Continuous-time Constrained Funnel Synthesis for Incrementally Quadratic Nonlinear Systems
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| Format: | Preprint |
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2025
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| _version_ | 1866918198278881280 |
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| author | Kim, Taewan Luo, Dayou Açıkmeşe, Behçet |
| author_facet | Kim, Taewan Luo, Dayou Açıkmeşe, Behçet |
| contents | This paper presents a convex optimization-based framework for synthesizing time-varying controlled invariant funnels and associated feedback control around a given nominal trajectory for nonlinear systems subject to bounded disturbances. Nonlinearities are modeled using incremental quadratic constraints, including Lipschitz, L-smooth, and sector-bounded nonlinearities. Funnel invariance is ensured via a DLMI. Together with pointwise-in-time LMIs for state and input constraints, we formulate a continuous-time funnel synthesis problem. To solve it using numerical optimal control techniques, the DLMI is reformulated into a differential matrix equality (DME) and an LMI, where the DME acts as a funnel dynamics equation. We explore different formulations of these funnel dynamics. Continuous-time constraint satisfaction is addressed through two convex methods: one based on intermediate constraint-checking points, and another using a successive convexification method with subgradients to handle nondifferentiable maximum eigenvalue functions. Theoretical justification is provided for the existence of a measurable and integrable subgradient for the latter. The method is demonstrated on two numerical examples: the control of a unicycle and a 6-degree-of-freedom quadrotor for obstacle avoidance. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_08868 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Continuous-time Constrained Funnel Synthesis for Incrementally Quadratic Nonlinear Systems Kim, Taewan Luo, Dayou Açıkmeşe, Behçet Optimization and Control This paper presents a convex optimization-based framework for synthesizing time-varying controlled invariant funnels and associated feedback control around a given nominal trajectory for nonlinear systems subject to bounded disturbances. Nonlinearities are modeled using incremental quadratic constraints, including Lipschitz, L-smooth, and sector-bounded nonlinearities. Funnel invariance is ensured via a DLMI. Together with pointwise-in-time LMIs for state and input constraints, we formulate a continuous-time funnel synthesis problem. To solve it using numerical optimal control techniques, the DLMI is reformulated into a differential matrix equality (DME) and an LMI, where the DME acts as a funnel dynamics equation. We explore different formulations of these funnel dynamics. Continuous-time constraint satisfaction is addressed through two convex methods: one based on intermediate constraint-checking points, and another using a successive convexification method with subgradients to handle nondifferentiable maximum eigenvalue functions. Theoretical justification is provided for the existence of a measurable and integrable subgradient for the latter. The method is demonstrated on two numerical examples: the control of a unicycle and a 6-degree-of-freedom quadrotor for obstacle avoidance. |
| title | Continuous-time Constrained Funnel Synthesis for Incrementally Quadratic Nonlinear Systems |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2511.08868 |