Progressive Barrier Lyapunov Functions for Nonlinear Constrained Control Systems
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912460771950592 |
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| author | Nohooji, Hamed Rahimi Voos, Holger |
| author_facet | Nohooji, Hamed Rahimi Voos, Holger |
| contents | This paper introduces the Progressive Barrier Lyapunov Function (p-BLF) for output- and full-state-constrained nonlinear control systems. Unlike traditional BLF methods, where control effort continuously increases as the state approaches the constraint boundaries, the p-BLF maintains minimal control effort in unconstrained regions and increases it progressively toward the boundaries. In contrast to previous methods with predefined safe zones and abrupt control activation, the p-BLF provides a smooth transition, improving continuity in the control response and enhancing stability by reducing chattering. Two forms of the p-BLF, logarithmic-based and rational-based, are developed to handle systems with either output constraints or full-state constraints. Theoretical analysis guarantees that all system states remain within the defined constraints, ensuring boundedness and stability of the closed-loop system. Simulation results validate the effectiveness of the proposed method in constrained nonlinear control. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_06288 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Progressive Barrier Lyapunov Functions for Nonlinear Constrained Control Systems Nohooji, Hamed Rahimi Voos, Holger Systems and Control This paper introduces the Progressive Barrier Lyapunov Function (p-BLF) for output- and full-state-constrained nonlinear control systems. Unlike traditional BLF methods, where control effort continuously increases as the state approaches the constraint boundaries, the p-BLF maintains minimal control effort in unconstrained regions and increases it progressively toward the boundaries. In contrast to previous methods with predefined safe zones and abrupt control activation, the p-BLF provides a smooth transition, improving continuity in the control response and enhancing stability by reducing chattering. Two forms of the p-BLF, logarithmic-based and rational-based, are developed to handle systems with either output constraints or full-state constraints. Theoretical analysis guarantees that all system states remain within the defined constraints, ensuring boundedness and stability of the closed-loop system. Simulation results validate the effectiveness of the proposed method in constrained nonlinear control. |
| title | Progressive Barrier Lyapunov Functions for Nonlinear Constrained Control Systems |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2411.06288 |