Hybrid Feedback for Affine Nonlinear Systems With Application to Global Obstacle Avoidance

• 成果类型: Article
• 署名作者: Wang, Miaomiao; Tayebi, Abdelhamid
• 署名单位: Huazhong University of Science & Technology; Lakehead University; Western University (University of Western Ontario)
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2024.3372463
• 发表日期: 2024
• 页码: 5546-5553
• 关键词: Switches; navigation; Nonlinear systems; robots; Lyapunov methods; Collision avoidance; asymptotic stability; affine nonlinear systems; navigation functions; obstacle avoidance; synergistic hybrid feedback

摘要

This article explores the design of hybrid feedback for a class of affine nonlinear systems with topological constraints that prevent global asymptotic stability. A new hybrid control strategy is introduced, which differs conceptually from the commonly used synergistic hybrid approaches. The key idea involves the construction of a generalized synergistic Lyapunov function whose switching variable can either remain constant or dynamically change between jumps. Based on this new hybrid mechanism, a generalized synergistic hybrid feedback control scheme, endowed with global asymptotic stability guarantees, is proposed. This hybrid control scheme is then improved through a smoothing mechanism that eliminates discontinuities in the feedback term. Moreover, the smooth hybrid feedback is further extended to a larger class of systems through the integrator backstepping approach. The proposed hybrid feedback schemes are applied to solve the global obstacle avoidance problem using a new concept of synergistic navigation functions. Finally, numerical simulation results are presented to illustrate the performance of the proposed hybrid controllers.