2 interpolation procedure is developed by tracking the feet of the characteristic lines from the integration nodes numerical results are illustrated for a linear advection diffusion equation with known analytical solution and for the viscous burgers equation the computed results support our expectations for a robust and highly accurate finite element slag method copyright 2012 john wiley sons ltd

a new error analysis of characteristics mixed fems for miscible displacement in porous media the method of characteristics type is especially effective for convection dominated diffusion problems due to the nature of characteristic temporal discretization the method allows one to use a large time step in many practical computations while all previous theoretical analyses always required certain restrictions on the time stepsize here we present a new analysis to establish unconditionally optimal error estimates for a modified method of characteristics with a mixed finite element approximation to the miscible displacement problem in mathbb r d d 2 3 for this purpose we introduce a new characteristic time discrete system we prove that the l 2 error bound the characteristic time discrete systemof the fully discrete method of characteristics to the time discrete system is tau independent and the numerical solution is bounded in w 1 infty norm unconditionally with the boundedness optimal error estimates are established in a traditional manner numerical results confirm our th

a generalized tracking and disturbance rejection problem for multidimensional behaviors in this paper we study a generalized tracking and disturbance rejection problem for multidimensional behaviors given a multidimensional plant our first goal is to design a compensator to be connected to the plant through regular partial interconnection in such a way that the overall controlled system is autonomous and stable when no exogenous signal acts on the system on the other hand when exogenous signals affect the controlled system evolution we want to impose that a suitable linear combination of the overall system trajectories is negligibile in a sense we will clarify within the paper this problem setup formalizes a number of classical control problems first of all tracking of some reference signal together with rejection of another disturbance signal the adopted approach is extremely general and it is based on the idea of describing all behavior trajectories as the sum of a transient signal and a steady state component a decomposition that relies on gabriel s localization theor

stability and stabilization of multidimensional input output systems in this paper we discuss stability and stabilization of continuous and discrete multidimensional input output io behaviors of dimension r which are described by linear systems of complex partial differential resp difference equations with constant coefficients where the signals are taken from various function spaces in particular from those of polynomial exponential functions stability is defined with respect to a disjoint decomposition of the r dimensional complex space into a stable and an unstable region with the standard stable region in the one dimensional continuous case being the set of complex numbers with negative real part a rational function is called stable if it has no poles in the unstable region an io behavior is called stable if the characteristic variety of its autonomous part has no points in the unstable region this is equivalent to the stability of its transfer matrix and an additional condition the system is called stabilizable if there is a compensator io system such that the output feedback system is well posed and stable we characterize stability and stabilizability and construct all stabilizing compensators of a stabilizable io system parametrization the theorems and proofs are new but essentially inspired and influenced by and related to the stabilization theorems concerning multidimensional io maps as developed for instance by bose guiver shankar sule xu lin ying zerz and quadrat and of course the seminal papers of vidyasagar youla and others in the one dimensional case in contrast to the existing literature the theorems and proofs of this paper do not need or employ the so called fractional representation approach i e various matrix fraction descriptions of the transfer matrix thus avoiding the often lengthy matrix computations and seeming to be of interest even for one dimensional systems at least to the author an important mathematical tool new in systems theory is gabriel s localization theory which only in the case of ideal convex shankar sule unstable regions coincides with the usual one algorithmic tests for stability stabilizability and ideal convexity and the algorithmic construction of stabilizing compensators are addressed but still encounter many difficulties see in particular the open problems listed by xu e

numerical method of characteristics for one dimensional blood flow mathematical modeling at the level of the full cardiovascular system requires the numerical approximation of solutions to a one dimensional nonlinear hyperbolic system describing flow in a single vessel this model is often simulated by computationally intensive methods like finite elements and discontinuous galerkin while some recent applications require more efficient approaches e g for real time clinical decision support phenomena occurring over multiple cardiac cycles iterative solutions to optimization inverse problems and uncertainty quantification further the high speed of pressure waves in blood vessels greatly restricts the time step needed for stability in explicit schemes we address both cost and stability by presenting an efficient and unconditionally stable method for approximating solutions to diagonal nonlinear hyperbolic systems theoretical analysis of the algorithm is given along with a comparison of our method to a discontinuous galerkin implementation lastly we demonstrate the utility of the proposed method by implementing it on small and large arterial networks of vessels whose elastic and geometrical parameters are physiologically relevant

