Robust filtering for 2-D state-delayed systems with NFT uncertainties

This paper is concerned with the robust filtering problem for two-dimensional (2-D) state-delayed systems with uncertainties represented by nonlinear fraction transformation. The authors first establish the stability H/sub /spl infin// performance and generalized H/sub 2/ performance criteria for the system. Based on the results, the authors propose efficient methods to solve the robust H/sub /spl infin// filtering, generalized H/sub 2/ filtering, and mixed generalized H/sub 2//H/sub /spl infin// filtering problems by using a parameter-dependent Lyapunov function approach. The methods involve solving linear matrix inequalities. Two examples are given to show the effectiveness of the proposed approach.     

New hybrid controller for systems with deterministic uncertainties

In this paper, a new hybrid controller for systems with deterministic uncertainties is developed. The proposed controller identifies and compensates deterministic uncertainties simultaneously. It is the combination of a time-domain feedback controller and a frequency-domain iterative learning controller. The feedback controller decreases system variability and reduces the effect of random disturbances. The iterative learning controller shapes the system input to suppress the error caused by deterministic uncertainties such as friction and backlash. The control scheme use only local input and output information, no system model is required. The uncertainties can be structured or unstructured. The effectiveness of the proposed controller is experimentally verified on a servo system with gearbox     

Robust filtering for bilinear uncertain stochastic discrete-timesystems

This paper deals with the robust filtering problem for uncertain bilinear stochastic discrete-time systems with estimation error variance constraints. The uncertainties are allowed to be norm-bounded and enter into both the state and measurement matrices. We focus on the design of linear filters, such that for all admissible parameter uncertainties, the error state of the bilinear stochastic system is mean square bounded, and the steady-state variance of the estimation error of each state is not more than the individual prespecified value. It is shown that the design of the robust filters can be carried out by solving some algebraic quadratic matrix inequalities. In particular, we establish both the existence conditions and the explicit expression of desired robust filters. A numerical example is included to show the applicability of the present method     

Robust H/sub 2/ filtering for a class of systems with stochastic nonlinearities

This paper addresses the robust H/sub 2/ filtering problem for a class of uncertain discrete-time nonlinear stochastic systems. The nonlinearities described by statistical means in this paper comprise some well-studied classes of nonlinearities in the literature. A technique is developed to tackle the matrix trace terms resulting from the nonlinearities, and the well-known S-procedure technique is adopted to cope with the uncertainties. A unified framework is established to solve the addressed robust H/sub 2/ filtering problem by using a linear matrix inequality approach. A numerical example is provided to illustrate the usefulness of the proposed method.     

Robust ℋ∞ filtering for continuous timevarying uncertain systems with deterministic input signals

Many dynamical systems involve not only process and measurement noise signals but also parameter uncertainty and known input signals. When ℒ₂ or ℋ_∞ filters that were designed based on a “nominal” model of the system are applied, the presence of parameter uncertainty will not only affect the noise attenuation property of the filter but also introduce a bias proportional to the known input signal, and the latter may be very appreciable. We introduce a finite-horizon robust ℋ_∞ filtering method that provides a guaranteed ℋ_∞ bound for the estimation error in the presence of both parameter uncertainty and a known input signal. This method is developed by using a game-theoretic approach, and the results generalize those obtained for cases without parameter uncertainty or without a known input signal. It is also demonstrated, via an example, that the proposed method provides significantly improved signal estimates     

Robust H/sub /spl infin// filtering for stochastic time-delay systems with missing measurements

In this paper, the robust H/sub /spl infin// filtering problem is studied for stochastic uncertain discrete time-delay systems with missing measurements. The missing measurements are described by a binary switching sequence satisfying a conditional probability distribution. We aim to design filters such that, for all possible missing observations and all admissible parameter uncertainties, the filtering error system is exponentially mean-square stable, and the prescribed H/sub /spl infin// performance constraint is met. In terms of certain linear matrix inequalities (LMIs), sufficient conditions for the solvability of the addressed problem are obtained. When these LMIs are feasible, an explicit expression of a desired robust H/sub /spl infin// filter is also given. An optimization problem is subsequently formulated by optimizing the H/sub /spl infin// filtering performances. Finally, a numerical example is provided to demonstrate the effectiveness and applicability of the proposed design approach.     

