quantum symmetries associated with the perk schultz model the quantum algebraic structures associated with a family of r matrices one extracts from the perk schultz model are studied starting with the quantum spaces one can define from the r matrices the author shows how different duality conditions at the level of quantum spaces manin s construction translate in different quantum groups and quantized universal enveloping algebras

connes embedding problem and winning strategies for quantum xor games we consider quantum xor games defined in the work of regev and vidick acm trans comput theory 7 43 2015 from the perspective of unitary correlations defined in the work of harris and paulsen integr equations oper theory 89 125 2017 we show that the winning bias of a quantum xor game in the tensor product model respectively the commuting model is equal to the norm of its associated linear functional on the unitary correlation set from the appropriate model we show that connes embedding problem has a positive answer if and only if every quantum xor game has entanglement bias equal to the commuting bias in particular the embedding problem is equivalent to determining whether every quantum xor game g with a winning strategy in the commuting model also has a winning strategy in the approximate finite dimensional model

a synchronous game for binary constraint systems recently slofstra proved that the set of quantum correlations is not closed we prove that the set of synchronous quantum correlations is not closed which implies his result by giving an example of a synchronous game that has a perfect quantum approximate strategy but no perfect quantum strategy we also exhibit a graph for which the quantum independence number and the quantum approximate independence number are different we prove new characterisations of synchronous quantum approximate correlations and synchronous quantum spatial correlations we solve the synchronous approximation problem of dykema and the second author which yields a new equivalence of connes embedding problem in terms of synchronous correlations

on some quantum r matrices associated with representations of uq sl 2 c when q is a root of unity the author constructs quantum r matrices associated with certain non cyclic irreducible representations of uq sl 2 c at roots of unity which are parametrized by one continuous parameter the author finds solutions for the two and three dimensional representations via baxterization the two dimensional case corresponds to the free fermion model of fan and wu 1970

boson fermion models for osp 1 2 and uq osp 1 2 a reducible representation of the simple lie superalgebra osp 1 2 is constructed from two pairs of boson and one pair of fermion creation and annihilation operators the representation contains in direct sum every distinct up to equivalence finite dimensional irreducible representation of osp 1 2 exactly once and so defines a model generalizing to osp 1 2 schwinger s boson model of su 2 the model of osp 1 2 is further generalized to a model of the quantum superalgebra uq osp 1 2 in the case that q is not a root of unity matrix elements of generators and basic properties of the r matrix known from previous studies are rederived using the boson fermion calculus

type i quantum superalgebras q supertrace and two variable link polynomials a new general eigenvalue formula for the eigenvalues of casimir invariants for the type i quantum superalgebras is applied to the construction of link polynomials associated with any finite dimensional unitary irrep for these algebras this affords a systematic construction of new two variable link polynomials associated with any finite dimensional irrep with a real highest weight for the type i quantum superalgebras in particular infinite families of nonequivalent two variable link polynomials are determined in fully explicit form

grothendieck s theorem past and present probably the most famous of grothendieck s contributions to banach space theory is the result that he himself described as the fundamental theorem in the metric theory of tensor products that is now commonly referred to as grothendieck s theorem gt in short or sometimes as grothendieck s inequality this had a major impact first in banach space theory roughly after 1968 then later on in c algebra theory roughly after 1978 more recently in this millennium a new version of gt has been successfully developed in the framework of operator spaces or non commutative banach spaces in addition gt independently surfaced in several quite unrelated fields in connection with bell s inequality in quantum mechanics in graph theory where the grothendieck constant of a graph has been introduced and in computer science where the grothendieck inequality is invoked to replace certain np hard problems by others that can be treated by semidefinite programming and hence solved in polynomial time in this expository paper we present a review of all these topics starting from the original gt we concentrate on the more recent developments and merely outline those of the first banach space period since detailed accounts of that are already available for instance the author s 1986 cbms notes

an iterative adaptive dynamic programming method for solving a class of nonlinear zero sum differential games in this paper a new iterative adaptive dynamic programming adp method is proposed to solve a class of continuous time nonlinear two person zero sum differential games the idea is to use the adp technique to obtain the optimal control pair iteratively which makes the performance index function reach the saddle point of the zero sum differential games if the saddle point does not exist the mixed optimal control pair is obtained to make the performance index function reach the mixed optimum stability analysis of the nonlinear systems is presented and the convergence property of the performance index function is also proved two simulation examples are given to illustrate the performance of the proposed method

