stochastic controllability and minimum energy control of systems with multiple delays in control in recent years various controllability problems for different types of linear dynamical systems have been considered in many publications and monographs

exponential stability of impulsive systems with application to uncertain sampled data systems we establish exponential stability of nonlinear time varying impulsive systems by employing lyapunov functions with discontinuity at the impulse times our stability conditions have the property that when specialized to linear impulsive systems the stability tests can be formulated as linear matrix inequalities lmis then we consider lti uncertain sampled data systems in which there are two sources of uncertainty the values of the process parameters can be unknown while satisfying a polytopic condition and the sampling intervals can be uncertain and variable we model such systems as linear impulsive systems and we apply our theorem to the analysis and state feedback stabilization we find a positive constant which determines an upper bound on the sampling intervals for which the stability of the closed loop is guaranteed the control design lmis also provide controller gains that can be used to stabilize the process we also consider sampled data systems with constant sampling intervals and provide results that are less conservative than the ones obtained for variable sampling intervals

brief paper a duality based convex optimization approach to l2 gain control of piecewise affine slab differential inclusions this paper introduces the dual parameter set of a piecewise affine pwa system this is a key concept to enable a convex formulation of pwa controller synthesis for pwa slab differential inclusions using a new convex relaxation another important contribution of the paper is to present pwa l 2 gain analysis and synthesis results for pwa systems whose output is also a pwa function of the state as opposed to a piecewise linear pwl function unlike other results existing in the literature the sufficient lmi conditions in this paper are valid for synthesis even when the pwa systems include sliding modes a numerical example with sliding modes illustrates the new approach

controllability for neutral stochastic functional differential inclusions with infinite delay in abstract space abstract in this paper sufficient conditions are given for the controllability of a class of partial stochastic functional differential inclusions with infinite delay in an abstract space with the help of the leray schauder nonlinear alternative an example is provided to illustrate the theory

on controllability of linear stochastic systems we discuss several concepts of controllability for partially observable stochastic systems complete controllability approximate controllability controllability and s controllability and show that complete and approximate controllability notions are equivalent and in turn are equivalent to the controllability for linear stochastic systems controlled by gaussian processes we derive necessary and sufficient conditions for these concepts of controllability these criteria reduce to the well known rank condition

approximate controllability of fractional nonlocal delay semilinear systems in hilbert spaces we study the existence and approximate controllability of a class of fractional nonlocal delay semilinear differential systems in a hilbert space the results are obtained by using semigroup theory fractional calculus and schauder s fixed point theorem multi delay controls and a fractional nonlocal condition are introduced furthermore we present an appropriate set of sufficient conditions for the considered fractional nonlocal multi delay control system to be approximately controllable an example to illustrate the abstract results is given

controllability of stochastic integrodifferential systems in this paper sufficient conditions for the complete controllability of a stochastic semilinear integrodifferential system in finite dimensional spaces are established using the resolvent matrix and the banach fixed point theorem an example is provided to illustrate the result

approximate controllability of semi linear neutral integro differential systems with finite delay abstract this paper considers the approximate controllability of semilinear neutral integrodifferential systems with finite delay in hilbert space since the considered equation admits nonlinear terms involving spatial derivatives the fraction power theory and norm are used to discuss the problem so that the established results can be applied to them the results are obtained by using the sadovskii fixed point theorem and the theory of analytic resolvent operator an example is presented to illustrate the applications of the obtained results

brief transfer equivalence and realization of nonlinear higher order input output difference equations two fundamental modelling problems in nonlinear discrete time control systems are studied using the language of differential forms the discrete time nonlinear single input single output systems to be studied are described by input output i o difference equations i e a high order difference equation relating the input the output and a finite number of their time shifts a new definition of equivalence is introduced which generalizes the notion of transfer equivalence well known for the linear case our definition is based upon the notion of an irreducible differential form of the system and was inspired by the analogous definition for continuous time systems the second problem to be addressed is the realization problem the i o difference equation is assumed to be in the irreducible form so that one can obtain an accessible and observable realization necessary and sufficient conditions are given for the existence of a local state space realization of the irreducible i o difference equation these conditions are formulated in terms of the integrability of certain subspaces of one forms classified according to their relative degree the sufficiency part of the proof gives a constructive procedure up to finding the integrating factors and integration of the set of one forms for obtaining a locally observable and accessible state space system if the system is not in the irreducible form one has first to apply the reduction procedure to transform the system into the irreducible form

controllability of non linear impulsive stochastic systems in this article we consider the finite dimensional dynamical control systems described by non linear impulsive stochastic differential equations sufficient conditions for the complete and approximate controllability of non linear impulsive stochastic systems are formulated and proved under the natural assumption that the corresponding linear system is appropriately controllable

