second order and moderate deviations asymptotics for successive refinement we derive the optimal second order coding region and moderate deviations constant for successive refinement source coding with a joint excess distortion probability constraint we consider two scenarios 1 a discrete memoryless source dms and arbitrary distortion measures at the decoders and 2 a gaussian memoryless source gms and quadratic distortion measures at the decoders for a dms with arbitrary distortion measures we prove an achievable second order coding region using type covering lemmas by kanlis and narayan and by no ingber and weissman we prove the converse using the perturbation approach by gu and effros when the dms is successively refinable the expressions for the second order coding region and the moderate deviations constant are simplified and easily computable for this case we also obtain new insights on the second order behavior compared with the scenario where separate excess distortion proabilities are considered for example we describe a dms for which the optimal second order region transitions from being characterizable by a bivariate gaussian to a univariate gaussian as the distortion levels are varied we then consider a gms with quadratic distortion measures to prove the direct part we make use of the sphere covering theorem by verger gaugry together with appropriately defined gaussian type classes to prove the converse we generalize kostina and verdu s one shot converse bound for point to point lossy source coding we remark that this proof is applicable to general successively refinable sources in the proofs of the moderate deviations results for both scenarios we follow a strategy similar to that for the second order asymptotics and use the moderate deviations principle

asymmetric evaluations of erasure and undetected error probabilities the problem of channel coding with the erasure option is revisited for discrete memoryless channels the interplay between the code rate the undetected and total error probabilities is characterized using the information spectrum method a sequence of codes of increasing blocklengths n is designed to illustrate this tradeoff furthermore for additive discrete memoryless channels with uniform input distribution we establish that our analysis is tight with respect to the ensemble average this is done by analyzing the ensemble performance in terms of a tradeoff between the code rate the undetected and total errors this tradeoff is parameterized by the threshold in a generalized likelihood ratio test two asymptotic regimes are studied first the code rate tends to the capacity of the channel at a rate slower than n 1 2 corresponding to the moderate deviations regime in this case both error probabilities decay subexponentially and asymmetrically the precise decay rates are characterized second the code rate tends to capacity at a rate of n 1 2 in this case the total error probability is asymptotically a positive constant while the undetected error probability decays as exp bn 1 2 for some b 0 the proof techniques involve the applications of a modified or shifted version of the gartner ellis theorem and the type class enumerator method to characterize the asymptotic behavior of a sequence of cumulant generating functions

on the order of approximation in approximative triadic decompositions of tensors abstract based on alder s 1984 result on the equivalence of algebraic and topological border rank of tensors over algebraically closed ground fields we give an upper bound for the order of approximation in approximative triadic decompositions we also treat the analogous question for real closed fields in particular we carry over alder s result to the case of real closed fields

asymptotic optimal control of uncertain nonlinear euler lagrange systems a sufficient condition to solve an optimal control problem is to solve the hamilton jacobi bellman hjb equation however finding a value function that satisfies the hjb equation for a nonlinear system is challenging for an optimal control problem when a cost function is provided a priori previous efforts have utilized feedback linearization methods which assume exact model knowledge or have developed neural network nn approximations of the hjb value function the result in this paper uses the implicit learning capabilities of the rise control structure to learn the dynamics asymptotically specifically a lyapunov stability analysis is performed to show that the rise feedback term asymptotically identifies the unknown dynamics yielding semi global asymptotic tracking in addition it is shown that the system converges to a state space system that has a quadratic performance index which has been optimized by an additional control element an extension is included to illustrate how a nn can be combined with the previous results experimental results are given to demonstrate the proposed controllers

minimum expected length of fixed to variable lossless compression without prefix constraints the minimum expected length for fixed to variable length encoding of an n block memoryless source with entropy h grows as nh o 1 where the term o 1 lies between 0 and 1 however this well known performance is obtained under the implicit constraint that the code assigned to the whole n block is a prefix code dropping the prefix constraint which is rarely necessary at the block level we show that the minimum expected length for a finite alphabet memoryless source with known distribution grows as nh 1 2 log n o 1 unless the source is equiprobable we also refine this result up to o 1 for those memoryless sources whose log probabilities do not reside on a lattice

nonasymptotic noisy lossy source coding this paper shows new general nonasymptotic achievability and converse bounds and performs their dispersion analysis for the lossy compression problem in which the compressor observes the source through a noisy channel while this problem is asymptotically equivalent to a noiseless lossy source coding problem with a modified distortion function nonasymptotically there is a noticeable gap in how fast their minimum achievable coding rates approach the common rate distortion function as evidenced both by the refined asymptotic analysis dispersion and the numerical results the size of the gap between the dispersions of the noisy problem and the asymptotically equivalent noiseless problem depends on the stochastic variability of the channel through which the compressor observes the source

