Concentration of Stochastic System Trajectories with Time-varying Contraction Conditions
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866915908345135104 |
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| author | Liu, Zishun Ma, Liqian Yu, Hongzhe Chen, Yongxin |
| author_facet | Liu, Zishun Ma, Liqian Yu, Hongzhe Chen, Yongxin |
| contents | We establish two concentration inequalities for nonlinear stochastic system under time-varying contraction conditions. The key to our approach is an energy function termed Averaged Moment Generating Function (AMGF). By combining it with incremental stability analysis, we develop a concentration inequality that bounds the deviation between the stochastic system state and its deterministic counterpart. As this inequality is restricted to single time instance, we further combine AMGF with martingale-based methods to derive a concentration inequality that bounds the fluctuation of the entire stochastic trajectory. Additionally, by synthesizing the two results, we significantly improve the trajectory-level concentration inequality for strongly contractive systems. Given the probability level $1-δ$, the derived inequalities ensure an $\mO(\sqrt{\log(1/δ))}$ bound on the deviation of stochastic trajectories, which is tight under our assumptions. Our results are exemplified through a case study on stochastic safe control. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_01403 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Concentration of Stochastic System Trajectories with Time-varying Contraction Conditions Liu, Zishun Ma, Liqian Yu, Hongzhe Chen, Yongxin Optimization and Control Systems and Control We establish two concentration inequalities for nonlinear stochastic system under time-varying contraction conditions. The key to our approach is an energy function termed Averaged Moment Generating Function (AMGF). By combining it with incremental stability analysis, we develop a concentration inequality that bounds the deviation between the stochastic system state and its deterministic counterpart. As this inequality is restricted to single time instance, we further combine AMGF with martingale-based methods to derive a concentration inequality that bounds the fluctuation of the entire stochastic trajectory. Additionally, by synthesizing the two results, we significantly improve the trajectory-level concentration inequality for strongly contractive systems. Given the probability level $1-δ$, the derived inequalities ensure an $\mO(\sqrt{\log(1/δ))}$ bound on the deviation of stochastic trajectories, which is tight under our assumptions. Our results are exemplified through a case study on stochastic safe control. |
| title | Concentration of Stochastic System Trajectories with Time-varying Contraction Conditions |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2604.01403 |