control of an unstable reaction diffusion pde with long input delay abstract a smith predictor like design for compensation of arbitrarily long input delays is available for general controllable possibly unstable lti finite dimensional systems such a design has not been proposed previously for problems where the plant is a pde we present a design and stability analysis for a prototype problem where the plant is a reaction diffusion parabolic pde with boundary control the plant has an arbitrary number of unstable eigenvalues and arbitrarily long delay with an unbounded input operator the predictor based feedback design extends fairly routinely within the framework of infinite dimensional backstepping however the stability analysis contains interesting features that do not arise in predictor problems when the plant is an ode the unbounded character of the input operator requires that the stability be characterized in terms of the h 1 rather than the usual l 2 norm of the actuator state the analysis involves an interesting structure of interconnected pdes of parabolic and first order hyperbolic types where the feedback gain kernel for the undelayed problem becomes an initial condition in a pde arising in the compensator design for the problem with input delay space and time variables swap their roles in an interesting manner throughout the analysis

characterizations of input to state stability for infinite dimensional systems we prove characterizations of input to state stability iss for a large class of infinite dimensional control systems including some classes of evolution equations over banach spaces time delay systems ordinary differential equations ode and switched systems these characterizations generalize well known criteria of iss proved by sontag and wang for ode systems for the special case of differential equations in banach spaces we prove even broader criteria for iss and apply these results to show that under some mild restrictions the existence of a noncoercive iss lyapunov functions implies iss we introduce the new notion of strong iss siss that is equivalent to iss in the ode case but is strictly weaker than iss in the infinite dimensional setting and prove several criteria for the siss property at the same time we show by means of counterexamples that many characterizations which are valid in the ode case are not true for general infinite dimensional systems

further facts about input to state stabilization previously published results about input to state stabilizability are shown to hold even for systems which are not linear in controls provided that a more general type of feedback is allowed applications to certain stabilization problems and coprime factorizations as well as comparisons to other results on input to state stability are briefly discussed

a sparse proximal implementation of the lp dual active set algorithm we present an implementation of the lp dual active set algorithm lp dasa based on a quadratic proximal approximation a strategy for dropping inactive equations from the constraints and recently developed algorithms for updating a sparse cholesky factorization after a low rank change although our main focus is linear programming the first and second order proximal techniques that we develop are applicable to general concave convex lagrangians and to linear equality and inequality constraints we use netlib lp test problems to compare our proximal implementation of lp dasa to simplex and barrier algorithms as implemented in cplex

position space renormalisation group for directed diffusion limited aggregation the author uses a position space renormalisation group transformation to show that directed diffusion limited aggregation and directed animals are in different universality classes

boundary stabilization of the phase field system by finite dimensional feedback controllers abstract we design here finite dimensional stabilizing feedback dirichlet boundary controllers for steady state solutions to the phase field system the feedback controllers are easily manageable from computational point of view since they are expressed in terms of the eigenfunctions j j 1 n n n corresponding to the eigenvalues j j 1 n of the laplace operator in r q q 2 3 the stabilizing algorithm we develop here is applicable under the assumption that the system j n j 1 n is linearly independent on the part of the boundary where the control is applied

exponential stabilization of the semilinear heat equation with nonlocal boundary conditions abstract the present work is devoted to the problem of boundary stabilization of the semilinear 1 d heat equation with nonlocal boundary conditions the stabilizing controller is finite dimensional linear given in an explicit form involving only the eigenfunctions of the laplace operator with nonlocal boundary conditions

comment on eden model on the manhattan lattice the author re examines the two parameter position space renormalisation group calculation for eden growth process on the square manhattan lattice sml first studied by chernoutsan and milosevic ibid vol 19 p 2237 1986 and find that contrary to the finding of the above authors eden processes on sml and on the ordinary square lattice are in the same universality class

exponential input to state stabilization of a class of diagonal boundary control systems with delay boundary control abstract this paper deals with the exponential input to state stabilization with respect to boundary disturbances of a class of diagonal infinite dimensional systems via delay boundary control the considered input delays are uncertain and time varying the proposed control strategy consists of a constant delay predictor feedback controller designed on a truncated finite dimensional model capturing the unstable modes of the original infinite dimensional system we show that the resulting closed loop system is exponentially input to state stable with fading memory of both additive boundary input perturbations and disturbances in the computation of the predictor feedback

new formulation of predictors for finite dimensional linear control systems with input delay we consider a one dimensional controlled reaction diffusion equation where the control acts on the boundary and is subject to a constant delay such a model is a paradigm for more general parabolic systems coupled with a transport equation we prove that this is possible to stabilize in h 1 norm this process by means of an explicit predictor based feedback control that is designed from a finite dimensional subsystem the implementation is very simple and efficient and is based on standard tools of pole shifting our feedback acts on the system as a finite dimensional predictor we compare our approach with the backstepping method