refined asymptotics for rate distortion using gaussian codebooks for arbitrary sources the rate distortion saddle point problem considered by lapidoth 1997 consists in finding the minimum rate to compress an arbitrary ergodic source when one is constrained to use a random gaussian codebook and minimum euclidean distance encoding is employed we extend lapidoth s analysis in several directions in this paper first we consider refined asymptotics in particular when the source is stationary and memoryless we establish the second order moderate and large deviation asymptotics of the problem second by random gaussian codebook lapidoth referred to a collection of random codewords each of which is drawn independently and uniformly from the surface of an n dimensional sphere to be more precise we term this as a spherical codebook we also consider i i d gaussian codebooks in which each random codeword is drawn independently from a product gaussian distribution we derive the second order moderate and large deviation asymptotics when i i d gaussian codebooks are employed in contrast to the recent work on the channel coding counterpart by scarlett tan and durisi 2017 the dispersions for spherical and i i d gaussian codebooks are identical the ensemble excess distortion exponents for both spherical and i i d gaussian codebooks are established for all rates furthermore we show that the i i d gaussian codebook has a strictly larger excess distortion exponent than its spherical counterpart for any rate greater than the ensemble rate distortion function derived by lapidoth

asymptotic entanglement transformation between w and ghz states we investigate entanglement transformations with stochastic local operations and classical communication in an asymptotic setting using the concepts of degeneration and border rank of tensors from algebraic complexity theory results well known in that field imply that ghz states can be transformed into w states at rate 1 for any number of parties as a generalization we find that the asymptotic conversion rate from ghz states to dicke states is bounded as the number of subsystems increases and the number of excitations is fixed by generalizing constructions of coppersmith and winograd and by using monotones introduced by strassen we also compute the conversion rate from w to ghz states

nonasymptotic and second order achievability bounds for coding with side information we present a novel nonasymptotic or finite blocklength achievability bounds for three side information problems in network information theory these include 1 the wyner ahlswede korner wak problem of almost lossless source coding with rate limited side information 2 the wyner ziv wz problem of lossy source coding with side information at the decoder and 3 the gel fand pinsker gp problem of channel coding with noncausal state information available at the encoder the bounds are proved using ideas from channel simulation and channel resolvability our bounds for all three problems improve on all previous nonasymptotic bounds on the error probability of the wak wz and gp problems in particular those derived by verdu using our novel nonasymptotic bounds we recover the general formulas for the optimal rates of these side information problems finally we also present achievable second order coding rates by applying the multidimensional berry esseen theorem to our new nonasymptotic bounds numerical results show that the second order coding rates obtained using our nonasymptotic achievability bounds are superior to those obtained using existing finite blocklength bounds

bayesian m ary hypothesis testing the meta converse and verdu han bounds are tight two alternative exact characterizations of the minimum error probability of bayesian m ary hypothesis testing are derived the first expression corresponds to the error probability of an induced binary hypothesis test and implies the tightness of the meta converse bound by polyanskiy et al the second expression is a function of an information spectrum measure and implies the tightness of a generalized verdu han lower bound the formulas characterize the minimum error probability of several problems in information theory and help to identify the steps where existing converse bounds are loose

the ziv zakai renyi bound for joint source channel coding shannon s capacity and rate distortion function combined with the separation principle provide tight bounds for the minimum possible distortion in joint source channel coding these bounds however are usually achievable only in the limit of a large block length in their 1973 paper ziv and zakai introduced a family of alternative capacity and rate distortion functions based on functionals satisfying the data processing inequality which potentially give tighter bounds for systems with a small block length there is a considerable freedom as to how to choose those functionals and the ways of finding the best possible functionals yielding the best bounds for a given source channel combination are not specified we examine recently conjectured high snr asymptotic expressions for the ziv zakai bounds based on the renyi divergence functional we derive nonasymptotic bounds on the ziv zakai renyi rate distortion function and capacity for a broad class of sources and additive noise channels which hold for arbitrary snr and prove the conjectured asymptotic expressions in the limit of a small distortion high snr the results lead to new bounds on the best achievable distortion in finite dimensional joint source channel coding examples are presented where the new bounds achieve significant improvement upon shannon s original bounds

adaptive tracking control of uncertain mimo nonlinear systems with input constraints in this paper adaptive tracking control is proposed for a class of uncertain multi input and multi output nonlinear systems with non symmetric input constraints the auxiliary design system is introduced to analyze the effect of input constraints and its states are used to adaptive tracking control design the spectral radius of the control coefficient matrix is used to relax the nonsingular assumption of the control coefficient matrix subsequently the constrained adaptive control is presented where command filters are adopted to implement the emulate of actuator physical constraints on the control law and virtual control laws and avoid the tedious analytic computations of time derivatives of virtual control laws in the backstepping procedure under the proposed control techniques the closed loop semi global uniformly ultimate bounded stability is achieved via lyapunov synthesis finally simulation studies are presented to illustrate the effectiveness of the proposed adaptive tracking control

a note on the gap between rank and border rank we study the tensor rank of the tensor corresponding to the algebra of n variate complex polynomials modulo the dth power of each variable as a result we find a sequence of tensors with a large gap between rank and border rank and thus a counterexample to a conjecture of rhodes at the same time we obtain a new lower bound on the tensor rank of tensor powers of the generalised w state tensor in addition we exactly determine the tensor rank of the tensor cube of the three party w state tensor thus answering a question of chen et al

brief paper inverse optimal stabilization for stochastic nonlinear systems whose linearizations are not stabilizable after considering the stabilization of a class of high order stochastic nonlinear systems which are neither necessarily feedback linearizable nor affine in the control input in this brief paper we further address the problem of state feedback inverse optimal stabilization in probability i e our redesigned stabilizing backstepping controller is also optimal with respect to meaningful cost functionals