parameter space methods for robust control design a guided tour the results obtained in studies of robust stability and stabilizability of control systems with parametric structured uncertainties are reviewed both the algebraic methods based upon characteristic equations and the methods using lyapunov functions and riccati equations are discussed and compared in the context of algebraic methods most promising are the kharitonov type approach and the optimization procedure of embedding a geometric figure of some kind inside the stability regions of the parameter space maximizing its size using minimax or some other mathematical programming technique in the framework of lyapunov s direct method the dominant approach has been a quadratic function estimation of stability regions in the parameter space in large sale systems the concept of vector lyapunov functions has been used with the possibility of choosing quadratic forms norm like functions and their combinations

regular almost interconnection of multidimensional behaviors reading the doctoral thesis of napp avelli 2007 i realized that gabriel s localization theory which i applied in context with the stabilization of multidimensional input output behaviors can also be used for the construction of regular almost interconnections of behaviors in arbitrary dimensions and not only in two dimensions in this paper i expose this theory in the language of quotient modules and derive an algorithm for arbitrary dimensions which has however not yet been implemented regular interconnections were introduced and discussed by willems ieee trans automat control 36 1991 pp 259 294 42 1997 pp 458 472 for one dimensional behaviors their multidimensional counterparts have been treated by rocha wood shankar zerz lomadze napp avelli and others since 1998 two dimensional almost direct sum decompositions and regular almost interconnections have been considered by valcher and bisiacco since 2000 and are also the main subject of napp avelli s thesis and his recent submitted paper roughly two behaviors are almost equal if they differ by finite dimensional behaviors only so the latter are considered negligible in this context two dimensional behaviors have special properties which are not discussed in the present paper i also briefly discuss other variants of regular almost interconnections where only stable autonomous behaviors are considered negligible

global low rank enhancement of decentralized control for large scale systems this note proposes a new control strategy which is computationally attractive for systems of large dimensions the main idea is to supplement decentralized feedback with a global additive term which is computed as a product of two low rank matrices this feature is of critical importance for systems that cannot be adequately stabilized using standard decentralized control the low rank matrices can be efficiently obtained using linear matrix inequalities and the resulting control is suitable for implementation in a multiprocessor environment simulations on a platoon of vehicles demonstrate that such a control can significantly improve the robustness of the closed loop system with respect to uncertain nonlinearities

a behavioral approach to identifiability of 2d scalar systems abstract a modelling procedure can be seen as an algorithm that analyzing a set of data provides a mathematical description of a phenomenon which is called a model in some cases the most suitable description of the data is a dynamical one and consequently the appropriate class of models to be considered is that of dynamical systems in this paper the particular case of noise free data with two dimensional support is considered the model class is constituted by systems of two dimensional difference equations and corresponds to the family of linear systems as defined in the behavioral approach in this setup two indices describing the identifiability of the model in the model class are introduced they provide information on the amount of data that is needed to identify a model in two directions how many trajectories are needed and how large their support should be

stabilization of nonlinear systems with moving equilibria this note provides a new method for the stabilization of nonlinear systems with parametric uncertainty unlike traditional techniques our approach does not assume that the equilibrium remains fixed for all parameter values the proposed method combines different optimization techniques to produce a robust control that accounts for uncertain parametric variations and the corresponding equilibrium shifts comparisons with analytical gain scheduling are provided

converting high order linear pdes to first order abstract a straightforward way requiring no calculations is offered to convert a system of high order constant coefficient linear pdes into a system of first order pdes

canonical forms for polynomial and quadratic differential operators we define the canonical representative for the equivalence class consistingof all polynomial and quadratic differential operators that take the same values on a given subspaceof c

multidimensional behaviours an algebraic approach to control theory for pde this paper gives an overview of the algebraic theory of multidimensional behaviours and it contains some new aspects as well some known results are restated with a new proof after a short introduction to behavioural systems theory we briefly describe the mathematical background of the algebraic approach then we study structural properties such as autonomy and over determined systems on the one hand and controllability and flat systems on the other

