paper pole assignment for distributed systems by finite dimensional control the question of pole assignment for a class of distributed systems by means of finite dimensional control is considered a finite dimensional compensator is usually designed based on a reduced order model and it is not a priori known what effect this will have on the original infinite dimensional system explicit formulas are derived which enable one to calculate the eigenvalues of the resulting closed loop system for a certain compensator design estimates are derived which can be used to guarantee stability a priori numerical results are also presented

random attractors for stochastic porous media equations perturbed by space time linear multiplicative noise unique existence of solutions to porous media equations driven by continuous linear multiplicative space time rough signals is proven for initial data in l 1 o on bounded domains o the generation of a continuous order preserving random dynamical system rds on l 1 o and the existence of a random attractor for stochastic porous media equations perturbed by linear multiplicative noise in space and time is obtained the random attractor is shown to be compact and attracting in l o norm uniform l bounds and uniform space time continuity of the solutions is shown general noise including fractional brownian motion for all hurst parameters is treated a pathwise wong zakai result for driving noise given by a continuous semimartingale is obtained for fast diffusion equations driven by continuous linear multiplicative space time rough signals existence of solutions is proven for initial data in l m 1 o

on the stochastic porous medium equation abstract in this paper we discuss an initial boundary value problem and a cauchy problem for the stochastic porous medium equation our basic estimates are based on the known results due to math sbornik 67 1965 609 642 arch rational mech anal 25 1967 64 80 by the procedure developed in trans amer math soc 354 2001 1117 1135 we obtain solutions over the given probability space rather than martingale solutions we will also establish the existence of invariant measures when the space domain is bounded

proper stable bezout factorizations and feedback control of linear time delay systems this paper deals with the existence and construction of proper stable bezout factorizations of transfer function matrices of linear time invariant systems with commensurate time delays existence of factorizations is characterized in terms of spectral controllability or spectral observability of the co canonical or canonical realization of the transfer function matrix an explicit procedure for computing proper stable bezout factorizations is given in terms of a specialized ring of pure and distributed time delays this procedure is utilized to construct finite dimensional stabilizing compensators and to construct feedback systems which assign the characteristic polynomial of the closed loop system

on spectrum distribution of completely controllable linear systems this paper is concerned with the placement of the spectrum of the closed loop operator a bk resulting from use of a linear feedback control law u kx in the infinite dimensional linear control system x ax bu for a class of systems in hilbert space with certain assumptions on the spectrum of the operator a a complete characterization of the achievable spectra is obtained the proofs are carried out in an operator theoretic context

nonresonance impulsive functional differential inclusions with variable times in this paper we investigate the existence of solutions for first and second order nonresonance impulsive functional differential inclusions with variable moments the proofs make use of the martelli fixed point theorem for condensing multivalued maps

on nonresonance impulsive functional differential inclusions with nonconvex valued right hand side in this paper we investigate the existence of solutions for first and second order nonresonance impulsive functional differential inclusions we shall rely on the schaefer s fixed point theorem combined with a selection theorem due to bressan and colombo for lower semicontinuous multivalued maps with nonempty closed and decomposable values

perturbation of strongly and polynomially stable riesz spectral operators abstract in this paper we consider bounded and relatively bounded finite rank perturbations of a riesz spectral operator generating a polynomially stable semigroup of linear operators on a hilbert space we concentrate on a commonly encountered situation where the spectrum of the unperturbed operator is contained in the open left half plane of the complex plane and approaches the imaginary axis asymptotically we present conditions on the perturbing operator such that the spectrum of the perturbed operator is contained in the open left half plane of the complex plane and additional conditions for the strong and polynomial stabilities of the perturbed semigroup we consider two applications of the perturbation results in the first example we apply the results to the perturbation of a polynomially stabilized one dimensional wave equation in the second example we consider the perturbation of a closed loop system consisting of a distributed parameter system and an observer based feedback controller solving the robust output regulation problem related to an infinite dimensional signal generator

