Discrete control of nonlinear stochastic systems driven by Levy process

In this paper, the stabilization is studied for a complex dynamic model which involves nonlinearities, uncertainty, and Levy noises. This paper also discusses the controller discretization and presents a new algorithm to obtain the upper bound for the sample interval through which the exponential stability of the discrete system can still be guaranteed. Firstly, an integral sliding surface is designed to obtain the sliding mode dynamics for the considered stochastic Levy process. By using Lyapunov theory, generalized Ito formula and some inequality techniques, the exponential stability is proved in the sense of mean square for sliding mode dynamics. The reachability of the sliding mode surface is also ensured by designing a sliding mode control law. Secondly, the continuous-time controller is discretized from the point of control cost, and the squared difference is analyzed for the states before and after the discretization. Different from those classical stochastic differential equations driven by Brownian motions, the noise is supposed to be Levy type and the squared difference is analyzed in different cases. Furthermore, we obtain the largest sampling interval through which the discretized controller can still stabilize the Levy process driven stochastic system. Finally, a simulation for a drill bit system is given to demonstrate the results under the algorithms. & COPY; 2023 The Franklin Institute. Published by Elsevier Inc. All rights reserved.

Automated summary

This paper studies the stabilization of a complex dynamic model with nonlinearities, uncertainty, and Levy noises. It proposes a new algorithm to determine the upper bound for the sample interval that ensures the exponential stability of the discrete system. Firstly, an integral sliding surface is designed using Lyapunov theory and generalized Ito formula to prove the exponential stability in mean square sense. Secondly, the continuous-time controller is discretized and the squared difference of states is analyzed. The largest sampling interval that stabilizes the Levy process driven stochastic system is obtained.