on stabilizability and sampling for infinite dimensional systems some questions either motivated by or related to time sampling regarding the stabilizability of infinite dimensional or distributed parameter systems are considered in particular these include the characteristics of those systems which are finite rank stabilizable and the preservation of stabilizability under sampling a pathological class of systems which when sampled may be rendered unstabilizable by arbitrarily small perturbations in the sampling rate is identified the approach taken in establishing these results is based upon a spectral decomposition of the infinitesimal generator of the underlying open loop semigroup the results obtained apply to control systems with dynamics described by broad classes of partial and functional differential equations that arise frequently in applications

on global stabilization of burgers equation by boundary control abstract although often referred to as a one dimensional cartoon of navier stokes equation because it does not exhibit turbulence the burgers equation is a natural first step towards developing methods for control of flows recent references include burns and kang nonlinear dynamics 2 1991 235 262 choi et al j fluid mech 253 1993 509 543 ito and kang siam j control optim 32 1994 831 854 ito and yan j math anal appl 227 1998 271 299 byrnes et al j dynam control systems 4 1998 457 519 and van ly et al numer funct anal optim 18 1997 143 188 while these papers have achieved tremendous progress in local stabilization and global analysis of attractors the problem of global asymptotic stabilization has remained open this problem is non trivial because for large initial conditions the quadratic convective term which is negligible in a linear local analysis dominates the dynamics we derive nonlinear boundary control laws that achieve global asymptotic stability we consider both the viscous and the inviscid burgers equation using both neumann and dirichlet boundary control we also study the case where the viscosity parameter is uncertain as well as the case of stochastic burgers equation for some of the control laws that would require the measurement in the interior of the domain we develop the observer based versions

closed form boundary state feedbacks for a class of 1 d partial integro differential equations in this paper a problem of boundary stabilization of a class of linear parabolic partial integro differential equations p i des in one dimension is considered using the method of backstepping avoiding spatial discretization required in previous efforts the problem is formulated as a design of an integral operator whose kernel is required to satisfy a hyperbolic p i de the kernel p i de is then converted into an equivalent integral equation and by applying the method of successive approximations the equation s well posedness and the kernel s smoothness are established it is shown how to extend this approach to design optimally stabilizing controllers an adaptation mechanism is developed to reduce the conservativeness of the inverse optimal controller and the performance bounds are derived for a broad range of physically motivated special cases feedback laws are constructed explicitly and the closed loop solutions are found in closed form a numerical scheme for the kernel p i de is proposed its numerical effort compares favorably with that associated with operator riccati equations

boundary feedback stabilization of a reaction diffusion equation with robin boundary conditions and state delay abstract this paper discusses the boundary feedback stabilization of a reaction diffusion equation with robin boundary conditions and in the presence of a time varying state delay the proposed control design strategy is based on a finite dimensional truncated model obtained via a spectral decomposition by an adequate selection of the number of modes of the original infinite dimensional system we show that the design performed on the finite dimensional truncated model achieves the exponential stabilization of the original infinite dimensional system in the presence of distributed disturbances we show that the closed loop system is exponentially input to state stable with fading memory

infinite dimensional lur e systems input to state stability and convergence properties we consider forced lur e systems in which the linear dynamic component is an infinite dimensional well posed system numerous physically motivated delay and partial differential equations are know

position space renormalisation group for isolated polymer chains we develop a cell position space renormalisation group psrg with which we study the scaling properties of isolated polymer chains we model a chain by a self avoiding walk constrained to a lattice for rescaling factors b s 6 we calculate recursion relations analytically on the square lattice with several different choices for the psrg weight function we also calculate implicit cell to cell transformations in which a cell of size b is rescaled to a cell of size b the results of these psrgs improve both as b increases and as b b 1 in addition we construct a true infinitesimal psrg transformation which appears to become exact as the dimensionality d approaches 1 we obtain the closed form expression for the correlation length exponent u d l d in d the flory formula deviates from this already at first order in d 1 we also develop a constant fugacity monte carlo method which enables us to simu late in an unbiased way within the grand canonical ensemble chains of up to lo3 bonds with this method we extend the psrg to larger cells b s 150 on the square lattice our numerical method provides high statistical accuracy for all cell sizes however in the range of b we study the asymptotic behaviour of our results appears to depend on the choice of weight function one weight function provides smooth behaviour as a function of b and with it we extrapolate to find u 0 756 0 004 further work is required to resolve the apparent anomalies in the results based on the other weight functions

sampled data boundary feedback control of 1 d parabolic pdes abstract the paper provides results for the application of boundary feedback control with zero order hold zoh to 1 d linear parabolic systems on bounded domains it is shown that the continuous time boundary feedback applied in a sample and hold fashion guarantees closed loop exponential stability provided that the sampling period is sufficiently small two different continuous time feedback designs are considered the reduced model design and the backstepping design the obtained results provide stability estimates for weighted 2 norms of the state and robustness with respect to perturbations of the sampling schedule is guaranteed

