Controller design for nonlinear systems subject to both input saturation and asymmetry time‐varying state constraints: A novel network‐based approach

Abstract

Summary In this article, the issues of asymmetric input saturation and asymmetric time‐varying state constraints are integrated into nonlinear systems for the first time, and a new adaptive tracking control strategy is proposed based on the multi‐dimensional Taylor network (MTN) method. Firstly, by introducing a continuous auxiliary function, the input saturation is transformed into a smooth model with bounded error. Secondly, MTNs are employed to estimate nonlinear functions, asymmetric barrier Lyapunov functions (ABLFs) are constructed to make all state variables meet asymmetric constraints, and then a novel control scheme with simple structure is developed via backstepping. Thirdly, according to the Lyapunov stability theory, it is proved that all signals in the closed‐loop systems are bounded, and all state variables do not violate the constraints. Finally, three examples show the effectiveness of the proposed scheme.

Adaptive tracking control for a class of stochastic nonlinear systems with input delay using multidimensional Taylor network

“…With this advantage, the MTN-based adaptive control scheme for stochastic nonlinear systems with unknown nonlinear functions, combined with the classical adaptive technique and backstepping method, has been designed and attracted wide attention [31,33,50,52]. At present, this control strategy has been widely used in nonlinear systems [53][54][55], stochastic systems [56][57][58], switching systems [59][60][61], and so on. However, like the above mentioned, there were few literatures on tracking control of stochastic nonlinear systems with input delay based on MTN, and most of them used Pade approximation to deal with the problem of input delay, while there is no scheme to compensate for the effect of input delay through auxiliary system, which promotes the research of this paper.…”