robustness of strongly and polynomially stable semigroups abstract in this paper we study the robustness properties of strong and polynomial stability of semigroups of operators we show that polynomial stability of a semigroup is robust with respect to a large and easily identifiable class of perturbations to its infinitesimal generator the presented results apply to general polynomially stable semigroups and bounded perturbations the conditions on the perturbations generalize well known criteria for the preservation of exponential stability of semigroups we also show that the general results can be improved if the perturbation is of finite rank or if the semigroup is generated by a riesz spectral operator the theory is applied to deriving concrete conditions for the preservation of stability of a strongly stabilized one dimensional wave equation

robust stabilization of infinite dimensional systems by finite dimensional controllers abstract the problem of robustly stabilizing an infinite dimensional system with transfer function g subject to an additive perturbation is considered it is assumed that g b 0 of systems introduced by callier and desoer 3 the perturbation satisfies w1 w2 c now write w1gw2 g1 g1 where g1 is rational and totally unstable and g2 is stable generalizing the finite dimensional results of glover 12 this family of perturbed systems is shown to be stabilizable if and only if min g 1 the smallest hankel singular value of g 1 a finite dimensional stabilizing controller is then given by k w 2 k 1 i g 2 k 1 1 w 1 where 2 is a rational approximation of g2 such that g 2 g 2 min g 1 and k1 robustly stabilizes g1 to margin the feedback system g k will then be stable if w1 w2

weak solutions to the stochastic porous media equation via kolmogorov equations the degenerate case a stochastic version of the porous medium equation with coloured noise is studied the corresponding kolmogorov equation is solved in the space l 2 h where is an infinitesimally excessive measure then a weak solution is constructed

tracking control for boundary controlled parabolic pdes with varying parameters combining backstepping and differential flatness the combination of backstepping based state feedback control and flatness based trajectory planning and feedforward control is considered for the design of an exponentially stabilizing tracking controller for a linear diffusion convection reaction system with spatially and temporally varying parameters and nonlinear boundary input for this in a first step the backstepping transformation is utilized to determine a state feedback controller which transforms the original distributed parameter system into an appropriately chosen exponentially stable distributed parameter target system of a significantly simpler structure in a second step the flatness property of the target system is exploited in order to determine the feedforward controller which allows us to realize the tracking of suitably prescribed trajectories for the system output this results in a systematic procedure for the design of an exponentially stabilizing tracking controller for the considered general linear diffusion convection reaction system with varying parameters whose applicability and tracking performance is evaluated in simulation studies

riesz basis property of a second order hyperbolic system with collocated scalar input output the closed loop form of a second order hyperbolic system with scalar collocated sensor actuator is considered the riesz basis property of the system is verified for diagonal semigroups based on an abstract result of one rank perturbation of discrete type operators in hilbert spaces a simplified proof for the abstract result is presented

on a random scaled porous media equation abstract it is shown that a random scaled porous media equation arising from a stochastic porous media equation with linear multiplicative noise through a random transformation is well posed in l in the fast diffusion case we show existence in l p

stochastic porous media equations and self organized criticality the existence and uniqueness of nonnegative strong solutions for stochastic porous media equations with noncoercive monotone diffusivity function and wiener forcing term is proven the finite time extinction of solutions with high probability is also proven in 1 d the results are relevant for self organized criticality behavior of stochastic nonlinear diffusion equations with critical states

attractors for random dynamical systems a criterion for existence of global random attractors for rds is established existence of invariant markov measures supported by the random attractor is proved for spde this yields invariant measures for the associated markov semigroup the results are applied to reation diffusion equations with additive white noise and to navier stokes equations with multiplicative and with additive white noise

probabilistic representation for solutions of an irregular porous media type equation we consider a porous media type equation over all of d d 1 with monotone discontinuous coefficient with linear growth and prove a probabilistic representation of its solution in terms of an associated microscopic diffusion the interest in such singular porous media equations is due to the fact that they can model systems exhibiting the phenomenon of self organized criticality one of the main analytic ingredients of the proof is a new result on uniqueness of distributional solutions of a linear pde on 1 with not necessarily continuous coefficients

riesz basis approach to the stabilization of a flexible beam with a tip mass using an abstract condition of riesz basis generation of discrete operators in the hilbert spaces we show in this paper that a sequence of generalized eigenfunctions of an euler bernoulli beam equation with a tip mass under boundary linear feedback control forms a riesz basis for the state hilbert space in the meanwhile an asymptotic expression of eigenvalues and the exponential stability are readily obtained the main results of siam j control optim 36 1998 pp 1962 1986 are concluded as a special case and the additional conditions imposed there are removed

