the construction of preconditioners for elliptic problems by substructuring i in earlier parts of this series of papers we constructed preconditioners for the discrete systems of equations arising from the numerical approximation of elliptic boundary value problems the resulting algorithms are well suited for implementation on computers with parallel architecture in this paper we will develop a technique which utilizes these earlier methods to derive even more efficient preconditioners the iterative algorithms using these new preconditioners converge to the solution of the discrete equations with a rate that is independent of the number of unknowns these preconditioners involve an incomplete chebyshev iteration for boundary interface conditions which results in a negligible increase in the amount of computational work theoretical estimates and the results of numerical experiments are given which demonstrate the effectiveness of the methods

restarted gmres preconditioned by deflation this paper presents a new preconditioning technique for the restarted gmres algorithm it is based on an invariant subspace approximation which is updated at each cycle numerical examples show that this deflation technique gives a more robust scheme than the restarted algorithm at a low cost of operations and memory

additive and multiplicative two level spectral preconditioning for general linear systems in this paper we introduce new preconditioning techniques for the solution of general symmetric and unsymmetric linear systems a x b these approaches borrow some ideas of the multigrid philosophy designed for the solution of linear systems arising from the discretization of elliptic partial differential equations we attempt to improve the convergence rate of a prescribed preconditioner m 1 in a two grid framework this preconditioner is viewed as a smoother and the coarse space is spanned by the eigenvectors associated with the smallest eigenvalues of m 1a we derive both additive and multiplicative variants of the resulting iterated two level preconditioners for unsymmetric linear systems that can also be adapted for hermitian positive definite problems we show that these two level preconditioners shift the smallest eigenvalues to one and tend to better cluster around one those eigenvalues that m 1 already succeeded in moving into the neighborhood of one we illustrate the behavior of our method through extensive numerical experiments on a set of general linear systems finally we show the effectiveness of these approaches on two challenging real applications the first comes from a nonoverlapping domain decomposition method in semiconductor device modeling the second from industrial electromagnetism applications

uniform decay in viscoelasticity for kernels with small non decreasingness zones abstract we consider a viscoelastic problem with a relaxation function which may be strictly increasing in some sub intervals that is we go beyond the zero which was a bound for the derivative of the kernel in the previous works it is proved that we have different types of decay rates including the exponential one provided that the rate and or the non decreasingness zone including the flat zone is small enough in a certain sense

energy decay rates for the semilinear wave equation with memory boundary condition and acoustic boundary conditions in this paper we consider the energy decay rates for the semilinear wave equation with memory boundary condition and acoustic boundary conditions motivated by results of gerbi and said houari 2011 2008 li and zhao 2011 liu and chen 2016 wu etal 2010 and lu etal 2011 we intend to study the energy decay rates for problem 1 1 1 6 by using the perturbed energy method and riemannian geometry method we obtained general energy decay rates

the use of bulk states to accelerate the band edge state calculation of a semiconductor quantum dot we present a new technique to accelerate the convergence of the folded spectrum method in empirical pseudopotential band edge state calculations for colloidal quantum dots we use bulk band states of the materials constituent of the quantum dot to construct initial vectors and a preconditioner we apply these to accelerate the convergence of the folded spectrum method for the interior states at the top of the valence and the bottom of the conduction band for large cdse quantum dots the number of iteration steps until convergence decreases by about a factor of 4 compared to previous calculations

control of discrete event systems with minimal switchings this paper studies the problem of controlling discrete event systems as formulated by ramadge and wonham 1987 an optimal d supervisor is introduced which requires a minimal number of switchings i e enabling and disabling controllable events a complete characterization of such controllers as well as a procedure for its construction is given an example to illustrate the result is also included

on a large class of kernels yielding exponential stability in viscoelasticity in this paper we prove exponential decay of solutions for a problem which appears in viscoelasticity the conditions on the admissible kernels are relaxed so as to allow for more kernels to be treated namely the smallness of the kernels is replaced by the smallness of the set where the kernel is flat this work extends previous works and improves in particular a recent result by pata 16 this is established by introducing two lemmas an idea due to pata and using the energy method