existence and controllability for fractional evolution inclusions of clarke s subdifferential type in this paper by using the method of the measure of noncompactness the fixed points theorem of multivalued maps and the properties of clarke s subdifferential we give the existence result and controllability for the fractional evolution inclusions of clarke s subdifferential type in a separable reflexive banach space

brief paper complete controllability of impulsive stochastic integro differential systems this paper is concerned with the controllability of impulsive stochastic integro differential systems sufficient conditions of complete controllability for impulsive stochastic integro differential systems are obtained by using schaefer s fixed point theorem a numerical example is provided to show the effectiveness of the proposed results

approximate controllability for semilinear second order stochastic evolution systems with infinite delay in this work we study the approximate controllability for a class of semilinear second order stochastic evolution systems with infinite delay the main technique is the fundamental solution theory

approximate controllability of backward stochastic evolution equations in hilbert spaces in this paper we examine the approximate controllability of a semilinear backward stochastic evolution equations in hilbert spaces with non lipschitz coefficient

stability analysis of piecewise affine systems using controlled invariant sets abstract this paper presents new stability conditions for closed loop piecewise affine pwa systems the result is based on controlled invariant sets for pwa systems which are defined by extending the notion of semi ellipsoidal invariant sets for constrained linear systems reported in previous research the paper shows that by proper use of the control input concatenations of semi ellipsoidal sets can be made invariant for the trajectories of pwa systems furthermore based on these controlled invariant sets the paper presents a result for stability of a closed loop pwa system which is less conservative than existing approaches in the literature in this result it is shown that a pwa system is stable inside the intersection of any level set for a local lyapunov function and the design set where the function is defined provided the flow points inwards at the boundaries of the intersection this result is less conservative than previous approaches and it enables the designer to have an estimation of a much larger region of exponential stability then it would be possible using previous results a numerical example is presented in which it is made clear by comparison with previous approaches that the estimated region of stability can be made significantly larger using the new stability conditions developed in this paper

controllability of the impulsive functional bbm equation with nonlinear term involving spatial derivative abstract for a broad class of control systems modeling real life problems delays and impulses are natural properties that do not modify their behavior so we conjecture that under certain conditions delays and abrupt changes as perturbations of a system do not modify properties such as controllability in this regard we prove the approximate controllability of the impulsive functional benjamin bona mahony bbm equation with nonlinear term involving spatial derivative this can be achieved using the technique avoiding fixed point theorems employed by a e bashirov et al in this case the delay helps us to prove the approximate controllability by pulling back the control solution to a fixed curve in a short time interval

on concepts of controllability for deterministic and stochastic systems the new necessary and sufficient conditions which are formulated in terms of convergence of a certain sequence of operators involving the resolvent of the negative of the controllability operator are found for deterministic linear stationary control systems to be completely and approximately controllable respectively these conditions are applied to study the s controllability a property of attaining an arbitrarily small neighborhood of each point in the state space with a probability arbitrarily close to one and c controllability the s controllability fortified with some uniformity of stochastic systems it is shown that the s controllability the c controllability of a partially observable linear stationary control system with an additive gaussian white noise disturbance on all the intervals 0 t for t 0 is equivalent to the approximate complete controllability of its deterministic part on all the intervals 0 t for t 0

controllability of semilinear stochastic systems the picard type approximation is used to derive sufficient conditions for approximate and complete controllability of semilinear stochastic systems with non lipschitz coefficients under the assumption that the corresponding linear system is appropriately controllable

controllability of semilinear stochastic systems in hilbert spaces we study the weak approximate and complete controllability properties of semilinear stochastic systems assuming controllability of the associated linear systems the results are obtained by using the banach fixed point theorem applications to stochastic heat equation are given

controllability of a backward fractional semilinear differential equation abstract in this paper we study the approximate controllability of a fractional semilinear differential equation involving the right fractional caputo derivative more precisely we construct by means of tikhonov type regularization method the controllability operator then under certain condition on this operator we obtain that the associate backward fractional linear system can be steered to an arbitrary small neighborhood of the state at initial time this allows us to prove the approximate controllability of the semilinear system

controllability observability and discrete time markovian jump linear quadratic control this paper is concerned with the controllability and observability of discrete time linear systems that possess randomly jumping parameters described by finite stale markov processes and the relationship between these properties and the solution of the infinite time jump linear quadratic jlq optimal control problem the solution of the markovian jlq problem with finite or infinite time horizons is known necessary and sufficient conditions for the existence of optimal constant control laws that lead to finite optimal expected costs as the time horizon becomes infinite are also known sufficient conditions for these steady state control laws to stabilize the controlled system are also available chizeck et al 1986 these conditions are not easy to test however various definitions of controllability and observability for stochastic systems exist in the literature these definitions are unfortunately not related to the steady state jlq control problem in a manner that is analogous to the role of deter

