output feedback stabilization control design for boolean control networks this paper investigates the output feedback stabilization of boolean control networks bcns by using the semi tensor product method and presents a number of new results first based on the algebraic expression of bcns a necessary and sufficient condition is presented for the existence of output feedback stabilizers second a constructive procedure is proposed to design output feedback stabilization controllers for bcns the study of an illustrative example shows that the new results obtained in this paper are very effective in designing output feedback stabilizers for bcns

perturbation theory for dual semigroups i the sun reflexive case soit a 0 le generateur infinitesimal d un co semigroupe d operateurs lineaires bornes to t sur un espace de banach x soit b un operateur lineaire borne sur x a 0 b engendre un co semigroupe t t sur x b agit hors de l espace x dans un espace plus grand y on donne une methode systematique pour construire un tel espace y

application of adaptive basis functions for a diagonal moment matrix solution of arbitrarily shaped three dimensional conducting body problems we present the application of specially constructed adaptive basis functions that generate a diagonal matrix in the method of moments solution procedure for the calculation of scattered electromagnetic fields from arbitrarily shaped conducting bodies excited by a plane electromagnetic wave the arbitrary body is modeled using planar triangular patches the crucial step in the solution procedure is the construction of the adaptive basis functions to generate the diagonal matrix this task is accomplished with the help of well known rwg basis functions the solution thus obtained is very efficient accurate and applicable to truly arbitrary bodies several numerical examples are presented to validate the new method

equivalent conditions for stabilizability of infinite dimensional systems with admissible control operators in this paper we study the optimizability of infinite dimensional systems with admissible control operators we show that under a weak condition such a system is optimizable if and only if the system can be split into an exponentially stable subsystem and an unstable subsystem that is exactly controllable in finite time the state space of the unstable subsystem equals the span of all unstable generalized eigenvectors of the original system this subsystem can be infinite dimensional furthermore the unstable poles satisfy a summability condition the state space of the exponentially stable subsystem is given by all vectors for which the action of the original c0 semigroup is stable

on the periodic trajectories of boolean control networks abstract in this note we first characterize the periodic trajectories or equivalently the limit cycles of a boolean network and their global attractiveness we then investigate under which conditions all the trajectories of a boolean control network may be forced to converge to the same periodic trajectory if every trajectory can be driven to such a periodic trajectory this is possible by means of a feedback control law

state feedback stabilization for boolean control networks state feedback stabilization for boolean control networks is investigated in this technical note based on the algebraic representation of logical dynamics in terms of the semi tensor product of matrices a necessary and sufficient condition is derived for the existence of a globally stabilizing state feedback controller and a general control design approach is proposed when global stabilization is feasible via state feedback instead of designing the logical form of a stabilizing feedback law directly we first construct its algebraic representation and then convert the algebraic representation back to the logical form an example is worked out to illustrate the proposed design procedure

observability reconstructibility and state observers of boolean control networks the aim of this paper is to introduce and characterize observability and reconstructibility properties for boolean networks and boolean control networks described according to the algebraic approach proposed by d cheng and co authors in the series of papers 3 6 7 and in the recent monography a complete characterization of these properties based both on the boolean matrices involved in the network description and on the corresponding digraphs is provided finally the problem of state observer design for reconstructible bns and bcns is addressed and two different solutions are proposed

comparison theorems for infinite dimensional riccati equations abstract comparison theorems are proved for the algebraic riccati equation in the framework of infinite dimensional hilbert spaces these theorems extend well known results for the finite dimensional case

semigroup generation and stabilization by a r bounded feedback perturbations abstract let a be a generator of a strongly continuous semigroup of operators and assume that c and h are operators such that a ch generates a strongly continuous semigroup sh t on x let 0 be a real number in the resolvent set of a and let 1 1 then there are some fairly unrestrictive conditions under which a 0 a ch 0 a also generates a strongly continuous semigroup sk t on x which has the same exponential growth rate as sh t given an input operator b we can use this to identify a class of feedback perturbations k such that a bk generates a strongly continuous semigroup we can also use this result to identify classes of feedbacks which can and cannot uniformly stabilize a system for example we show that if the control on a cantilever beam in the state space h02 0 1 l2 0 1 is a moment force on the free end then we cannot stabilize the beam with an a 1 2 bounded feedback but we can find an a e 1 4 bounded feedback for any e 0 which does stabilize the beam