on decay and blow up of the solution for a viscoelastic wave equation with boundary damping and source terms abstract in this paper we consider the decay and blow up properties of a viscoelastic wave equation with boundary damping and source terms we first extend the decay result for the case of linear damping obtained by lu et al on a viscoelastic equation with nonlinear boundary damping and source terms global existence and decay of the solution nonlinear analysis real world applications 12 1 2011 295 303 to the nonlinear damping case under weaker assumption on the relaxation function g t then we give an exponential decay result without the relation between g t and g t for the linear damping case provided that g l 1 0 is small enough finally we establish two blow up results one is for certain solutions with nonpositive initial energy as well as positive initial energy for both the linear and nonlinear damping cases the other is for certain solutions with arbitrarily positive initial energy for the linear damping case

optimality of energy estimates for the wave equation with nonlinear boundary velocity feedbacks we consider the wave equation damped by a nonlinear boundary velocity feedback q ut first we consider the case where q has a linear growth at infinity we prove that the usual decay rate estimates proved by nakao differential integral equations 8 1995 pp 681 688 haraux and zuazua arch rational mech anal 100 1988 pp 191 206 conrad leblond and marmorat in proceedings of the fifth international federation of automatic control symposium on control of distributed parameter systems perpignan 1989 pp 101 116 zuazua siam j control optim 28 1990 pp 466 477 and komornik in control and estimation of distributed parameter systems nonlinear phenomena internat ser numer math 118 birkhauser basel 1994 pp 253 266 when q has a polynomial behavior at zero and by the second author esaim control optim calc var 4 1999 pp 419 444 in the general case are in fact optimal in one space dimension more generally we prove that the energy decays exactly like the solution of an explicit and simple ordinary differential equation next we study the problem when q is bounded at infinity we prove that strong solutions decay exponentially to zero and we exhibit a sequence of weak solutions for which the associated energy decays to zero at infinity as slowly as the iterated logarithms go to infinity at infinity

aggregation and multi level control in discrete event dynamic systems abstract in this paper we consider the problem of higher level aggregate modeling and control of discrete event dynamic systems deds modeled as finite state automata in which some events are controllable some are observed and some represent events to be tracked the higher level models considered correspond to associating specified sequences of events in the original system to single macroscopic events in the higher level model we also consider the problem of designing a compensator that can be used to restrict microscopic behavior so that the system will only produce strings of these primitive sequences or tasks with this lower level control in place we can construct higher level models which typically have many fewer states and events than the original system the use of these higher level models allow us to decrease the computational complexity of problems involving complex interconnected deds

global existence and asymptotic behavior for a coupled hyperbolic system with localized damping abstract in this paper we investigate the global existence and energy decay rate for the solution of a coupled hyperbolic system the semi explicit energy decay rate is established by using piecewise multiplier techniques and weighted integral inequality we extend the energy decay result in alabau boussouira f alabau boussouira convexity and weighted integral inequalities for energy decay rates of nonlinear dissipative hyperbolic systems appl math optim 51 2005 61 105 for a single equation to the coupled hyperbolic system

on the uniform decay in viscoelastic problems in rn in this paper we consider a linear cauchy viscoelastic problem we show that for compactly supported initial data and for an exponentially decaying relaxation function the decay of the first energy of solution is polynomial the finite speed propagation is used to compensate for the lack of poincare s inequality in r n

general stability result for viscoelastic wave equations in this paper we consider a viscoelastic equation and establish an explicit and general decay rate result without imposing restrictive assumptions on the behavior of the relaxation function at infinity our result allows a wider class of relaxation functions and improves earlier results in the literature

on convexity for energy decay rates of a viscoelastic equation with boundary feedback abstract in this paper we consider a viscoelastic equation with a nonlinear feedback localized on a part of the boundary we establish an explicit and general decay rate result using some properties of the convex functions our result is obtained without imposing any restrictive growth assumption on the damping term and strongly weakening the usual assumptions on the relaxation function

asymptotic stability and energy decay rates for solutions of the wave equation with memory in a star shaped domain we study the asymptotic stability and give the energy decay rates for solutions of the wave equation with boundary dissipation of the memory type

energy decay rates via convexity for some second order evolution equation with memory and nonlinear time dependent dissipation abstract the stabilization of the following abstract integro differential equation u t a u t 0 t g t s a u s d s q t u t f u t is investigated we establish the general decay rate of the solution energy in terms of the behavior of the nonlinear feedback and the relaxation function g without imposing any restrictive growth assumption on the damping at the origin and strongly weakening the usual assumption of the relaxation function g our approach is based on the multiplier method and make use of some properties of the convex functions these decay results can be applied to various concrete models we shall study some examples to illustrate our result