on the approximate controllability of fractional evolution equations with compact analytic semigroup in this paper we discuss the approximate controllability of fractional evolution equations involving caputo fractional derivative the results are obtained with the help of the theory of fractional calculus semigroup theory and the schauder s fixed point theorem under the assumption that the corresponding linear system is approximately controllable finally an example is provided to illustrate the obtained results

controllability of linear stochastic systems abstract we discuss several concepts of controllability for stochastic systems and derive sufficient and in most cases also necessary algebraic conditions for the controllability of the state and the output of white and colored noise linear systems these criteria reduce to the well known deterministic ones in the absence of noise

a guide to completeness and complexity for modal logics of knowledge and belief abstract we review and re examine possible worlds semantics for propositional logics of knowledge and belief with three particular points of emphasis 1 we show how general techniques for finding decision procedures and complete axiomatizations apply to models for knowledge and belief 2 we show how sensitive the difficulty of the decision procedure is to such issues as the choice of modal operators and the axiom system and 3 we discuss how notions of common knowledge and distributed knowledge among a group of agents fit into the possible worlds framework as far as complexity is concerned we show among other results that while the problem of deciding satisfiability of an s5 formula with one agent is np complete the problem for many agents is pspace complete adding a distributed knowledge operator does not change the complexity but once a common knowledge operator is added to the language the problem becomes complete for exponential time

controllability of stochastic semilinear functional differential equations in hilbert spaces in this paper approximate and exact controllability for semilinear stochastic functional differential equations in hilbert spaces is studied sufficient conditions are established for each of these types of controllability the results are obtained by using the banach fixed point theorem applications to stochastic heat equation are given

brief paper stability of sampled data piecewise affine systems under state feedback this paper addresses stability of sampled data piecewise affine pwa systems consisting of a continuous time plant and a discrete time emulation of a continuous time state feedback controller the paper presents conditions under which the trajectories of the sampled data closed loop system will exponentially converge to a neighborhood of the origin moreover the size of this neighborhood will be related to bounds on perturbation parameters related to the sampling procedure in particular related to the sampling period finally it will be shown that when the sampling period converges to zero the performance of the stabilizing continuous time pwa state feedback controller can be recovered by the emulated controller

on controlability of linear systems with stochastic jump parameters this note studies the notion of stochastic e controllability in probability for linear systems subject to sudden jumps in parameter values by using a lyapunov like approach sufficient conditions are obtained in terms of a set of coupled bernoulli equations the potential use of the results is illustrated by an example

controllability of linear stochastic systems we discuss several concepts of controllability for partially observable stochastic systems complete controllability approximate controllability and stochastic controllability we show that complete and approximate controllability notions are equivalent and in turn they are equivalent to the stochastic controllability for linear stochastic systems controlled with gaussian processes we derive necessary and sufficient conditions for these concepts of controllability these criteria reduce to the well known rank condition

sufficient conditions for stabilization of sampled data nonlinear systems via discrete time approximations given a parameterized by sampling period t family of approximate discrete time models of a sampled nonlinear plant and given a family of controllers stabilizing the family of plant models for all t sufficiently small we present conditions which guarantee that the same family of controllers semi globally practically stabilizes the exact discrete time model of the plant for sufficiently small sampling periods when the family of controllers is locally bounded uniformly in the sampling period the inter sample behavior can also be uniformly bounded so that the time varying sampled data model of the plant is uniformly semi globally practically stabilized the result justifies controller design for sampled data nonlinear systems based on the approximate discrete time model of the system when sampling is sufficiently fast and the conditions we propose are satisfied our analysis is applicable to a wide range of time discretization schemes and general plant models

partial approximate controllability of nonlocal fractional evolution equations via approximating method abstract in this paper we study partial approximate controllability of semilinear nonlocal fractional evolution equations in hilbert spaces by using fractional calculus variational approach and approximating technique we give the approximate problem of the control system and get the compactness of approximate solution set then new sufficient conditions for the partial approximate controllability of the control system are obtained when the compactness conditions or lipschitz conditions for the nonlocal function are not required finally we apply our abstract results to the partial approximate controllability of the semilinear heat equation and delay equation

