Joint adaptive power allocation and interference suppression algorithms based on theMSER criterion for wireless sensor networks

In this study, a two-hop wireless sensor network with multiple relay nodes is considered where the amplify-and-forward （AF） scheme is employed. Two algorithms are presented to jointly consider interference suppression and power allocation （PA） based on the minimization of the symbol error rate （SER） criterion. A stochastic gradient （SG） algorithm is developed on the basis of the minimum-SER （MSER） criterion to jointly update the parameter vectors that allocate the power levels among the relay sensors subject to a total power constraint and the linear receiver. In addition, a conjugate gradient （CG） algorithm is developed on the basis of the SER criterion. A centralized algorithm is designed at the fusion center. Destination nodes transmit the quantized information of the PA vector to the relay nodes through a limited-feedback channel. The complexity and convergence analysis of the proposed algorithms are carried out. Simulation results show that the proposed two adaptive algorithms significantly outperform the other previously reported algorithms.     

On stabilization for a class of nonlinear stochastic time-delay systems： a matrix inequality approach

This paper treats the feedback stabilization of nonlinear stochastic time-delay systems with state and control-dependent noise. Some locally （globally） robustly stabilizable conditions are given in terms of matrix inequalities that are independent of the delay size. When it is applied to linear stochastic time-delay systems, sufficient conditions for the state-feedback stabilization are presented via linear matrix inequalities. Several previous results are extended to more general systems with both state and control-dependent noise, and easy computation algorithms are also given.     

Iterative learning control for nonlinear systems with uncertain state delay and arbitrary initial error

Most of the existing iterative learning control algorithms proposed for time-delay systems are based on the condition that the time-delay is precisely available, and the initial state is reset to the desired one or a fixed value at the start of each operation, which makes great limitation on the practical application of corresponding results. In this paper, a new iterative learning control algorithm is studied for a class of nonlinear system with uncertain state delay and arbitrary initial error. This algorithm needs to know only the boundary estimation of the state delay, and the initial state is updated, while the convergence of the system is guaranteed. Without state disturbance and output measurement noise, the system output will strictly track the desired trajectory after successive iteration. Furthermore, in the presence of state disturbance and measurement noise, the tracking error will be bounded uniformly. The convergence is strictly proved mathematically, and sufficient conditions are obtained. A numerical example is shown to demonstrate the effectiveness of the proposed approach.     

Optimal linear estimators for systems with random measurement delays

This paper is concerned with the optimal linear estimation problem for linear discrete-time stochastic systems with random measurement delays. A new model that describes the random delays is constructed where possible the largest delay is bounded. Based on this new model, the optimal linear estimators including filter, predictor and smoother are developed via an innovation analysis approach. The estimators are recursively computed in terms of the solutions of a Riccati difference equation and a Lyapunov difference equation. The steady-state estimators are also investigated. A sufficient condition for the convergence of the optimal linear estimators is given. A simulation example shows the effectiveness of the proposed algorithms.     

Basic principle and rational user in interactive evolutionary computation

As is the basic principle in interactive evolutionary computation （IEC） that the optima evolved by the algorithm should be the individuals that the user is most satisfied with. A rational user will keep consistent dominated relationship between the assigned fitness and his/her preference for the individuals. Even for rational users, it is unavoidable that the fitness he/she assigned contains noise. The result that the fitness noise caused by a rational user will not damage the basic principle in IEC is concluded. In order to prove the conclusion, two theorems separately named as strong condition and weak condition are put forward. The experiments and their results validate the theorems. As the successive issue, the relationship between the two conditions, the relationship between weak condition and fitness scaling, the true fitness in IEC, the definition of noise in IEC and so on are discussed. The results establish necessary foundation for future research.     

Recursive estimation algorithms for power controls of wireless communication networks

Power control problems for wireless communication networks are investigated in direct-sequence codedivision multiple-access （DS/CDMA） channels. It is shown that the underlying problem can be formulated as a constrained optimization problem in a stochastic framework. For effective solutions to this optimization problem in real time, recursive algorithms of stochastic approximation type are developed that can solve the problem with unknown system components. Under broad conditions, convergence of the algorithms is established by using weak convergence methods.     

Infinite time horizon nonzero-sum linear quadratic stochastic differential games with state and control-dependent noise

This paper discusses the infinite time horizon nonzero-sum linear quadratic （LQ） differential games of stochastic systems governed by Itoe＇s equation with state and control-dependent noise. First, the nonzero-sum LQ differential games are formulated by applying the results of stochastic LQ problems. Second, under the assumption of mean-square stabilizability of stochastic systems, necessary and sufficient conditions for the existence of the Nash strategy are presented by means of four coupled stochastic algebraic Riccati equations. Moreover, in order to demonstrate the usefulness of the obtained results, the stochastic H-two/H-infinity control with state, control and external disturbance-dependent noise is discussed as an immediate application.     