root locii for systems defined on hilbert spaces the root locus is an important tool for analyzing the stability and time constants of linear finite dimensional systems as a parameter often the gain is varied however many systems are modelled by partial differential equations or delay equations these systems evolve on an infinite dimensional space and their transfer functions are not rational in this paper a rigorous definition of the root locus for infinite dimensional systems is given and it is shown that the root locus is well defined for a large class of infinite dimensional systems as for finite dimensional systems any limit point of a branch of the root locus is a zero however the asymptotic behavior can be quite different from that for finite dimensional systems this point is illustrated with a number of examples it is shown that the familiar pole zero interlacing property for collocated systems with a hermitian state matrix extends to infinite dimensional systems with self adjoint generator this interlacing property is also shown to hold for collocated systems with a skew adjoint generator

controller design for distributed systems based on hankel norm approximations a procedure for obtaining a finite dimensional reduced order model for a class of distributed systems is developed it is based on a combination of a modal approximation and an optimal hankel norm approximation and the approximation error can be accurately predicted the reduced order model can be used to design a precompensator for the original system as its performance and robust stability characteristics can be deduced from the reduced order model and finitely many modal parameters the procedure is applied to a parabolic system

robust control of flexible structures a case study a comparison is made between three partial differential equation models for a flexible beam with different types of damping and varying parameter values robust controllers can be designed to stabilize all linear systems whose transfer functions lie within a ball in the l norm given a nominal model for our flexible beam we calculate which sets of models can be stabilized by the same finite dimensional robust controller by stabilize we mean here that the poles of the system are moved to the left of the line re s 0

the substitution theorem for semilinear stochastic partial differential equations abstract in this article we establish a substitution theorem for semilinear stochastic evolution equations see s depending on the initial condition as an infinite dimensional parameter due to the infinite dimensionality of the initial conditions and of the stochastic dynamics existing finite dimensional results do not apply the substitution theorem is proved using malliavin calculus techniques together with new estimates on the underlying stochastic semiflow applications of the theorem include dynamic characterizations of solutions of stochastic partial differential equations spde s with anticipating initial conditions and non ergodic stationary solutions in particular our result gives a new existence theorem for solutions of semilinear stratonovich spde s with anticipating initial conditions

stochastic generalized porous media and fast diffusion equations abstract we present a generalization of krylov rozovskii s result on the existence and uniqueness of solutions to monotone stochastic differential equations as an application the stochastic generalized porous media and fast diffusion equations are studied for finite reference measures where the drift term is given by a negative definite operator acting on a time dependent function which belongs to a large class of functions comparable with the so called n functions in the theory of orlicz spaces

stochastic variational inequalities and applications to the total variation flow perturbed by linear multiplicative noise in this work we introduce a new method to prove the existence and uniqueness of a variational solution to the stochastic nonlinear diffusion equation rm d x t rm div left frac nabla x t nabla x t right rm d t x t rm d w t rm in 0 infty times mathcal o where mathcal o is a bounded and open domain in mathbb r n n geqq 1 and w t is a wiener process of the form w t sum infty k 1 mu k e k beta k t e k in c 2 overline mathcal o cap h 1 0 mathcal o and beta k k in mathbb n are independent brownian motions this is a stochastic diffusion equation with a highly singular diffusivity term one main result established here is that for all initial conditions in l 2 mathcal o it is well posed in a class of continuous solutions to the corresponding stochastic variational inequality thus one obtains a stochastic version of the minimal total variation flow the new approach developed here also allows us to prove the finite time extinction of solutions in dimensions 1 leqq n leqq3 which is another main result of this work

a direct approach to compensator design for distributed parameter systems we present a direct approach to finite order compensator design for distributed parameter systems i e one that is not based on reduced order modelling instead we use a parametrization around an initial compensator which displays both controller order and closed loop stability in a convenient way the main result is an existence theorem which holds for a wide class of linear time invariant systems parabolic delay damped hyperbolic the most important assumptions are bounded inputs and outputs finitely many unstable modes completeness of eigenvectors an example is included to illustrate the feasibility of our method for purposes of design