arbitrary decays in linear viscoelasticity it is by now well known that a necessary condition for the exponential polynomial decay of the energy of a problem arising in viscoelasticity is that the kernel which appears in the memory term itself be of exponential polynomial type by a kernel of exponential polynomial type we mean that the product of this kernel with an exponential polynomial function is summable some researchers have started from this condition to seek other sufficient conditions ensuring exponential or polynomial decay of the energy in this work we generalize these works to an arbitrary decay not necessarily of an exponential or polynomial rate

adaptively preconditioned gmres algorithms the restarted gmres algorithm proposed by saad and schultz siam j sci statist comput 7 1986 pp 856 869 is one of the most popular iterative methods for the solution of large linear systems of equations ax b with a nonsymmetric and sparse matrix this algorithm is particularly attractive when a good preconditioner is available the present paper describes two new methods for determining preconditioners from spectral information gathered by the arnoldi process during iterations by the restarted gmres algorithm these methods seek to determine an invariant subspace of the matrix a associated with eigenvalues close to the origin and to move these eigenvalues so that a higher rate of convergence of the iterative methods is achieved

observability of discrete event dynamic systems a finite state automaton is adopted as a model for discrete event dynamic systems deds observations are assumed to be a subset of the event alphabet observability is defined as having perfect knowledge of the current state at points in time separated by bounded numbers of transitions a polynomial test for observability is given it is shown that an observer may be constructed and implemented in polynomial time and space a bound on the cardinality of the observer state space is also presented a notion of resiliency is defined for observers and a test for resilient observability and a procedure for the construction of a resilient observer are presented

a sparse approximate inverse preconditioner for the conjugate gradient method a method for computing a sparse incomplete factorization of the inverse of a symmetric positive definite matrix a is developed and the resulting factorized sparse approximate inverse is used as an explicit preconditioner for conjugate gradient calculations it is proved that in exact arithmetic the preconditioner is well defined if a is an h matrix the results of numerical experiments are presented

decay rate estimates for wave equations of memory type with acoustic boundary conditions abstract a wave equation of memory type u u 0 t g t s u s d s 0 with acoustic boundary conditions is considered this work is devoted to investigating the influence of the kernel function g and proving general rates of decay of solutions when g does not necessarily decay exponentially

uniform stabilization of the wave equation by nonlinear boundary feedback the question of uniformly stabilizing the solution of the wave equation y delta y 0 in omega times 0 infty omega is a bounded domain of bf r n by means of a nonlinear feedback law of the following form is studied partial y partial v k x g y on gamma 0 times 0 infty y 0 on gamma 1 times 0 infty gamma 0 gamma 1 being a suitable partition of the boundary of omega and g a continuous nondecreasing function such that g 0 0 we choose k x in l infty k x geqq 0 such that k x vanishes linearly at the interface points x in bar gamma 0 cap bar gamma 1 then if g s behaves like s p 1 s as s to 0 with p 1 and linearly as s to infty it is proved that the energy of every solution decays like t 2 p 1 as t to infty in the case where p 1 the exponential decay rate is proved

moore gibson thompson equation with memory part ii general decay of energy abstract we study a temporally third order moore gibson thompson equation with a memory term previously it was known that in non critical regime the global solutions exist and the energy functionals decay to zero more precisely it is known that the energy has exponential decay if the memory kernel decays exponentially the current work is a generalization of the previous one part i in that it allows the memory kernel to be more general and shows that the energy decays the same way as the memory kernel does exponentially or not

a class of spectral two level preconditioners it is well known that the convergence of krylov methods for solving the linear system often depends to a large extent on the eigenvalue distribution in many cases it is observed that removing the smallest eigenvalues can greatly improve the convergence several techniques have been proposed in the past few years that attempt to tackle this problem the proposed approaches can be split into two main families depending on whether the scheme enlarges the generated krylov space or adaptively updates the preconditioner in this paper we follow the second approach and propose a class of preconditioners both for unsymmetric and for symmetric linear systems that can also be adapted for symmetric positive definite problems we effectively solve the preconditioned system exactly in the low dimensional space associated with the smallest eigenvalues and use this to update the preconditioned residual this update results in shifting eigenvalues from close to the origin to near to one for the new preconditioner this is ideal when there are only a few eigenvalues near the origin while all the others are close to one because the updated preconditioned system becomes close to the identity we illustrate the performance of our method through extensive numerical experiments on a set of general linear systems finally we show the advantages of the preconditioners for solving dense linear systems arising in electromagnetism applications which were the main motivation for this work