P-Tree Structures and Event Horizon: Efficient Event-Set Implementations

This paper describes efficient data structures, namely the Indexed P-tree, Block P-tree, and Indexed-Block P-tree （or/P-tree, BP-tree, and IBP-tree, respectively, for short）, for maintaining future events in a general purpose discrete event simulation system, and studies the performance of their event set algorithms under the event horizon principle. For comparison reasons, some well-known event set algorithms have been selected and studied, that is, the Dynamic-heap and the P-tree algorithms. To gain insight into the performance of the proposed event set algorithms and allow comparisons with the other selected algorithms, they are tested under a wide variety of conditions in an experimental way. The time needed for the execution of the Hold operation is taken as the measure for estimating the average time complexity of the algorithms. The experimental results show that the BP-tree algorithm and the IBP-tree algorithm behave very well with the event set of all the sizes and their performance is almost independent of the stochastic distributions.     

Asymptotic behavior of asynchronous stochastic approximation

The pathwise convergence of a distributed, asynchronous stochastic approximation (SA) scheme is analyzed. The conditions imposed on the step size and noise are the weakest in comparison with the existing ones. The step sizes in different processors are allowed to be different, and the time-delays between processors are also allowed to be different and even time-varying.     

Robust sliding mode control of general time-varying delay stochastic systems with structural uncertainties

This paper presents a new robust sliding mode control （SMC） method with well-developed theoretical proof for general uncertain time-varying delay stochastic systems with structural uncertainties and the Brownian noise （Wiener process）. The key features of the proposed method are to apply singular value decomposition （SVD） to all structural uncertainties and to introduce adjustable parameters for control design along with the SMC method. It leads to a less-conservative condition for robust stability and a new robust controller for the general uncertain stochastic systems via linear matrix inequality （LMI） forms. The system states are able to reach the SMC switching surface as guaranteed in probability 1. Furthermore, it is theoretically proved that the proposed method with the SVD and adjustable parameters is less conservatism than the method without the SVD. The paper is mainly to provide all strict theoretical proofs for the method and results.     

Recursive identification of Hammerstein systems with dead-zone nonlinearity in the presence of bounded noise

The existing identification algorithms for Hammerstein systems with dead-zone nonlinearity are restricted by the noise-free condition or the stochastic noise assumption. Inspired by the practical bounded noise assumption, an improved recursive identification algorithm for Hammerstein systems with dead-zone nonlinearity is proposed. Based on the system parametric model, the algorithm is derived by minimising the feasible parameter membership set. The convergence conditions are analysed, and the adaptive weighting factor and the adaptive covariance matrix are introduced to improve the convergence. The validity of this algorithm is demonstrated by two numerical examples, including a practical DC motor case.     

Convergence Analysis of Weighted Stochastic Gradient Identification Algorithms Based on Latest‐Estimation for ARX Models

In this paper, weighted stochastic gradient (WSG) algorithms for ARX models are proposed by modifying the standard stochastic gradient identification algorithms. In the proposed algorithms, the correction term is a weighting combination of the correction terms of the standard stochastic gradient (SG) algorithm in the current and last recursive steps. In addition, a latest estimation based WSG (LE‐WSG) algorithm is also established. The convergence performance of the proposed LE‐WSG algorithm is then analyzed. It is shown by a numerical example that both the WSG and LE‐WSG algorithms can possess faster convergence speed and higher convergence precision compared with the standard SG algorithms if the weighting factor is appropriately chosen.     

Almost sure convergence of stochastic approximation algorithms with non-additive noise

Stochastic approximation algorithms with non-additive noise are discussed. In studying strong convergence of such algorithms, traditionally one assumes that the iterates return to a bounded or compact set infinitely often, or that the function under consideration grows with certain rate. The usual projection algorithms require that the bounded projection region is known beforehand. It is desirable to weaken these ‘boundedness’ conditions. By introducing randomly varying truncations, Chen and Zhu (1986) achieved this for stochastic approximation algorithms with additive noise. Here, we extend their result to a more general setting.     

