Researchers have proposed a double-channel event-triggered adaptive tracking control scheme for nonstrict-feedback nonlinear systems, addressing critical challenges like "algebraic loops" and "jumps of virtual control laws (JVCL)" in traditional control methods. This innovation significantly reduces communication bandwidth usage, offering a new approach for efficient control of complex industrial systems.
In industrial settings, numerous devices such as ball and beam systems, vehicle coupled turning models, and multi-link manipulators can be described as nonstrict-feedback nonlinear systems. Controlling these systems poses multiple challenges: "algebraic loop" issues often arise in traditional backstepping control designs; event-triggered control (ETC) frequently suffers from communication congestion due to clustered state transmission; and jumps in virtual control laws can disrupt system stability. To tackle these problems, a research team including Yingjie Deng and Fangcheng Liu from Yanshan University developed this novel control scheme.
The core innovations of the scheme are threefold: 1) Taking advantage of the bounded characteristic of fuzzy basis functions, the proposed scheme includes merely one adaptive law in each step of the virtual control laws. 2) The devised virtual control laws are not involved in the final control input but presented for the analysis use. This train of thought can unite the event-triggered control (ETC) design in both channels and solve the jumps of virtual control laws (JVCL) problem flexibly. 3) The proposed separate transmission principle ensures the effective utilization of the unoccupied channel in the inter-event time. In comparison to the conventional event-triggered mechanism, the communication bandwidth is significantly decreased.
"This design achieves an excellent balance between control precision and communication efficiency," the research team stated. "In simulations of a third-order nonlinear system, the proposed scheme (DETC-ST) achieved a tracking error of only 0.1014, which is less than that of the traditional clustered transmission scheme (ETC-CT). The scheme without solving the JVCL problem (ETC-WJ) is difficult to ensure closed-loop system stability. Moreover, it only requires the bandwidth of 1 state, while traditional schemes need at least the bandwidth of 4 states."
The scheme also performed well in simulation validation on a single-link manipulator system, with bounded state tracking errors, stable convergence of adaptive laws, and event intervals in both SC and CA channels meeting design requirements, confirming its engineering practicality. Theoretical analysis proves that all tracking and estimation errors of the system are ultimately bounded, and there is no "Zeno behavior".
Beyond industrial control, the design of this scheme can provide references for scenarios requiring precise regulation and efficient communication, such as multi-agent collaboration and remote robot control. Currently, the scheme has the limitation of increased computational burden on the sensor side. The research team plans to explore controller-side centralized adaptive law designs in the future to further enhance its engineering application value.
This paper "Double-channel event-triggered adaptive tracking control of nonstrict-feedback nonlinear systems with separate state transmission" was published in Advanced Equipment.
Deng Y, Liu F, Xu Y, Li F, Ni T, et al. Double-channel event-triggered adaptive tracking control of nonstrict-feedback nonlinear systems with separate state transmission. Adv. Equip. 2025(1):0003, https://doi.org/10.55092/ae20250003 .
