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

Abstract

AbstractThe 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.