WMF self-tuning Kalman estimators for multisensor singular system

For the multisensor linear stochastic singular system with unknown noise variances, the weighted measurement fusion (WMF) self-tuning Kalman estimation problem is solved in this paper. The consistent estimates of these unknown noise variances are obtained based on the correlation method. Applying the WMF method and the singular value decomposition (SVD) method yields the WMF reduced-order subsystems. Based on these consistent estimates of unknown noise variances and the new non-singular systems, the WMF self-tuning Kalman estimators of the state components and white noise deconvolution estimators are presented. Then the WMF self-tuning Kalman estimators of the original state are presented, and their convergence has been proved by dynamic error system analysis (DESA) method and dynamic variance error system analysis (DVESA) method. A simulation example of 3-sensors circuits systems verifies the effectiveness, the accuracy relationship and the convergence.     

Performance analysis of multi-innovation gradient type identification methods

It is well-known that the stochastic gradient (SG) identification algorithm has poor convergence rate. In order to improve the convergence rate, we extend the SG algorithm from the viewpoint of innovation modification and present multi-innovation gradient type identification algorithms, including a multi-innovation stochastic gradient (MISG) algorithm and a multi-innovation forgetting gradient (MIFG) algorithm. Because the multi-innovation gradient type algorithms use not only the current data but also the past data at each iteration, parameter estimation accuracy can be improved. Finally, the performance analysis and simulation results show that the proposed MISG and MIFG algorithms have faster convergence rates and better tracking performance than their corresponding SG algorithms.     

Parameter identification of wiener models by multi-innovation algorithms

An output nonlinear Wiener system is rewritten as a standard least squares form by reconstructing the input-output items of its difference equation. Multi-innovation based stochastic gradient (MISG) algorithm and its derivate algorithms are introduced to formulate identification methods of Wiener models. In order to increase the convergence performance of stochastic gradient (SG) algorithm, the scalar innovation in SG algorithm is expanded to an innovation vector which contains more information about input-output data. Furthermore, a proper forgetting factor for SG algorithm is introduced to get a faster convergence rates. The comparisons of convergence performance and estimation errors of proposed algorithms are illustrated by two numerical simulation examples.     

On convergence of the unscented Kalman–Bucy filter using contraction theory

Contraction theory entails a theoretical framework in which convergence of a nonlinear system can be analysed differentially in an appropriate contraction metric. This paper is concerned with utilising stochastic contraction theory to conclude on exponential convergence of the unscented Kalman–Bucy filter. The underlying process and measurement models of interest are Itô-type stochastic differential equations. In particular, statistical linearisation techniques are employed in a virtual–actual systems framework to establish deterministic contraction of the estimated expected mean of process values. Under mild conditions of bounded process noise, we extend the results on deterministic contraction to stochastic contraction of the estimated expected mean of the process state. It follows that for the regions of contraction, a result on convergence, and thereby incremental stability, is concluded for the unscented Kalman–Bucy filter. The theoretical concepts are illustrated in two case studies.     

Consistency of the extended gradient identification algorithm for multi-input multi-output systems with moving average noises

The consistency of identification algorithms for systems with colored noises is a main topic in system identification. This paper focuses on the extended stochastic gradient (ESG) identification algorithm for the multivariable linear systems with moving average noises. By integrating the noise regression terms and the noise model parameters into the information matrix and the parameter vector, and based on the gradient search principle, the ESG algorithm is presented. The unknown noise terms in the information matrix are replaced with their estimates. The convergence analysis shows that the parameter estimation error converges to zero under a persistent excitation condition. Two simulation examples are given to illustrate the effectiveness of the algorithm.     

OBE算法对误差界低估的鲁棒性

研究了具有未知但有界(UBB)误差系统辨识的最优定界椭球(OBE)算法对误差界 低估的鲁棒性.证明了在一定的条件下,即使误差界低估,任何OBE算法都能保持其收敛性. 这一结论可用于具有UBB误差的实际系统参数估计中,以期获得不太保守的结果.     

Development of multivariable PID controller gains in presence of measurement noise

This paper examines the ability of a multivariable PID controller rejecting measurement noise without the use of any external filter. The work first provides a framework for the design of the PID gains comprising of necessary and sufficient conditions for boundedness of trajectories and zero-error convergence in presence of measurement noise. It turns out that such convergence requires time-varying gains. Subsequently, novel recursive algorithms providing optimal and sub-optimal time-varying PID gains are proposed for discrete-time varying linear multiple-input multiple-output (MIMO) systems. The development of the proposed optimal algorithm is based on minimising a stochastic performance index in presence of erroneous initial conditions, white measurement noise, and white process noise. The proposed algorithms are shown to reject measurement noise provided that the system is asymptotically stable and the product of the input–output coupling matrices is full-column rank. In addition, convergence results are presented for discretised continuous-time plants. Simulation results are included to illustrate the performance capabilities of the proposed algorithms.