Adaptive fixed-time fuzzy control for delayed recycling continuous stirred tank reactor with asymmetric time-varying full-state constraints

Recently, there are some results concerning stability and finite-time stability control for continuous stirred tank reactors (CSTR). However, when considering the control of time- delay CSTR systems or fixed-time stability of CSTR systems, there are relatively few articles involved. In this paper, we first consider the CSTR system that includes both of the above factors simultaneously, that is, the adaptive fixed-time fuzzy control design problem for a CSTR with a delayed recycle stream and asymmetric time-varying full-state constraints. Firstly, based on existing works, we present an improved practical fixed-time stability criterion, which can be applied to more complex nonlinear systems. Then, we construct time-varying asymmetric integral barrier Lyapunov functions to handle asymmetric time-varying full-state constraints. Next, fuzzy logic systems are used to approximate the unknown functions of the system, and a sliding mode differentiator is introduced to avoid the "explosion of complexity" of the time derivative of the virtual controller. Furthermore, using the improved practical fixed-time stability criterion, we present the adaptive fixed-time fuzzy controller design processes that can ensure tracking performance in a fixed-time, and states of the system never violate their constraint bounds. Finally, a simulation example is provided to verify the effectiveness of the proposed control strategy.