an lmi condition for the robustness of constant delay linear predictor feedback with respect to uncertain time varying input delays abstract this paper discusses the robustness of the constant delay predictor feedback in the case of an uncertain time varying input delay specifically we study the stability of the closed loop system when the predictor feedback is designed based on the knowledge of the nominal value of the time varying delay by resorting to an adequate lyapunov krasovskii functional we derive an lmi based sufficient condition ensuring the exponential stability of the closed loop system for small enough variations of the time varying delay around its nominal value these results are extended to the feedback stabilization of a class of diagonal infinite dimensional boundary control systems in the presence of a time varying delay in the boundary control input

iss like estimates for nonlinear parabolic pdes with variable coefficients on higher dimensional domains abstract this paper presents a maximum principle based approach in the establishment of iss like estimates for a class of nonlinear parabolic partial differential equations pdes with variable coefficients and different types of nonlinear boundary conditions on higher dimensional domains comparing with the existing literature the iss like estimates established in this paper are independent of the nonlinear terms of the pdes technical development on iss analysis of the considered systems is detailed and an example of establishing iss like estimates for a nonlinear parabolic equation with respectively a nonlinear robin boundary condition and a nonlinear dirichlet boundary condition is provided to illustrate the application of the developed method

improving the run time and quality of nested dissection ordering when performing sparse matrix factorization the ordering of matrix rows and columns has a dramatic impact on the factorization time this paper describes an approach to the reordering problem that produces significantly better orderings than prior methods the algorithm is a hybrid of nested dissection and minimum degree ordering and combines an assortment of different algorithmic advances new or improved algorithms are described for graph compression multilevel partitioning and separator improvement when these techniques are combined the resulting orderings average 39 better than minimum degree over a suite of test matrices while requiring roughly 2 7 times the run time of liu s multiple minimum degree

dual multilevel optimization we study the structure of dual optimization problems associated with linear constraints bounds on the variables and separable cost we show how the separability of the dual cost function is related to the sparsity structure of the linear equations as a result techniques for ordering sparse matrices based on nested dissection or graph partitioning can be used to decompose a dual optimization problem into independent subproblems that could be solved in parallel the performance of a multilevel implementation of the dual active set algorithm is compared with cplex simplex and barrier codes using netlib linear programming test problems

stability of higher order discrete time lur e systems abstract we consider discrete time lur e systems obtained by applying nonlinear feedback to a system of higher order difference equations arma models the arma model relates the inputs and outputs of the linear system and does not involve any internal or state variables a stability theory subsuming results of circle criterion type is developed including criteria for input to output stability a concept which is very much reminiscent of input to state stability

feedback stabilization of a 1 d linear reaction diffusion equation with delay boundary control the goal of this paper is to design a stabilizing feedback boundary control for a reaction diffusion partial differential equation pde where the boundary control is subject to a constant delay while the equation may be unstable without any control for this system which is equivalent to a parabolic equation coupled with a transport equation a prediction based control is explicitly computed by splitting the infinite dimensional system into two parts a finite dimensional unstable part and a stable infinite dimensional part a finite dimensional delayed controller is computed for the unstable part and it is shown that this controller stabilizes the whole pde the proof is based on an explicit expression of the classical artstein transformation combined with an adequately designed lyapunov function a numerical simulation illustrates the constructive feedback design method

input to state stability and inverse optimality of linear time varying delay predictor feedbacks for linear systems with time varying input delay and additive disturbances we show that the basic predictor feedback control law is inverse optimal with respect to a meaningful differential game problem and establish its robustness to constant multiplicative perturbations appearing at the system input both of these properties of the basic predictor feedback controller have not been established so far even for the constant delay case we then show that the basic predictor feedback controller when applied through a low pass filter is again inverse optimal and study its input to state stability as well as its robustness to the low pass filter time constant properties all of the stability and inverse optimality proofs are based on the infinite dimensional backstepping transformation which allows us to construct appropriate lyapunov functionals a numerical example is also provided

parallel multilevel series k way partitioning scheme for irregular graphs in this paper we present a parallel formulation of a multilevel k way graph partitioning algorithm a key feature of this parallel formulation is that it is able to achieve a high degree of concurrency while maintaining the high quality of the partitions produced by the serial multilevel k way partitioning algorithm in particular the time taken by our parallel graph partitioning algorithm is only slightly longer than the time taken for re arrangement of the graph among processors according to the new partition experiments with a variety of finite element graphs show that our parallel formulation produces high quality partitionings in a short amount of time for example a 128 way partitioning of graphs with one million vertices can be computed in a little over two seconds on a 128 processor cray t3d furthermore the quality of the partitions produced is comparable edge cuts within 5 to those produced by the serial multilevel k way algorithm thus our parallel algorithm makes it feasible to perform frequent repartitioning of graphs in dynamic computations without compromising the partitioning quality