general decay and blow up of solution for a quasilinear viscoelastic problem with nonlinear source abstract in this paper we consider a quasilinear viscoelastic wave equation in canonical form with the homogeneous dirichlet boundary condition we prove that for certain class of relaxation functions and certain initial data in the stable set the decay rate of the solution energy is similar to that of the relaxation function this result improves earlier ones obtained by messaoudi and tatar s a messaoudi n e tatar global existence and uniform stability of solutions for a quasilinear viscoelastic problem math methods appl sci 30 2007 665 680 in which only the exponential and polynomial decay rates are considered conversely for certain initial data in the unstable set there are solutions that blow up in finite time the last result is new since it allows a larger class of initial energy which may take positive values

a two level ilu preconditioner for electromagnetic applications computational electromagnetics based on the solution of the integral form of maxwell s equations with boundary element methods require the solution of large and dense linear systems for large scale problems the solution is obtained by using iterative krylov type methods provided that a fast method for performing matrix vector products is available in addition for ill conditioned problems some kind of preconditioning technique must be applied to the linear system in order to accelerate the convergence of the iterative method and improve its performance for many applications it has been reported that incomplete factorizations often suffer from numerical instability due to the indefiniteness of the coefficient matrix in this context approximate inverse preconditioners based on frobenius norm minimization have emerged as a robust and highly parallel alternative in this work we propose a two level ilu preconditioner for the preconditioned gmres method the computation and application of the preconditioner is based on graph partitioning techniques numerical experiments are presented for different problems and show that with this technique it is possible to obtain robust ilu preconditioners that perform competitively compared with frobenius norm minimization preconditioners

integro differential equations of hyperbolic type with positive definite kernels abstract the main purpose of this work is to study the damping effect of memory terms associated with singular convolution kernels on the asymptotic behavior of the solutions of second order evolution equations in hilbert spaces for kernels that decay exponentially at infinity and possess strongly positive definite primitives the exponential stability of weak solutions is obtained in the energy norm it is also shown that this theory applies to several examples of kernels with possibly variable sign and to a problem in nonlinear viscoelasticity

energy decay rate for a coupled hyperbolic system with nonlinear damping abstract in this paper we investigate the energy decay rate for the solution of a coupled hyperbolic system the explicit energy decay rate is established by using multiplier techniques and constructing a suitable energy functional

uniform decay of solutions for a quasilinear system of viscoelastic equations abstract in this paper we consider a system of two coupled quasilinear viscoelastic equations in canonical form with dirichlet boundary condition we use the perturbed energy method to show that the dissipations given by the viscoelastic terms are strong enough to ensure uniform decay with exponential and polynomial rates of the solutions energy which extends some existing results for a single equation to the case of a coupled system

on supervisor reduction in discrete event systems abstract a supervisory controller supervisor s for a discrete event system can be modelled on a recognizer r for the language corresponding to the supervisory task to be accomplished it is shown that simpler reduced supervisors can be constructed by the use of covers of the state set of r and that any mildly restricted supervisor is a reduction of r in this sense the reduction procedure is time exponential with respect to the size of the state set of r

energy decay rates for von karman system with memory and boundary feedback abstract in this paper we study the von karman plate model with long range memory and boundary nonlinear feedback we establish an explicit and general decay rate result using some properties of the convex functions our result is obtained without imposing any restrictive growth assumption on the damping term and strongly weakening the usual assumptions on the relaxation function

uniform energy decay rates for nonlinear viscoelastic wave equation with nonlocal boundary damping abstract in this paper we consider the uniform decay estimates of solutions for the viscoelastic wave equation u t t 0 u 0 t g t s div a x u s d s b x h u t 0 in 0 under weak assumptions on the functions g h and f we prove the energy functional decays exponentially or polynomially to zero as the time goes to infinity by introducing brief lyapunov functions and precise priori estimates

