arXiv subjects

Lihua Xie

Publications and source records attributed to Lihua Xie.

At least 253 records · Page 14Linked to original sources

arXiv2016

Data Rate for Distributed Consensus of Multi-agent Systems with High Order Oscillator Dynamics

Distributed consensus with data rate constraint is an important research topic of multi-agent systems. Some results have been obtained for consensus of multi-agent systems with integrator dynamics, but it remains challenging for general high-order systems, especially in the presence of unmeasurable states. In this paper, we study the quantized consensus problem for a special kind of high-order systems and investigate the corresponding data rate required for achieving consensus. The state matrix of each agent is a 2m-th order real Jordan block admitting m identical pairs of conjugate poles on the unit circle; each agent has a single input, and only the first state variable can be measured. The case of harmonic oscillators corresponding to m=1 is first investigated under a directed communication topology which contains a spanning tree, while the general case of m >= 2 is considered for a connected and undirected network. In both cases it is concluded that the sufficient number of communication bits to guarantee the consensus at an exponential convergence rate is an integer between $m$ and $2m$, depending on the location of the poles.

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arXiv2016

A Bregman Splitting Algorithm for Distributed Optimization over Networks

We consider distributed optimization problems in which a group of agents are to collaboratively seek the global optimum through peer-to-peer communication networks. The problem arises in various application areas, such as resource allocation, sensor fusion and distributed learning. We propose a general efficient distributed algorithm--termed Distributed Forward-Backward Bregman Splitting (D-FBBS)--to simultaneously solve the above primal problem as well as its dual based on Bregman method and operator splitting. The proposed algorithm allows agents to communicate asynchronously and thus lends itself to stochastic networks. This algorithm belongs to the family of general proximal point algorithms and is shown to have close connections with some existing well-known algorithms when dealing with fixed networks. However, we will show that it is generally different from the existing ones due to its effectiveness in handling stochastic networks. With proper assumptions, we establish a non-ergodic convergence rate of o(1/k) in terms of fixed point residuals over fixed networks both for D-FBBS and its inexact version (ID-FBBS) which is more computationally efficient and an ergodic convergence rate of O(1/k) for D-FBBS over stochastic networks respectively. We also apply the proposed algorithm to sensor fusion problems to show its superior performance compared to existing methods.

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arXiv2016

Continuous-Time Distributed Algorithms for Extended Monotropic Optimization Problems

This paper studies distributed algorithms for the extended monotropic optimization problem, which is a general convex optimization problem with a certain separable structure. The considered objective function is the sum of local convex functions assigned to agents in a multi-agent network, with private set constraints and affine equality constraints. Each agent only knows its local objective function, local constraint set, and neighbor information. We propose two novel continuous-time distributed subgradient-based algorithms with projected output feedback and derivative feedback, respectively, to solve the extended monotropic optimization problem. Moreover, we show that the algorithms converge to the optimal solutions under some mild conditions, by virtue of variational inequalities, Lagrangian methods, decomposition methods, and nonsmooth Lyapunov analysis. Finally, we give two examples to illustrate the applications of the proposed algorithms.

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arXiv2016

Exact Joint Sparse Frequency Recovery via Optimization Methods

Frequency recovery/estimation from discrete samples of superimposed sinusoidal signals is a classic yet important problem in statistical signal processing. Its research has recently been advanced by atomic norm techniques which exploit signal sparsity, work directly on continuous frequencies, and completely resolve the grid mismatch problem of previous compressed sensing methods. In this work we investigate the frequency recovery problem in the presence of multiple measurement vectors (MMVs) which share the same frequency components, termed as joint sparse frequency recovery and arising naturally from array processing applications. To study the advantage of MMVs, we first propose an $\ell_{2,0}$ norm like approach by exploiting joint sparsity and show that the number of recoverable frequencies can be increased except in a trivial case. While the resulting optimization problem is shown to be rank minimization that cannot be practically solved, we then propose an MMV atomic norm approach that is a convex relaxation and can be viewed as a continuous counterpart of the $\ell_{2,1}$ norm method. We show that this MMV atomic norm approach can be solved by semidefinite programming. We also provide theoretical results showing that the frequencies can be exactly recovered under appropriate conditions. The above results either extend the MMV compressed sensing results from the discrete to the continuous setting or extend the recent super-resolution and continuous compressed sensing framework from the single to the multiple measurement vectors case. Extensive simulation results are provided to validate our theoretical findings and they also imply that the proposed MMV atomic norm approach can improve the performance in terms of reduced number of required measurements and/or relaxed frequency separation condition.

