Random Coefficient Matrices Research Articles

A novel two-layer fuzzy neural network for solving inequality-constrained [formula omitted]-minimization problem with applications

In this paper, we propose a novel two-layer fuzzy neural network model (TLFNN) for solving the inequality-constrained ℓ1-minimization problem. The stability and global convergence of the proposed TLFNN model are detailedly analyzed using the Lyapunov theory. Compared with the existing three-layer neural network model (TLNN) recently designed by Yang et al., the proposed TLFNN model possesses less storage, stronger robustness, faster convergence rate and higher convergence accuracy. These advantages are illustrated by some numerical experiments, where it is shown that the TLFNN model can achieve a convergence accuracy of 10−13 within 5s while the TLNN model can only acquire 10−6 in 105s when some random coefficient matrices are applied. Since the linear equality-constrained conditions can be equivalently transformed into double inequality-constrained ones, some simulation experiments for sparse signal reconstruction show that the proposed TLFNN model also has less convergence time and stronger robustness than the existing state-of-the-art neural network models for the equality-constrained ℓ1-minimization problem.

Harmonic-wavelet approach for response spectrum estimation of vehicle and bridge systems with uncertain parameters subjected to stochastic excitation

Vehicle and bridge systems (VBSs) are subjected to stochastic excitations. Significant research effort has been devoted to the stochastic response analysis of VBSs. In most previous studies, VBSs have been treated as deterministic systems with certain parameters. However, the real VBSs always have uncertain parameters, such as the mass and spring stiffness of the vehicles and elastic modulus of the bridge material, which significantly affect the response power spectrum (RPS) estimation. Moreover, the equations of motion of the VBSs are essentially second-order differential equations with time-dependent and random coefficient matrices, and the excitation-response spectral relation cannot be directly described using the frequency response functions. These properties render the available methods unsuitable for the RPS estimation of the VBSs when both structural uncertainty and stochastic excitations are considered. In the present study, a harmonic-wavelet approach is proposed to estimate the time-varying RPSs of the VBSs with random parameters. The second-order differential equations of motion of VBSs with random parameters are first transformed into linear algebraic equations with random coefficient matrices using a harmonic-wavelet analysis technique; then, the excitation-response spectral relation of VBSs is derived based on these linear algebraic equations. Finally, the RPSs of VBSs with uncertain parameters are solved using the perturbation technique. The accuracy of the proposed method was verified by comparing it with the Monte Carlo method using a numerical example of railway VBS. The numerical simulation results show that the parameter uncertainties significantly affect the RPSs of the VBSs and increase the amplitude of the time-varying RPSs. The uncertainty of vehicle stiffness was the most sensitive factor for vehicle RPSs, and the bridge elastic modulus was the most sensitive factor for the bridge RPSs.

Scaled Tracking Consensus in Discrete-Time Second-Order Multiagent Systems With Random Packet Dropouts

This article focuses on the issue of scaled tracking consensus for discrete-time second-order multiagent systems under random packet dropouts, where the cases with a static leader and a dynamic leader are considered, respectively. The scaled tracking consensus means that all agents reach a consensus value determined by the leader but with different scales, and the phenomenon of packet dropout on each communication link is described as a Bernoulli variable independent of other communication links. By virtue of random environment-based scaled consensus algorithms, it is shown how to reconstruct the original system into augmented error systems with random coefficient matrices. With the kind assistance of substochastic matrix and super-stochastic matrix, sufficient conditions for the cases with a static leader and a dynamic leader are derived, respectively. Moreover, computer simulations are performed to demonstrate the dynamics of network agents under random packet dropouts.

Stability Properties of Systems of Linear Stochastic Differential Equations with Random Coefficients

This work is concerned with the stability properties of linear stochastic differential equations with random (drift and diffusion) coefficient matrices, and the stability of a corresponding random transition matrix (or exponential semigroup). We consider a class of random matrix drift coefficients that involves random perturbations of an exponentially stable flow of deterministic (time-varying) drift matrices. In contrast with more conventional studies, our analysis is not based on the existence of Lyapunov functions, and it does not rely on any ergodic properties. These approaches are often difficult to apply in practice when the drift/diffusion coefficients are random. We present rather weak and easily checked perturbation-type conditions for the asymptotic stability of time-varying and random linear stochastic differential equations. We provide new log-Lyapunov estimates and exponential contraction inequalities on any time horizon as soon as the fluctuation parameter is sufficiently small. These seem to be the first results of this type for this class of linear stochastic differential equations with random coefficient matrices.

Consensus seeking in heterogeneous second-order multi-agent systems with switching topologies and random link failures

Abstract In this paper, we consider the issue of consensus among the agents with heterogeneous dynamics under random link failures that obey Bernoulli distribution. The heterogeneous multi-agent systems (MASs) are composed of hybrid dynamic agents including first-order dynamic agents and second-order dynamic agents, and the communication topologies are assumed to be directed and time-varying. The failure control protocol is designed by randomly utilizing the previous one- or two-step states information sent by the neighbors. A criterion for the heterogeneous consensus is established by constructing augmented systems with nonnegative random coefficient matrices for the switching topologies. With the help of graph theory and stochastic matrix theory, a sufficient condition related to switching topologies is established to ensure the realization of heterogeneous consensus. Numerical examples are finally provided to validate the theoretical result.