finite dimensional compensators for parabolic distributed systems with unbounded control and observation it is proved that for a class of parabolic distributed parameter systems with unbounded control and observation there exists a finite dimensional compensator using dynamic output feedback finite dimensional means here that the dynamics relating the input to the output is finite dimensional a constructive design algorithm is presented and several examples are considered

nonlinear fokker planck equations driven by gaussian linear multiplicative noise abstract existence of a strong solution in h 1 r d is proved for the stochastic nonlinear fokker planck equation d x div d x d t x d t x d w in 0 t r d x 0 x respectively for a corresponding random differential equation here d 1 w is a wiener process in h 1 r d d c 1 r d r d and is a continuous monotonically increasing function satisfying some appropriate sublinear growth conditions which are compatible with the physical models arising in statistical mechanics the solution exists for x l 1 l and preserves positivity if is locally lipschitz the solution is unique pathwise lipschitz continuous with respect to initial data in h 1 r d stochastic fokker planck equations with nonlinear drift of the form d x div a x d t x d t x d w are also considered for lipschitzian continuous functions a r r d

fault detection for linear distributed parameter systems using finite dimensional functional observers abstractin this article finite dimensional residual generators are directly designed for riesz spectral systems with bounded input and output operators to detect faults this is achieved by using finite dimensional observers that can estimate linear functionals of the state without spillover these observers allow for a decoupling of the unknown disturbances from the estimation error dynamics under mild assumptions then a finite dimensional residual generator is obtained by approximately decoupling the state from the residual that is generated by the observer states and the outputs it is shown that the resulting approximation error can be made small by increasing the observer order then fault detection with the finite dimensional residual generator can be assured by introducing a time varying threshold a faulty euler bernoulli beam with structural damping illustrates the proposed finite dimensional fault detection approach

harnack inequality and applications for stochastic generalized porous media equations by using coupling and girsanov transformations the dimension free harnack inequality and the strong feller property are proved for transition semigroups of solutions to a class of stochastic generalized porous media equations as applications explicit upper bounds of the l p norm of the density as well as hypercontractivity ultracontractivity and compactness of the corresponding semigroup are derived

harnack inequality and strong feller property for stochastic fast diffusion equations abstract as a continuation to f y wang harnack inequality and applications for stochastic generalized porous media equations ann probab 35 2007 1333 1350 where the harnack inequality and the strong feller property are studied for a class of stochastic generalized porous media equations this paper presents analogous results for stochastic fast diffusion equations since the fast diffusion equation possesses weaker dissipativity than the porous medium one does some technical difficulties appear in the study as a compensation to the weaker dissipativity condition a sobolev nash inequality is assumed for the underlying self adjoint operator in applications some concrete examples are constructed to illustrate the main results

strong solutions for stochastic partial differential equations of gradient type unique existence of analytically strong solutions to stochastic partial differential equations spde with drift given by the subdifferential of a quasi convex function and with general multiplicative noise is proven the proof applies a genuinely new method of weighted galerkin approximations based on the distance defined by the quasi convex function spatial regularization of the initial condition analogous to the deterministic case is obtained the results yield a unified framework which is applied to stochastic generalized porous media equations stochastic generalized reaction diffusion equations and stochastic generalized degenerated p laplace equations in particular higher regularity for solutions of such spde is obtained

finite dimensional compensators for linear distributed control systems with delays in outputs abstract in this paper we are concerned with linear control systems of infinite dimension with delays in outputs an asymptotic compensator of finite order is proposed the compensator provides a control law that stabilizes a wide class of distributed systems moreover the compensator is invariant with respect to small bounded perturbations of the system parameters

the variational approach to hamilton jacobi equations driven by a gaussian noise abstract the global existence and uniqueness of viscosity solutions to the cauchy problem for the hamilton jacobi equations in r n driven by additive and multiplicative wiener processes are studied for convex hamiltonians via variational techniques the finite speed of propagation is also established in the multiplicative noise case for equations with lipschitzian hamiltonians

well posedness of nonlinear diffusion equations with nonlinear conservative noise we prove the pathwise well posedness of stochastic porous media and fast diffusion equations driven by nonlinear conservative noise as a consequence the generation of a random dynamical system is obtained this extends results of the second author and souganidis who considered analogous spatially homogeneous and first order equations and earlier works of lions perthame and souganidis