Robust filtering for a class of stochastic uncertain nonlineartime-delay systems via exponential state estimation

We investigate the robust filter design problem for a class of nonlinear time-delay stochastic systems. The system under study involves stochastics, unknown state time-delay, parameter uncertainties, and unknown nonlinear disturbances, which are all often encountered in practice and the sources of instability. The aim of this problem is to design a linear, delayless, uncertainty-independent state estimator such that for all admissible uncertainties as well as nonlinear disturbances, the dynamics of the estimation error is stochastically exponentially stable in the mean square, independent of the time delay. Sufficient conditions are proposed to guarantee the existence of desired robust exponential filters, which are derived in terms of the solutions to algebraic Riccati inequalities. The developed theory is illustrated by numerical simulation     

Robust peak-to-peak filtering for Markov jump systems

The peak-to-peak filtering problem is studied for a class of Markov jump systems with uncertain parameters. By re-constructing the system, the dynamic filtering error system is obtained. The objective is to design a peak-to-peak filter such that the induced L_∞ gain from the unknown inputs to the estimated errors is minimized or guaranteed to be less or equal to a prescribed value. By using appropriate stochastic Lyapunov–Krasovskii functional, sufficient conditions are initially established on the existence of mode-dependent peak-to-peak filter which also guarantees the stochastic stability of the filtering error dynamic systems. The design criterions are presented in the form of linear matrix inequalities and then described as an optimization problem. Simulation results demonstrate the validity of the proposed approaches.     

Improved stability criterion for uncertain stochastic delay systems with nonlinear uncertainties

Based on an integral inequality, a stability criterion for uncertain stochastic delay systems with nonlinear uncertainties is obtained in terms of a linear matrix inequality. The restriction used to bound some trace term in the existing methods is removed. The advantage of the proposed method is verified by a numerical example.     

Robust filtering for discrete time piecewise impulsive systems

This paper investigates the filtering problems for the discrete time piecewise impulsive system. First, the robust H_∞ filtering problem and generalized H₂ filtering problem for the discrete time piecewise impulsive system are introduced. Then, linear matrix inequality (LMI) conditions are proposed for the design of H_∞ and generalized H₂ filters such that the resulting discrete time piecewise impulsive filtering error system is globally stable with guaranteed H_∞ or H₂ performance. Finally, a numerical simulation is also given to illustrate the effectiveness of the proposed approaches.     

Robust joint optimization for MIMO AF multiple-relay systems with correlated channel uncertainties

In the paper, robust joint optimization of the source/relays precoders and destination equalizer is proposed for non-regenerative dual-hop multiple-input multiple-output (MIMO) amplify-and-forward (AF) multiple-relay systems with correlated channel uncertainties. By taking the imperfect channel state information (CSI) into consideration, the robust transceiver/relays joint optimization is developed based on the minimum mean-squared error (MMSE) criterion under individual power constraints at the source and relays. The optimization problem of precoding and amplifying matrices under power constraints belongs to neither concave nor convex so that a nonlinear matrix-form conjugate gradient (MCG) algorithm is applied to explore local optimal solutions. Simulation results illustrate that the robust transceiver/relays joint architecture for an AF-MIMO multiple-relay system outperforms the non-robust transceiver/relays design.     

Robust filtering for discrete nonlinear fractional transformation systems

In this brief, we consider robust filtering problems for uncertain discrete-time systems. The uncertain plants under consideration possess nonlinear fractional transformation (NFT) representations which are a generalization of the classical linear fractional transformation (LFT) representations. The proposed NFT is more practical than the LFT, and moreover, it leads to substantial performance gains as well as computational savings. For this class of systems, we derive linear-matrix inequality characterizations for H/sub 2/, & H/sub /spl infin//, and mixed filtering problems. Our approach is finally validated through a number of examples.     

Robust filtering for discrete-time systems with saturation and its application to transmultiplexers

This paper considers the problem of robust filtering for discrete-time linear systems subject to saturation. A generalized dynamic filter architecture is proposed, and a filter design method is developed. Our approach incorporates the conventional linear H/sub 2/ and H/sub /spl infin// filtering as well as a regional l/sub 2/ gain filtering feature developed specially for the saturation nonlinearity and is applicable to the digital transmultiplexer systems for the purpose of separating filterbank design. It turns out that our filter design can be carried out by solving a constrained optimization problem with linear matrix inequality (LMI) constraints. Simulations show that the resultant separating filters possess satisfactory reconstruction performance while working in the linear range and less degraded reconstruction performance in the presence of saturation.     