asymptotic behavior of solutions of the one dimensional wave equation with a nonlinear boundary stabilizer the modeling of nonlinear passive damping devices or boundary frictions of an otherwise linear vibrating system often results in nonlinear elastic dissipative boundary conditions such systems occur increasingly often in engineering applications whose control and stability analysis appear much more complex than the classical linear distributed parameter systems this paper uses the method of characteristics and nonlinear semigroup theory to study the effect of nonlinear boundary stabilization and analyze the asymptotic behavior of solutions of such systems the authors are able to determine the omega limit set of the dynamical system and the asymptotic rates of various solutions to the omega limit set

smoothing effect and propagations of singularities for viscoelastic plates abstract we study dissipative models for plates and we show that the solutions have a smoothing effect on the initial data for viscous plates while for materials with memory the solution propagates singularities that is the solution of the plate equation of memory type is as regular as the initial data moreover we show that when both dissipations are present the memory type prevails in the sense that the solution propagates singularities finally we prove the existence of global solutions for non linear dissipative equations with small data which decay exponentially as time goes to infinity

exponential energy decay of solutions of viscoelastic wave equations abstract in this paper we consider the nonlinear viscoelastic equation u t t u 0 t g t u d u t u p 1 u in 0 with initial conditions and dirichlet boundary condition under some appropriate assumption on g by introducing a potential well we establish the global existence result for the equation above furthermore we investigate explicit exponential energy decay of the viscoelastic wave equation under the potential well

output stabilizability of discrete event dynamic systems the authors investigate the problem of designing stabilizing feedback compensators for discrete event dynamic systems deds modeled as finite state automata in which some transition events are controllable and some events are observed the problem of output stabilization is defined as the construction of a compensator such that all state trajectories in the closed loop system go through a given set e infinitely often the authors also define a stronger notion of output stabilizability which requires that the state not only pass through e infinitely often but that the set of instants when the state is in e and one knows it is in e is also infinite necessary and sufficient conditions are presented for both notions the authors also introduce and characterize a notion of resiliency that corresponds to the system being able to recover from observation errors in addition they provide some general bounds for the algorithms considered and discuss several conditions under which far smaller bounds can be achieved

using spectral low rank preconditioners for large electromagnetic calculations for solving large dense complex linear systems that arise in electromagnetic calculations we perform experiments using a general purpose spectral low rank update preconditioner in the context of the gmres method preconditioned by an approximate inverse preconditioner the goal of the spectral preconditioner is to improve the convergence properties by shifting by one the smallest eigenvalues of the original preconditioned system numerical experiments on parallel distributed memory computers are presented to illustrate the efficiency of this technique on large and challenging real life industrial problems copyright 2004 john wiley sons ltd

general decay rate estimates for viscoelastic dissipative systems abstract the linear viscoelastic equation is considered we prove uniform decay rates of the energy by assuming a nonlinear feedback acting on the boundary without imposing any restrictive growth assumption on the damping term and strongly weakening the usual assumptions on the relaxation function our estimate depends both on the behavior of the damping term near zero and on the behavior of the relaxation function at infinity the proofs are based on the multiplier method and on a general lemma about convergent and divergent series for obtaining the uniform decay rates

projection and deflation method for partial pole assignment in linear state feedback two projection methods are proposed for partial pole placement in linear control systems these methods are of interest when the system is very large and only a few of its poles must be assigned the first method is based on computing an orthonormal basis of the left invariant subspace associated with the eigenvalues to be assigned and then solving a small inverse eigenvalue problem resulting from projecting the initial problem into that subspace the second method can be regarded as a variant of the weilandt deflation technique used in eigenvalue methods

global nonexistence of positive initial energy solutions for a viscoelastic wave equation abstract in this paper we consider the nonlinear viscoelastic equation u t u t t u 0 t g t u d u t m 2 u t u p 2 u in 0 t with initial conditions and dirichlet boundary conditions for nonincreasing positive functions g we prove the nonexistence of global solutions with positive initial energy

two level algebraic domain decomposition preconditioners using jacobi schwarz smoother and adaptive coarse grid corrections we investigate two level preconditioners on the extended linear system arising from the domain decomposition method the additive schwarz method is used as a smoother and the coarse grid space is constructed by using the ritz vectors obtained in the arnoldi process the coarse grid space can be improved adaptively as the ritz vectors become a better approximation of the eigenvectors numerical tests on the model problem demonstrate the efficiency