distributed system transfer functions of exponential order o is a real number we construct a transfer function algebra of fractions viz f o for modelling possibly unstable distributed systems such that i fcirc in f o is holomorphic in re s o i e is o stable iff fcirc is o exponentially stable and ii we allow delay in the direct input output transmission of the system this algebra is a a restriction of the algebra b o developed by callier and desoer 1978 1980 a b an extension of the algebra of proper rational functions such that the exponential order properties of the latter transfer functions of lumped systems are maintained the algebra f o can be used for modelling and feedback system design it is shown that standard semigroup systems are better modelled by a transfer function in f o rather than b o

probabilistic representation for solutions of an irregular porous media type equation the degenerate case summary we consider a possibly degenerate porous media type equation over all of r d with d 1 with monotone discontinuous coefficients with linear growth and prove a probabilistic representation of its solution in terms of an associated microscopic diffusion this equation is motivated by some singular behaviour arising in complex self organized critical systems the main idea consists in approximating the equation by equations with monotone non degenerate coefficients and deriving some new analytical properties of the solution

some algebraic aspects of the strong stabilizability of time delay linear systems this note considers some algebraic aspects of the output feedback strong stabilizability of time delay linear systems a sufficient condition for the existence of a stable finite dimensional stabilizing compensator for a single input single output siso time delay system is given an illustrative example is also given and two open problems are posed

spectral factorization by symmetric extraction for distributed parameter systems the spectral factorization problem of a scalar coercive spectral density is considered in the framework of the callier desoer algebra of distributed parameter system transfer functions criteria are given for the infinite product representation of a meromorphic coercive spectral density of finite order and for the convergence of infinite product representations of spectral factors i e for the convergence of the symmetric extraction method for solving the spectral factorization problem of such spectral density these convergence criteria are applied to the solution of the linear quadratic optimal control problem by spectral factorization for a specific class of semigroup hilbert state space systems with a riesz spectral generator the speed of convergence of the symmetric extraction method is also considered as an example a damped vibrating string model is handled

existence of strong solutions for stochastic porous media equation under general monotonicity conditions this paper addresses existence and uniqueness of strong solutions to stochastic porous media equations dx x dt b x dw t in bounded domains of r d with dirichlet boundary conditions here is a maximal monotone graph in r r possibly multivalued with

model reference adaptive control for spectral systems in this paper we investigate a model reference adaptive control problem for the class of distributed parameter systems generated by spectral operators first we present an equivalent static input output representation for the spectral system using filtered values generated from the inputs and the outputs next we design and analyse a model reference adaptive control system for systems with unknown input and output distribution functions

stochastic nonlinear schrodinger equations abstract this paper is devoted to the well posedness of stochastic nonlinear schrodinger equations in the energy space h 1 r d and is a continuation of our recent work barbu et al 2014 we allow general complex coefficients in the noise thus covering both the conservative and non conservative case the latter being important to include quantum measurement effects in the underlying physical model we consider both focusing and defocusing nonlinearities and prove global well posedness in h 1 r d including also the pathwise continuous dependence on initial conditions with exponents of the nonlinearity in exactly the same sharp range as in the deterministic case in particular in the special conservative case this work improves earlier results in de bouard and debussche 2003 where the critical exponents could not be reached for d 6 in the defocusing and for d 4 in the focusing case respectively moreover the local existence uniqueness and blowup alternative are also established for the energy critical case the approach presented here is mainly based on the rescaling approach already used in barbu et al 2014 to study the l 2 case and also on the strichartz estimates established in marzuola et al 2008 for large perturbations of the laplacian

stabilization problem in hilbert spaces the stabilization problem for linear systems on hilbert spaces is examined necessary and sufficient conditions for the state stabilization by a linear bounded feedback are given using these results and similar methods necessary and sufficient conditions for output stabilization are given

finite dimensional regulators for a class of infinite dimensional systems abstract we show that the direct approach developed by the author for stabilization of certain classes of distributed parameter systems can be extended to cover regulation problems as well an iterative design algorithm is presented together with proof that the algorithm will converge after a finite number of steps the procedure is illustrated with an example of a constant disturbance acting on a delay system