nonlinear h sub spl infin control and its application to rigid spacecraft the problem of h sub spl infin control of a rigid spacecraft with three control torques and disturbances is addressed the hamilton jacobi isaacs inequality for h sub spl infin feedback design is solved an h sub spl infin suboptimal feedback is given and the stability properties of the closed loop system are studied

strong converses in source coding relative to a fidelity criterion two strong converses are obtained for an abstract alphabet stationary ergodic source coded relative to an appropriate fidelity criterion it is shown that given a distortion rate point d r that lies below the rate distortion curve 1 block codes that operate at rate level r must encode sample source blocks at a rate exceeding d with probability tending to one as the block length tends to infinity and 2 variable rate codes that operate at distortion level d must encode sample source blocks at a rate exceeding r with probability tending to one as the block length tends to infinity the previously known weak converses guarantee only that the indicated probabilities remain bounded away from zero as block length tends to infinity the proofs of the strong converses involve sample converses in source coding theory

lossy compression via sparse linear regression computationally efficient encoding and decoding we propose computationally efficient encoders and decoders for lossy compression using a sparse regression code the codebook is defined by a design matrix and codewords are structured linear combinations of columns of this matrix the proposed encoding algorithm sequentially chooses columns of the design matrix to successively approximate the source sequence it is shown to achieve the optimal distortion rate function for independent identically distributed i i d gaussian sources under the squared error distortion criterion for a given rate the parameters of the design matrix can be varied to tradeoff distortion performance with encoding complexity an example of such a tradeoff as a function of the block length n is the following with computational resource space or time per source sample of o n log n 2 for a fixed distortion level above the gaussian distortion rate function the probability of excess distortion decays exponentially in n the sparse regression code is robust in the following sense for any ergodic source the proposed encoder achieves the optimal distortion rate function of an i i d gaussian source with the same variance simulations show that the encoder has good empirical performance especially at low and moderate rates

l sub 2 gain analysis of nonlinear systems and nonlinear state feedback h sub infinity control previously obtained results on l2 gain analysis of smooth nonlinear systems are unified and extended using an approach based on hamilton jacobi equations and inequalities and their relation to invariant manifolds of an associated hamiltonian vector field on the basis of these results a nonlinear analog is obtained of the simplest part of a state space approach to linear h sub infinity control namely the state feedback h sub infinity optimal control problem furthermore the relation with h sub infinity control of the linearized system is dealt with

rateless lossy compression via the extremes we begin by presenting a simple lossy compressor operating at near zero rate the encoder merely describes the indices of the few maximal source components while the decoder s reconstruction is a natural estimate of the source components based on this information this scheme turns out to be near optimal for the memoryless gaussian source in the sense of achieving the zero rate slope of its distortion rate function motivated by this finding we then propose a scheme comprised of iterating the above lossy compressor on an appropriately transformed version of the difference between the source and its reconstruction from the previous iteration the proposed scheme achieves the rate distortion function of the gaussian memoryless source under squared error distortion when employed on any finite variance ergodic source it further possesses desirable properties and we respectively refer to as infinitesimal successive refinability ratelessness and complete separability its storage and computation requirements are of order no more than n 2 log beta n per source symbol for beta 0 at both the encoder and the decoder though the details of its derivation construction and analysis differ considerably we discuss similarities between the proposed scheme and the recently introduced sparse regression codes of venkataramanan et al

pointwise redundancy in lossy data compression and universal lossy data compression we characterize the achievable pointwise redundancy rates for lossy data compression at a fixed distortion level pointwise redundancy refers to the difference between the description length achieved by an nth order block code and the optimal nr d bits for memoryless sources we show that the best achievable redundancy rate is of order o spl radic n in probability this follows from a second order refinement to the classical source coding theorem in the form of a one sided central limit theorem moreover we show that along almost any source realization the description lengths of any sequence of block codes operating at distortion level d exceed nr d by at least as much as c spl radic nloglogn infinitely often corresponding direct coding theorems are also given showing that these rates are essentially achievable the above rates are in sharp contrast with the expected redundancy rates of order o log n reported by various authors our approach is based on showing that the compression performance of an arbitrary sequence of codes is essentially bounded below by the performance of shannon s random code we obtain partial generalizations of the above results for arbitrary sources with memory and we prove lossy analogs of barron s lemma barron 1985

inverse optimal design of input to state stabilizing nonlinear controllers we show that input to state stabilizability as defined by sontag 1989 1995 is both necessary and sufficient for the solvability of a hamilton jacobi isaacs equation associated with a meaningful differential game problem similar to but more general than the nonlinear h sub spl infin problem the significance of the result stems from the fact that constructive solutions to the input to state stabilization problem are available presented in the paper and that as shown here inverse optimal controllers possess margins on input to state stability against a certain class of input unmodeled dynamics rather than completion of squares the main tools in our analysis are legendre fenchel transformations and the general form of young s inequality