control of large scale systems in a multiprocessor environment in this paper a new approach is proposed for designing robust controllers for large scale systems the method utilizes linear matrix inequalities lmi to produce control structures that are suitable for a multiprocessor environment it is shown that appropriate gain matrices can be obtained with only a modest computational effort and that the interprocessor communication can be minimized

brief stability preserving interpolation methods for the synthesis of gain scheduled controllers synthesis of gain scheduled controllers for nonlinear plants often requires that a parameter varying controller be generated from a finite set of linear time invariant controllers we propose interpolation methods for this task with the property that stability of the linearized closed loop system is preserved for all values of the scheduling parameter in addition slow variation arguments are presented that establish local stability of the nonlinear closed loop system with gain scheduled controller

a behavioral approach to the pole structure of one dimensional and multidimensional linear systems we use the tools of behavioral theory and commutative algebra to produce a new definition of a finite pole of a linear system this definition agrees with the classical one and allows a direct dynamical interpretation it also generalizes immediately to the case of a multidimensional nd system we make a natural division of the poles into controllable and uncontrollable poles when the behavior in question has latent variables we make a further division into observable and unobservable poles in the case of a one dimensional 1d state space model the uncontrollable and unobservable poles correspond respectively to the input and output decoupling zeros whereas the observable controllable poles are the transmission poles most of these definitions can be interpreted dynamically in both the 1d and nd cases and some can be connected to properties of kernel representations we also examine the connections between poles transfer matrices and their left and right matrix fraction descriptions mfds we find behavioral results which correspond to the concepts that a controllable system is precisely one with no input decoupling zeros and an observable system is precisely one with no output decoupling zeros we produce a decomposition of a behavior as the sum of subbehaviors associated with various poles this is related to the integral representation theorem which describes every system trajectory as a sum of integrals of polynomial exponential trajectories

a constructive solution to interconnection and decomposition problems with multidimensional behaviors by a multidimensional behavior we mean the solution space of a linear constant coefficient system of partial difference or differential equations within the behavioral framework a natural concept of interconnection has been introduced by j c willems the regular interconnection problem can be formulated as follows given a behavior the plant find if possible another behavior a controller such that their interconnection is not redundant and is equal to a certain desired behavior we give a constructive solution to this problem which is in terms of polynomial matrix equations that can be solved using the theory of grobner bases we also study a dual problem concerning the existence of direct sum decompositions of multidimensional behaviors finally we present a unified framework for studying both problems as special cases of constructing relative complements in the lattice of behaviors

unconditional stability and error estimates of modified characteristics fems for the navier stokes equations the paper is concerned with the unconditional stability and convergence of characteristics type methods for the time dependent navier stokes equations we present optimal error estimates in l 2 l2 and h 1 h1 norms for a typical modified characteristics finite element method unconditionally while all previous works require certain time step restrictions the analysis is based on an iterated characteristic time discrete system with which the error function is split into a temporal error and a spatial error with a rigorous analysis to the characteristic time discrete system we prove that the difference between the numerical solution and the solution of the time discrete system is tau independent where tau denotes the time stepsize thus numerical solution in w 1 infty w1 is bounded and optimal error estimates can be obtained in a traditional way numerical results confirm our analysis and show clearly the unconditional stability and convergence of the modified characteristics finite element method for the time dependent navier stokes equations the approach used in this paper can be easily extended to many other characteristics based methods

the lattice structure of behaviors if a linear continuous shift invariant distributed system is considered as a dynamical system converting input signals to output signals then this information is encapsulated in the impulse response or the transfer function of the system the set of all transfer functions has the structure of a ring corresponding to the operations of parallel and cascade connections of two systems however in the behavioral theory of willems a system is not described in terms of its input output transformation property indeed the concept of a behavior does not even need the notions of inputs and outputs and is therefore more fundamental than the classical concept of a system given by its transfer function the question then arises as to what is the structure of the set of all behaviors this paper argues that the relevant structure here is that of a modular lattice

