Adaptive Neural Dynamic-Memory Event-Triggered Control of High-Order Random Nonlinear Systems With Deferred Output Constraints

Shanlin Liu, Ben Niu, Guangdeng Zong, Xudong Zhao, Ning Xu

Abstract: This paper investigates the deferred output constraint (DOC) issues of high-order random nonlinear systems. The DOC indicates that the system output is constrained within a given range after the system running for a period of time, rather than being constrained at the beginning. This leads to an obstacle that the well used barrier Lyapunov function method is invalid because it is not defined at the initial stage. For this reason, a prescribed-time scaling function and a barrier function are introduced. Then, to more accurately describe the disturbances in nature, this paper considers a more common stochastic process than white noise, which is called colored noise. In addition, a dynamic-memory event-triggered mechanism (DMETM) that takes into account the influence of historical information of internal dynamic variables on trigger conditions is proposed to reduce the waste of communication resources. With the assistance of Lyapunov stability theory and backstepping approach, it is shown that our developed DMETM-based control scheme can guarantee that all signals are bounded in the presence of colored noises. Ultimately, two simulation examples are included to demonstrate the effectiveness of the proposed theory. Note to Practitioners—Since higher-order nonlinear systems can describe nonlinear features in system dynamics, some complex actual systems such as induction motorcycles and space vehicles can be modeled as such systems. In engineering applications, controlled systems are usually affected by random noises from external environment, thus colored noises are introduced in this paper. Compared with white noises, colored noises can describe disturbances in nature more accurately and reasonably. In addition, to ensure that practical systems such as car operation systems and robotic arm systems can work safely, their DOC issues need to be considered. However, the traditional barrier Lyapunov functions (BLFs) cannot solve the DOC problems because they are not defined in the initial stage, hence the prescribed-time scaling and barrier functions are proposed. Meanwhile, to circumvent the problem of limited communication bandwidth, a DMETM with delay terms of internal variables is devised.