identification of nonlinear spatiotemporal dynamical systems with nonuniform observations using reproducing kernel based integral least square regulation the identification of nonlinear spatiotemporal dynamical systems given by partial differential equations has attracted a lot of attention in the past decades several methods such as searching principle based algorithms partially linear kernel methods and coupled lattice methods have been developed to address the identification problems however most existing methods have some restrictions on sampling processes in that the sampling intervals should usually be very small and uniformly distributed in spatiotemporal domains these are actually not applicable for some practical applications in this paper to tackle this issue a novel kernel based learning algorithm named integral least square regularization regression ilsrr is proposed which can be used to effectively achieve accurate derivative estimation for nonlinear functions in the time domain with this technique a discretization method named inverse meshless collocation is then developed to realize the dimensional reduction of the system to be identified thereafter with this novel inverse meshless collocation model the ilsrr and a multiple kernel based learning algorithm a multistep identification method is systematically proposed to address the identification problem of spatiotemporal systems with pointwise nonuniform observations numerical studies for benchmark systems with necessary discussions are presented to illustrate the effectiveness and the advantages of the proposed method

approximate controllability of semilinear functional equations in hilbert spaces in this paper approximate and complete controllability for semilinear functional differential systems is studied in hilbert spaces sufficient conditions are established for each of these types of controllability the results address the limitation that linear systems in infinite dimensional spaces with compact semigroup cannot be completely controllable the conditions are obtained by using the schauder fixed point theorem when the semigroup is compact and the banach fixed point theorem when the semigroup is not compact

approximate controllability of evolution systems with nonlocal conditions we study the approximate controllability for the abstract evolution equations with nonlocal conditions in hilbert spaces assuming the approximate controllability of the corresponding linearized equation we obtain sufficient conditions for the approximate controllability of the semilinear evolution equation the results we obtained are a generalization and continuation of the recent results on this issue at the end an example is given to show the application of our result

semantical considerations on nonmonotonic logic abstract commonsense reasoning is nonmonotonic in the sense that we often draw on the basis of partial information conclusions that we later retract when we are given more complete information some of the most interesting products of recent attempts to formalize nonmonotonic reasoning are the nonmonotonic logics of mcdermott and doyle 1 2 these logics however all have peculiarities that suggest they do not quite succeed in capturing the intuitions that prompted their development in this paper we reconstruct nonmonotonic logic as a model of an ideally rational agent s reasoning about his own beliefs for the resulting system called autoepistemic logic we define an intuitively based semantics for which we can show autoepistemic logic to be both sound and complete we then compare autoepistemic logic with the approach of mcdermott and doyle showing how it avoids the peculiarities of their nonmonotonic logic

on the relation between default and autoepistemic logic abstract default logic is a formal means of reasoning about defaults what normally is the case in the absence of contradicting information autoepistemic logic on the other hand is meant to describe the consequences of reasoning about ignorance what must be true if a certain fact is not known although the motivation and formal character of these two systems are different a closer analysis shows that they share a common trait which is the indexical nature of certain elements in the theory in this paper we compare the expressive power of the two systems first we give an effective translation of default logic into autoepistemic logic default theories can thus be embedded into autoepistemic logic we also present a more surprising result the reverse translation is also possible so that every set of sentences in autoepistemic logic can be effectively rewritten as a default theory the formal equivalence of these two differing systems is thus established this analysis gives an interpretive semantics to default logic and yields insight into the nature of defaults in autoepistemic reasoning

exact controllability of stochastic differential equations with multiplicative noise abstract one proves that the n d stochastic controlled equation d x t a t x t d t x t d w t b t u t d t where lip r n r d r n a t r n and b t r n r n is invertible is exactly controllable with high probability in each y r n such that y 0 on each finite interval 0 t an application to approximate controllability of the stochastic heat equation is given the case where b r m r n 1 m n and the pair a b satisfies the kalman rank condition is also studied

a framework for stabilization of nonlinear sampled data systems based on their approximate discrete time models a unified framework for design of stabilizing controllers for sampled data differential inclusions via their approximate discrete time models is presented both fixed and fast sampling are considered in each case sufficient conditions are presented which guarantee that the controller that stabilizes a family of approximate discrete time plant models also stabilizes the exact discrete time plant model for sufficiently small integration and or sampling periods previous results in the literature are extended to cover 1 continuous time plants modeled as differential inclusions 2 general approximate discrete time plant models 3 dynamical discontinuous controllers modeled as difference inclusions and 4 stability with respect to closed arbitrary not necessarily compact sets

on stabilizability and exact observability of stochastic systems with their applications this paper mainly studies the stabilizability and exact observability of stochastic linear controlled systems and their applications with the aid of the operator spectrum a necessary and sufficient condition is given for the stabilizability of stochastic systems some new concepts such as unremovable spectrum and strong solution are introduced an unremovable spectral theorem and a stochastic popov belevith hautus criterion for exact observability are presented as applications a comparison theorem for stochastic algebraic riccati equations and a result on lyapunov type equations are obtained