linear quadratic control and quadratic differential forms for multidimensional behaviors this paper deals with systems described by constant coefficient linear partial differential equations nd systems from a behavioral point of view in this context we treat the linear quadratic control problem where the performance functional is the integral of a quadratic differential form we look for characterizations of the set of stationary trajectories and of the set of local minimal trajectories with respect to compact support variations turning out that they are equal if the system is dissipative finally we provide conditions for regular implementability of this set of trajectories and give an explicit representation of an optimal controller

decentralized control through parameter space optimization the decentralized control problem for linear dynamic systems is revisited using a parameter space approach which enables the definition of the decentralized feedbacks from the existence of non empty parameter convex sets the convexity property enables the derivation of efficient numerical algorithms based on standard approaches in convex programming the continuous time and discrete time cases are investigated and the decentralized control design is also treated to meet other important assignments such as optimal h2 performance index absolute stability h prescribed attenuation and robustness against actuator failures some numerical experiments illustrate the potential of this new control design

a modified backward time discretization for nonlinear parabolic equations using patch approximations a modified backward difference time discretization is presented for galerkin approximations for the nonlinear parabolic equation in mathbb r d q x u u t sum i j 1 d frac partial partial x i left a ij x u frac partial u partial x j right sum i 1 d b i x u frac partial u partial x i f x t u this procedure uses a local approximation of the coefficients based on patches of finite elements to update the coefficient matrix at each time step and allows for efficient use of such direct methods for solving linear systems of equations as nested dissection optimal order error estimates and almost optimal order work requirements are derived an alternating direction variant is also presented which has both optimal order error estimates and optimal order work requirements

state space realization of 2 d finite dimensional behaviours this paper deals with the state space realization of autonomous autoregressive two dimensional 2 d systems in the context of the behavioural approach an arbitrary autoregressive 2 d system sig

on interconnections control and feedback the purpose of this paper is to study interconnections and control of dynamical systems in a behavioral context we start with an extensive physical example which serves to illustrate that the familiar input output feedback loop structure is not as universal as we have been taught to believe this leads to a formulation of control problems in terms of interconnections subsequently we study interconnections of linear time invariant systems from this vantage point let us mention two of the results obtained the first one states that any polynomial can be achieved as the characteristic polynomial of the interconnection with a given plant provided the plant is not autonomous the second result states that any subsystem of a controllable system can be implemented by means of a singular feedback control law these results yield pole placement and stabilization of controllable plants as a special case these ideas are finally applied to the stabilization of a nonlinear system around an operating point

strong controlled invariance of behavioural nd systems abstractin this paper we give a stronger version of the notion of behavioral controlled invariance introduced in pereira rocha 2017 in the context of regular partial interconnections in such interconnections the variables are divided into two sets the variables to be controlled and the variables on which it is allowed to enforce restrictions control variables moreover regularity means that the restrictions of the controller do not overlap with the ones already implied by the laws of the original behavior a complete characterization of strong controlled invariance for nd behaviors is derived making use of a special controller behavior known as the canonical controller

algebraic aspects of two dimensional convolutional codes two dimensional 2d codes are introduced as linear shift invariant spaces of admissible signals on the discrete plane convolutional and in particular basic codes are characterized both in terms of their internal properties and by means of their input output representations the algebraic structure of the class of all encoders that correspond to a given convolutional code is investigated and the possibility of obtaining 2d decoders free from catastrophic errors as veil as efficient syndrome decoders is considered some aspects of the state space implementation of 2d encoders and decoders via finite memory 2d system are discussed

h sub 2 norm optimization with constrained dynamic output feedback controllers decentralized and reliable control this paper addresses some open problems in the area of dynamic output feedback control design the first one is the structurally constrained decentralized control problem and the second is related to robust and reliable control a necessary and sufficient condition for decentralized and quadratic stabilizability is given and used to provide a solution to the h sub 2 norm optimization problem a numerical cross decomposition algorithm is developed and satisfactorily applied to find the solution of some illustrative examples a comprehensive benchmark validates the results