pi regulation of a reaction diffusion equation with delayed boundary control the general context of this work is the feedback control of an infinite dimensional system so that the closed loop system satisfies a fading memory property and achieves the setpoint tracking of a given reference signal more specifically this paper is concerned with the proportional integral pi regulation control of the left neumann trace of a one dimensional reaction diffusion equation with a delayed right dirichlet boundary control in this setting the studied reaction diffusion equation might be either open loop stable or unstable the proposed control strategy goes as follows first a finite dimensional truncated model that captures the unstable dynamics of the original infinite dimensional system is obtained via spectral decomposition the truncated model is then augmented by an integral component on the tracking error of the left neumann trace after resorting to the artstein transformation to handle the control input delay the pi controller is designed by pole shifting stability of the resulting closed loop infinite dimensional system consisting of the original reaction diffusion equation with the pi controller is then established thanks to an adequate lyapunov function in the case of a time varying reference input and a time varying distributed disturbance our stability result takes the form of an exponential input to state stability iss estimate with fading memory finally another exponential iss estimate with fading memory is established for the tracking performance of the reference signal by the system output in particular these results assess the setpoint regulation of the left neumann trace in the presence of distributed perturbations that converge to a steady state value and with a time derivative that converges to zero numerical simulations are carried out to illustrate the efficiency of our control strategy

stabilization of linear heat equation with a heat source at intermediate point by boundary control in this paper the stabilization of a linear heat equation with a heat source at intermediate point is discussed applying the backstepping method firstly we prove the existence of kernels in the forward and inverse transformation by some special techniques secondly we obtain the exponential stability with any prescribed decay rate of a closed loop system finally the effectiveness of the explicit feedback stabilization controller design is illustrated with some numerical examples

on the stabilizability of the burgers equation by receding horizon control a receding horizon framework for stabilization of a class of infinite dimensional controlled systems is presented no terminal costs or constraints are used to ensure asymptotic stability of the controlled system the key assumption is a stabilizability assumption which can be guaranteed for example for the burgers equations with periodic and with homogeneous neumann boundary conditions numerical experiments validate the theoretical results comparisons to the case with terminal penalties acting as control lyapunov functions are included

integral control of linear systems with actuator nonlinearities lower bounds for the maximal regulating gain closing the loop around an exponentially stable single input single output regular linear system subject to a globally lipschitz and nondecreasing actuator nonlinearity and compensated by an integral controller is known to ensure asymptotic tracking of constant reference signals provided that 1 the steady state gain of the linear part of the plant is positive 2 the positive integrator gain is sufficiently small and 3 the reference value is feasible in a very natural sense here lower bounds are derived for the maximal regulating gain for various special cases including systems with nonovershooting step response and second order systems with a time delay in the input or output the lower bounds are given in terms of open loop frequency step response data and the lipschitz constant of the nonlinearity and are hence readily obtainable

eden model on the manhattan lattice the authors study the eden growth model on the square manhattan lattice sml for this purpose it has been necessary to extend the standard eden model in such a way that each act of growing is conceived as a directional process by applying the position space renormalisation group technique they find that the eden processes on the sml and on the ordinary square lattice are in different universality classes this finding and corresponding fractal dimensions are compared with results obtained for similar models of irreversible kinetic processes

monotonicity methods for input to state stability of nonlinear parabolic pdes with boundary disturbances we introduce a monotonicity based method for studying input to state stability iss of nonlinear parabolic equations with boundary inputs we first show that a monotone control system is iss if an

local input to state stability characterizations and counterexamples abstract we show that a nonlinear locally uniformly asymptotically stable infinite dimensional system is automatically locally input to state stable liss provided the nonlinearity possesses some sort of uniform continuity with respect to external inputs also we prove that liss is equivalent to existence of a liss lyapunov function we show by means of a counterexample that if this uniformity is not present then the equivalence of local asymptotic stability and local iss does not hold anymore using a modification of this counterexample we show that in infinite dimensions a uniformly globally asymptotically stable at zero globally stable and locally iss system possessing an asymptotic gain property does not have to be iss in contrast to finite dimensional case

boundary control of a nonhomogeneous flexible wing with bounded input disturbances this note deals with the boundary control problem of a nonhomogeneous flexible wing evolving under unsteady aerodynamic loads the wing is actuated at its tip by flaps and is modeled by a distributed parameter system consisting of two coupled partial differential equations based on the proposed boundary control law the well posedness of the underlying cauchy problem is first investigated by resorting to the semigroup theory then a lyapunov based approach is employed to assess the stability of the closed loop system in the presence of bounded input disturbances

presolving in linear programming most modern linear programming solvers analyze the lp problem before submitting it to optimization some examples are the solvers whizard tomlin and welch 1983 ob1 lustig et al 1994 osl forrest and tomlin 1992 sciconic 1990 and cplex bixby 1994 the purpose of the presolve phase is to reduce the problem size and to discover whether the problem is unbounded or infeasible in this paper we present a comprehensive survey of presolve methods moreover we discuss the restoration procedure in detail i e the procedure that undoes the presolve computational results on the netlib problems gay 1985 are reported to illustrate the efficiency of the presolve methods