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arXiv2016

Towards a Unified Resilience Analysis: State Estimation against Integrity Attacks

We consider the problem of resilient state estimation in the presence of integrity attacks. There are m sensors monitoring the state and p of them are under attack. The sensory data collected by the compromised sensors can be manipulated arbitrarily by the attacker. The classical estimators such as the least squares estimator may not provide a reliable estimate under the so-called (p,m)-sparse attack. In this work, we are not restricting our efforts in studying whether any specific estimator is resilient to the attack or not, but instead we aim to present the generic sufficient and necessary conditions for resilience by considering a general class of convex optimization based estimators. The sufficient and necessary conditions are shown to be tight, with a trivial gap. We further specialize our result to scalar sensor measurements case and present some conservative but verifiable results for practical use. Experimental simulations tested on the IEEE 14-bus test system validate the theoretical analysis.

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arXiv2016

An Improved DOA Estimation Algorithm for Circular and Non-Circular Signals with High Resolution

In this paper, an improved direction-of-arrival (DOA) estimation algorithm for circular and non-circular signals is proposed. Most state-of-the-art algorithms only deal with the DOA estimation problem for the maximal non-circularity rated and circular signals. However, common non-circularity rated signals are not taken into consideration. The proposed algorithm can estimates not only the maximal non-circularity rated and circular signals, but also the common non-circularity rated signals. Based on the property of the non-circularity phase and rate, the incident signals can be divided into three types as mentioned above, which can be estimated separately. The interrelationship among these signals can be reduced significantly, which means the resolution performance among different types of signals is improved. Simulation results illustrate the effectiveness of the proposed method.

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arXiv2016

Vandermonde Decomposition of Multilevel Toeplitz Matrices with Application to Multidimensional Super-Resolution

The Vandermonde decomposition of Toeplitz matrices, discovered by Carathéodory and Fejér in the 1910s and rediscovered by Pisarenko in the 1970s, forms the basis of modern subspace methods for 1D frequency estimation. Many related numerical tools have also been developed for multidimensional (MD), especially 2D, frequency estimation; however, a fundamental question has remained unresolved as to whether an analog of the Vandermonde decomposition holds for multilevel Toeplitz matrices in the MD case. In this paper, an affirmative answer to this question and a constructive method for finding the decomposition are provided when the matrix rank is lower than the dimension of each Toeplitz block. A numerical method for searching for a decomposition is also proposed when the matrix rank is higher. The new results are applied to studying MD frequency estimation within the recent super-resolution framework. A precise formulation of the atomic $\ell_0$ norm is derived using the Vandermonde decomposition. Practical algorithms for frequency estimation are proposed based on relaxation techniques. Extensive numerical simulations are provided to demonstrate the effectiveness of these algorithms compared to the existing atomic norm and subspace methods.

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arXiv2016

Robust State Estimation against Sparse Integrity Attacks

We consider the problem of robust state estimation in the presence of integrity attacks. There are $m$ sensors monitoring a dynamical process. Subject to the integrity attacks, $p$ out of $m$ measurements can be arbitrarily manipulated. The classical approach such as the MMSE estimation in the literature may not provide a reliable estimate under this so-called $(p,m)$-sparse attack. In this work, we propose a robust estimation framework where distributed local measurements are computed first and fused at the estimator based on a convex optimization problem. We show the sufficient and necessary conditions for robustness of the proposed estimator. The sufficient and necessary conditions are shown to be tight, with a trivial gap. We also present an upper bound on the damage an attacker can cause when the sufficient condition is satisfied. Simulation results are also given to illustrate the effectiveness of the estimator.

