A Robust Observer-Based Control Method for Nonlinear Systems Based on Random Bit Errors

In this paper, the observer-based control problem is studied for nonlinear discrete-time systems with parameter uncertainty under the binary encoding scheme. In the network transmission processes of the measurement signal (from the sensor to the observer) and the control signal (from the controller to the actuator), the binary encoding scheme using the probabilistic quantization is employed to alleviate the burden and enhance the security of signal transmission through the network. Random bit errors are taken into account, which occur inevitably due to the influence of channel noises in binary symmetric channels and are described by Bernoulli distributed random variables. The effect of random bit errors is expressed by equivalent stochastic noises, which promotes the analysis and design afterwards. Stochastic nonlinearities are under consideration, which are characterized through statistical properties and cover several classes of common nonlinearities. Parameter uncertainty is included to reflect the model imprecision. The aim of this paper is to design suitable observer and controller so that the dynamics of the closed-loop system is exponentially ultimately bounded in mean square and fulfills the specified <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$H_{\infty}$</tex> performance constraint in the presence of parameter uncertainty, stochastic nonlinearities and random bit errors. According to Lyapunov stability theory and matrix inequality technique, a sufficient criterion is obtained conveniently for the design of the observer and the state feedback controller. Gain parameters of the observer and controller are computed directly via solving the acquired linear matrix inequalities. Effectiveness of the proposed control method is verified through a numerical simulation.