gmres with deflated restarting a modification is given of the gmres iterative method for nonsymmetric systems of linear equations the new method deflates eigenvalues using wu and simon s thick restarting approach siam j matrix anal appl 22 2000 pp 602 616 it has the efficiency of implicit restarting but is simpler and does not have the same numerical concerns the deflation of small eigenvalues can greatly improve the convergence of restarted gmres also it is demonstrated that using harmonic ritz vectors is important because then the whole subspace is a krylov subspace that contains certain important smaller subspaces

general decay rate estimate for a viscoelastic equation with weakly nonlinear time dependent dissipation and source terms a viscoelastic wave equation in canonical form with weakly nonlinear time dependent dissipation and source terms is investigated in this paper for a wider class of relaxation functions and without imposing any restrictive growth assumption on the damping term at the origin we establish an explicit and general energy decay rate result

stability and stabilizability of discrete event dynamic systems a finite state automaton is adopted as a model for discrete event dynamic systems deds stabdity is defined as wslting a given set e mtinitely often stabilizability is defined as choosing state feedback such that the closed loop system is stable these notions are proposed as properties of resiliency or error recovery an important ingredient in stability is shown to be a notion of transition function invariance relations between our notions of stability and invariance and the notions of safety fairness hvelock deadlock etc in computer science literature are pointed out connections are established between our notions of invariance and the classical notions of a invariance and a 11 invariance of linear systems polynomial algorithms for testing stability and stabilizabdity and for constructing a stabilizing control law are also presented

the thermoelastic and viscoelastic contact of two rods we consider the thermoelastic and viscoelastic contact problem of two rods and prove the existence of a weak solution using a penalization method and compensated compactness moreover for the thermoelastic contact we show that the weak solution converges to zero exponentially as time goes to infinity and for the viscoelastic contact we prove that the weak solution decays to zero with the same rates as the relaxation functions do

note on intrinsic decay rates for abstract wave equations with memory in this paper we consider a viscoelastic abstract wave equation with memory kernel satisfying the inequality g h g 0 s 0 where h s is a given continuous positive increasing and convex function such that h 0 0 we shall develop an intrinsic method based on the main idea introduced by lasiecka and tataru uniform boundary stabilization of semilinear wave equation with nonlinear boundary dissipation differential and integral equations 6 507 533 1993 for determining decay rates of the energy given in terms of the function h s this will be accomplished by expressing the decay rates as a solution to a given nonlinear dissipative ode we shall show that the obtained result while generalizing previous results obtained in the literature is also capable of proving optimal decay rates for polynomially decaying memory kernels h s sp and for the full range of admissible parameters p 1 2 while such result has been known for certain restrictive ranges of the parameters p 1 3 2

on the supermal controllable sublanguage of a given language the concept of controllable language has been shown to play a basic role in the existence theory of supervisory controls for discrete event processes in this paper the supremal controllable sublanguage s of a given language l is characterized as the largest fixpoint of a monotone operator omega in the case where the languages involved are regular it is shown that the fixpoint s can be computed as the limit of the finite sequence k j given by k j 1 omega k j k 0 l an effective computational algorithm is developed and three examples are provided for illustration

general decay and blow up of solutions for a system of viscoelastic wave equations with nonlinear boundary source terms abstract in this work an initial boundary value problem for a system of viscoelastic wave equations with nonlinear boundary source term of the form u i t t u i u i t t 0 t g i t s u i s d s u i t 0 in 0 t u i x 0 i x u i t x 0 i x in u i x t 0 on 0 0 t u i t t u i 0 t g i t s u i s d s u i t f i u 0 on 1 0 t where i 1 l l 2 is considered in a bounded domain in r n n 1 by the faedo galerkin approximation method we obtain existence and uniqueness of weak solutions under appropriate assumptions on initial data and the relaxation functions we establish general decay and blow up results associated to solution energy estimates for lifespan of solutions are also given

blow up in a nonlinear viscoelastic wave equation with strong damping abstract in this paper we consider the nonlinear viscoelastic equation u t t u 0 t g t u d u t u p 2 u in 0 t with initial conditions and dirichlet boundary conditions for nonincreasing positive functions g we show the finite time blow up of some solutions whose initial data have arbitrarily high initial energy