controllability of probabilistic boolean control networks based on transition probability matrices in this paper we propose a new approach to investigate the controllability and reachability of probabilistic boolean control networks pbcns with forbidden states we first give a simple algebraic formula for the transition probability between two states in a given number of time step while avoiding a set of forbidden states then we construct the controllability matrix based on a new operator and some necessary and sufficient conditions are obtained for the controllability and reachability of pbcns a numerical example is given to illustrate the efficiency of the obtained results

lq optimal control of infinite dimensional systems by spectral factorization abstract we consider the standard lq optimal control of an exponentially stabilizable and detectable infinite dimensional semigroup state space system with bounded sensing and control it is reported that the reachable restriction of the lq optimal state feedback operator can be identified 1 by solving a spectral factorization problem delivering a bistable spectral factor with entries in the distributed proper stable transfer function algebra and 2 by obtaining any constant solution of an operator diophantine equation over the properties of the restricted solution feedback operator are discussed it is shown in particular that the lq optimal state feedback operator and its reachable restriction coincide whenever the unreachable state components are unobservable these theoretical results are applied to a simple model of heat diffusion with collocated sensor and actuator leading to an approximation procedure converging exponentially fast to the lq optimal state feedback operator this procedure is based on approximate spectral factorization by symmetric extraction and on simple residue calculus

robust stabilizability of normalized coprime factors the infinite dimensional case the problem of robustly stabilizing a linear system subject to h bounded perturbations in the numerator and the denominator of its normalized left coprime factorization is considered for a class of infinite dimensional systems this class has possible unbounded finite rank input and output operators which include many delay and distributed systems the optimal stability margin is expressed in terms of the solutions of the control and filter algebraic riccati equations

output tracking control of boolean control networks via state feedback this paper investigates the state feedback based output tracking control of boolean control networks bcns with a constant reference signal by using the semi tensor product method based on the algebraic expression of bcns and by constructing a series of reachable sets a general procedure is proposed for the design of the state feedback laws for bcns to track a constant reference signal the study of an illustrative example shows that the obtained new results are effective in designing state feedback based output tracking controllers for bcns to track a constant reference signal

necessary conditions for exponential stabilizability of distributed parameter systems with infinite dimensional unbounded feedback abstract in this paper we consider distributed parameter control systems of the form x t ax t bu t where x t is in the state space x u t is in an infinite dimensional control space u and b is an unbounded input operator which is admissible in a standard sense we find necessary conditions for there to exist a compact operator k x u such that a bk generates a c 0 semigroup which is of exponential growth type in particular for every a must have at most finitely many eigenvalues of finite multiplicity in re z furthermore the part of a corresponding to the remaining spectrum must generate a semigroup with type at most we apply this to a model for a clamped euler bernoulli plate with dirichlet control applied to the entire boundary we show that a compact state feedback cannot exponentially stabilize the plate in the state space of maximum regularity

the equivalence issue of two kinds of controllers in boolean control networks abstract in this paper the equivalence issue between state feedback controller and free sequence controller in boolean control network bcn is investigated based on the algebraic representation of boolean networks we prove that a boolean control network can be stabilized to a cycle or a fixed point via free sequence controller if and only if there is a state feedback controller which can derive the boolean control network to the cycle or the fixed point then two algorithms are provided to find the state feedback controller after that we prove that a bcn can be globally controllable by free sequence controller while the bcn is not necessarily globally controllable by state feedback controller at last an example is given to illustrate the results

isolated nonnegative solutions of infinite dimensional algebraic riccati equations abstract for an infinite dimensional continuous or discrete time linear system based on the study of the representation of nonnegative solutions of the algebraic riccati equation are we get some sufficient and necessary conditions for a nonnegative solution of are to be isolated in the set of all nonnegative solution of are with respect to the norm topology the strong operator topology and weak operator topology respectively

