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., ℓ 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.
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 that exploit signal sparsity, work directly on continuous frequencies, and completely resolve the grid mismatch problem of previous compressed sensing methods. In this paper, 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 ℓ 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 ℓ 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.
This paper studies the finite-time consensus tracking control for multirobot systems. We prove that finite-time consensus tracking of multiagent systems can be achieved on the terminal sliding-mode ...surface. Also, we show that the proposed error function can be modified to achieve relative state deviation between agents. These results are then applied to the finite-time consensus tracking control of multirobot systems with input disturbances. Simulation results are presented to validate the analysis.
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.
This paper investigates the joint effect of agent dynamic, network topology and communication data rate on consensusability of linear discrete-time multi-agent systems. Neglecting the finite ...communication data rate constraint and under undirected graphs, a necessary and sufficient condition for consensusability under a common control protocol is given, which explicitly reveals how the intrinsic entropy rate of the agent dynamic and the communication graph jointly affect consensusability. The result is established by solving a discrete-time simultaneous stabilization problem. A lower bound of the optimal convergence rate to consensus, which is shown to be tight for some special cases, is provided as well. Moreover, a necessary and sufficient condition for formationability of multi-agent systems is obtained. As a special case, the discrete-time second-order consensus is discussed where an optimal control gain is designed to achieve the fastest convergence. The effects of undirected graphs on consensability/formationability and optimal convergence rate are exactly quantified by the ratio of the second smallest to the largest eigenvalues of the graph Laplacian matrix. An extension to directed graphs is also made. The consensus problem under a finite communication data rate is finally investigated.
This brief addresses the trajectory tracking control problem of a fully actuated surface vessel subjected to asymmetrically constrained input and output. The controller design process is based on the ...backstepping technique. An asymmetric time-varying barrier Lyapunov function is proposed to address the output constraint. To overcome the difficulty of nondifferentiable input saturation, a smooth hyperbolic tangent function is employed to approximate the asymmetric saturation function. A Nussbaum function is introduced to compensate for the saturation approximation and ensure the system stability. The command filters and auxiliary systems are integrated with the control law to avoid the complicated calculation of the derivative of the virtual control in backstepping. In addition, the bounds of uncertainties and disturbances are estimated and compensated with an adaptive algorithm. With the proposed control, the constraints will never be violated during operation, and all system states are bounded. Simulation results and comparisons with standard method illustrate the effectiveness and advantages of the proposed controller.
This technical note studies quantized output feedback control of discrete-time linear systems using a finite-level quantizer. The main objective is to find a quantization strategy which is easily ...implementable and achieves asymptotic stabilization. Based on a known logarithmic quantization scheme, we introduce a simple dynamic scaling method for the quantizer. A suboptimal approach for the optimization of the number of quantization levels and the design of a corresponding quantized dynamic output feedback controller is given. The robustness of the dynamic quantization scheme with respect to input disturbances is also examined.
A novel method is proposed in this note for stability analysis of systems with a time-varying delay. Appropriate Lyapunov functional and augmented Lyapunov functional are introduced to establish some ...improved delay-dependent stability criteria. Less conservative results are obtained by considering the additional useful terms (which are ignored in previous methods) when estimating the upper bound of the derivative of Lyapunov functionals and introducing the new free-weighting matrices. The resulting criteria are extended to the stability analysis for uncertain systems with time-varying structured uncertainties and polytopic-type uncertainties. Numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method
We consider the stability properties of sampled-data networked linear systems with Markovian packet losses. A binary Markov chain is used to characterize the packet loss phenomenon of the network. We ...show that the sampled-data system under consideration can be considered as a randomly sampled system with an i.i.d. random sampling period. Necessary and sufficient conditions for the stochastic stability properties are established. Those conditions are based on the relationships of stability properties between the systems evolving in deterministic continuous time, deterministic discrete time, and random discrete time. In addition, the asymptotic stability of the system is also studied by using Lyapunov exponent method.
Direction of arrival (DOA) estimation is a classical problem in signal processing with many practical applications. Its research has recently been advanced owing to the development of methods based ...on sparse signal reconstruction. While these methods have shown advantages over conventional ones, there are still difficulties in practical situations where true DOAs are not on the discretized sampling grid. To deal with such an off-grid DOA estimation problem, this paper studies an off-grid model that takes into account effects of the off-grid DOAs and has a smaller modeling error. An iterative algorithm is developed based on the off-grid model from a Bayesian perspective while joint sparsity among different snapshots is exploited by assuming a Laplace prior for signals at all snapshots. The new approach applies to both single snapshot and multi-snapshot cases. Numerical simulations show that the proposed algorithm has improved accuracy in terms of mean squared estimation error. The algorithm can maintain high estimation accuracy even under a very coarse sampling grid.
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