lossy joint source channel coding in the finite blocklength regime this paper finds new tight finite blocklength bounds for the best achievable lossy joint source channel code rate and demonstrates that joint source channel code design brings considerable performance advantage over a separate one in the nonasymptotic regime a joint source channel code maps a block of k source symbols onto a length n channel codeword and the fidelity of reproduction at the receiver end is measured by the probability e that the distortion exceeds a given threshold d for memoryless sources and channels it is demonstrated that the parameters of the best joint source channel code must satisfy nc kr d nv k v d q 1 e where c and v are the channel capacity and channel dispersion respectively r d and v d are the source rate distortion and rate dispersion functions and q is the standard gaussian complementary cumulative distribution function symbol by symbol uncoded transmission is known to achieve the shannon limit when the source and channel satisfy a certain probabilistic matching condition in this paper we show that even when this condition is not satisfied symbol by symbol transmission is in some cases the best known strategy in the nonasymptotic regime

channel coding rate in the finite blocklength regime this paper investigates the maximal channel coding rate achievable at a given blocklength and error probability for general classes of channels new achievability and converse bounds are given which are tighter than existing bounds for wide ranges of parameters of interest and lead to tight approximations of the maximal achievable rate for blocklengths n as short as 100 it is also shown analytically that the maximal rate achievable with error probability isclosely approximated by c v n q 1 where c is the capacity v is a characteristic of the channel referred to as channel dispersion and q is the complementary gaussian cumulative distribution function

moderate deviations in channel coding we consider block codes whose rate converges to the channel capacity with increasing blocklength at a certain speed and examine the best possible decay of the probability of error for discrete memoryless channels we prove that a moderate deviation principle holds for all convergence rates between the large deviation and the central limit theorem regimes

variable length compression allowing errors this paper studies the fundamental limits of the minimum average length of lossless and lossy variable length compression allowing a nonzero error probability epsilon for lossless compression we give nonasymptotic bounds on the minimum average length in terms of erokhin s rate distortion function and we use those bounds to obtain a gaussian approximation on the speed of approach to the limit which is quite accurate for all but small blocklengths 1 epsilon k h mathsf s k v mathsf s 2 pi 1 2 mathop rm exp q 1 left epsilon right 2 2 where q 1 left cdot right is the functional inverse of the standard gaussian complementary cumulative distribution function and v mathsf s is the source dispersion a nonzero error probability thus not only reduces the asymptotically achievable rate by a factor of 1 epsilon but this asymptotic limit is approached from below i e larger source dispersions and shorter blocklengths are beneficial variable length lossy compression under an excess distortion constraint is shown to exhibit similar properties

phase synchronization control of complex networks of lagrangian systems on adaptive digraphs this paper presents a formation control and synchronization method that utilizes adaptive network topologies for a class of complex dynamical networks comprised of a large number of highly nonlinear euler lagrange el systems a time varying and switching network topology constructed by the adaptive graph laplacian matrix relaxes the standard requirement of consensus stability even permitting exponential synchronization on an unbalanced digraph or a weakly connected digraph that can sporadically lose connectivity the time varying graph laplacian matrix is adapted by an adaptive control scheme based on relative positions and errors of synchronization and tracking the adaptive graph laplacian is integrated with a phase synchronization controller that synchronizes the relative motions of el systems moving in elliptical orbits thereby yielding a smaller synchronization error than an uncoupled tracking control law in the presence of bounded disturbances and modeling errors an example of reconfiguring hundreds of spacecraft in low earth orbit shows the effectiveness of the proposed phase synchronization controller for a large number of complex el systems moving in periodic elliptical orbits

strong successive refinability and rate distortion complexity tradeoff we investigate the second order asymptotics source dispersion of the successive refinement problem similar to the classical definition of a successively refinable source we say that a source is strongly successively refinable if successive refinement coding can achieve the second order optimum rate including the dispersion terms at both decoders we establish a sufficient condition for strong successive refinability we show that any discrete source under hamming distortion and the gaussian source under quadratic distortion are strongly successively refinable we also demonstrate how successive refinement ideas can be used in point to point lossy compression problems in order to reduce complexity we give two examples the binary hamming and gaussian quadratic cases in which a layered code construction results in a low complexity scheme that attains optimal performance for example when the number of layers grows with the block length n we show how to design an o n log n algorithm that asymptotically achieves the rate distortion bound

a lower bound analysis of hamming distortion for a binary ceo problem with joint source channel coding a two node binary chief executive officer ceo problem is investigated noise corrupted versions of a binary sequence are forwarded by two nodes to a single destination node over orthogonal additive white gaussian noise awgn channels we first reduce the binary ceo problem to a binary multiterminal source coding problem of which an outer bound for the rate distortion region is derived the distortion function is then established by evaluating the relationship between the binary ceo and multiterminal source coding problems a lower bound approximation on the hamming distortion hd is obtained by minimizing a distortion function subject to constraints obtained based on the source channel separation theorem encoding decoding algorithms using concatenated convolutional codes and a joint decoding scheme are used to verify the lower bound on the hd it is found that the theoretical lower bounds on the hd and the computer simulation based bit error rate performance curves have the same tendencies the differences in the threshold signal to noise ratio between the theoretical lower bounds and those obtained by simulations are around 1 5 db in awgn channel the theoretical lower bound on the hd in block rayleigh fading channel is also evaluated by performing monte carlo simulation