complete controllability of nonlinear stochastic impulsive functional systems abstract this paper is concerned with the controllability of a kind of nonlinear stochastic impulsive functional systems sufficient conditions for the complete controllability of the nonlinear stochastic impulsive functional systems are obtained by using schauder fixed point theorem a numerical example is given to illustrate the effectiveness of the theoretical results

partial controllability concepts the main results in theory of controllability are formulated for deterministic or stochastic control systems given in a standard form i e given as a first order differential equation driven by an infinitesimal generator of strongly continuous semigroup in an abstract hilbert or banach space and disturbed by a deterministic function or by a white noise process at the same time some deterministic or stochastic linear systems can be written in a standard form if the state space is enlarged respectively the ordinary controllability conditions for them are too strong since they assume extended state space it is reasonable to introduce partial controllability concepts which assume original state space in this paper we study necessary and sufficient conditions of partial controllability for deterministic and stochastic linear control systems given in a standard form and their implications to particular cases

asymptotic stability of sampled data piecewise affine slab systems this paper addresses stability analysis of closed loop sampled data piecewise affine pwa slab systems in particular we study the case in which a pwa plant is in feedback with a discrete time emulation of a pwa controller we consider the sampled data system as a continuous time system with a variable time delay the contributions of this work are threefold first we present a modified lyapunov krasovskii functional lkf for studying pwa systems with time delays that is less conservative when compared to previously suggested alternatives second based on the new lkf sufficient conditions are provided for asymptotic stability of sampled data pwa slab systems to the origin these conditions become linear matrix inequalities lmis in the case of a piecewise linear pwl controller finally we present an algorithm for finding a lower bound on the maximum delay that preserves asymptotic stability therefore the output of the algorithm provides an upper bound on the minimum sampling frequency that guarantees asymptotic stability of the sampled data system the new results are successfully applied to a unicycle example

approximate controllability of second order semilinear stochastic system with nonlocal conditions in this paper the approximate controllability of second order semilinear stochastic system involving nonlocal conditions is studied by using sadovskii s fixed point theorem with stochastic analysis theory we derive a new set of sufficient conditions for the approximate controllability of second order semilinear stochastic system with nonlocal conditions under the assumption that the corresponding linear system is approximately controllable finally an application to a second order semilinear stochastic system with nonlocal initial condition is provided to illustrate the obtained theory

nonmonotonic logic ii nonmonotonic modal theories tradmonal logics suffer from the monotomclty problem new axioms never mvahdate old theorems one way to get nd of this problem ts to extend traditional modal logic in the following way the operator m usually read possible is extended so that mp is true whenever p is consistent with the theory then any theorem of this form may be mvahdated if p s added as an axiom this extension results m nonmonotomc versions of the systems t 4 and 5 these systems are complete in that a theorem is provable in a theory based on one of them just if it is true m all noncommittal models of that theory where a noncommittal model ts one m which as many thmgs are possible as possible nonmonotomc 4 is probably the most interesting of the three since it is stronger than ordinary 4 but has all the usual inferential machinery of 4 there is a straightforward proof procedure for the sententlal subset of nonmonotomc 4 this approach to nonmonotonlc logic may be applied to several problems in knowledge representation for aruficml mtelhgence its main advantages over competmg approaches are that tt factors out problems of resource hmltattons and allows the symbol m to appear m any context since m is a meaningful part of the language

stability of sampled data piecewise affine systems a time delay approach this paper addresses the stability analysis of sampled data piecewise affine pwa systems consisting of a continuous time plant in feedback connection with a discrete time emulation of a continuous time state feedback controller the sampled data system is first considered as a continuous time system with a variable time delay conditions under which the trajectories of the sampled data closed loop system will converge to an attracting invariant set are then presented it is also shown that when the sampling period converges to zero these conditions coincide with sufficient conditions for non fragility of the stabilizing continuous time pwa state feedback controller the results are successfully applied to a helicopter example

on the approximate controllability of semilinear fractional differential systems fractional differential equations have wide applications in science and engineering in this paper we consider a class of control systems governed by the semilinear fractional differential equations in hilbert spaces by using the semigroup theory the fractional power theory and fixed point strategy a new set of sufficient conditions are formulated which guarantees the approximate controllability of semilinear fractional differential systems the results are established under the assumption that the associated linear system is approximately controllable further we extend the result to study the approximate controllability of fractional systems with nonlocal conditions an example is provided to illustrate the application of the obtained theory