second order boundary value problems with integral boundary conditions abstract in this paper we investigate the existence of positive solutions of nonlocal second order boundary value problems with integral boundary conditions

stability of nonnegative lur e systems a stability instability trichotomy for a class of nonnegative continuous time lur e systems is derived asymptotic exponential and input to state stability concepts are considered the presented trichotomy rests on perron frobenius theory absolute stability theory and recent input to state stability results for lur e systems applications of the results derived arise in various fields including density dependent population dynamics and two examples are discussed in detail

semi global incremental input to state stability of discrete time lur e systems abstract we present sufficient conditions for semi global incremental input to state stability of a class of forced discrete time lur e systems the results derived are reminiscent of well known absolute stability criteria such as the small gain theorem and the circle criterion we derive a natural sufficient condition which guarantees that asymptotically almost periodic inputs generate asymptotically almost periodic state trajectories as a corollary we obtain sufficient conditions for the converging input converging state property to hold

backstepping boundary control of burgers equation with actuator dynamics in this paper we propose a backstepping boundary control law for burgers equation with actuator dynamics while the control law without actuator dynamics depends only on the signals u 0 t and u 1 t the backstepping control also depends on ux 0 t ux 1 t uxx 0 t and uxx 1 t making the regularity of the control inputs the key technical issue of the paper with elaborate lyapunov analysis we prove that all these signals are suciently regular and the closed loop system including the boundary dynamics is globally h 3 stable and well posed c 2000 elsevier science b v all rights reserved

boundary stabilisation to non stationary solutions for deterministic and stochastic parabolic type equations abstractin this work we design explicit finite dimensional boundary feedback laws for stabilisation to trajectories for parabolic type equations the simple form of the feedback allows to write the solution of the corresponding closed loop equation in a mild formulation via a kernel then taking advantage of this the stability is shown as an application null stabilisation for stochastic parabolic type equations is deduced as well as far as we know the present work is the first result on boundary feedback stabilisation to trajectories and for stochastic parabolic type equations with stability guaranteed independent of how large the level of the noise is

response to the comment on eden model on the manhattan lattice the authors respond to the numerical simulation result obtained by botet ibid vol 19 p 2233 1986 which implies that the eden aggregates should be compact objects and comment on the validity of the renormalisation group approach to the same problem

blow up of solutions for semilinear heat equation with nonlinear nonlocal boundary condition abstract in this paper we consider a semilinear heat equation u t u c x t u p for x t 0 with nonlinear and nonlocal boundary condition u 0 k x y t u l d y and nonnegative initial data where p 0 and l 0 we prove global existence theorem for max p l 1 some criteria on this problem which determine whether the solutions blow up in a finite time for sufficiently large or for all nontrivial initial data or the solutions exist for all time with sufficiently small or with any initial data are also given

a de giorgi iteration based approach for the establishment of iss properties for burgers equation with boundary and in domain disturbances this note addresses input to state stability iss properties with respect to w r t boundary and in domain disturbances for burgers equation the developed approach is a combination of the method of de giorgi iteration and the technique of lyapunov functionals by adequately splitting the original problem into two subsystems the iss properties in l 2 norm for burgers equation have been established using this method moreover as an application of de giorgi iteration iss in l infty norm w r t in domain disturbances and actuation errors in boundary feedback control for a one dimensional linear unstable reaction diffusion equation have also been established it is the first time that the method of de giorgi iteration is introduced in the iss theory for infinite dimensional systems and the developed method can be generalized for tackling some problems on multidimensional spatial domains and to a wider class of nonlinear partial differential equations

construction of lyapunov functions for interconnected parabolic systems an iiss approach this paper is devoted to two issues the first one is to provide lyapunov based tools to establish integral input to state stability iiss and input to state stability iss for some classes of nonlinear parabolic equations the other one is to provide a stability criterion for interconnections of iiss parabolic systems the results addressing the former problem allow us to overcome obstacles arising in tackling the latter one the results for the latter problem are a small gain condition and a formula of lyapunov functions which can be constructed for interconnections whenever the small gain condition holds it is demonstrated that for interconnections of partial differential equations the choice of a right state and input spaces is crucial in particular for iiss subsystems which are not iss as illustrative examples stability of two highly nonlinear reaction diffusion systems is established by the proposed small gain criterion

iss in different norms for 1 d parabolic pdes with boundary disturbances for one dimensional parabolic partial differential equations with disturbances at both boundaries and distributed disturbances we provide input to state stability iss estimates in various norms due to the lack of an iss lyapunov functional for boundary disturbances the proof methodology uses i an eigenfunction expansion of the solution and ii a finite difference scheme the iss estimate for the sup norm leads to a refinement of the well known maximum principle for the heat equation finally the obtained results are applied to quasi static thermoelasticity models that involve nonlocal boundary conditions small gain conditions that guarantee the global exponential stability of the zero solution for such models are derived

