Probabilistic-Constrained H ∞ Tracking Control for a Class of Stochastic Nonlinear Systems Subject to DoS Attacks and Measurement Outliers

Abstract

In this study, the probabilistic-constrained <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {H}_{\infty }$ </tex-math></inline-formula> tracking control problem is addressed for a class of stochastic nonlinear systems subject to measurement outliers, stochastic nonlinearities and DoS attacks. The considered systems have the following characters: 1) an unequal redundant-channel communication protocol is adopted to resist the DoS attacks and enhance the reliability of packet transmission. Different from some existing redundant-channel approaches, the considered two channels have different transmission abilities. 2) The measurement outliers (e.g., some unexpected large amplitude disturbances) are concerned and a saturation-function-based observer is proposed to avert the side effects from measurement outliers. 3) The DoS jamming attacks are considered in this paper, and an aperiodic DoS model is utilized. 4) Both sector-bounded nonlinear function and stochastic nonlinear function are involved in the considered systems, which makes the considered systems more general. To compensate the negative effect of the DoS jamming attacks and enhance the reliability of the packet transmission, a novel redundant-channel-based switching protocol is proposed to schedule data transmission when the plant suffers malicious cyber attacks. The primary objective of the present study is to design tracking controller such that the prescribed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {H}_{\infty }$ </tex-math></inline-formula> control performance is reached and probabilistic constraints on the tracking error are satisfied simultaneously. To achieve this objective, a probabilistic-constrained <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {H}_{\infty }$ </tex-math></inline-formula> tracking control algorithm is established to obtain tracking controller gains and minimize the prescribed set of the constraint. Finally, two simulation examples are used to validate the practicability of our devised strategy.