Robust Mean Square Research Articles

Relay Precoder Optimization in MIMO-Relay Networks With Imperfect CSI

In this paper, we consider robust joint designs of relay precoder and destination receive filters in a nonregenerative multiple-input multiple-output (MIMO) relay network. The network consists of multiple source-destination node pairs assisted by a MIMO-relay node. The channel state information (CSI) available at the relay node is assumed to be imperfect. We consider robust designs for two models of CSI error. The first model is a stochastic error (SE) model, where the probability distribution of the CSI error is Gaussian. This model is applicable when the imperfect CSI is mainly due to errors in channel estimation. For this model, we propose robust minimum sum mean square error (SMSE), MSE-balancing, and relay transmit power minimizing precoder designs. The next model for the CSI error is a norm-bounded error (NBE) model, where the CSI error can be specified by an uncertainty set. This model is applicable when the CSI error is dominated by quantization errors. In this case, we adopt a worst-case design approach. For this model, we propose a robust precoder design that minimizes total relay transmit power under constraints on MSEs at the destination nodes. We show that the proposed robust design problems can be reformulated as convex optimization problems that can be solved efficiently using interior-point methods. We demonstrate the robust performance of the proposed design through simulations.

Reliable H ∞ filter design for T–S fuzzy model‐based networked control systems with random sensor failure

SUMMARYThis paper investigates robust and reliable H ∞ filter design for a class of nonlinear networked control systems: (i) a T‐S fuzzy model with its own uncertainties is used to approximate the nonlinear dynamics of the plant, (ii) a new sensor failure model with uncertainties is proposed, and (iii) the signal transfer of the closed‐loop system is under a networked communication scheme and therefore is subject to time delay, packet loss, and/or packet out of order. Four new theorems are proved to cover the conditions for the robust mean square stability of the systems under study in terms of LMIs, and a decoupling method for the filter design is developed. Two examples, one of them is based on a model of an inverted pendulum, are provided to demonstrate the design method. Copyright © 2011 John Wiley & Sons, Ltd.

T–S Fuzzy Model-Based Robust Stabilization for Networked Control Systems With Probabilistic Sensor and Actuator Failure

The system studied in this paper has four main features: 1) It is a networked controlled system (NCS), and therefore, the signal transfer is subject to random delay and/or loss; 2) it is a nonlinear system approximated by a Takegi--Sugeno (T-S) fuzzy model; 3) its multisensors and multiactuators are subject to various possible faults/failures; and 4) there are uncertainties in the plant model parameters. A comprehensive model is first developed in this paper to cover these features for a class of NCS nonlinear systems. This model has removed some limitations of similar models in the published literature. Then, the Lyapunov functional and the linear matrix inequality (LMI) are applied to develop two new stability conditions (Theorems 1 and 2). These conditions and an algorithm are used to design a controller to achieve robust mean square stability of the system. Finally, two examples are used to demonstrate the application of the modeling and the controller design method developed.

Parameter-dependent robust stability for uncertain Markovian jump systems with time delay

In this paper, the problem of parameter-dependent robust stability analysis is addressed for uncertain Markovian jump linear systems (MJLSs) with polytopic parameter uncertainties and time-varying delay. By constructing parameter-dependent Lyapunov functional, some sufficient conditions are developed to enable robust exponential mean square stability for the systems. New parameter-dependent robust stability criteria for MJLSs are established in the form of linear matrix inequalities (LMIs), which can be solved efficiently by the interior-point algorithm. Finally, a numerical example is given to demonstrate the effectiveness of the proposed approach.

Feedback predictive control for constrained fuzzy systems with Markovian jumps

In this paper, a feedback model predictive control method is presented to tackle control problems with constrained multivariables for uncertain discrete-time nonlinear Markovian jump systems. An uncertain Markovian jump fuzzy system (MJFS) is obtained by employing the Takagi-Sugeno (T-S) fuzzy model to represent a discrete-time nonlinear system with norm bounded uncertainties and Markovain jump parameters. To achieve more generality, the transition probabilities of the Markov chain are assumed to be partly unknown and partly accessible. The predictive formulation adopts an on-line optimization paradigm that utilizes the closed-loop state feedback controller and is solved using the standard semi-definite programming (SDP). To reduce the on-line computational burden, a mode independent control move is calculated at every sampling time based on a stochastic fuzzy Lyapunov function (FLF) and a parallel distributed compensation (PDC) scheme. The robust mean square stability, performance minimization and constraint satisfaction properties are guaranteed under the control move for all admissible uncertainties. A numerical example is given to show the efficiency of the developed approach. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

H∞ synchronization of general chaotic systems with random perturbations

In this paper, the H∞ synchronization of general chaotic systems with random perturbations is investigated, in which perturbation is a random process of Brownian motion. Based on stochastic Lyapunov stability theory, linear matrix inequalities, and It formula and H∞ control method combined with feedback control laws, some new asymptotic synchronization schemes are established which guarantee robust stochastical mean square asymptotical synchronization for drive system and noise-perturbed response system, as well as achieving a prescribed stochastic robust H∞ performance level. These schemes are in a simple form and easy to work with Matlab. Finally, simulations show that the proposed results are correct and effective.

Research on robust mean square stability of networked control systems with packet dropout

Research on robust mean square stability of networked control systems with packet dropout

Robust Control of Systems over a Communication Network with Queues

Abstract In this paper the problem of robust control of linear dynamic systems in the presence of unmodeled dynamic and communication network with queues is considered. The generalized plant (plant with unmodeled dynamics- queue with feedback linearization- random delay of up-link) modeled in the form of discrite-time Markov jump linear system. On the other hand the down-link is time stamped (setting a delay line which covers all possible delays assuming that there exists a known upper bound on the delay) and generalized controller is with augmented state. For such feedback control systems the robust mean square stability is proved.

Robust exponential stability for delayed uncertain Hopfield neural networks with Markovian jumping parameters

This Letter is concerned with delay-dependent robust exponential mean square stability for delayed uncertain Hopfield neural networks with Markovian jumping parameters. Time delays here are discrete and distributed time-varying delays. Based on Lyapunov–Krasovskii stability theory, delay-dependent stability conditions are derived in terms of linear matrix inequalities (LMIs). Finally, numerical examples are given to illustrate the effectiveness of the proposed method.

Robust MMSE receiver employing Hampel-type nonlinear preprocessing for DS-CDMA communication in impulsive noise

A robust minimum mean square error receiver using Hampel-type nonlinear preprocessing is proposed for mitigating both unknown multiple-access interference and impulsive noise. Simulation results are presented to demonstrate the performance of the proposed receiver structure for three distinct nonlinearities in the presence of additive impulsive Gaussian noise.

LMI-based robust H∞ control of uncertain linear jump systems with time-delays

This paper examines the robust mean square stabilization and robust H ∞ control problem for a class of linear systems. The systems under consideration involve time delays, parameter uncertainties, and jumping parameters which may be seen as, for example, failures that occur in the systems at certain probabilities. The uncertain parameters are assumed to be time-varying and satisfy boundness conditions. A systematic approach via linear matrix inequalities (LMI) is proposed to solve the problem of concern. Sufficient conditions for robust mean square stabilization and robust H ∞ control are given in the form of LMI and the control law is computed using standard LMI techniques.