stabilisation of parabolic semilinear equations abstractwe design here a finite dimensional feedback stabilising dirichlet boundary controller for the equilibrium solutions to parabolic equations these results extend that ones in barbu 2013 which provide a feedback controller expressed in terms of the eigenfunctions j corresponding to the unstable eigenvalues j j 1n of the operator corresponding to the linearised equation in barbu 2013 the stabilisability result is conditioned by the require of linear independence of j j 1n on the part of the boundary where control acts in this work we design a similar control as in barbu 2013 and show that it assures the stability of the system this time we drop the require of linear independence and any other additional hypothesis some examples are provided in order to illustrate the acquired results more exactly boundary stabilisation of the heat equation and the fitzhugh nagumo equation

approximate controllability of the semilinear heat equation this article is concerned with the study of approximate controllability for the semilinear heat equation in a bounded domain when the control acts on any open and nonempty subset of or on a part of the boundary in the case of both an internal and a boundary control the approximate controllability in l p for 1 p l in the case of the interior control we also prove approximate controllability in c 0 the proof combines a variational approach to the controllability problem for linear equations and a fixed point method we also prove that the control can be taken to be of quasi bang bang form

input to state stability of discrete time lur e systems an input to state stability theory which subsumes results of circle criterion type is developed in the context of discrete time lur e systems the approach developed is inspired by the complexified aizerman conjecture

global steady state controllability of one dimensional semilinear heat equations we investigate the problem of exact boundary controllability of semilinear one dimensional heat equations we prove that it is possible to move from any steady state to any other by means of a boundary control provided that both are in the same connected component of the set of steady states the proof is based on an effective feedback stabilization procedure which is implemented

iss property with respect to boundary disturbances for a class of riesz spectral boundary control systems abstract this paper deals with the establishment of input to state stability iss estimates for infinite dimensional systems with respect to both boundary and distributed disturbances first a new approach is developed for the establishment of iss estimates for a class of riesz spectral boundary control systems satisfying certain eigenvalue constraints second a concept of weak solutions is introduced in order to relax the disturbances regularity assumptions required to ensure the existence of classical solutions the proposed concept of weak solutions that applies to a large class of boundary control systems which is not limited to the riesz spectral ones provides a natural extension of the concept of both classical and mild solutions assuming that an iss estimate holds true for classical solutions we show the existence the uniqueness and the iss property of the weak solutions

on continuity of solutions for parabolic control systems and input to state stability abstract we study minimal conditions under which mild solutions of linear evolutionary control systems are continuous for arbitrary bounded input functions this question naturally appears when working with boundary controlled linear partial differential equations here we focus on parabolic equations which allow for operator theoretic methods such as the holomorphic functional calculus moreover we investigate stronger conditions than continuity leading to input to state stability with respect to orlicz spaces this also implies that the notions of input to state stability and integral input to state stability coincide if additionally the uncontrolled equation is dissipative and the input space is finite dimensional

cell renormalisation of growth processes true self avoiding walks and growing animals the authors present a generating function formalism for growth processes in general and introduce a new cell renormalisation scheme as examples they treat the true self avoiding walk and the eden process or growing animals in two and three dimensions using small cells the results in both cases indicate a substantial increase in the fractal dimension d compared with their equilibrium counterparts the case of the eden process may however suggest a peculiar convergence behaviour as the cell size b tends to infinity

universality of neighbour avoiding and self avoiding walks on the square lattice it is shown that within position space renormalisation group psrg theory neighbour avoiding walks naws and self avoiding walks saws on the square lattice obey the same end to end distance critical exponent nu this universality is shown by applying a recent finite lattice renormalisation transformation to ordinary and oriented naw and saw problems and then using an exact equivalence between saws on an oriented lattice and naws on its covering lattice the universality class includes several oriented walk problems

input to state stability of differential inclusions with applications to hysteretic and quantized feedback systems input to state stability iss of a class of differential inclusions is proved every system in the class is of lur e type a feedback interconnection of a linear system and a set valued nonlinearity applications of the iss results in the context of feedback interconnections with a hysteresis operator or a quantization operator in the feedback path are developed

infinite dimensional input to state stability and orlicz spaces in this work the relation between input to state stability and integral input to state stability is studied for linear infinite dimensional systems with an unbounded control operator although a special focus is laid on the case l infty general function spaces are considered for the inputs we show that integral input to state stability can be characterized in terms of input to state stability with respect to orlicz spaces since we consider linear systems the results can also be formulated in terms of admissibility for parabolic diagonal systems with scalar inputs both stability notions with respect to l infty are equivalent