nearly optimal control laws for nonlinear systems with saturating actuators using a neural network hjb approach the hamilton jacobi bellman hjb equation corresponding to constrained control is formulated using a suitable nonquadratic functional it is shown that the constrained optimal control law has the largest region of asymptotic stability ras the value function of this hjb equation is solved for by solving for a sequence of cost functions satisfying a sequence of lyapunov equations le a neural network is used to approximate the cost function associated with each le using the method of least squares on a well defined region of attraction of an initial stabilizing controller as the order of the neural network is increased the least squares solution of the hjb equation converges uniformly to the exact solution of the inherently nonlinear hjb equation associated with the saturating control inputs the result is a nearly optimal constrained state feedback controller that has been tuned a priori off line

general eigenvalue formula for casimir invariants of type i quantum superalgebras induced invariant forms and the multiplicity labeling problem are investigated for typical summands of the tensor product of an arbitrary finite dimensional irreducible representation and a typical one for the type i quantum superalgebras the results are applied to obtain a general eigenvalue formula for casimir invariants corresponding to an arbitrary finite dimensional irreducible reference representation

old and new link polynomials from the theory of exactly solvable models abstract a general theory is presented to construct link polynomials topological invariants for knots and links from exactly solvable integrable models representations of the braid group and the markov traces on the representations are made through the general theory which is based on fundamental properties of the models various examples leading to alexander jones kauffman and new link polynomials are explicitly shown in a word the soliton theory contains an essence of the knot theory

on a non commutative analogue of a classical result of namioka and phelps abstract a classical result of namioka and phelps states that the square is a test object to verify semi simplexity in the tensor theory of convex compact sets by using the quantization of generalized namioka phelps test spaces we formulate a nuclearity criterion for c algebras which establishes a non commutative version of their result the proof we suggest covers the nuclearity characterization via non commutative polyhedron outlined by effros 8 several matrix systems studied by farenick and paulsen 13 are shown to be test systems for nuclearity we also prove that the standard namioka phelps test space is c nuclear we propose a partition of unity property for c algebras which distinguishes nuclear c algebras among the others

on quantum spin chain spectra and the structure of hecke algebras and q groups at roots of unity we combine statistical mechanical and algebraic lie theory techniques to investigate the ordinary representation theory of the quotients of the hecke algebras when q is a root of unity we show how to determine the main invariants of these algebras the standard module contents of the indecomposable projective modules in general n we give complete explicit results in the cases n 2 3 these results are used to determine the q variation energy level convergences in invariant quantum spin chains

free fermions and the alexander conway polynomial we show how the conway alexander polynomial arises from theq deformation of z2 graded sl n n algebras in the simplestsl 1 1 case we then establish connection between classical knot theory and its modern versions based on quantum groups we first shown how the crystal and the fundamental group of the complement of a knot give rise naturally to the burau representation of the braid group the burau matrix is then transformed into theu q sl 1 1 r matrix by going to the exterior power algebra using a det str identity this allows us to recover the state model of k2 89 as well we also show how theu q sl 1 1 algebra describes free fermions propagating on the knot diagram we rewrite the conway alexander polynomial as a berezin integral and thus as an apparently new determinant

bounding the set of quantum correlations we introduce a hierarchy of conditions necessarily satisfied by any distribution p ensuremath alpha ensuremath beta representing the probabilities for two separate observers to obtain outcomes ensuremath alpha and ensuremath beta when making local measurements on a shared quantum state each condition in this hierarchy is formulated as a semidefinite program among other applications our approach can be used to obtain upper bounds on the quantum violation of an arbitrary bell inequality it yields for instance tight bounds for the violations of the collins et al inequalities

perfect commuting operator strategies for linear system games linear system games are a generalization of mermin s magic square game introduced by cleve and mittal they show that perfect strategies for linear system games in the tensor product model of entanglement correspond to finite dimensional operator solutions of a certain set of non commutative equations we investigate linear system games in the commuting operator model of entanglement where alice and bob s measurement operators act on a joint hilbert space and alice s operators must commute with bob s operators we show that perfect strategies in this model correspond to possibly infinite dimensional operator solutions of the non commutative equations the proof is based around a finitely presented group associated with the linear system which arises from the non commutative equations

connes embedding problem and tsirelson s problem we show that tsirelson s problem concerning the set of quantum correlations and connes embedding problem on finite approximations in von neumann algebras known to be equivalent to kirchberg s qwep conjecture are essentially equivalent specifically tsirelson s problem asks whether the set of bipartite quantum correlations generated between tensor product separated systems is the same as the set of correlations between commuting c algebras connes embedding problem asks whether any separable ii1 factor is a subfactor of the ultrapower of the hyperfinite ii1 factor we show that an affirmative answer to connes question implies a positive answer to tsirelson s conversely a positive answer to a matrix valued version of tsirelson s problem implies a positive one to connes problem