lyapunov stability of 2d finite dimensional behaviours in this article we investigate a lyapunov approach to the stability of finite dimensional 2d systems we use the behavioural framework and consider a notion of stability following the ideas in pillai and shankar h pillai and s shankar 1998 a behavioral approach to control of distributed systems siam journal of control and optimization 37 388 408 rocha p rocha 2008 stabilization of multidimensional behaviors multidimensional systems and signal processing 19 273 286 valcher m valcher 2000 characteristic cones and stability properties of two dimensional autonomous behaviors ieee transactions on circuits and systems part i cas 47 290 302 we characterise stability in terms of the existence of a quadratic lyapunov function and provide a constructive algorithm for the computation of all such lyapunov functions

l2 stability the cases of infinite dimensional discrete autonomous systems and 2 d autonomous systems abstract in this paper we analyze l 2 stability of infinite dimensional discrete autonomous systems given in a state space form with state transition matrix being a laurent polynomial matrix a 1 in the shift operator we give sufficient conditions and necessary conditions for l 2 stability of such systems we then use the theory of l 2 stability thus developed to analyze l 2 stability of discrete 2 d autonomous systems we achieve this by showing how a discrete 2 d autonomous system can be converted to an equivalent infinite dimensional state space discrete autonomous system where the state transition matrix turns out to be a laurent polynomial matrix in the shift operator finally we provide some easy to check numerical tests for l 2 stability of the above mentioned type of systems

minimal grobner bases and the predictable leading monomial property abstract we focus on grobner bases for modules of univariate polynomial vectors over a ring we identify a useful property the predictable leading monomial plm property that is shared by minimal grobner bases of modules in f x q no matter what positional term order is used the plm property is useful in a range of applications and can be seen as a strengthening of the wellknown predictable degree property row reducedness a terminology introduced by forney in the 70 s because of the presence of zero divisors minimal grobner bases over a finite ring of the type z p r where p is a prime integer and r is an integer 1 do not necessarily have the plm property in this paper we show how to derive from an ordered minimal grobner basis a so called minimal grobner p basis that does have a plm property we demonstrate that minimal grobner p bases lend themselves particularly well to derive minimal realization parametrizations over z p r applications are in coding and sequences over z p r

gain scheduling dynamic linear controllers for a nonlinear plant abstract for a general type of nonlinear tracking problem we consider gain scheduling based on a family of linear dynamic controllers designed for a family of plant linearizations about constant operating points a necessary and sufficient condition for the existence of gain scheduled controllers satisfying appropriate requirements is presented using this condition the impact of linear controller configuration on the existence of a gain scheduled controller can be assessed and ad hoc approaches to scheduling can be analyzed

a finite element alternating direction method combined with a modified method of characteristics for convection diffusion problems a finite element alternating direction method is combined with a modified method of characteristics to solve convection diffusion problems this approach combines the attractive attributes of the modified method of characteristics with those of the alternating direction method for convection dominated problems the modified method of characteristics has much smaller time truncation errors than those of standard methods hence larger timesteps can be taken to integrate the convection diffusion equation the alternating direction method reduces multidimensional problems to a series of uncoupled one dimensional problems which results in very low execution times and storage the method has the ability to solve problems on curved structured grids the accuracy of this procedure is demonstrated by linear and nonlinear convection dominated diffusion problems in two space dimensions the procedure can be generalized to more than two dimensions

a new approach to control design with overlapping information structure constraints in this paper a new strategy is proposed for decentralized state feedback design with overlapping information structure constraints the method combines linear matrix inequalities and the inclusion principle in a way that eliminates controllability problems that are inherent to standard decentralized control design in the expanded space this approach can be extended to include an important class of uncertain nonlinearities and its validity is demonstrated through applications to strings of moving vehicles

trajectory control and interconnection of 1d and nd systems in this paper we examine the relationship between control viewed as concatenation of trajectories and control viewed as interconnection of systems we show that for one dimensional linear time invariant systems the ability to obtain a given subsystem by regular interconnection a prerequisite for any feedback type structure is equivalent to the ability to drive any trajectory into that subsystem however in the case of multidimensional systems the former is a stronger property than the latter trajectory controllability can however be expressed as a regular interconnection of behaviors in an extended variable space by introducing latent or auxiliary variables this leads as a by product to the notion of controlling a system by means of latent variables