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arXiv2015

Nash Equilibrium Computation in Subnetwork Zero-Sum Games with Switching Communications

In this paper, we investigate a distributed Nash equilibrium computation problem for a time-varying multi-agent network consisting of two subnetworks, where the two subnetworks share the same objective function. We first propose a subgradient-based distributed algorithm with heterogeneous stepsizes to compute a Nash equilibrium of a zero-sum game. We then prove that the proposed algorithm can achieve a Nash equilibrium under uniformly jointly strongly connected (UJSC) weight-balanced digraphs with homogenous stepsizes. Moreover, we demonstrate that for weighted-unbalanced graphs a Nash equilibrium may not be achieved with homogenous stepsizes unless certain conditions on the objective function hold. We show that there always exist heterogeneous stepsizes for the proposed algorithm to guarantee that a Nash equilibrium can be achieved for UJSC digraphs. Finally, in two standard weight-unbalanced cases, we verify the convergence to a Nash equilibrium by adaptively updating the stepsizes along with the arc weights in the proposed algorithm.

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arXiv2015

Convex Optimization Based State Estimation against Sparse Integrity Attacks

We consider the problem of robust estimation in the presence of integrity attacks. There are m sensors monitoring the state and p of them are under attack. The malicious measurements collected by the compromised sensors can be manipulated arbitrarily by the attacker. The classical estimators such as the least squares estimator may not provide a reliable estimate under the so-called (p,m)-sparse attack. In this work, we are not restricting our efforts in studying whether any specific estimator is resilient to the attack or not, but instead we aim to present some generic sufficient and necessary conditions for robustness by considering a general class of convex optimization based estimators. The sufficient and necessary conditions are shown to be tight, with a trivial gap.

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arXiv2015

Mean Square Stabilization of Vector LTI Systems over Power Constrained Lossy Channels

This paper studies the mean square stabilization problem of vector LTI systems over power constrained lossy channels. The communication channel is with packet dropouts, additive noises and input power constraints. To overcome the difficulty of optimally allocating channel resources among different sub-dynamics, schedulers are designed with time division multiplexing of channels. An adaptive TDMA (Time Division Multiple Access) scheduler is proposed first, which is shown to be able to achieve a larger stabilizability region than the conventional TDMA scheduler, and is optimal under some special cases. In particular, for two-dimensional systems, an optimal scheduler is designed, which provides the necessary and sufficient condition for mean square stabilization.

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arXiv2015

Enhancing Sparsity and Resolution via Reweighted Atomic Norm Minimization

The mathematical theory of super-resolution developed recently by Candès and Fernandes-Granda states that a continuous, sparse frequency spectrum can be recovered with infinite precision via a (convex) atomic norm technique given a set of uniform time-space samples. This theory was then extended to the cases of partial/compressive samples and/or multiple measurement vectors via atomic norm minimization (ANM), known as off-grid/continuous compressed sensing (CCS). However, a major problem of existing atomic norm methods is that the frequencies can be recovered only if they are sufficiently separated, prohibiting commonly known high resolution. In this paper, a novel (nonconvex) sparse metric is proposed that promotes sparsity to a greater extent than the atomic norm. Using this metric an optimization problem is formulated and a locally convergent iterative algorithm is implemented. The algorithm iteratively carries out ANM with a sound reweighting strategy which enhances sparsity and resolution, and is termed as reweighted atomic-norm minimization (RAM). Extensive numerical simulations are carried out to demonstrate the advantageous performance of RAM with application to direction of arrival (DOA) estimation.

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arXiv2015

Distributed Inference for Relay-Assisted Sensor Networks With Intermittent Measurements Over Fading Channels

In this paper, we consider a general distributed estimation problem in relay-assisted sensor networks by taking into account time-varying asymmetric communications, fading channels and intermittent measurements. Motivated by centralized filtering algorithms, we propose a distributed innovation-based estimation algorithm by combining the measurement innovation (assimilation of new measurement) and local data innovation (incorporation of neighboring data). Our algorithm is fully distributed which does not need a fusion center. We establish theoretical results regarding asymptotic unbiasedness and consistency of the proposed algorithm. Specifically, in order to cope with time-varying asymmetric communications, we utilize an ordering technique and the generalized Perron complement to manipulate the first and second moment analyses in a tractable framework. Furthermore, we present a performance-oriented design of the proposed algorithm for energy-constrained networks based on the theoretical results. Simulation results corroborate the theoretical findings, thus demonstrating the effectiveness of the proposed algorithm.

