Event-triggered adaptive neural networks control for fractional-order nonstrict-feedback nonlinear systems with unmodeled dynamics and input saturation

Event‐triggered adaptive tracking control for uncertain fractional‐order nonstrict‐feedback nonlinear systems via command filtering

“…From the literature, 49 the event‐triggered mechanism with a dynamic threshold condition is formulated as follows $$$$ u(t)=\varpi \left({t}_k\right),t\in \left[{t}_k,{t}_{k+1}\right), $$$$ $$$$ {t}_{k+1}=\operatorname{inf}\left\{t\ge {t}_k:|\varpi (t)-u(t)|\ge {\hslash}_1|u(t)|+{\hslash}_3(t)\right\}, $$$$ where $$$ {t}_k\left(k\in {N}^{+}\right) $$$ represents triggering instants with the initial time $$$ {t}_0=0 $$$, $$$ \varpi (t) $$$ and $$$ u(t) $$$ stand for the input and output signal, respectively. $$$ {\hslash}_3(t) $$$ is the dynamic threshold condition which is defined as <...…”

“…From the literature, 49 the event-triggered mechanism with a dynamic threshold condition is formulated as follows…”

“…Note that, most event‐triggered control approaches are based on static threshold conditions, being set as a predefined constant, which cannot reach requirements in certain practical cases particularly while the current state deviates the desired state considerably in short periods 46,47 . Relatively, a dynamic triggering threshold condition, which is designed as a function related to the tracking error directly, has been exploited in References 48 and 49. This makes the times of updating controller can be adjusted dynamically based on the tracking error, which enhances the control performance under event‐triggered control.…”

Adaptive neural consensus tracking control of distributed nonlinear multiagent systems with unmodeled dynamics

“…Therefore, a variety of better design schemes have been developed. In reference 37, the paper focuses on the intelligent‐estimation‐based tracking controller design problem for a class of switched non‐lower triangular nonlinear systems with unmodeled dynamics and an output constraint. In reference 38, an adaptive NNs control scheme is developed for a class of multiple‐input and multiple‐output uncertain nonlinear systems with unmeasured states and unmodeled dynamics.…”

On characterisations of the input to state stability properties for conformable fractional order bilinear systems

“…Following this work, the input‐to‐state practical stability of fractional‐order systems was further extended in ref. [9] and the notion of Mittag–Leffler ISS Lyapunov function was proposed in order to design an event‐triggered adaptive neural networks controller for fractional systems under Caputo derivative. Moreover, the Lyapunov characterisation of Mittag–Leffler input‐to‐state stability of the fractional differential equations with exogenous inputs was presented in ref.…”