large violation of bell inequalities with low entanglement in this paper we obtain violations of general bipartite bell inequalities of order frac sqrt n log n with n inputs n outputs and n dimensional hilbert spaces moreover we construct explicitly up to a random choice of signs all the elements involved in such violations the coefficients of the bell inequalities povms measurements and quantum states analyzing this construction we find that even though entanglement is necessary to obtain violation of bell inequalities the entropy of entanglement of the underlying state is essentially irrelevant in obtaining large violation we also indicate why the maximally entangled state is a rather poor candidate in producing large violations with arbitrary coefficients however we also show that for bell inequalities with positive coefficients in particular games the maximally entangled state achieves the largest violation up to a logarithmic factor

more about the nonstandard r matrix associated with suq 2 the markov trace is constructed for the general r matrices associated with suq 2 at q a root of unity the relationship between the r matrices derived based on quantum algebra and those obtained by akutsu et al 1991 is clarified

on the statistical independence of algebras of observables we reexamine various notions of statistical independence presently in use in algebraic quantum theory establishing alternative characterizations for such independence some of which are also valid without assuming that the observable algebras mutually commute in addition in the context which holds in concrete applications to quantum theory the equivalence of three major notions of statistical independence is proven

optimal control for unknown discrete time nonlinear markov jump systems using adaptive dynamic programming in this paper we develop and analyze an optimal control method for a class of discrete time nonlinear markov jump systems mjss with unknown system dynamics specifically an identifier is established for the unknown systems to approximate system states and an optimal control approach for nonlinear mjss is developed to solve the hamilton jacobi bellman equation based on the adaptive dynamic programming technique we also develop detailed stability analysis of the control approach including the convergence of the performance index function for nonlinear mjss and the existence of the corresponding admissible control neural network techniques are used to approximate the proposed performance index function and the control law to demonstrate the effectiveness of our approach three simulation studies one linear case one nonlinear case and one single link robot arm case are used to validate the performance of the proposed optimal control method

perfect embezzlement of entanglement van dam and hayden introduced a concept commonly referred to as embezzlement where for any entangled quantum state there is an entangled catalyst state from which a high fidelity approximation of can be produced using only local operations we investigate a version of this where the embezzlement is perfect i e the fidelity is 1 we prove that perfect embezzlement is impossible in a tensor product framework even with infinite dimensional hilbert spaces and infinite entanglement entropy then we prove that perfect embezzlement is possible in a commuting operator framework we prove this using the theory of c algebras and we also provide an explicit construction next we apply our results to analyze perfect versions of a nonlocal game introduced by regev and vidick finally we analyze the structure of perfect embezzlement protocols in the commuting operator model showing that they require infinite dimensional hilbert spaces

operator systems from discrete groups we express various sets of quantum correlations studied in the theoretical physics literature in terms of different tensor products of operator systems of discrete groups we thus recover earlier results of tsirelson and formulate a new approach for the study of quantum correlations to do this we formulate a general framework for the study of operator systems arising from discrete groups we study in detail the operator system of the free group mathbb f n on n generators as well as the operator systems of the free products of finitely many copies of the two element group mathbb z 2 we examine various tensor products of group operator systems including the minimal the maximal and the commuting tensor products we introduce a new tensor product in the category of operator systems and formulate necessary and sufficient conditions for its equality to the commuting tensor product in the case of group operator systems

solutions of the nonadditive ybe by spectral parameter factorization and re yang baxterization r matrix solutions for the nonadditive yang baxter equation are obtained in arbitrary dimension using a factorization ansatz in spectral parameters a symmetry transformation determined for the particle conserving r matrix is used to formulate a re yang baxterization scheme with multicomponent spectral parameters extending the notion of conventional yang baxterization the possible scope for such a transformation which has a striking resemblance to reshetikhin s deformation of r matrices but extended now to include spectral parameters is discussed

bounds on the distance between a unital quantum channel and the convex hull of unitary channels motivated by the recent resolution of asymptotic quantum birkhoff conjecture aqbc we attempt to estimate the distance between a given unital quantum channel and the convex hull of unitary channels we provide two lower bounds on this distance by employing techniques from quantum information and operator algebras respectively we then show how to apply these results to construct some explicit counterexamples to aqbc we also point out an interesting connection between the grothendieck s inequality and aqbc