potential integrals for uniform and linear source distributions on polygonal and polyhedral domains formulas for the potentials due to uniform and linearly varying source distributions defined on simply shaped domains are systematically developed and presented domains considered are infinite planar strips infinite cylinders of polygonal cross sections planar surfaces with polygonal boundaries and volumetric regions with polyhedral boundaries the expressions obtained are compact in form and their application in the numerical solution of electromagnetics problems by the method of moments is illustrated

logistic models of structured population growth abstract a general model of structured population dynamics with logistic type nonlinearity is considered the model consists of a semilinear hyperbolic partial differential equation with a linear boundary condition and an initial value the logistic nonlinearity corresponds to increased mortality as the population increases the problem is treated as an abstract semilinear evolution equation sufficient conditions are given for the solutions to converge to an equilibrium solution applications are made to age structured populations size structured populations multispecies structured populations and cell populations

robustness of linear systems abstract in this paper we consider linear systems which are stable and examine the robustness of this property the perturbations are assumed to have unbounded structure and we determine the smallest perturbation which destroys stability we begin with an abstract analysis of the problem but in later sections specialize to three types of systems those whose mild solutions are given in terms of 1 a strongly continuous semigroups 2 b resolvent operators integrodifferential systems 3 c evolution operators time varying systems for b a banach space l2 t0 t b denotes the space of all square integrable functions defined on t0 t with values in b for b1 b2 banach spaces t0 t denotes the space of strongly measurable functions f t0 t l b1 b2 with ess sup f b 1 t0 l b1 b2 denotes the space of strongly measurable functions f t0 l b1 b2 with f t 0 and k l1 t0

characteristic matrices and spectral properties of evolutionary systems in this paper we introduce the notion of a characteristic matrix for a large class of unbounded operators and study the precise connection between characteristic matrices and spectral properties of evolutionary systems in particular we study so called multiplicity theorems several examples will illustrate our results

application of the method of moments to acoustic scattering from multiple bodies of arbitrary shape the method proposed in this paper provides a computational technique for solving acoustic scattering problems associated with arbitrarily shaped three dimensional bodies in particular using the free space green s function along with the associated boundary conditions on the surface of the body integral equations to calculate the velocity potential and the exterior field of the scattering body are derived the equations are then solved by approximating the scatterers by planar triangular patches and using the method of moments test cases are shown involving single and multiple bodies of spherical cylindrical and cubical geometry the method presented in this paper is novel simple and efficient and yet general enough to obtain the sonic fields scattered by multiple arbitrarily shaped bodies oriented in random fashion

spectral properties of finite dimensional perturbed linear semigroups abstract many interesting cauchy problems arising in applications can be treated as finite dimensional perturbations of relatively simple problems in most applications these perturbations take place via boundary conditions it is the aim of this paper to investigate such cauchy problems and especially the spectral properties of the corresponding generators some general results are obtained that unify several well known results for functional differential equations and age dependent population dynamics applications to control problems as well as some nonlinear generalizations will appear in forthcoming papers

equivalence of input output stability and exponential stability abstract for a large class of well posed infinite dimensional systems we show that if their state space realisation is exponentially stabilizable and detectable then exponential stability of the system operator is equivalent to input output stability

a new method to generate an almost diagonal matrix in the boundary integral equation formulation in this work a new numerical procedure is developed to generate an almost diagonal matrix for the solution of boundary integral equation formulation dealing with acoustic scattering problems the major drawback of the traditional boundary integral equation procedure resulting in a dense system matrix is eliminated in this new procedure by grouping the basis functions into a cluster the geometry of the structure is modeled by planar triangles and the basis functions are defined on the nodes by doing so one can get a benefit of a smaller size matrix to begin with furthermore by grouping these node based basis functions into a cluster an almost diagonal matrix is generated thus the solution procedure developed in this work may be utilized for very large scattering problems since the required computer resources are very low the solution procedure developed in this work is validated for the scattering cross section of the simple shapes with the closed form solutions wherever available and with the other numerical solution procedures

null controllability with vanishing energy linear null controllable systems for which an arbitrary initial state can be transferred to the origin with arbitrarily small energy are characterized theorems are stated in terms of an associated algebraic riccati equation and in terms of the spectrum of the linear part of the system the results so obtained allow us to determine ornstein uhlenbeck operators for which the liouville theorem about bounded harmonic functions holds