Bounds on the Reliability of RaptorQ Codes in the Finite-Length Regime

In this paper we analyze the bounds on the reliability of RaptorQ codes under maximum likelihood decoding, especially in the finite-length regime. RaptorQ code ensembles by a high-order low density generator-matrix (LDGM) code as pre-code and an inner Luby transform (LT) code. By investigating the rank of the product of two random coefficient matrices of the high-order LDGM code and the inner LT code, we derive the expressions for the upper and lower bounds of decoding failure probability (DFP) on the RaptorQ code. Then, the accuracy of our derived theoretical bounds are verified through the Monte Carlo simulations with different degree distributions and short packets. The high accuracy bounds are then exploited to design near-optimum finite-length RaptorQ codes, enabling a tight control on the tradeoff between decoding complexity and DFP.

Joint estimation of target state and ionospheric height bias in over‐the‐horizon radar target tracking

Up to now, all over-the-horizon radar-based tracking methods have the prerequisite that the virtual ionospheric height, as the key ionosphere state, should be known, or should be estimated from the provided ionospheric measurements, or at least the prior statistical information of the ionosphere should be given. However, the ionospheric height is intermittently evolving and hence deviates from its nominal value. Therefore, no matter the virtual ionospheric height is directly given by ionosondes or estimated from the ionospheric measurements or prior statistical information, it may have ionospheric height bias. Here, the authors propose the problem of joint estimation of target state and ionospheric height bias in clutters. The problem is reformulated as the multi-rate state estimation with random coefficient matrices. Then, the linear minimum mean square error estimator with causality constraints is designed and extended to the non-linear measurement model via iterative optimisation. The proposed method is shown effective in the simulation about tracking one target in the case of four resolvable propagation modes.

Performance Analysis of Raptor Codes Under Maximum Likelihood Decoding

In this paper, we analyze the maximum likelihood decoding performance of Raptor codes with a systematic low-density generator-matrix code as the pre-code. By investigating the rank of the product of two random coefficient matrices, we derive upper and lower bounds on the decoding failure probability. The accuracy of our analysis is validated through simulations. Results of extensive Monte Carlo simulations demonstrate that for Raptor codes with different degree distributions and pre-codes, the bounds obtained in this paper are of high accuracy. The derived bounds can be used to design near-optimum Raptor codes with short and moderate lengths.

L2-stability of Discrete-time Kalman Filter with Random Coefficients under Incorrect Covariance

This paper studies the L2-stability of Kalman filter for discrete-time linear stochastic systems. Two main features, i.e., random coefficient matrices and incorrect covariances of process noise, measurement noise and initial value, are emphasized. Under suitable conditions, including boundedness of coefficient matrices, conditional observability and boundedness of initial error and noises, L2-stability of Kalman filter is achieved. The equivalence between Kalman filter and state-space least squares algorithm is established. Based on this equivalence, L2-stability of state estimation error by state-space least squares is also obtained. A numerical example is given to demonstrate the effectiveness of Kalman filtering algorithm.

Novel Data Association Algorithm Based on Integrated Random Coefficient Matrices Kalman Filtering

We present a novel data association algorithm based on an integrated random coefficient matrices Kalman filtering (DAIRKF) for the multiple targets and sensors tracking association problem. The basic idea of this algorithm is to integrate all targets and measurements which need to be associated to a new whole system. Then the random coefficient matrices Kalman filtering is applied to this integrated dynamic system to derive the estimates of these target states. Since this algorithm violates some independence conditions for the optimality of the random coefficient matrices Kalman filtering, it is suboptimal in the mean square error (MSE) sense. Nevertheless, in some degree, there is still a correct theoretical basis in DAIRKF and the idea of this algorithm is significantly different from that of joint probabilistic data association (JPDA). Moreover, we can extend the single-sensor DAIRKF algorithm to a multisensor DAIRKF (MSDAIRKF) algorithm with high survivability in poor environment. The computation burden of MSDAIRKF grows linearly as the number of sensors increases. Numerical examples show that the new algorithm works significantly better than JPDA in many cases.

Regularly varying multivariate time series

Extreme values of a stationary, multivariate time series may exhibit dependence across coordinates and over time. The aim of this paper is to offer a new and potentially useful tool called tail process to describe and model such extremes. The key property is the following fact: existence of the tail process is equivalent to multivariate regular variation of finite cuts of the original process. Certain remarkable properties of the tail process are exploited to shed new light on known results on certain point processes of extremes. The theory is shown to be applicable with great ease to stationary solutions of stochastic autoregressive processes with random coefficient matrices, an interesting special case being a recently proposed factor GARCH model. In this class of models, the distribution of the tail process is calculated by a combination of analytical methods and a novel sampling algorithm.