a note on graded yang baxter solutions as braid monoid invariants we construct two osp n mod 2m solutions of the graded yang baxter equation by using the algebraic braid monoid approach the factorizable s matrix interpretation of these solutions is also discussed

h _ infty tracking control of completely unknown continuous time systems via off policy reinforcement learning this paper deals with the design of an h infty tracking controller for nonlinear continuous time systems with completely unknown dynamics a general bounded l 2 gain tracking problem with a discounted performance function is introduced for the h infty tracking a tracking hamilton jacobi isaac hji equation is then developed that gives a nash equilibrium solution to the associated min max optimization problem a rigorous analysis of bounded l 2 gain and stability of the control solution obtained by solving the tracking hji equation is provided an upper bound is found for the discount factor to assure local asymptotic stability of the tracking error dynamics an off policy reinforcement learning algorithm is used to learn the solution to the tracking hji equation online without requiring any knowledge of the system dynamics convergence of the proposed algorithm to the solution to the tracking hji equation is shown simulation examples are provided to verify the effectiveness of the proposed method

neural network based online simultaneous policy update algorithm for solving the hji equation in nonlinear h_ infty control it is well known that the nonlinear h state feedback control problem relies on the solution of the hamilton jacobi isaacs hji equation which is a nonlinear partial differential equation that has proven to be impossible to solve analytically in this paper a neural network nn based online simultaneous policy update algorithm spua is developed to solve the hji equation in which knowledge of internal system dynamics is not required first we propose an online spua which can be viewed as a reinforcement learning technique for two players to learn their optimal actions in an unknown environment the proposed online spua updates control and disturbance policies simultaneously thus only one iterative loop is needed second the convergence of the online spua is established by proving that it is mathematically equivalent to newton s method for finding a fixed point in a banach space third we develop an actor critic structure for the implementation of the online spua in which only one critic nn is needed for approximating the cost function and a least square method is given for estimating the nn weight parameters finally simulation studies are provided to demonstrate the effectiveness of the proposed algorithm

link polynomials related to the new braid group representations by introducing a modified diagonal matrix h the properties of markov moves are examined for the non standard representations of the braid group associated with the fundamental representations of an bn cn and dn it is shown that link polynomials can be constructed from those braid group representations the skein relations of link polynomials are obtained explicitly

causal independence and the energy level density of states in local quantum field theory within the general framework of local quantum field theory a physically motivated condition on the energy level density of well localized states is proposed and discussed it is shown that any model satisfying this condition obeys a strong form of the principle of causal statistical independence which manifests itself in a specific algebraic structure of the local algebras split property it is also shown that the proposed condition holds in a free field theory

state convertibility in the von neumann algebra framework we establish a generalisation of the fundamental state convertibility theorem in quantum information to the context of bipartite quantum systems modelled by commuting semi finite von neumann algebras namely we establish a generalisation to this setting of nielsen s theorem on the convertibility of quantum states under local operations and classical communication locc schemes along the way we introduce an appropriate generalisation of locc operations and connect the resulting notion of approximate convertibility to the theory of singular numbers and majorisation in von neumann algebras as an application of our result in the setting of mathrm ii 1 factors we show that the entropy of the singular value distribution relative to the unique tracial state is an entanglement monotone in the sense of vidal thus yielding a new way to quantify entanglement in that context building on previous work in the infinite dimensional setting we show that trace vectors play the role of maximally entangled states for general mathrm ii 1 factors examples are drawn from infinite spin chains quasi free representations of the car and discretised versions of the ccr

tensor products of operator systems abstract the purpose of the present paper is to lay the foundations for a systematic study of tensor products of operator systems after giving an axiomatic definition of tensor products in this category we examine in detail several particular examples of tensor products including a minimal maximal maximal commuting maximal injective and some asymmetric tensor products we characterize these tensor products in terms of their universal properties and give descriptions of their positive cones we also characterize the corresponding tensor products of operator spaces induced by a certain canonical inclusion of an operator space into an operator system we examine notions of nuclearity for our tensor products which on the category of c algebras reduce to the classical notion we exhibit an operator system s which is not completely order isomorphic to a c algebra yet has the property that for every c algebra a the minimal and maximal tensor product of s and a are equal

