observer based adaptive fuzzy decentralized control for stochastic large scale nonlinear systems with unknown dead zones this paper studies the problem of adaptive fuzzy decentralized output feedback control for a class of uncertain stochastic large scale nonlinear systems the considered systems have unknown nonlinear functions unknown dead zones unmodeled dynamics and unmeasurable state variables therefore fuzzy logic systems are utilized to approximate the unknown nonlinear functions and a fuzzy state observer is established to estimate the unmeasurable states based on the backstepping design and the supply changing function technique a robust adaptive fuzzy decentralized output feedback control approach is developed the proposed control approach can ensure the closed loop system to be input state practically stable isps in probability and accommodate the unmodeled dynamics and unknown dead zones as well the effectiveness of the proposed control approach is illustrated by a simulation example

finite time fault detection filter design for discrete time interconnected systems with average dwell time abstract in this paper we present an approach to finite time robust fault detection filter design for interconnected systems with disconnected interconnections among these subsystems taking various disconnected interconnections into account a switched scheme is proposed to analysis these complex cases by modeling these cases of disconnections into independent subsystems a switching signal is introduced to specify which subsystem is activated in the aid of the average dwell time method sufficient conditions on existence of the desired filter are derived in term of linear matrices inequalities which guarantee the augmented system is finite time boundedness and achieve the h performance a numerical example is used to illustrate the effectiveness of the proposed approach

decentralized adaptive fuzzy output feedback control of stochastic nonlinear large scale systems with dynamic uncertainties in this paper centralized and decentralized adaptive fuzzy output feedback control schemes are investigated for a class of stochastic nonlinear interconnected large scale systems with dynamic uncertainties and unmeasured states fuzzy systems are used to approximate the unknown nonlinear functions decentralized k filters are designed to estimate the unmeasured states an available dynamic signal is introduced to dominate the unmodeled dynamics by combining dynamic surface control dsc technique with backstepping design the condition in which the approximation errors are assumed to be bounded is avoided using the defined compact set in the stability analysis the unknown smooth interconnections and black box functions are effectively dealt with using it o formula and chebyshev s inequality it is shown that all the signals in the closed loop system are bounded in probability and the error signals are semi globally uniformly ultimately bounded in mean square or the sense of four moment simulation results demonstrate the effectiveness of the proposed approach

adaptive fault tolerant stabilization for nonlinear systems with markovian jumping actuator failures and stochastic noises in this paper we consider the fault tolerant stabilization problem for a class of nonlinear systems with uncertain parameters uncertainties caused by markovian jumping actuator failures and stochastic noises are also taken into consideration different from most existing results the number of actuator failures may be infinite and stochastic functions related to multi markovian variables have been introduced to denote the failure scaling factors for the actuators which is practical but challenging three main difficulties arise first is how to establish fundamentals for systems involving multi markovian variables and stochastic noises including the joint transition probability the infinitesimal generator the existence and uniqueness of the solution and so on second is how to handle the extra transition rate related terms appearing in the infinitesimal generator of the lyapunov function last is how to cope with the involved higher order hessian term in the ito stochastic differentiation by proposing a new adaptive fault tolerant control scheme the boundedness in probability of all the closed loop signals has been ensured an example of altitude fault tolerant control for a generic hypersonic air vehicle is presented to show the effectiveness of the proposed scheme

minimal and maximal operator spaces and operator systems in entanglement theory abstract we examine k minimal and k maximal operator spaces and operator systems and investigate their relationships with the separability problem in quantum information theory we show that the matrix norms that define the k minimal operator spaces are equal to a family of norms that have been studied independently as a tool for detecting k positive linear maps and bound entanglement similarly we investigate the k super minimal and k super maximal operator systems that were recently introduced and show that their cones of positive elements are exactly the cones of k block positive operators and unnormalized states with schmidt number no greater than k respectively we characterize a class of norms on the k super minimal operator systems and show that the completely bounded versions of these norms provide a criterion for testing the schmidt number of a quantum state that generalizes the recently developed separability criterion based on trace contractive maps

adaptive partial state feedback control for stochastic high order nonlinear systems with stochastic input to state stable inverse dynamics this paper aims to solve the adaptive stabilization problem for a class of stochastic high order nonlinear systems with stochastic inverse dynamics and nonlinear parameterization under the weaker assumptions on stochastic inverse dynamic and nonlinear functions by generalizing the adding a power integrator technique using the idea of changing supply function and parameter separation technique a smooth adaptive partial state feedback controller is constructed to render the closed loop system globally stable in probability and all states can be regulated to the origin almost surely the effectiveness of the designed controller is demonstrated by a simulation example

