Adaptive Nussbaum design using composite triggering condition for stochastic nonlinear systems with multiple unknown control directions

Abstract

The traditional Nussbaum-type functions encounter challenges when extended to systems with multiple unknown control directions, as the coupling between the Nussbaum-type function and Nussbaum-type gain may lead to mutual elimination. To address this issue, a novel Nussbaum-type function is introduced to handle multiple unknown control directions for stochastic systems. The stability of the proposed Nussbaum-based design can be guaranteed using the Lyapunov analysis. To conserve computational resources, a static composite event-triggered mechanism is integrated with intermittent feedback in the Nussbaum-based design. In contrast to conventional event-triggering mechanisms that depend solely on control signals, the presented design incorporates tracking errors into the event-triggering conditions. Moreover, to further alleviate computational burdens, we further develop a dynamic composite event-triggered mechanism. With the overall design scheme, bounded tracking errors and reduced computational burden can be ensured. Simulation examples validate the efficacy of the proposed adaptive Nussbaum composite event-based robust control design.