conic approach to quantum graph parameters using linear optimization over the completely positive semidefinite cone we investigate the completely positive semidefinite cone mathcal cs n a new matrix cone consisting of all n times n matrices that admit a gram representation by positive semidefinite matrices of any size in particular we study relationships between this cone and the completely positive and the doubly nonnegative cone and between its dual cone and trace positive noncommutative polynomials we use this new cone to model quantum analogues of the classical independence and chromatic graph parameters alpha g and chi g which are roughly obtained by allowing variables to be positive semidefinite matrices instead of 0 1 scalars in the programs defining the classical parameters we can formulate these quantum parameters as conic linear programs over the cone mathcal cs n using this conic approach we can recover the bounds in terms of the theta number and define further approximations by exploiting the link to trace positive polynomials

closed sets of correlations answers from the zoo we investigate the conditions under which a set of multipartite nonlocal correlations can describe the distributions achievable by distant parties conducting experiments in a consistent universe several questions are posed such as are all such sets nested i e contained into one another are they discrete or do they form a continuum how many of them are supraquantum are there non trivial polytopes among them we answer some of these questions or relate them to established conjectures in complexity theory by introducing a zoo of physically consistent sets which can be characterized efficiently via either linear or semidefinite programming as a bonus we use the zoo to derive for the first time concrete impossibility results in nonlocality distillation this article is part of a special issue of journal of physics a mathematical and theoretical devoted to 50 years of bell s theorem

h sub spl infin control via measurement feedback for general nonlinear systems this paper shows how the problem of local disturbance attenuation via measurement feedback with internal stability can be solved for a nonlinear system of rather general structure the solution of the problem is shown to be related to the existence of solutions of a pair of hamilton jacobi inequalities in n independent variables which are associated with state feedback and respectively output injection design

graded solutions of the yang baxter relation and link polynomials from a family of graded solvable models the authors derive representations of the braid group associated with the lie superalgebra gl m mod n and give explicitly a general form of the markov traces on the representations the braid operators thus obtained satisfy the hecke algebra the authors construct composite solvable models and obtain link polynomials from the braid operators for the composite models

new hierarchy of colored braid group representations novel solutions of the yang baxter relation for a series of multistate vertex models are presented in the braid group limit the obtained family of solutions gives a sequence of colored braid group representations possible generalizations of the multivariable alexander polynomial are discussed

on non semisplit extensions tensor products and exactness of group c algebras we show the existence of a block diagonal extensionb of the suspensions a of the reduced groupc algebraa c sl 2 such that there is only onec norm on the algebraic tensor productb op b butb is not nuclear even not exact thus the class of exactc algebras is not closed under extensions the existence comes from a new established tensorial duality between the weak expectation property wep of lance and the local variant llp of the lifting property we characterize the local lifting property of separable unitalc algebrasa as follows a has the local lifting property if and only if ext s a is a group wheres a is the suspension ofa if moreovera is the quotient algebra of ac algebra withwep for brevity a isqwep but does not satisfyllp then there exists a quasidiagonal extensionb of the suspensions a by the compact operators such that on the algebraic tensor productb op b there is only onec norm the question if everyc algebra isqwep remains open but we obtain the following results onqwep ac algebrac isqwep if and only ifc isqwep a von neumannii 1 factorn with separable predualn isqwep if and only ifn is a von neumann subfactor of the ultrapower of the hyperfiniteii 1 factor ifg is a maximally almost periodic discrete non amenable group with haagerup s herz schur multiplier constant g 1 then the universal groupc algebrac g is not exact but the reduced groupc albegrac g is exact and isqwep but does not satisfywep andllp we study functiorial properties of the classes ofc algebras satisfyingwep llp resp beingqwep as applications we obtain some unexpected relations between some open questions onc algebras

free products of completely positive maps and spectral sets let f be the free group on n generators and for each word w e f let 1 wi be its length haagerup lo showed that for each 0 r 1 the function h wp r is a positive definite function on f consider the positive definite function q n rinl on h then the free product function cpi cpr on ff z h coincides with h and the result was extended this way by de michele and fig talamanca 7 and by boiejko 4 51 in s it is proved that the free product of the unital positive defined functions ui gi z z is still positive defined on the free product group gi the correspondence between the positive defined functions on a discrete group g and the completely positive maps on the full c algebra c g and the isomorphism c g g2 n c g z c g suggested we consider amalgamated products of unital linear maps on the amalgamated product of a family of unital c algebras over a c subalgebra in section 3 we prove that the amalgamated product of a family of unital completely positive b bimodule maps qi a c is completely positive on the biggest amalgamated free product i a i as an application of our main result in section 2 we obtain some results concerning the dilation of noncommutative families of operators