decentralised adaptive output feedback stabilisation for stochastic time delay systems via lasalle yoshizawa type theorem abstractthis paper deals with the decentralised output feedback stabilisation problem for a class of large scale stochastic time delay nonlinear systems a general theorem is firstly given to guarantee the global existence and uniqueness of the solution for stochastic time delay systems in addition a stochastic version of the well known lasalle yoshizawa theorem with time varying delay is initially proposed for the controller design and stability analysis then for a class of large scale stochastic systems with time varying delays totally decentralised adaptive delay dependent controllers are designed by using k filter and backstepping approach via lasalle yoshizawa type theorem and constructing a general lyapunov function it is shown that all signals in the closed loop system are bounded almost surely and the solution is almost surely asymptotically stable finally a simulation example is given to illustrate the effectiveness of the results of this paper

quantum gate fidelity in terms of choi matrices we provide new results for computing and comparing the quantum gate fidelity of quantum channels via their choi matrices we extend recent work that showed that there exist non dual pairs of quantum channels with equal gate fidelity by providing an explicit characterization of all such channels we use our characterization to show that when the dimension is 2 or 3 under slightly stronger hypotheses the gate fidelity of two channels is equal if and only if their difference equals the difference of some unital map and its dual a fact that has been shown to be false when the dimension is 4 or larger we also present a formula for the minimum gate fidelity of a channel in terms of a well studied norm on a compression of its choi matrix as a consequence several new ways of bounding and approximating the minimum gate fidelity follow including a simple semidefinite program to compute it for qubit channels

adaptive output feedback tracking of stochastic nonlinear systems we address the adaptive stabilization and tracking problems for a class of output feedback canonical systems driven by wiener noises of unknown covariance filtered transformation and backstepping techniques are employed in the stochastic control design we obtain two adaptive controllers that guarantee the global stability in probability for vanishing perturbations or the input to state stability in probability for nonvanishing perturbations respectively the tracking error can converge to a small residual set around the origin in the sense of mean quartic value

cones of positive maps and their duality relations the structure of cones of positive and k positive maps acting on a finite dimensional hilbert space is investigated special emphasis is given to their duality relations to the sets of superpositive and k superpositive maps we characterize k positive and k superpositive maps with regard to their properties under taking compositions a number of results obtained for maps are also rephrased for the corresponding cones of block positive k block positive separable and k entangled operators due to the jamiolkowski choi isomorphism generalizations to a situation where no such simple isomorphism is available are also made employing the idea of mapping cones as a side result to our discussion we show that extreme entanglement witnesses which are optimal should be of special interest in entanglement studies

the lower semicontinuity of optimal solution sets abstract we provide a sufficient condition which guarantees the lower semicontinuity of the optimal solution set for a general nonlinear programming problem it is shown that the same condition is both sufficient and necessary for convex programming problems that satisfy the slater condition

a class of operator equilibrium problems in this paper we consider a class of operator equilibrium problems oep for short with operator solutions and derive a minty type lemma for this class of problems further using this lemma and kkm theorem we establish some existence theorems for oep the theorems presented in this paper generalize improve and unify many known results

a family of norms with applications in quantum information theory we consider a family of vector and operator norms defined by the schmidt decomposition theorem for quantum states we use these norms to tackle two fundamental problems in quantum information theory the classification problem for k positive linear maps and entanglement witnesses and the existence problem for nonpositive partial transpose bound entangled states we begin with an analysis of the norms showing that the vector norms can be explicitly calculated and we derive several inequalities in order to bound the operator norms and compute them in special cases we then use the norms to establish what appears to be the most general spectral test for k positivity currently available showing how it implies several other known tests as well as some new ones building on this work we frame the nonpositive partial transpose bound entangled problem as a concrete problem on a specific limit specifically that a particular entangled werner state is bound entangled if and only if a certain norm inequality ho

on generalized operator quasi equilibrium problems abstract in this paper we will introduce the generalized operator equilibrium problem and generalized operator quasi equilibrium problem which generalize the operator equilibrium problem due to kazmi and raouf k r kazmi a raouf a class of operator equilibrium problems j math anal appl 308 2005 554 564 into multi valued and quasi equilibrium problems using a fan browder type fixed point theorem in s park foundations of the kkm theory via coincidences of composites of upper semicontinuous maps j korean math soc 31 1994 493 519 and an existence theorem of equilibrium for 1 person game in x p ding w k kim k k tan equilibria of non compact generalized games with l majorized preferences j math anal appl 164 1992 508 517 as basic tools we prove new existence theorems on generalized operator equilibrium problem and generalized operator quasi equilibrium problem which includes operator equilibrium problems