the rate distortion function and excess distortion exponent of sparse regression codes with optimal encoding this paper studies the performance of sparse regression codes for lossy compression with the squared error distortion criterion in a sparse regression code code words are linear combinations of subsets of columns of a design matrix it is shown that with minimum distance encoding sparse regression codes achieve the shannon rate distortion function for i i d gaussian sources r d as well as the optimal excess distortion exponent this completes a previous result which showed that r d and the optimal exponent were achievable for distortions below a certain threshold the proof of the rate distortion result is based on the second moment method a popular technique to show that a non negative random variable x is strictly positive with high probability in our context x is the number of code words within target distortion d of the source sequence we first identify the reason behind the failure of the standard second moment method for certain distortions and illustrate the different failure modes via a stylized example we then use a refinement of the second moment method to show that r d is achievable for all distortion values finally the refinement technique is applied to suen s correlation inequality to prove the achievability of the optimal gaussian excess distortion exponent

coordinate independent adaptive attitude tracking control design for spacecraft robust to time varying system uncertainties abstractin this paper we consider the adaptive attitude control of spacecraft with time varying inertial properties we use a coordinate independent approach for the purpose of designing the control and estimation laws in terms of the rotation matrices representing the spacecraft body frame and reference tracking signals this method helps to overcome the difficulties regarding the attitude representation on so 3 such as ambiguities associated with quaternion representation and inherent singularities inside euler parameters we model the time variations in inertial parameters in two different ways and design adaptive control schemes for each case as the first uncertain dynamic model we consider a setting of spacecraft with multiple moving appendages and based on this model design an adaptive control scheme with three different versions where frobenious norm is used in measuring the deviation of the estimated inertia tensors from their actual values the proposed adaptive control scheme is later ex

one shot lossy quantum data compression we provide a framework for one shot quantum rate distortion coding in which the goal is to determine the minimum number of qubits required to compress quantum information as a function of the probability that the distortion incurred upon decompression exceeds some specified level we obtain a one shot characterization of the minimum qubit compression size for an entanglement assisted quantum rate distortion code in terms of the smooth max information a quantity previously employed in the one shot quantum reverse shannon theorem next we show how this characterization converges to the known expression for the entanglement assisted quantum rate distortion function for asymptotically many copies of a memoryless quantum information source finally we give a tight finite blocklength characterization for the entanglement assisted minimum qubit compression size of a memoryless isotropic qubit source subject to an average symbolwise distortion constraint

quaternion based adaptive output feedback attitude control of spacecraft using chebyshev neural networks this paper investigates the problem of output feedback attitude control of an uncertain spacecraft two robust adaptive output feedback controllers based on chebyshev neural networks cnn termed adaptive neural networks nn controller i and adaptive nn controller ii are proposed for the attitude tracking control of spacecraft the four parameter representations quaternion are employed to describe the spacecraft attitude for global representation without singularities the nonlinear reduced order observer is used to estimate the derivative of the spacecraft output and the cnn is introduced to further improve the control performance through approximating the spacecraft attitude motion the implementation of the basis functions of the cnn used in the proposed controllers depends only on the desired signals and the smooth robust compensator using the hyperbolic tangent function is employed to counteract the cnn approximation errors and external disturbances the adaptive nn controller ii can efficiently avoid the over estimation problem i e the bound of the cnns output is much larger than that of the approximated unknown function and hence the control input may be very large existing in the adaptive nn controller i both adaptive output feedback controllers using cnn can guarantee that all signals in the resulting closed loop system are uniformly ultimately bounded for performance comparisons the standard adaptive controller using the linear parameterization of spacecraft attitude motion is also developed simulation studies are presented to show the advantages of the proposed cnn based output feedback approach over the standard adaptive output feedback approach

nearest neighbor decoding for additive non gaussian noise channels we study the performance of a transmission scheme employing random gaussian codebooks and nearest neighbor decoding over a power limited additive non gaussian noise channel we show that the achievable rates depend on the noise distribution only via its power and thus coincide with the capacity region of a white gaussian noise channel with signal and noise power equal to those of the original channel the results are presented for single user channels as well as multiple access channels and are extended to fading channels with side information at the receiver

the tensor rank of tensor product of two three qubit w states is eight abstract we show that the tensor rank of tensor product of two three qubit w states is not less than eight combining this result with the recent result of m christandl a k jensen and j zuiddam that the tensor rank of tensor product of two three qubit w states is at most eight we deduce that the tensor rank of tensor product of two three qubit w states is eight we also construct the upper bound of the tensor rank of tensor product of many three qubit w states

model free optimal tracking control via critic only q learning model free control is an important and promising topic in control fields which has attracted extensive attention in the past few years in this paper we aim to solve the model free optimal tracking control problem of nonaffine nonlinear discrete time systems a critic only q learning coql method is developed which learns the optimal tracking control from real system data and thus avoids solving the tracking hamilton jacobi bellman equation first the q learning algorithm is proposed based on the augmented system and its convergence is established using only one neural network for approximating the q function the coql method is developed to implement the q learning algorithm furthermore the convergence of the coql method is proved with the consideration of neural network approximation error with the convergent q function obtained from the coql method the adaptive optimal tracking control is designed based on the gradient descent scheme finally the effectiveness of the developed coql method is demonstrated through simulation studies the developed coql method learns with off policy data and implements with a critic only structure thus it is easy to realize and overcome the inadequate exploration problem

