Hybrid Feedback for Affine Nonlinear Systems with Application to Global Obstacle Avoidance (Extended Version)
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866909133992624128 |
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| author | Wang, Miaomiao Tayebi, Abdelhamid |
| author_facet | Wang, Miaomiao Tayebi, Abdelhamid |
| contents | This paper 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_04104 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Hybrid Feedback for Affine Nonlinear Systems with Application to Global Obstacle Avoidance (Extended Version) Wang, Miaomiao Tayebi, Abdelhamid Systems and Control This paper 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. |
| title | Hybrid Feedback for Affine Nonlinear Systems with Application to Global Obstacle Avoidance (Extended Version) |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2305.04104 |