approximate controllability for stochastic evolution inclusions of clarke s subdifferential type in this paper we deal with the approximate controllability of stochastic evolution inclusions of clarke s subdifferential type firstly by using stochastic analysis nonsmooth analysis theory of operator semigroups and fixed point theorems of multivalued maps we show the existence of mild solutions for the stochastic evolution inclusions then we provide a sufficient condition to guarantee the approximate controllability of the stochastic evolution inclusions actually our results cover a broader class of inclusion problems involving time depending operators finally an example is included to illustrate the applicability of the main results

approximate controllability of stochastic differential systems driven by a levy process in this paper we are concerned with the approximate controllability of stochastic differential systems driven by teugels martingales associated with a levy process we derive the approximate controllability with the coefficients in the system satisfying some non lipschitz conditions which include classic lipschitz conditions as special cases the desired result is established by means of standard picard s iteration

on controllability of second order nonlinear impulsive differential systems abstract many dynamical systems in physics chemistry biology and engineering sciences have impulsive dynamical behaviors due to abrupt jumps at certain instants during the dynamical processes the mathematical models of such processes are called differential systems with impulse effect this paper studies the exact controllability issue of certain types of second order nonlinear impulsive control differential systems sufficient conditions are formulated and proved for the exact controllability of such systems without imposing a compactness condition on the cosine family of operators we establish controllability results by using a fixed point analysis approach finally an example is presented to illustrate the utility of the proposed result the results improve some recent results

null controllable region of delta operator systems subject to actuator saturation abstractin this paper we give exact description of null controllable regions for delta operator systems subject to actuator saturation the null controllable region is in terms of a set of extremal trajectories of anti stable subsystems for the delta operator system with real eigenvalues or complex eigenvalues the description is simplified to an explicit formula which is used to characterise the boundary of a null controllable region the relations of null controllable regions are shown separately for continuous time systems discrete time systems and delta operator systems two numerical examples are given to illustrate the effectiveness of the proposed techniques on null controllable regions

optimal feedback control and controllability for hyperbolic evolution inclusions of clarke s subdifferential type abstract in this paper by applying the weak closedness of multi valued maps and the properties of clarke s subdifferential we consider new results of optimal feedback control and controllability for hyperbolic evolution inclusions of clarke s subdifferential type we omit the condition that the evolution operator and the values of multi valued map are compact our main results can be applied to the problems of hyperbolic partial differential equations and hemivariational inequalities

approximate controllability of fractional delay dynamic inclusions with nonlocal control conditions we introduce a nonlocal control condition and the notion of approximate controllability for fractional order quasilinear control inclusions approximate controllability of a fractional control nonlocal delay quasilinear functional differential inclusion in a hilbert space is studied the results are obtained by using the fractional power of operators multi valued analysis and sadovskii s fixed point theorem main result gives an appropriate set of sufficient conditions for the considered system to be approximately controllable as an example a fractional partial nonlocal control functional differential inclusion is considered

stochastic controllability of linear systems with markovian jumps abstract the notion of stochastic controllability for linear systems subject to markovian jumps in parameter values is studied an algebraic necessary and sufficient condition is obtained in terms of an easily computable rank test

piecewise affine state feedback for piecewise affine slab systems using convex optimization abstract this paper shows that lyapunov based state feedback controller synthesis for piecewise affine pwa slab systems can be cast as an optimization problem subject to a set of linear matrix inequalities lmis analytically parameterized by a vector furthermore it is shown that continuity of the control inputs at the switchings can be guaranteed by adding equality constraints to the problem without affecting its parameterization structure finally it is shown that piecewise affine state feedback controller synthesis for piecewise affine slab systems to maximize the decay rate of a quadratic control lyapunov function can be cast as a set of quasi concave optimization problems analytically parameterized by a vector before casting the synthesis in the format presented in this paper lyapunov based piecewise affine state feedback controller synthesis could only be formulated as a bi convex optimization program which is very expensive to solve globally thus the fundamental importance of the contributions of the paper relies on the fact that for the first time the piecewise affine state feedback synthesis problem has been formulated as a convex problem with a parameterized set of lmis that can be relaxed to a finite set of lmis and solved efficiently to a point near the global optimum using available software furthermore it is shown for the first time that in some situations the global can be exactly found by solving only one concave problem

robust controllability of linear stochastic uncertain systems the paper extends the concept of robust controllability via linear state feedback to stochastic uncertain systems we show that the controllability of a stochastic uncertain system can be characterized using solutions to a game type differential riccati equation