fixed length lossy compression in the finite blocklength regime this paper studies the minimum achievable source coding rate as a function of blocklength n and probability that the distortion exceeds a given level d tight general achievability and converse bounds are derived that hold at arbitrary fixed blocklength for stationary memoryless sources with separable distortion the minimum rate achievable is shown to be closely approximated by r d v d n q 1 where r d is the rate distortion function v d is the rate dispersion a characteristic of the source which measures its stochastic variability and q 1 is the inverse of the standard gaussian complementary cumulative distribution function

rigid body attitude stabilization with attitude and angular rate constraints abstract in this paper a solution to the problem of rest to rest three axis attitude reorientation of a fully actuated rigid body under multiple attitude constraint zones and angular velocity limits is presented based on the unit quaternion parameterized attitude constrained zones a quadratic potential function is developed with a global minimum locating at the desired attitude and high potential closing to the constrained zones in addition to limit the magnitude of the angular velocity another logarithmic potential function is also designed using these two potential functions and sliding mode control technique a nonlinear attitude control law is obtained to guarantee asymptotic convergence of the closed loop system with consideration of attitude and angular rate constraints and external disturbances the effectiveness of the constrained attitude control method is demonstrated through numerical simulation

equivocations exponents and second order coding rates under various renyi information measures we evaluate the asymptotics of equivocations their exponents as well as their second order coding rates under various renyi information measures specifically we consider the effect of applying a hash function on a source and we quantify the level of non uniformity and dependence of the compressed source from another correlated source when the number of copies of the sources is large unlike previous works that use shannon information measures to quantify randomness information or uniformity we define our security measures in terms of a more general class of information measures the renyi information measures and their gallager type counterparts a special case of these renyi information measure is the class of shannon information measures we prove tight asymptotic results for the security measures and their exponential rates of decay we also prove bounds on the second order asymptotics and show that these bounds match when the magnitudes of the second order coding rates are large we do so by establishing new classes non asymptotic bounds on the equivocation and evaluating these bounds using various probabilistic limit theorems asymptotically

passivity based adaptive attitude control of a rigid spacecraft an adaptive control scheme for the attitude control of a rigid spacecraft is derived using a linear parameterization of the equation of motion the tracking error is described with the euler parameter vector global convergence of the tracking error to zero is shown using passivity theory this allows for the use of time varying positive definite feedback gain matrices and the results can easily be extended to other passive parameter update laws

inverse optimal adaptive control for attitude tracking of spacecraft the attitude tracking control problem of a rigid spacecraft with external disturbances and an uncertain inertia matrix is addressed using the adaptive control method the adaptive control laws proposed in this paper are optimal with respect to a family of cost functionals this is achieved by the inverse optimality approach without solving the associated hamilton jacobi isaacs partial differential hjipd equation directly the design of the optimal adaptive controllers is separated into two stages by means of integrator backstepping and a control lyapunov argument is constructed to show that the inverse optimal adaptive controllers achieve h sub spl infin disturbance attenuation with respect to external disturbances and global asymptotic convergence of tracking errors to zero for disturbances with bounded energy the convergence of adaptive parameters is also analyzed in terms of invariant manifold numerical simulations illustrate the performance of the proposed control algorithms

optimal zero delay coding of markov sources stationary and finite memory codes the optimal zero delay coding of a finite state markov source is considered the existence and structure of optimal codes are studied using a stochastic control formulation prior results in the literature established the optimality of deterministic markov walrand varaiya type coding policies for the finite time horizon problem and the optimality of both deterministic nonstationary and randomized stationary policies for the infinite time horizon problem our main result here shows that for any irreducible and aperiodic markov source with a finite alphabet deterministic and stationary markov coding policies are optimal for the infinite horizon problem in addition the finite block length time horizon performance of an optimal stationary and markov coding policy is shown to approach the infinite time horizon optimum at a rate o 1 t the results are extended to systems where zero delay communication takes place across a noisy channel with noiseless feedback

linear programming based converses for finite blocklength lossy joint source channel coding a linear programming lp based framework is presented for obtaining converses for finite blocklength lossy joint source channel coding problems the framework applies for any loss criterion generalizes certain previously known converses and also extends to multi terminal settings the finite blocklength problem is posed equivalently as a nonconvex optimization problem and using a lift and project like method a close but tractable lp relaxation of this problem is derived lower bounds on the original problem are obtained by the construction of feasible points for the dual of the lp relaxation a particular application of this approach leads to new converses which recover and improve on the converses of kostina and verdu for finite blocklength lossy joint source channel coding and lossy source coding for finite blocklength channel coding the lp relaxation recovers the converse of polyanskiy poor and verdu and leads to a new improvement on the converse of wolfowitz showing thereby that our lp relaxation is asymptotically tight with increasing blocklengths for channel coding lossless source coding and joint source channel coding with the excess distortion probability as the loss criterion using a duality based argument a new converse is derived for finite blocklength joint source channel coding for a class of source channel pairs employing this converse the lp relaxation is also shown to be tight for all blocklengths for the minimization of the expected average symbolwise hamming distortion of a q ary uniform source over a q ary symmetric memoryless channel for any q in mathbb n the optimization formulation and the lift and project method are extended to networked settings and demonstrated by obtaining an improvement on a converse of zhou et al for the successive refinement problem for successively refinable source distortion measure triplets

