A Sandwich Control System with Dual Stochastic Impulses

Chuanlin Liao, Dan Tu, Yuming Feng, Wei Zhang,Zitao Wang, and B. O. Onasanya

Dear editor,

Along with the progress of science and technology and the development of social civilization, control system brings an increasingly significant function in daily life. The application field of control system is very wide, for instance, in mobile technology [1],artificial earth satellite [2], pest control [3], etc.

Ribeiro [4] first put forward the concept of random pulse in 1967.At present, impulsive control is used in networked control [5], secure communication [6], etc. In the 21st century, the impulsive control has been used in synchronization of coupled system, intelligent fault identification, image encryption, etc. [7]–[9]. Meanwhile, alternate control is often applied to traffic, irrigation of crop and current switching control [10]–[12], etc. Adaptive control is often used in robots [13], neural networks [14], etc.

At present, there are lots of means to stabilize a nonlinear system.For example, impulsive control [1]–[9], [15]–[17], alternate control[10]–[12], adaptive control [13], [14], [18], etc. In this letter, the goal is to devise some superior control systems after researching the general means of system control being used currently.

Fig. 1. Operating principle of SCSDSI within one control cycle T.

then, system (2) has global exponential stability.

Proof: The Lyapunov function constructed is shown as follow:

x(0)=(2,−1,−2)TFig. 2. The chaotic phenomena of Chua’s oscillator with .

Therefore, the Chua’s system (15) is exponentially stable by Theorem 1. The time response curves of Chua’s oscillator, using the proposed method, are shown in Fig. 3.

Fig. 3. The time response curves of Chua’s oscillator by using SCSDSI.

Conclusions: In this letter, a new model of Sandwich control system with dual stochastic impulses (SCSDSI), where the exact time of occurrence of impulses is uncertain, was proposed. It established that the chaotic Chua’s circuit can be controlled by this new method.In fact, by this method, a host of other nonlinear systems in robotics,electronics and other fields can be controlled.

Acknowledgments: This work was supported by the Foundation of Chongqing Municipal Key Laboratory of Institutions of Higher Education ([2017]3), and Foundation of Chongqing Development and Reform Commission (2017[1007]).