Lyapunov Matrix-Based Guaranteed Cost Dynamic Positioning Control for Unmanned Marine Vehicles With Time Delay

Xin Yang, Li-Ying Hao, Tieshan Li, Yang Xiao, Guoyong Liu

Abstract: This paper presents the design of a Lyapunov matrix-based guaranteed cost dynamic positioning controller for unmanned marine vehicles (UMVs) under time delays. Compared to traditional time delays compensation methods. This article first introduces a novel Lyapunov matrix-based complete type Lyapunov--Krasovskii functional (LKF), incorporating more comprehensive information about time delays and system states. The strategy employs the linear matrix inequality (LMI) method and Jensen's inequality to derive sufficient conditions for the existence of the controller under the constructed complete LKF framework. The proposed controller ensures that the state errors of UMVs asymptotically converge to zero, with the adaptive $H_{\infty}$ performance index not exceeding $\gamma_{0}$, and that the cost function has an upper bound. Finally, the effectiveness of the proposed approach is verified through simulation results.

Submission Number: 173