risk sensitive adaptive trackers for strict feedback systems with output measurements this note investigates the control of stochastic nonlinear systems with parametric uncertainty the class of systems considered are single input single output and in strict feedback form with the performance measured with respect to a risk sensitive cost criterion the uncertainty in the system description is assumed to be linearly parameterized where the unmeasured parameters are generated by stochastic differential equations by employing the backstepping design technique on the estimates of the unmeasured states provided by a simple state estimator an output feedback adaptive controller is constructed which maintains an arbitrarily small average value for the risk sensitive cost the controller designed achieves boundedness in probability for all closed loop signals and under certain conditions the tracking error converges to zero almost surely

semicontinuity of the solution set of parametric multivalued vector quasiequilibrium problems abstract in this paper we establish sufficient conditions for the solution set of parametric multivalued vector quasiequilibrium problems to be semicontinuous all kinds of semicontinuity are considered lower semicontinuity upper semicontinuity hausdorff upper semicontinuity and closedness moreover we investigate both the weak and strong solutions of quasiequilibrium problems

disguising quantum channels by mixing and channel distance trade off we consider the reverse problem of the distinguishability of two quantum channels which we call the disguising problem given two quantum channels the goal here is to make the two channels identical by mixing with some other channels with minimal mixing probabilities this quantifies how much one channel can disguise as the other in addition the possibility to trade off between the two mixing probabilities allows one channel to be more preserved less mixed at the expense of the other we derive lower and upper bounds of the trade off curve and apply them to a few example channels optimal trade off is obtained in one example we relate the disguising problem and the distinguishability problem by showing that the former can lower and upper bound the diamond norm we also show that the disguising problem gives an upper bound on the key generation rate in quantum cryptography

choi matrices norms and entanglement associated with positive maps on matrix algebras abstract we study positive maps of b k into b h for finite dimensional hilbert spaces k and h our main emphasis is on how choi matrices and estimates of their norms with respect to mapping cones reflect various properties of the maps special attention will be given to entanglement properties and k positive maps

spectral conditions for positive maps we provide partial classification of positive linear maps in matrix algebras which is based on a family of spectral conditions this construction generalizes the celebrated choi example of a map which is positive but not completely positive it is shown how the spectral conditions enable one to construct linear maps on tensor products of matrix algebras which are positive but only on a convex subset of separable elements such maps provide basic tools to study quantum entanglement in multipartite systems

semicontinuity of the solution multifunctions of the parametric generalized operator equilibrium problems abstract in this paper we first introduce the parametric form of the generalized operator equilibrium problem and generalized operator quasi equilibrium problem due to kum and kim s kum w k kim on generalized operator quasi equilibrium problems j math anal appl 345 2008 559 565 next we consider the upper and lower semicontinuity properties for the parametric generalized operator equilibrium problem simply pgoep and the parametric generalized operator quasi equilibrium problem simply pgoqep our semicontinuity properties of the solution sets for pgoep and pgoqep can be suitable for the stability properties of many kinds of nonlinear problems e g the operator equilibrium problem operator quasi equilibrium problem operator variational like inequality problem operator variational inequality problem operator minimization problem and vector equilibrium problem

an algorithm to explore entanglement in small systems a quantum state s entanglement across a bipartite cut can be quantified with entanglement entropy or more generally schmidt norms using only schmidt decompositions we present a simple iterative algorithm to maximize schmidt norms depending on the choice of norm the optimizing states maximize or minimize entanglement possibly across several bipartite cuts at the same time and possibly only among states in a specified subspace recognizing that convergence but not success is certain we use the algorithm to explore topics ranging from fermionic reduced density matrices and varieties of pure quantum states to absolutely maximally entangled states and minimal output entropy of channels

how often is a random quantum state k entangled the set of trace preserving positive maps acting on density matrices of size d forms a convex body we investigate its nested subsets consisting of kpositive maps where k 2 d working with the measure induced by the hilbert schmidt distance we derive asymptotically tight bounds for the volumes of these sets our results strongly suggest that the inner set of k 1 positive maps forms a small fraction of the outer set of k positive maps these results are related to analogous bounds for the relative volume of the sets of k entangled states describing a bipartite d d system

the inverse eigenvalue problem for entanglement witnesses abstract we consider the inverse eigenvalue problem for entanglement witnesses which asks for a characterization of their possible spectra or equivalently of the possible spectra resulting from positive linear maps of matrices we completely solve this problem in the two qubit case and we derive a large family of new necessary conditions on the spectra in arbitrary dimensions we also establish a natural duality relationship with the set of absolutely separable states and we completely characterize witnesses i e separating hyperplanes of that set when one of the local dimensions is 2