all i know a study in autoepistemic logic abstract current approaches to formalizing nonmonotonic reasoning using logics of belief require the definition of new metalogical properties over sets of sentences this research attempts to show how some of these patterns of reasoning can be captured using only the classical notions of logic satisfiability validity implication this is done by extending a logic of belief so that it is possible to say that only a certain proposition or finite set of them is believed this research also extends previous approaches to handle quantifiers and equality provides a semantic account of certain types of nonmonotonicity and through a simple proof theory allows formal derivations to be generated

possible world semantics and autoepistemic reasoning abstract the possible world semantics of modal logic has been employed to study the nonmonotonic reasoning formalism moore s autoepistemic logic only kripke structure which is also known as a standard model has been used to represent the autoepistemic expansions of modal theories here we argue that the mode of autoepistemic reasoning which is formalized by autoepistemic logic is not necessarily associated with a standard model another model of the possible world semantics the minimal model is helpful in knowledge representation and belief reasoning in particular the minimal model can be used as a structure to represent all the autoepistemic expansions of a modal theory we extend the minimal model with standard model to deal with both knowledge and belief and introduce a null value called unknown to provide a refined model for knowledge and belief we also present a notion of epistemic base of basic sentences to identify the possible worlds in a minimal model by reformulating moore s autoepistemic logic with respect to epistemic base some reasonable modal theories that do not have any autoepistemic expansion will have generalized autoepistemic expansions

a converse lyapunov theorem for strong global recurrence abstract a converse lyapunov theorem is established for discrete time stochastic systems modeled by a set valued mapping under mild regularity conditions for this class of systems it is shown that strong global recurrence is a necessary and sufficient condition for the existence of a smooth lyapunov function that decreases in expected value along solutions outside of the set that is strongly globally recurrent robustness of strong global recurrence to sufficiently small perturbations is also established

approximate controllability of semilinear deterministic and stochastic evolution equations in abstract spaces various sufficient conditions for approximate controllability of linear evolution systems in abstract spaces have been obtained but approximate controllability of semilinear control systems usually requires some complicated and limited assumptions in this paper we show the approximate controllability of the abstract semilinear deterministic and stochastic control systems under the natural assumption that the associated linear control system is approximately controllable the results are obtained using new properties of symmetric operators which are proved in this paper compact semigroups the schauder fixed point theorem and or the contraction mapping principle

controllability stabilizability and continuous time markovian jump linear quadratic control consideration is given to the control of continuous time linear systems that possess randomly jumping parameters which can be described by finite state markov processes the relationship between appropriately defined controllability stabilizability properties and the solution of the infinite time jump linear quadratic jlq optimal control problems is also examined although the solution of the continuous time markov jlq problem with finite or infinite time horizons is known only sufficient conditions for the existence of finite cost constant stabilizing controls for the infinite time problem appear in the literature in this paper necessary and sufficient conditions are established these conditions are based on new definitions of controllability observability stabilizability and detectability that are appropriate for continuous time markovian jump linear systems these definitions play the same role for the jlq problem as the deterministic properties do for the linear quadratic regulator lqr problem

controllability of non linear stochastic systems complete controllability of a semi linear stochastic system assuming controllability of the associated linear sytem is studied it is also shown that a non linear stochastic system is locally null controllable provided that the corrsponding linearized system is controllable

sampled data piecewise affine differential inclusions this paper addresses exponential stability and stabilization of sampled data piecewise affine differential inclusions pwadi with an unknown nonuniform sampling rate the contributions of this paper are threefold first given a controller sufficient conditions for exponential stability of closed loop sampled data pwadi are presented using a piecewise smooth krasovskii functional second assuming the controller is piecewise linear and the krasovskii functional is piecewise quadratic the stability conditions are cast as linear matrix inequalities lmis third sufficient conditions for sampled data controller synthesis for pwadi are formulated in terms of lmis with the maximum allowable sampling period as a parameter the effectiveness of the approach is shown via a pwadi example that is motivated by a nonlinear system

on partial s controllability of semilinear partially observable systems in this paper the partial s controllability of semilinear partially observable control systems is investigated the essence of study is the presence of partial observations we define a weakened partial s controllability concept for partially observable systems a sufficient condition for this controllability concept is proved the method of proof differs from the traditional proofs by fixed point theorems the obtained result is demonstrated with examples