unbounded violation of tripartite bell inequalities we prove that there are tripartite quantum states constructed from random unitaries that can lead to arbitrarily large violations of bell inequalities for dichotomic observables as a consequence these states can withstand an arbitrary amount of white noise before they admit a description within a local hidden variable model this is in sharp contrast with the bipartite case where all violations are bounded by grothendieck s constant we will discuss the possibility of determining the hilbert space dimension from the obtained violation and comment on implications for communication complexity theory moreover we show that the violation obtained from generalized greenberger horne zeilinger ghz states is always bounded so that in contrast to many other contexts ghz states do not lead to extremal quantum correlations in this case in order to derive all these physical consequences we will have to obtain new mathematical results in the theories of operator spaces and tensor norms in particular we will prove the existence of bounded but not completely bounded trilinear forms from commutative c algebras finally we will relate the existence of diagonal states leading to unbounded violations with a long standing open problem in the context of banach algebras

tsirelson s problem and asymptotically commuting unitary matrices in this paper we consider quantum correlations of bipartite systems having a slight interaction and reinterpret tsirelson s problem and hence kirchberg s and connes s conjectures in terms of finite dimensional asymptotically commuting positive operator valued measures we also consider the systems of asymptotically commuting unitary matrices and formulate the stronger kirchberg conjecture

estimating quantum chromatic numbers abstract we develop further the new versions of quantum chromatic numbers of graphs introduced by the first and fourth authors we prove that the problem of computation of the commuting quantum chromatic number of a graph is solvable by an sdp algorithm and describe an hierarchy of variants of the commuting quantum chromatic number which converge to it we introduce the tracial rank of a graph a parameter that gives a lower bound for the commuting quantum chromatic number and parallels the projective rank and prove that it is multiplicative we describe the tracial rank the projective rank and the fractional chromatic numbers in a unified manner that clarifies their connection with the commuting quantum chromatic number the quantum chromatic number and the classical chromatic number respectively finally we present a new sdp algorithm that yields a parameter larger than the lovasz number and is yet a lower bound for the tracial rank of the graph we determine the precise value of the tracial rank of an odd cycle

geometry of the set of synchronous quantum correlations we provide a complete geometric description of the set of synchronous quantum correlations for the three experiment two outcome scenario we show that these correlations form a closed set moreover every correlation in this set can be realized using projection valued measures on a hilbert space of dimension no more than 16

online actor critic algorithm to solve the continuous time infinite horizon optimal control problem in this paper we discuss an online algorithm based on policy iteration for learning the continuous time ct optimal control solution with infinite horizon cost for nonlinear systems with known dynamics that is the algorithm learns online in real time the solution to the optimal control design hj equation this method finds in real time suitable approximations of both the optimal cost and the optimal control policy while also guaranteeing closed loop stability we present an online adaptive algorithm implemented as an actor critic structure which involves simultaneous continuous time adaptation of both actor and critic neural networks we call this synchronous policy iteration a persistence of excitation condition is shown to guarantee convergence of the critic to the actual optimal value function novel tuning algorithms are given for both critic and actor networks with extra nonstandard terms in the actor tuning law being required to guarantee closed loop dynamical stability the convergence to the optimal controller is proven and the stability of the system is also guaranteed simulation examples show the effectiveness of the new algorithm

multi player non zero sum games online adaptive learning solution of coupled hamilton jacobi equations in this paper we present an online adaptive control algorithm based on policy iteration reinforcement learning techniques to solve the continuous time ct multi player non zero sum nzs game with infinite horizon for linear and nonlinear systems nzs games allow for players to have a cooperative team component and an individual selfish component of strategy the adaptive algorithm learns online the solution of coupled riccati equations and coupled hamilton jacobi equations for linear and nonlinear systems respectively this adaptive control method finds in real time approximations of the optimal value and the nzs nash equilibrium while also guaranteeing closed loop stability the optimal adaptive algorithm is implemented as a separate actor critic parametric network approximator structure for every player and involves simultaneous continuous time adaptation of the actor critic networks a persistence of excitation condition is shown to guarantee convergence of every critic to the actual optimal value function for that player a detailed mathematical analysis is done for 2 player nzs games novel tuning algorithms are given for the actor critic networks the convergence to the nash equilibrium is proven and stability of the system is also guaranteed this provides optimal adaptive control solutions for both non zero sum games and their special case the zero sum games simulation examples show the effectiveness of the new algorithm

