H∞ filtering with randomly occurring sensor saturations and missing measurements

• Published in: Automatica (Oxford) Vol. 48; no. 3; pp. 556 - 562
• Main Authors: Wang, Zidong, Shen, Bo, Liu, Xiaohui
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01.03.2012; Elsevier
• Subjects: Applied sciences; Computer science; control theory; systems; Computer systems and distributed systems. User interface; Control system analysis; Control theory. Systems; Detection, estimation, filtering, equalization, prediction; Exact sciences and technology; Information, signal and communications theory; Missing measurements; Modelling and identification; Nonlinear systems; Random incomplete information; Randomly occurring sensor saturations; Regional [formula omitted] filters; Signal and communications theory; Signal, noise; Software; Telecommunications and information theory; Missing measurements; Randomly occurring sensor saturations; Nonlinear systems; Random incomplete information; Regional H∞ filters; Probabilistic approach; Saturation; Measurement sensor; Gain margin; H infinite control; Non linear control; Semi definite programming; Conditional probability; filters; Non linear system; Modeling; Convex programming; Asymptotic stability; Uncertain system; Regional H; Filter; System identification; Incomplete information; Sensor array; Ellipsoid
• DOI: 10.1016/j.automatica.2012.01.008
• ISSN: 0005-1098

In this paper, the H∞ filtering problem is investigated for a class of nonlinear systems with randomly occurring incomplete information. The considered incomplete information includes both the sensor saturations and the missing measurements. A new phenomenon of sensor saturation, namely, randomly occurring sensor saturation (ROSS), is put forward in order to better reflect the reality in a networked environment such as sensor networks. A novel sensor model is then established to account for both the ROSS and missing measurement in a unified representation by using two sets of Bernoulli distributed white sequences with known conditional probabilities. Based on this sensor model, a regional H∞ filter with a certain ellipsoid constraint is designed such that the filtering error dynamics is locally mean-square asymptotically stable and the H∞-norm requirement is satisfied. Note that the regional l2 gain filtering feature is specifically developed for the random saturation nonlinearity. The characterization of the desired filter gains is derived in terms of the solution to a convex optimization problem that can be easily solved by using the semi-definite program method. Finally, a simulation example is employed to show the effectiveness of the filtering scheme proposed in this paper.