the dispersion of nearest neighbor decoding for additive non gaussian channels we study the second order asymptotics of information transmission using random gaussian codebooks and nearest neighbor decoding over a power limited stationary memoryless additive non gaussian noise channel we show that the dispersion term depends on the non gaussian noise only through its second and fourth moments thus complementing the capacity result lapidoth 1996 which depends only on the second moment furthermore we characterize the second order asymptotics of point to point codes over k sender interference networks with non gaussian additive noise specifically we assume that each user s codebook is gaussian and that nn decoding is employed i e that interference from the k 1 unintended users gaussian interfering signals is treated as noise at each decoder we show that while the first order term in the asymptotic expansion of the maximum number of messages depends on the power of the interfering codewords only through their sum this does not hold for the second order term

non asymptotic converse bounds and refined asymptotics for two source coding problems in this paper we revisit two multi terminal lossy source coding problems the lossy source coding problem with side information available at the encoder and one of the two decoders which we term as the kaspi problem kaspi 1994 and the multiple description coding problem with one semi deterministic distortion measure which we refer to as the fu yeung problem fu and yeung 2002 for the kaspi problem we first present the properties of optimal test channels subsequently we generalize the notion of the distortion tilted information density for the lossy source coding problem to the kaspi problem and prove a non asymptotic converse bound using the properties of optimal test channels and the well defined distortion tilted information density finally for discrete memoryless sources we derive refined asymptotics which includes the second order large and moderate deviations asymptotics in the converse proof of second order asymptotics we apply the berry esseen theorem to the derived non asymptotic converse bound the achievability proof follows by first proving a type covering lemma tailored to the kaspi problem then properly taylor expanding the well defined distortion tilted information densities and finally applying the berry esseen theorem we then generalize the methods used in the kaspi problem to the fu yeung problem as a result we obtain the properties of optimal test channels for the minimum sum rate function a non asymptotic converse bound and refined asymptotics for discrete memoryless sources since the successive refinement problem is a special case of the fu yeung problem as a by product we obtain a non asymptotic converse bound for the successive refinement problem which is a strict generalization of the non asymptotic converse bound for successively refinable sources zhou tan and motani 2017

on the redundancy of lossy source coding with abstract alphabets the redundancy problem of lossy source coding with abstract source and reproduction alphabets is considered for coding at a fixed rate level it is shown that for any fixed rate r 0 and any memoryless abstract alphabet source p satisfying some mild conditions there exists a sequence c sub n sub n 1 sup spl infin of block codes at the rate r such that the distortion redundancy of c sub n defined as the difference between the performance of c sub n and the distortion rate function d p r of p is upper bounded by spl part d p r spl part r ln n 2n o ln n n for coding at a fixed distortion level it is demonstrated that for any d 0 and any memoryless abstract alphabet source p satisfying some mild conditions there exists a sequence c sub n sub n 1 sup spl infin of block codes at the fixed distortion d such that the rate redundancy of c sub n defined as the difference between the performance of c sub n and the rate distortion function r p d of p is upper bounded by 7ln n 6n o ln n n these results strengthen the traditional berger s 1968 1971 abstract alphabet source coding theorem and extend the positive redundancy results of zhang yang and wei see ibid vol 43 no 1 p 71 91 1997 and ibid vol 42 p 803 21 1996 on lossy source coding with finite alphabets and the redundancy result of wyner see ibid vol 43 p 1452 64 1997 on block coding of memoryless gaussian sources

on finite block length quantization distortion we investigate the upper and lower bounds on the quantization distortions for independent and identically distributed continuous sources in the finite block length regime we derive a lower bound on the quantization distortion as well as an upper bound on the quantization distortion based on random quantization codebooks moreover we apply the obtained bounds to the continuous gaussian source for the gaussian source we propose a computationally tractable method to numerically compute the upper and lower bounds for both bounded and unbounded quantization codebooks numerical results show that the gap between the upper and lower bounds is small for the block length of several hundreds and the upper and lower bounds are tighter than those proposed in the existing works

sample converses in source coding theory the rate and distortion performance of a sequence of codes along a sample sequence of symbols generated by a stationary ergodic information source are studied two results are obtained 1 the source sample sequence is encoded by an arbitrary sequence of block codes which operate at a fixed rate level r and a sample converse is obtained which states that with probability one the lower limit of the code sample distortions is lower bounded by d r the value of the distortion rate function at r 2 the source sample sequence is encoded by an arbitrary sequence of variable rate codes which operate at a fixed distortion level d and a sample converse is obtained which states that with probability one the lower limit of the code sample rates is lower bounded by r d the value of the rate distortion function at d a novel ergodic theorem is used to obtain both sample converses

critical behavior in lossy source coding the following critical phenomenon was recently discovered when a memoryless source is compressed using a variable length fixed distortion code the fastest convergence rate of the pointwise compression ratio to r d is either o spl radic n or o log n we show it is always o spl radic n except for discrete uniformly distributed sources