parallel interior point solver for structured linear programs issues of implementation of an object oriented library for parallel interior point methods are addressed the solver can easily exploit any special structure of the underlying optimization problem in particular it allows a nested embedding of structures and by this means very complicated real life optimization problems can be modelled the efficiency of the solver is illustrated on several problems arising in the optimization of networks the sequential implementation outperforms the state of the art commercial optimization software the parallel implementation achieves speed ups of about 3 1 3 9 on 4 processors parallel systems and speed ups of about 10 12 on 16 processors parallel systems

linear systems with delayed controls a reduction linear systems with delayed control action are transformed into systems without delays under an absolute continuity condition the new system is an ordinary differential control equation in the general case the new system is a measure differential control system it is shown how the controllability stabilization and various optimization problems can be analyzed via the reduced systems

stability and convergence properties of forced infinite dimensional discrete time lur e systems incremental stability and convergence properties for forced infinite dimensional discrete time lur e systems are addressed lur e systems have a linear and nonlinear component and arise as the fe

delay robustness of linear predictor feedback without restriction on delay rate robustness is established for the predictor feedback for linear time invariant systems with respect to possibly time varying perturbations of the input delay with a constant nominal delay the prior results have addressed qualitatively constant delay perturbations robustness of stability in l 2 norm of actuator state and delay perturbations with restricted rate of change robustness of stability in h 1 norm of actuator state the present work provides simple formulas that allow direct and accurate computation of the least upper bound of the magnitude of the delay perturbation for which the exponential stability in supremum norm on the actuator state is preserved while the prior work has employed lyapunov krasovskii functionals constructed via backstepping the present work employs a particular form of small gain analysis two cases are considered the case of measurable possibly discontinuous time varying perturbations and the case of constant perturbations

iss with respect to boundary disturbances for 1 d parabolic pdes due to unbounded input operators in partial differential equations pdes with boundary inputs there has been a long held intuition that input to state stability iss properties and finite gains cannot be established with respect to disturbances at the boundary this intuition has been reinforced by many unsuccessful attempts as well as by the success in establishing iss only with respect to the derivative of the disturbance contrary to this intuition we establish such a result for parabolic pdes our methodology does not rely on the transformation of the boundary disturbance to a distributed input and the stability analysis is performed in time varying subsets of the state space the obtained results are used for the comparison of the gain coefficients of transport pdes with respect to inlet disturbances and for the establishment of the iss property with respect to control actuator errors for parabolic systems under boundary feedback control

stability of infinite dimensional sampled data systems suppose that a static state feedback stabilizes a continuous time linear infinite dimensional control system we consider the following question if we construct a sampled data controller by applying an idealized sample and hold process to a continuous time stabilizing feedback will this sampled data controller stabilize the system for all sufficiently small sampling times here the state space x and the control space u are hilbert spaces the system is of the form x t ax t bu t where a is the generator of a strongly continuous semigroup on x and the continuous time feedback is u t fx t the answer to the above question is known to be yes if x and u are finite dimensional spaces in the infinite dimensional case if f is not compact then it is easy to find counterexamples therefore we restrict attention to compact feedback we show that the answer to the above question is yes if b is a bounded operator from u into x moreover if b is unbounded we show that the answer yes remains correct provided that the semigroup generated by a is analytic we use the theory developed for static state feedback to obtain analogous results for dynamic output feedback control

generalized sampled data stabilization of well posed linear infinite dimensional systems we consider well posed linear infinite dimensional systems the outputs of which are sampled in a generalized sense using a suitable weighting function under certain natural assump tions on the system the weighting function and the sampling period we show that there exists a generalized hold function such that unity sampled data feedback renders the closed loop system exponentially stable in the state space sense as well as l 2 stable in the input output sense to illustrate our main result we describe an application to a structurally damped euler bernoulli beam

sampled data boundary feedback control of 1 d linear transport pdes with non local terms abstract the paper provides results for the application of boundary feedback control with zero order hold zoh to 1 d inhomogeneous linear transport partial differential equations on bounded domains with constant velocity and non local terms it is shown that the emulation design based on the recently proposed continuous time boundary feedback designed by means of backstepping guarantees closed loop exponential stability provided that the sampling period is sufficiently small it is also shown that contrary to the parabolic case a smaller sampling period implies a faster convergence rate with no upper bound for the achieved convergence rate the obtained results provide stability estimates for the sup norm of the state and robustness with respect to perturbations of the sampling schedule is guaranteed

stabilization of well posed infinite dimensional systems by dynamic sampled data feedback it is shown that a set of six natural conditions is necessary and sufficient for the existence of a finite dimensional stabilizing sampled data controller for a well posed infinite dimensional system the underlying stability concept for the sampled data system is reminiscent of the notion of input to state stability from nonlinear control theory

