Variance-constrained multiobjective control and filtering for nonlinear stochastic systems: A survey

The multiobjective control and filtering problems for nonlinear stochastic systems with variance constraints are surveyed. First, the concepts of nonlinear stochastic systems are recalled along with the introduction of some recent advances. Then, the covariance control theory, which serves as a practical method for multi-objective control design as well as a foundation for linear system theory, is reviewed comprehensively. The multiple design requirements frequently applied in engineering practice for the use of evaluating system performances are introduced, including robustness, reliability, and dissipativity. Several design techniques suitable for the multi-objective variance-constrained control and filtering problems for nonlinear stochastic systems are discussed. In particular, as a special case for the multi-objective design problems, the mixed H 2 / H ∞ control and filtering problems are reviewed in great detail. Subsequently, some latest results on the variance-constrained multi-objective control and filtering problems for the nonlinear stochastic systems are summarized. Finally, conclusions are drawn, and several possible future research directions are pointed out

A kepstrum approach to filtering, smoothing and prediction

The kepstrum (or complex cepstrum) method is revisited and applied to the problem of spectral factorization where the spectrum is directly estimated from observations. The solution to this problem in turn leads to a new approach to optimal filtering, smoothing and prediction using the Wiener theory. Unlike previous approaches to adaptive and self-tuning filtering, the technique, when implemented, does not require a priori information on the type or order of the signal generating model. And unlike other approaches - with the exception of spectral subtraction - no state-space or polynomial model is necessary. In this first paper results are restricted to stationary signal and additive white noise

Analysis of a non-minimum phase acoustic beamformer

The two input Griffiths-Jim acoustic beamformer is analysed in the frequency domain using a Wiener type formulation. Unlike previous solutions the approach here is to look at the problem of non-minimum phase acoustic transfer functions which are encountered in many real filtering problems. The polynomial transfer function approach gives an elegant way of obtaining the frequency response of the beamformer and gives new insight to the problem in general

The Optimal Projection Equations for Reduced-Order State Estimation: The Singular Measurement Noise Case

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/57879/1/OptProjSingStateEstTAC1987.pd

Filtering, smoothing, and prediction using a control-loop spectral factorization method for coloured noise

A method for the linear least-squares estimation of random signals contaminated with random noise is shown that uses a new method of spectral factorization. It is shown that the optimal filter can be written entirely in terms of the two spectral factors of signal plus noise and noise-alone, and can be applied to the general case of coloured and white additive noise. The method of spectral factorization used is novel and uses control-system methodology

Robust H-infinity sliding mode control for nonlinear stochastic systems with multiple data packet losses

This is the post-print version of this Article. The official published version can be accessed from the link below - Copyright @ 2012 John Wiley & SonsIn this paper, an ∞ sliding mode control (SMC) problem is studied for a class of discrete-time nonlinear stochastic systems with multiple data packet losses. The phenomenon of data packet losses, which is assumed to occur in a random way, is taken into consideration in the process of data transmission through both the state-feedback loop and the measurement output. The probability for the data packet loss for each individual state variable is governed by a corresponding individual random variable satisfying a certain probabilistic distribution over the interval [0 1]. The discrete-time system considered is also subject to norm-bounded parameter uncertainties and external nonlinear disturbances, which enter the system state equation in both matched and unmatched ways. A novel stochastic discrete-time switching function is proposed to facilitate the sliding mode controller design. Sufficient conditions are derived by means of the linear matrix inequality (LMI) approach. It is shown that the system dynamics in the specified sliding surface is exponentially stable in the mean square with a prescribed ∞ noise attenuation level if an LMI with an equality constraint is feasible. A discrete-time SMC controller is designed capable of guaranteeing the discrete-time sliding mode reaching condition of the specified sliding surface with probability 1. Finally, a simulation example is given to show the effectiveness of the proposed method.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the U.K. under Grant GR/S27658/01, the Royal Society of the U.K., the National Natural Science Foundation of China under Grant 61028008 and the Alexander von Humboldt Foundation of German

Bibliographic Review on Distributed Kalman Filtering

In recent years, a compelling need has arisen to understand the effects of distributed information structures on estimation and filtering. In this paper, a bibliographical review on distributed Kalman filtering (DKF) is provided.\ud The paper contains a classification of different approaches and methods involved to DKF. The applications of DKF are also discussed and explained separately. A comparison of different approaches is briefly carried out. Focuses on the contemporary research are also addressed with emphasis on the practical applications of the techniques. An exhaustive list of publications, linked directly or indirectly to DKF in the open literature, is compiled to provide an overall picture of different developing aspects of this area

An interim report of research on stochastic and adaptive systems

Interim report."March 20, 1981."Includes bibliographies.Air Force Office of Scientific Research Grant AFOSR-77-3281Cby Michael Athans, Sanjoy K. Mitter, Lena Valavani