tensor rank is not multiplicative under the tensor product the tensor rank of a tensor t is the smallest number r such that t can be decomposed as a sum of r simple tensors let s be a k tensor and let t be an l tensor the tensor product of s and t is a k l tensor tensor rank is sub multiplicative under the tensor product we revisit the connection between restrictions and degenerations a result of our study is that tensor rank is not in general multiplicative under the tensor product this answers a question of draisma and saptharishi specifically if a tensor t has border rank strictly smaller than its rank then the tensor rank of t is not multiplicative under taking a sufficiently hight tensor product power the tensor kronecker product from algebraic complexity theory is related to our tensor product but different namely it multiplies two k tensors to get a k tensor nonmultiplicativity of the tensor kronecker product has been known since the work of strassen it remains an open question whether border rank and asymptotic rank are multiplicative under the tensor product interestingly lower bounds on border rank obtained from generalized flattenings including young flattenings multiply under the tensor product

inverse optimal stabilization of a rigid spacecraft the authors present an approach for constructing optimal feedback control laws for regulation of a rotating rigid spacecraft they employ the inverse optimal control approach which circumvents the task of solving a hamilton jacobi equation and results in a controller optimal with respect to a meaningful cost functional the inverse optimality approach requires the knowledge of a control lyapunov function and a stabilizing control law of a particular form for the spacecraft problem they are both constructed using the method of integrator backstepping the authors give a characterization of nonlinear stability margins achieved with the inverse optimal control law

second order asymptotics in fixed length source coding and intrinsic randomness there is a difference between the optimal rates of fixed length source coding and intrinsic randomness when we care about the second order asymptotics we prove this difference for general information sources and then investigate independent and identically distributed i i d random variables and markovian variables as examples the difference is demonstrated through an investigation of the second order asymptotic behavior of the rates a universal fixed length source code attaining the second order optimal rate is also proposed the difference between the rates of fixed length source coding and intrinsic randomness proves that the outputs of fixed length source codes are not uniformly distributed

joint source channel coding with feedback this paper quantifies the fundamental limits of variable length transmission of a general possibly analog source over a memoryless channel with noiseless feedback under a distortion constraint we consider excess distortion average distortion and guaranteed distortion d semifaithful codes in contrast to the asymptotic fundamental limit a general conclusion is that allowing variable length codes and feedback leads to a sizable improvement in the fundamental delay distortion tradeoff in addition we investigate the minimum energy required to reproduce k source samples with a given fidelity after transmission over a memoryless gaussian channel and we show that the required minimum energy is reduced with feedback and an average rather than maximal power constraint

state feedback spl hscr sub spl infin suboptimal control of a rigid spacecraft a state feedback spl hscr sub spl infin suboptimal control problem on tso 3 for a rigid spacecraft with three control torques and disturbances is addressed the hamilton jacobi inequality associated with a corresponding state feedback spl hscr sub spl infin suboptimal control problem on ts sup 3 is solved globally the spl hscr sub spl infin suboptimal state feedback on ts sup 3 involves the euler parameters and solves the original problem on tso 3 when the initial values of the euler parameters are appropriately chosen

the attitude control problem a general framework for the analysis of the attitude tracking control problem for a rigid body is presented a large family of globally stable control laws is obtained by using the globally nonsingular unit quaternion representation in a lyapunov function candidate whose form is motivated by the consideration of the total energy of the rigid body the controllers share the common structure of a proportional derivative feedback plus some feedforward which can be zero the model independent case the coriolis torque compensation or an adaptive compensation these controller structures are compared in terms of the requirement on the a priori model information guaranteed transient performance and robustness the global stability of the luh walker paul robot end effector controller is also analyzed in this framework

the redundancy of source coding with a fidelity criterion 1 known statistics the problem of redundancy of source coding with respect to a fidelity criterion is considered for any fixed rate r 0 and any memoryless source with finite source and reproduction alphabets and a common distribution p the nth order distortion redundancy d sub n r of fixed rate coding is defined as the minimum of the difference between the expected distortion per symbol of any block code with length n and rate r and the distortion rate function d p r of the source p it is demonstrated that for sufficiently large n d sub n r is equal to spl part spl part r d p r ln n 2n o ln n n where spl part spl part r d p r is the partial derivative of d p r evaluated at r and assumed to exist for any fixed distortion level d 0 and any memoryless source p the nth order rate redundancy r sub n d of coding at fixed distortion level d or by using d semifaithful codes is defined as the minimum of the difference between the expected rate per symbol of any d semifaithful code of length n and the rate distortion function r p d of p evaluated at d it is proved that for sufficiently large n r sub n d is upper bounded by ln n n o ln n n and lower bounded by in n 2n o in n n as a by product the lower bound of r sub n d derived in this paper gives a positive answer to a conjecture proposed by yu and speed 1993

a case where interference does not affect the channel dispersion in 1975 carleial presented a special case of an interference channel called the very strong interference regime in which the interference does not reduce the capacity of the constituent point to point gaussian channels in this paper we show that in the strictly very strong interference regime the dispersions are similarly unaffected more precisely in this paper we characterize the second order coding rates of the gaussian interference channel in the strictly very strong interference regime in other words we characterize the speed of convergence of rates of optimal block codes toward a boundary point of the rectangular capacity region these second order coding rates are expressed in terms of the average probability of error and variances of appropriately defined information densities which coincide with the dispersion of the single user gaussian channel this allows us to conclude that the dispersions are unaffected by interference in this channel model