a strict control lyapunov function for a diffusion equation with time varying distributed coefficients in this paper a strict lyapunov function is developed in order to show the exponential stability and input to state stability iss properties of a diffusion equation for nonhomogeneous media such media can involve rapidly time varying distributed diffusivity coefficients based on this lyapunov function a control law is derived to preserve the iss properties of the system and improve its performance a robustness analysis with respect to disturbances and estimation errors in the distributed parameters is performed on the system precisely showing the impact of the controller on the rate of convergence and iss gains this is important in light of a possible implementation of the control since in most cases diffusion coefficient estimates involve a high degree of uncertainty an application to the safety factor profile control for the tore supra tokamak illustrates and motivates the theoretical results a constrained control law incorporating nonlinear shape constraints in the actuation profiles is designed to behave as close as possible to the unconstrained version albeit with the equivalent of a variable gain finally the proposed control laws are tested under simulation first in the nominal case and then using a model of tore supra dynamics where they show adequate performance and robustness with respect to disturbances

boundary feedback stabilization of an unstable heat equation in this paper we study the problem of boundary feedback stabilization for the unstable heat equation ut x t uxx x t a x u x t this equation can be viewed as a model of a heat conducting rod in which not only is the heat being diffused mathematically due to the diffusive term uxx but also the destabilizing heat is generating mathematically due to the term a u with a 0 we show that for any given continuously differentiable function a and any given positive constant l we can explicitly construct a boundary feedback control law such that the solution of the equation with the control law converges to zero exponentially at the rate of l this is a continuation of the recent work of boskovic krstic and liu ieee trans automat control 46 2001 pp 2022 2028 and balogh and krstic european j control 8 2002 pp 165 176

real space renormalisation theory of self avoiding walks on a manhattan lattice the real space renormalisation group theory is applied to the self avoiding walk saw problem on a two dimensional oriented lattice known as the manhattan lattice a finite lattice renormalisation transformation is used to calculate the connectivity constant mu and the size exponent nu a more general saw model is defined that contains the oriented and nonoriented lattice problems as special cases a renormalisation group analysis of this model provides evidence that the saw on the manhattan lattice is the same universality class as the ordinary nonoriented saw problem

input to state stability of a clamped free damped string in the presence of distributed and boundary disturbances this note establishes the exponential input to state stability eiss property for a clamped free damped string with respect to distributed and boundary disturbances while efficient methods for establishing iss properties for distributed parameter systems with respect to distributed disturbances have been developed during the last decades establishing iss properties with respect to boundary disturbances remains challenging one of the well known methods for well posedness analysis of systems with boundary inputs is the use of a lifting operator for transferring the boundary disturbance to a distributed one however the resulting distributed disturbance involves time derivatives of the boundary perturbation thus the subsequent iss estimate depends on its amplitude and may not be expressed in the strict form of iss properties to solve this problem we show for a clamped free damped string equation that the projection of the original system trajectories in an adequate riesz basis can be used to establish the desired eiss property

small gain stability analysis of certain hyperbolic parabolic pde loops abstract this work provides stability results in the spatial sup norm for hyperbolic parabolic loops in one spatial dimension the results are obtained by an application of the small gain stability analysis two particular cases are selected for the study because they contain challenges typical of more general systems to which the results are easily generalizable but at the expense of less pedagogical clarity and more notational clutter i the feedback interconnection of a parabolic pde with a first order zero speed hyperbolic pde with boundary disturbances and ii the feedback interconnection by means of a combination of boundary and in domain terms of a parabolic pde with a first order hyperbolic pde the first case arises in the study of the movement of chemicals underground and includes the wave equation with kelvin voigt damping as a subcase the second case arises when we apply backstepping to a pair of hyperbolic pdes that is obtained by ignoring diffusion phenomena moreover the second case arises in the study of parabolic pdes with distributed delays in the first case we provide sufficient conditions for iss in the spatial sup norm with respect to boundary disturbances in the second case we provide delay independent sufficient conditions for exponential stability in the spatial sup norm

input to state stability with respect to boundary disturbances for a class of semi linear parabolic equations abstract this paper studies the input to state stability iss properties for a class of semi linear parabolic partial differential equations pdes with respect to boundary disturbances in order to avoid the appearance of time derivatives of the disturbances in iss estimates some technical inequalities are first developed which allow directly dealing with the boundary conditions and establishing the iss based on the method of lyapunov functionals the well posedness analysis of the considered problem is carried out and the conditions for iss are derived two examples are used to illustrate the application of the developed method

brief input to state stability for a class of lurie systems we analyze input to state stability iss for the feedback interconnection of a linear block and a nonlinear element this study is of importance for establishing robustness against actuator nonlinearities and disturbances in the absolute stability framework we prove iss from a positive real property of the linear block by restricting the sector nonlinearity to grow unbounded as its argument tends to infinity when this growth condition is violated examples show that the iss property is lost the result is used to give a simple proof of boundedness for negative resistance oscillators such as the van der pol oscillator in a separate application we relax the minimum phase assumption of an earlier boundedness result for systems with nonlinearities that grow faster than linear