successive galerkin approximation algorithms for nonlinear optimal and robust control nonlinear optimal control and nonlinear h infinity control are two of the most significant paradigms in nonlinear systems theory unfortunately these problems require the solution of hamilton jacobi equations which are extremely difficult to solve in practice to make matters worse approximation techniques for these equations are inherently prone to the so called curse of dimensionality while there have been many attempts to approximate these equations solutions resulting in closed loop control with well defined stability and robustness have remained elusive this paper describes a recent breakthrough in approximating the hamilton jacobi bellman and hamilton jacobi isaacs equations successive approximation and galerkin approximation methods are combined to derive a novel algorithm that produces stabilizing closed loop control laws with well defined stability regions in addition we show how the structure of the algorithm can be exploited to reduce the amount of computation from exponential to po

approximate gauss newton methods for nonlinear least squares problems the gauss newton algorithm is an iterative method regularly used for solving nonlinear least squares problems it is particularly well suited to the treatment of very large scale variational data assimilation problems that arise in atmosphere and ocean forecasting the procedure consists of a sequence of linear least squares approximations to the nonlinear problem each of which is solved by an inner direct or iterative process in comparison with newton s method and its variants the algorithm is attractive because it does not require the evaluation of second order derivatives in the hessian of the objective function in practice the exact gauss newton method is too expensive to apply operationally in meteorological forecasting and various approximations are made in order to reduce computational costs and to solve the problems in real time here we investigate the effects on the convergence of the gauss newton method of two types of approximation used commonly in data assimilation first we examine truncated gauss newton methods where the inner linear least squares problem is not solved exactly and second we examine perturbed gauss newton methods where the true linearized inner problem is approximated by a simplified or perturbed linear least squares problem we give conditions ensuring that the truncated and perturbed gauss newton methods converge and also derive rates of convergence for the iterations the results are illustrated by a simple numerical example a practical application to the problem of data assimilation in a typical meteorological system is presented

on a one dimensional system associated with a gl m mod n vertex model a one dimensional 1d system associated with a gl m mod n vertex model is investigated the author adds a chemical potential term so that the model reduces to the supersymmetric t j model for m n 2 1 it is conjectured that the ground state of the model possesses su m symmetry in the rational limit the observation by kawakami and yang on the t j model is extended to a more general theorem of the 1d field theory the t j model is just an example of the present model and such systems can be described by a multi component gaussian model compactified on tori with different radii

online optimal control of affine nonlinear discrete time systems with unknown internal dynamics by using time based policy update in this paper the hamilton jacobi bellman equation is solved forward in time for the optimal control of a class of general affine nonlinear discrete time systems without using value and policy iterations the proposed approach referred to as adaptive dynamic programming uses two neural networks nns to solve the infinite horizon optimal regulation control of affine nonlinear discrete time systems in the presence of unknown internal dynamics and a known control coefficient matrix one nn approximates the cost function and is referred to as the critic nn while the second nn generates the control input and is referred to as the action nn the cost function and policy are updated once at the sampling instant and thus the proposed approach can be referred to as time based adp novel update laws for tuning the unknown weights of the nns online are derived lyapunov techniques are used to show that all signals are uniformly ultimately bounded and that the approximated control signal approaches the optimal control input with small bounded error over time in the absence of disturbances an optimal control is demonstrated simulation results are included to show the effectiveness of the approach the end result is the systematic design of an optimal controller with guaranteed convergence that is suitable for hardware implementation

iterative adaptive dynamic programming for solving unknown nonlinear zero sum game based on online data h infty control is a powerful method to solve the disturbance attenuation problems that occur in some control systems the design of such controllers relies on solving the zero sum game zsg but in practical applications the exact dynamics is mostly unknown identification of dynamics also produces errors that are detrimental to the control performance to overcome this problem an iterative adaptive dynamic programming algorithm is proposed in this paper to solve the continuous time unknown nonlinear zsg with only online data a model free approach to the hamilton jacobi isaacs equation is developed based on the policy iteration method control and disturbance policies and value are approximated by neural networks nns under the critic actor disturber structure the nn weights are solved by the least squares method according to the theoretical analysis our algorithm is equivalent to a gauss newton method solving an optimization problem and it converges uniformly to the optimal solution the online data can also be used repeatedly which is highly efficient simulation results demonstrate its feasibility to solve the unknown nonlinear zsg when compared with other algorithms it saves a significant amount of online measurement time