dynamical consistency in hierarchical supervisory control a hierarchical control theory is presented founded upon the trace dynamical consistency property which is an extension of the notion of dynamical consistency dc to the supervisory case of automata with disablable transitions partitions of a system state space are considered for which both the trace dc and the non blocking in block controllability ibc conditions hold it is shown that low level non blocking controllable languages project up to such languages in the high level system and that when the non blocking ibc condition also holds high level non blocking controllable languages map down to such languages in the low level system it is demonstrated that the resulting pairs of low level and high level languages satisfy a version of the hierarchical consistency condition found in the existing language based hierarchical supervisory control theory the structures produced in the formulation of hierarchical control in this paper permit efficient regulator design and in particular repeated re design for hierarchy compatible language specifications such specifications consist of low level languages whose maximal controllable sublanguages are realizable by a combination of a high level possibly history dependent regulator and a set of state dependent low level regulators specified block wise an algorithm is proposed which facilitates the construction of non blocking ibc partitions of systems with vocalized states examples are presented including a material transfer line with re entrant flow and a double queue

on the exponential decay of waves with memory in this paper we consider general linear damped wave equations with memory we establish energy estimates that under the assumption of exponentially bounded kernels induce exponential decaying solutions numerical waves that mimic their continuous counterpart are also introduced using a finite element approach

global existence and uniform decay for a nonlinear viscoelastic equation with damping abstract in this paper we investigate a nonlinear viscoelastic equation with linear damping global existence of weak solutions and the uniform decay estimates for the energy have been established

on asymptotically efficient solutions for a class of supervisory control problems we consider restricted sequences of forbidden string and forbidden state problems and show the limiting problem instance defined by a sequence has a solution if and only if each problem instance in the sequence has a solution furthermore the supervisor that enforces the desired behavior in the limiting problem instance also enforces the desired behavior in each problem instance in the sequence in essence the storage requirement for supervisory control of each instance is bounded above by that of the limiting problem instance in addition if the limiting problem instance is available a similar observation can be made regarding the complexity of supervisory control this observation coupled with recent results on the solvability of the supervisory control problem involving certain classes of nonregular behaviors and finite representations of infinite state systems is suggested as an effective procedure to combat the computational and storage issues in supervisory control we conclude with an incomplete list of future research directions

minimizing the cardinality of an events set for supervisors of discrete event dynamical systems in this paper we study sufficient observation and work spaces for supervisors of a class of discrete event dynamical systems deds we use finite state automata to model a deds the finite automata generates a formal language defined over the set of events in the deds a supervisor is a feedback system that observes a generated trace of events and dynamically disables or enables a subset of controllable events such that the closed loop system behaves as desired we model the desired behavior of the deds by a sublanguage defined over the set of events a sufficient observation space is a collection of events whose observation by a supervisor is enough to realize a given desired behavior a sufficient work space is a sufficient observation space such that the control action of the supervisor is limited to only the controllable elements of the work space we construct algorithms to evaluate a sufficient work or observation space the reduction of work or observation spaces results in reducing the number of event detectors communication and command channels between the supervisor and the plant

on the existence of finite state supervisors for arbitrary supervisory control problems given two prefix closed languages k l spl sube spl sigma where k spl sube l represents the desired closed loop behavior and l is the open loop behavior there exists a finite state supervisor that enforces k in the closed loop if and only if there is a regular prefix closed language m spl sube spl sigma such that 1 m spl sigma sub u spl cup l spl sube m and 2 m spl cup l k in this paper we show that this is equivalent to 1 the controllability of sup spl lcub p spl sube k spl cup l spl macr spl verbar pr p p spl rcub with respect to spl sigma and 2 the regularity of sup spl lcub p spl sube k spl cup l spl macr spl verbar pr p p spl rcub where l spl macr spl sigma spl minus l and pr spl middot is the set of prefixes of strings in the language argument we use this property to investigate the issue of deciding the existence of a finite state supervisor for different representations we also present some properties of the language sup spl lcub p spl sube k spl cup l spl macr spl verbar pr p p spl rcub along with implications to the synthesis of solutions to the supervisory control problem with the fewest states