$α$-stability of Differentially Flat Systems with Application to Newton-Raphson Tracking Control for Vehicle Dynamics
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866916058293600256 |
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| author | Sabry, Aadila Ali Notomista, Gennaro |
| author_facet | Sabry, Aadila Ali Notomista, Gennaro |
| contents | This paper studies the $α$-stability property of differentially flat nonlinear dynamical systems. The results build off the recently introduced notion of $α$-stability, which is particularly amenable to characterize the ability of a system to track dynamic output reference signals. We consider systems controlled using the Newton-Raphson tracking controller, which results in closed-form control policies, therefore it is computationally efficient, and it has been shown to be effective to control a large variety of mobile robots, including autonomous vehicles. The main results of the paper consist in sufficient conditions for the $α$-stability of differentially flat systems and for the equivalence between the proposed control algorithm and the Newton-Raphson tracking controller applied directly to the nonlinear dynamics. We demonstrate the behavior of the proposed controller applied to the kinematic unicycle and dynamic bicycle models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_29231 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | $α$-stability of Differentially Flat Systems with Application to Newton-Raphson Tracking Control for Vehicle Dynamics Sabry, Aadila Ali Notomista, Gennaro Dynamical Systems Systems and Control This paper studies the $α$-stability property of differentially flat nonlinear dynamical systems. The results build off the recently introduced notion of $α$-stability, which is particularly amenable to characterize the ability of a system to track dynamic output reference signals. We consider systems controlled using the Newton-Raphson tracking controller, which results in closed-form control policies, therefore it is computationally efficient, and it has been shown to be effective to control a large variety of mobile robots, including autonomous vehicles. The main results of the paper consist in sufficient conditions for the $α$-stability of differentially flat systems and for the equivalence between the proposed control algorithm and the Newton-Raphson tracking controller applied directly to the nonlinear dynamics. We demonstrate the behavior of the proposed controller applied to the kinematic unicycle and dynamic bicycle models. |
| title | $α$-stability of Differentially Flat Systems with Application to Newton-Raphson Tracking Control for Vehicle Dynamics |
| topic | Dynamical Systems Systems and Control |
| url | https://arxiv.org/abs/2605.29231 |