adaptive tracking for stochastic nonlinear systems with markovian switching the problem of the adaptive tracking for a class of stochastic nonlinear systems with stationary markovian switching is considered in this note an ito formula is proposed for stochastic integral equations with an integral about martingale measure an adaptive backstepping controller is designed such that the closed loop system has a unique solution that is globally bounded in probability and l4 norm of the tracking error converges to an arbitrarily small neighborhood of zero a simulation example demonstrates the efficiency of the proposed scheme

decentralized adaptive output feedback controller design for stochastic nonlinear interconnected systems in this paper the controller design for a class of stochastic interconnected systems with both parametric uncertainties and unknown nonlinear interactions is presented the diffusion terms considered are dependent on the outputs of local subsystems and allowed to be unbounded first by employing decentralized state observers totally decentralized adaptive tracking controllers with suitable parameter adaptive laws are designed to ensure the boundedness in probability of all the signals in the closed loop system it is shown that the tracking errors converge to small residual sets around the origin then for systems with relaxed diffusion vector fields a decentralized adaptive stabilizing scheme is proposed to ensure the boundedness in probability of all signals in the closed loop system

on the dimension of subspaces with bounded schmidt rank we consider the question of how large a subspace of a given bipartite quantum system can be when the subspace contains only highly entangled states this is motivated in part by results of hayden et al e print arxiv quant ph 0407049 commun math phys 265 95 2006 which show that in large d d dimensional systems there exist random subspaces of dimension almost d2 all of whose states have entropy of entanglement at least logd o 1 it is also a generalization of results on the dimension of completely entangled subspaces which have connections with the construction of unextendible product bases here we take as entanglement measure the schmidt rank and determine for every pair of local dimensions da and db and every r the largest dimension of a subspace consisting only of entangled states of schmidt rank r or larger this exact answer is a significant improvement on the best bounds that can be obtained using the random subspace techniques in hayden et al we also determine the converse the l

solution sensitivity of variational inequalities our goal is to show that the continuity of the solutions of monotone variational inequalities with respect to perturbations is independent from the geometrical properties of reflexive banach spaces

operator spaces with few completely bounded maps we construct several examples of hilbertian operator spaces with few completely bounded maps in particular we give an example of a separable 1 hilbertian operator space x 0 such that whenever x is an infinite dimensional quotient of x 0 x is a subspace of x and t x rightarrow x is a completely bounded map then t i x s where s is compact hilbert schmidt and s 2 16 s cb s 2 moreover every infinite dimensional quotient of a subspace of x 0 fails the operator approximation property we also show that every banach space can be equipped with an operator space structure without the operator approximation property

fixed points of commutative super operators in this paper we study fixed points of commutative super operators first under some circumstances we discuss the question of necessary and sufficient conditions for the set of fixed points of a super operator to be non trivial then we establish a structure lemma to completely characterize this set using this lemma we show that if a commutative super operator is also a generalized luders operator then its fixed points are precisely those operators intertwining the two sequences of operation elements associated with it specifically the main results of weihua and junde 2010 j phys a math theor 43 395206 are special cases of our results

decentralized adaptive output feedback stabilization for large scale stochastic nonlinear systems in this paper the problem of decentralized adaptive output feedback stabilization is investigated for large scale stochastic nonlinear systems with three types of uncertainties including parametric uncertainties nonlinear uncertain interactions and stochastic inverse dynamics under the assumption that the inverse dynamics of the subsystems are stochastic input to state stable an adaptive output feedback controller is constructively designed by the backstepping method it is shown that under some general conditions the closed loop system trajectories are bounded in probability and the outputs can be regulated into a small neighborhood of the origin in probability in addition the equilibrium of interest is globally stable in probability and the outputs can be regulated to the origin almost surely when the drift and diffusion vector fields vanish at the origin the contributions of the work are characterized by the following novel features 1 even for centralized single input single output systems this paper presents a first result in stochastic nonlinear adaptive output feedback asymptotic stabilization 2 the methodology previously developed for deterministic large scale systems is generalized to stochastic ones at the same time novel small gain conditions for small signals are identified in the setting of stochastic systems design 3 both drift and diffusion vector fields are allowed to be dependent not only on the measurable outputs but some unmeasurable states 4 parameter update laws are used to counteract the parametric uncertainty existing in both drift and diffusion vector fields which may appear nonlinearly 5 the concept of stochastic input to state stability and the method of changing supply functions are adapted for the first time to deal with stochastic and nonlinear inverse dynamics in the context of decentralized control