PID Control for Uncertain Systems with Integral Measurements and DoS Attacks Using a Binary Encoding Scheme

In this paper, an observer-based proportional-integral-derivative (PID) controller is designed for a class of uncertain nonlinear systems with integral measurements, denial-of-service (DoS) attacks and bounded stochastic noises under a binary encoding scheme (BES). Parameter uncertainty is involved with a norm-bounded multiplicative expression. Integral measurements are considered to reflect the delayed signal collection of sensor. For communication, BES is put into use in the signal transmission process from the sensor to the observer and from the controller to the actuator. Random bit flipping is described that may take place caused by channel noises, whose impact is described by a stochastic noise. Randomly occurring DoS attacks are taken account of that may appear due to the shared network, which block the transmitted signals totally. Three sets of Bernoulli-distributed random variables are adopted to reveal the random occurrence of uncertainties, bit flipping and DoS attacks. The aim of this paper is to design an observer-based PID controller which guarantees that the closed-loop system reaches exponential ultimate boundedness in mean square (EUBMS). By virtue of Lyapunov stability theory, stochastic analysis technique and matrix inequality method, a sufficient condition is developed for designing the observer-based PID controller such that the closed-loop system achieves EUBMS performance, and the ultimate upper bound of the controlled output is bounded and such a bound is minimized. The gain matrices of the observer-based controller are acquired explicitly by virtue of solving the solution to an optimized issue with several matrix inequality constraints. Two simulation examples are given which indicate the usefulness of the proposed control method in this paper adequately.