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arXiv2015

Mean Square Capacity of Power Constrained Fading Channels with Causal Encoders and Decoders

This paper is concerned with the mean square stabilization problem of discrete-time LTI systems over a power constrained fading channel. Different from existing research works, the channel considered in this paper suffers from both fading and additive noises. We allow any form of causal channel encoders/decoders, unlike linear encoders/decoders commonly studied in the literature. Sufficient conditions and necessary conditions for the mean square stabilizability are given in terms of channel parameters such as transmission power and fading and additive noise statistics in relation to the unstable eigenvalues of the open-loop system matrix. The corresponding mean square capacity of the power constrained fading channel under causal encoders/decoders is given. It is proved that this mean square capacity is smaller than the corresponding Shannon channel capacity. In the end, numerical examples are presented, which demonstrate that the causal encoders/decoders render less restrictive stabilizability conditions than those under linear encoders/decoders studied in the existing works.

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arXiv2015

Distributed Parameter Estimation with Quantized Communication via Running Average

In this paper, we consider the parameter estimation problem over sensor networks in the presence of quantized data and directed communication links. We propose a two-stage algorithm aiming at achieving the centralized sample mean estimate in a distributed manner. Different from the existing algorithms, a running average technique is utilized in the proposed algorithm to smear out the randomness caused by the probabilistic quantization scheme. With the running average technique, it is shown that the centralized sample mean estimate can be achieved both in the mean square and almost sure senses, which is not observed in the conventional consensus algorithms. In addition, the rates of convergence are given to quantify the mean square and almost sure performances. Finally, simulation results are presented to illustrate the effectiveness of the proposed algorithm and highlight the improvements by using running average technique.

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arXiv2015

On Gridless Sparse Methods for Line Spectral Estimation From Complete and Incomplete Data

This paper is concerned about sparse, continuous frequency estimation in line spectral estimation, and focused on developing gridless sparse methods which overcome grid mismatches and correspond to limiting scenarios of existing grid-based approaches, e.g., $\ell_1$ optimization and SPICE, with an infinitely dense grid. We generalize AST (atomic-norm soft thresholding) to the case of nonconsecutively sampled data (incomplete data) inspired by recent atomic norm based techniques. We present a gridless version of SPICE (gridless SPICE, or GLS), which is applicable to both complete and incomplete data without the knowledge of noise level. We further prove the equivalence between GLS and atomic norm-based techniques under different assumptions of noise. Moreover, we extend GLS to a systematic framework consisting of model order selection and robust frequency estimation, and present feasible algorithms for AST and GLS. Numerical simulations are provided to validate our theoretical analysis and demonstrate performance of our methods compared to existing ones.

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arXiv2015

Optimization-based State Estimation under Bounded Disturbances

This paper studies an optimization-based state estimation approach for discrete-time nonlinear systems under bounded process and measurement disturbances. We first introduce a full information estimator (FIE), which is given as a solution to minimize a cost function by using all the available measurements. Then, we prove that the FIE of an incrementally input/output-to-state stable system is robustly globally asymptotically stable under a certain class of cost functions. Moreover, the implications and relationships with related results in the literature are discussed. Finally, a simple example is included to illustrate the theoretical results.

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arXiv2015

An Improved Stability Condition for Kalman Filtering with Bounded Markovian Packet Losses

In this paper, we consider the peak-covariance stability of Kalman filtering subject to packet losses. The length of consecutive packet losses is governed by a time-homogeneous finite-state Markov chain. We establish a sufficient condition for peak-covariance stability and show that this stability check can be recast as a linear matrix inequality (LMI) feasibility problem. Comparing with the literature, the stability condition given in this paper is invariant with respect to similarity state transformations; moreover, our condition is proved to be less conservative than the existing results. Numerical examples are provided to demonstrate the effectiveness of our result.

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