non monotone stochastic generalized porous media equations abstract by using the nash inequality and a monotonicity approximation argument existence and uniqueness of strong solutions are proved for a class of non monotone stochastic generalized porous media equations moreover we prove for a large class of stochastic pde that the solutions stay in the smaller l 2 space provided the initial value does so that some recent results in the literature are considerably strengthened

an algorithmic test for checking stability of feedback spectral systems abstract given a certain class of regular spectral systems an algorithm is presented that is designed to test the stability properties of the feedback interconnection of such a system and either a bounded state feedback operator or a finite dimensional linear time invariant controller the applicability of this test is independent of the method used to design the feedback controller and is designed to provide a separate independent method for verifying whether or not the plant controller interconnection is exponentially stable the test is particularly well suited to problems involving certain partial differential equations pde with spatially varying coefficients or complicated boundary shapes

solving the linear quadratic optimal control problem for infinite dimensional systems abstract calculation of the solutions to linear quadratic optimal control problems for infinite dimensional systems is considered the sequence of solutions to a sequence of approximating finite dimensional problems converges to the optimal control for the infinite dimensional system if certain assumptions such as uniform stabilizability are satisfied we use this result to calculate controllers for the infinite dimensional system that are arbitrarily close to optimal a one dimensional heat equation and a problem of acoustic noise control are used to illustrate the algorithm the numerical results are discussed

robustness of polynomial stability with respect to unbounded perturbations abstract in this paper we present conditions for the preservation of strong and polynomial stability of a strongly continuous semigroup under unbounded finite rank perturbations of its infinitesimal generator in addition we also improve recent perturbation results for bounded finite rank perturbations the results are illustrated with two examples in the first one we consider the preservation of stability of a one dimensional wave equation that has been stabilized polynomially with boundary feedback in the second example we find conditions for the preservation of polynomial stability of a multiplication semigroup under unbounded rank one perturbations

spectral determination for a cantilever beam the eigenvalue specification problem is discussed for a beam with one end clamped and the other end free which is allowed to have some structural damping and has a moment force at the free end acting as a control the spectrum and eigenvectors of the uncontrolled system are first analyzed and are then used to construct the feedback element which solves the problem it is shown how this feedback element can be numerically approximated and a spillover result is proved for the approximation in the case where there is no damping this method yields a bounded feedback law which exponentially stabilizes the beam

optimal control of stochastic fitzhugh nagumo equation abstractthis paper is concerned with the existence and uniqueness of solution for the optimal control problem governed by the stochastic fitzhugh nagumo equation driven by a gaussian noise first order conditions of optimality are also obtained

output and error feedback regulator designs for linear infinite dimensional systems abstract this manuscript addresses the output regulation problem for linear distributed parameter systems dpss with bounded input and unbounded output operators we introduce novel methods for the design of the output feedback and error feedback regulators in the output feedback regulator design the measurements available for the regulator do not belong to the set of controlled outputs the proposed output feedback regulator with the injection of the measurement y m t and reference y r t can realize both the plant and the exosystem states estimation disturbance rejection and reference signal tracking simultaneously moreover new design approach provides an alternative choice for seeking the output injection gain in a traditional error feedback regulator design the regulator parameters are easily configured to solve the output regulation problems and to ensure the stability of the closed loop systems the results are demonstrated via computer simulation in two types of representative systems the parabolic partial differential equation pde system and the first order hyperbolic pde system

stabilization of a coupled transport diffusion system with boundary input we consider the problem of stabilizing a coupled transport diffusion system with boundary input the system is described by two linear transport diffusion equations and is not asymptotically stable in order to stabilize the system with boundary input sensor influence functions are assumed to be located at interior of the domain first we formulate the system as an evolution equation with unbounded output operators in a hilbert space using variable transformation next we derive a reduced order model with a finite dimensional state variable for the infinite dimensional system then a stabilizing controller is constructed for the reduced order model under an additional assumption it is shown that the finite dimensional controller together with a residual mode filter plays a role of a finite dimensional stabilizing controller for the original infinite dimensional system if the order of the residual mode filter is chosen sufficiently large finally the validity of the design method is demonstrated through a numerical simulation