policy iterations on the hamilton jacobi isaacs equation for h_ infty state feedback control with input saturation an hinfin suboptimal state feedback controller for constrained input systems is derived using the hamilton jacobi isaacs hji equation of a corresponding zero sum game that uses a special quasi norm to encode the constraints on the input the unique saddle point in feedback strategy form is derived using policy iterations on both players the hji equation is broken into a sequence of differential equations linear in the cost for which closed form solutions are easier to obtain policy iterations on the disturbance are shown to converge to the available storage function of the associated l2 gain dissipative dynamics the resulting constrained optimal control feedback strategy has the largest domain of validity within which l2 performance for a given gamma is guaranteed

the yang baxter equation and invariants of links on considere le fait que l on peut construire des invariants d isotopie p et f pour des liens en utilisant certaines solutions des equations de yang baxter

an integrable sl 2 1 vertex model for the spin quantum hall critical point an integrable vertex model associated to the lie superalgebra sl 2 1 is constructed for the description of the spin quantum hall critical phase the model involves r matrix solutions of the yang baxter equation with respect to both the vector representation of sl 2 1 and its dual and an inhomogenity in the spectral parameters on the torus the model can be mapped onto a chalker coddington type network model

neurodynamic programming and zero sum games for constrained control systems in this paper neural networks are used along with two player policy iterations to solve for the feedback strategies of a continuous time zero sum game that appears in l2 gain optimal control suboptimal hinfin control of nonlinear systems affine in input with the control policy having saturation constraints the result is a closed form representation on a prescribed compact set chosen a priori of the feedback strategies and the value function that solves the associated hamilton jacobi isaacs hji equation the closed loop stability l2 gain disturbance attenuation of the neural network saturated control feedback strategy and uniform convergence results are proven finally this approach is applied to the rotational translational actuator rtac nonlinear benchmark problem under actuator saturation offering guaranteed stability and disturbance attenuation

synchronous correlation matrices and connes embedding conjecture in the work of paulsen et al j funct anal in press preprint arxiv 1407 6918 the concept of synchronous quantum correlation matrices was introduced and these were shown to correspond to traces on certain c algebras in particular synchronous correlation matrices arose in their study of various versions of quantum chromatic numbers of graphs and other quantum versions of graph theoretic parameters in this paper we develop these ideas further focusing on the relations between synchronous correlation matrices and microstates we prove that connes embedding conjecture is equivalent to the equality of two families of synchronous quantum correlation matrices we prove that if connes embedding conjecture has a positive answer then the tracial rank and projective rank are equal for every graph we then apply these results to more general non local games

super yangian double dy gl 1 1 and its gauss decomposition we extend the yangian double to the super or graded case and give its drinfel d generators a realization by gauss decomposition

quantum superalgebras at roots of unity and non abelian symmetries of integrable models we consider integrable vertex models whose boltzmann weights r matrices are trigonometric solutions to the graded yang baxter equation as is well known the latter can be generically constructed from quantum affine superalgebras uq these algebras do not form a symmetry algebra of the model for generic values of the deformation parameter q when periodic boundary conditions are imposed if q is evaluated at a root of unity we demonstrate that in certain commensurate sectors one can construct non abelian subalgebras which are translation invariant and commute with the transfer matrix and therefore with all charges of the model in the line of argument we introduce the restricted quantum superalgebra uresq and investigate its root of unity limit we prove several new formulae involving supercommutators of arbitrary powers of the chevalley serre generators and derive higher order quantum serre relations as well as an analogue of lustzig s quantum frobenius theorem for superalgebras

policy iteration adaptive dynamic programming algorithm for discrete time nonlinear systems this paper is concerned with a new discrete time policy iteration adaptive dynamic programming adp method for solving the infinite horizon optimal control problem of nonlinear systems the idea is to use an iterative adp technique to obtain the iterative control law which optimizes the iterative performance index function the main contribution of this paper is to analyze the convergence and stability properties of policy iteration method for discrete time nonlinear systems for the first time it shows that the iterative performance index function is nonincreasingly convergent to the optimal solution of the hamilton jacobi bellman equation it is also proven that any of the iterative control laws can stabilize the nonlinear systems neural networks are used to approximate the performance index function and compute the optimal control law respectively for facilitating the implementation of the iterative adp algorithm where the convergence of the weight matrices is analyzed finally the numerical results and analysis are presented to illustrate the performance of the developed method

two parametric solution to graded yang baxter equation and two parametric uuvgl 1 mod 1 algebra as a hopf algebra the authors discuss a two parametric solution of the graded yang baxter equation ybe and perform the yang baxterization to obtain the solution to the quantum ybe in the formalism developed previously they present the two parametric quantized superalgebra uuvgl 1 mod 1 and prove that this algebra is a hopf algebra with the hopf operations explicitly provided