autoepistemic logic autoepistemic logic is one of the principal modes of nonmonotonic reasoning it unifies several other modes of nonmonotonic reasoning and has important application in logic programming in the paper a theory of autoepistemic logic is developed this paper starts with a brief survey of some of the previously known results then the nature of nonmonotonicity is studied by investigating how membership of autoepistemic statements in autoepistemic theories depends on the underlying objective theory a notion similar to set theoretic forcing is introduced expansions of autoepistemic theories are also investigated expansions serve as sets of consequences of an autoepistemic theory and they can also be used to define semantics for logic programs with negation theories that have expansions are characterized and a normal form that allows the description of all expansions of a theory is introduced our results imply algorithms to determine whether a theory has a unique expansion sufficient conditions stratification that imply existence of a unique expansion are discussed the definition of stratified theories is extended and under some additional assumptions efficient algorithms for testing whether a theory is stratified are proposed the theorem characterizing expansions is applied to two classes of theories k1 theories and ae programs in each case simple hypergraph characterization of expansions of theories from each of these classes is given finally connections with stable model semantics for logic programs with negation is discussed in particular it is proven that the problem of existence of stable models is np complete authors abstract

bsdes with general filtration driven by levy processes and an application in stochastic controllability abstract in this paper we introduce a weak version of the strong solution the adapted solution used in pardoux and peng 1990 2 i e the transposition solution to the backward stochastic differential equation bsde with general filtration and random jumps and study the corresponding well posedness the main tools that we employ are the riesz representation theorem and the banach fixed point theorem without using the martingale representation theorem as an application we give a definition of controllability to the stochastic linear control system in the sense of the transposition solution and provide a kalman type rank condition to guarantee this property

partial controllability of stochastic linear systems the controllability concepts for linear stochastic differential equations driven by different kinds of noise processes can be reduced to the partial controllability concepts for the same systems driven by correlated white noises based on this fact in this article we study the conditions of exact and approximate controllability for linear stochastic control systems under various kinds of noise processes including correlated white noises as well as coloured wide band and shifted white noises it is proved that such systems are never exactly controllable while their approximate controllability is equivalent to the approximate controllability of the associated linear deterministic systems at all past time moments

on controllability conception for stochastic systems the controllability notions for partially observed stochastic systems are defined their relation with complete and approximate controllabilities is shown in particular it is proven that the approximate controllability condition is necessary and the complete controllability condition is sufficient for the partially observed linear gaussian control system to attain the arbitrarily small neighborhood of each point in the state space with probability arbitrarily closely to one

controllability of stochastic systems with distributed delays in control in this article we are concerned with the problem of relative controllability for non linear stochastic systems with distributed delays in control in finite dimensional spaces sufficient criteria for the relative controllability of the non linear stochastic system are established some special cases are also considered the results are obtained by using the banach fixed point theorem an example is provided to illustrate the technique

controllability of stochastic linear systems in the paper necessary and sufficient conditions for various types of stochastic controllability of the linear stochastic system of the form d x ax d t bu d t c d w r x 0 x 0 are given some possible extensions are indicated as well

a matrosov theorem for strong global recurrence a theorem on nested matrosov functions is presented for time varying stochastic set valued discrete time systems satisfying mild regularity conditions it establishes sufficient conditions for uniform strong global recurrence of an open bounded set in general matrosov functions are required to satisfy less rigid requirements than typical lyapunov functions that satisfy a strict decrease condition along trajectories

controllability of nonlinear stochastic control systems abstract in the paper sufficient conditions for deterministic weak controllability of nonlinear ito equations of the form d x t f x t t 1 m u t t g t x t d t j 1 l h j x t dw j 1 0 x 0 p r n are given

non monotonic logic i abstract non monotonic logical systems are logics in which the introduction of new axioms can invalidate old theorems such logics are very important in modeling the beliefs of active processes which acting in the presence of incomplete information must make and subsequently revise assumptions in light of new observations we present the motivation and history of such logics we develop model and proof theories a proof procedure and applications for one non monotonic logic in particular we prove the completeness of the non monotonic predicate calculus and the decidability of the non monotonic sentential calculus we also discuss characteristic properties of this logic and its relationship to stronger logics logics of incomplete information and truth maintenance systems

stochastic minimum energy control abstract we give the solution to the minimum energy control problem for linear stochastic systems the problem is as follows given an exactly controllable system find the control process with the minimum expected energy that transfers the system from a given initial state to a desired final state the solution is found in terms of a certain forward backward stochastic differential equation of hamiltonian type

approximate controllability of semilinear neutral evolution systems with delay this paper considers the approximate controllability for a class of neutral control systems governed by semilinear neutral delayed equations sufficient conditions for approximate controllability are established by constructing fundamental solutions and using resolvent condition banach contraction mapping principle and techniques on fractional power operators the obtained results improve some existing analogous ones on this topic to some extent an example is presented finally to illustrate the applications of the obtained results

control problems for semi linear retarded integro differential equations by the fredholm theory in this paper we deal with the approximate controllability for semi linear retarded functional integro differential equations by using the fredholm theory in hilbert spaces we no longer require t