Robust Kalman filters for linear time-varying systems withstochastic parametric uncertainties

We present a robust recursive Kalman filtering algorithm that addresses estimation problems that arise in linear time-varying systems with stochastic parametric uncertainties. The filter has a one-step predictor-corrector structure and minimizes an upper bound of the mean square estimation error at each step, with the minimization reduced to a convex optimization problem based on linear matrix inequalities. The algorithm is shown to converge when the system is mean square stable and the state space matrices are time invariant. A numerical example consisting of equalizer design for a communication channel demonstrates that our algorithm offers considerable improvement in performance when compared with conventional Kalman filtering techniques     

Robust resource allocation scheme under channel uncertainties for LTE-A systems

Wireless Networks - Nowadays, resource allocation is one of the major problems in the cellular networks. Due to the increasing number of autonomous heterogeneous devices in future mobile networks,...     

Joint state filtering and parameter estimation for linear stochastic time-delay systems

This paper presents the joint state filtering and parameter estimation problem for linear stochastic time-delay systems with unknown parameters. The original problem is reduced to the mean-square filtering problem for incompletely measured bilinear time-delay system states over linear observations. The unknown parameters are considered standard Wiener processes and incorporated as additional states in the extended state vector. To deal with the new filtering problem, the paper designs the mean-square finite-dimensional filter for incompletely measured bilinear time-delay system states over linear observations. A closed system of the filtering equations is then derived for a bilinear time-delay state over linear observations. Finally, the paper solves the original joint estimation problem. The obtained solution is based on the designed mean-square filter for incompletely measured bilinear time-delay states over linear observations, taking into account that the filter for the extended state vector also serves as the identifier for the unknown parameters. In the example, performance of the designed state filter and parameter identifier is verified for a linear time-delay system with an unknown multiplicative parameter over linear observations.     

Robust state estimation for two-dimensional stochastic time-delay systems with missing measurements and sensor saturation

In this paper, the robust state estimation problem is investigated for a class of uncertain two-dimensional (2-D) systems with state delays and stochastic disturbances. The imperfect measurement output is subject to probabilistic data missing and sensor saturations. The missing phenomenon of the sensor measurement is governed by a stochastic variable satisfying the Bernoulli random binary distribution law, and the sensor saturation is considered to reflect the limited capacity of the communication networks. The parameter uncertainties are assumed to be norm-bounded and enter into the linear part of the system model in both directions. Through available but imperfect output measurements, a state estimator is designed to estimate the system states in the presence of data missing, sensor saturation, parameter uncertainties as well as stochastic perturbations. By defining an energy-like functional and conducting some stochastic analysis, several sufficient criteria in terms of matrix inequalities are established, which not only ensure the existence of the desired estimator gains but also guarantee the globally robustly asymptotic stability in the mean square of the estimation error dynamics. Finally, two numerical examples are exploited to show the effectiveness of the design method proposed in this paper.     

Robust H_{\infty } filtering for uncertain two-dimensional continuous systems with time-varying delays

This paper deals with the problem of delay-dependent robust $H_{\infty }$ H ∞ filtering for uncertain two-dimensional (2-D) continuous systems described by Roesser state space model with time-varying delays, with the uncertain parameters assumed to be of polytopic type. A sufficient condition for $H_{\infty }$ H ∞ noise attenuation is derived in terms of linear matrix inequalities, so a robust $H_{\infty }$ H ∞ filter can be obtained by solving a convex optimization problem. Finally, some examples are provided to illustrate the effectiveness of the proposed methodology.     

Reduced-order H/sub /spl infin// filtering for stochastic systems

This paper deals with the reduced-order H/sub /spl infin// filtering problem for stochastic systems. Necessary and sufficient conditions are obtained for the existence of solutions to the continuous-time and discrete-time problems in terms of certain linear matrix inequalities (LMIs) and a coupling nonconvex rank constraint condition. Furthermore, when these conditions are feasible, an explicit parametrization of all desired reduced-order filters corresponding to a feasible solution is given. In particular, when the reduced-order filter is restricted to be a static one, then simple conditions expressed by LMIs only without any rank constraints are derived, and a parametrization of all solutions is also given. Finally, an illustrative example is provided to show the effectiveness of the proposed approach.