Free Final Time Adaptive Mesh Covariance Steering via Sequential Convex Programming
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866908893007839232 |
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| author | Pilipovsky, Joshua |
| author_facet | Pilipovsky, Joshua |
| contents | In this paper we develop a sequential convex programming (SCP) framework for free-final-time covariance steering of nonlinear stochastic differential equations (SDEs) subject to both additive and multiplicative diffusion. We cast the free-final-time objective through a time-normalization and introduce per-interval time-dilation variables that induce an adaptive discretization mesh, enabling the simultaneous optimization of the control policy and the temporal grid. A central difficulty is that, under multiplicative noise, accurate covariance propagation within SCP requires retaining the first-order diffusion linearization and its coupling with time dilation. We therefore derive the exact local linear stochastic model (preserving the multiplicative structure) and introduce a tractable discretization that maintains the associated diffusion terms, after which each SCP subproblem is solved via conic/semidefinite covariance-steering relaxations with terminal moment constraints and state/control chance constraints. Numerical experiments on a nonlinear double-integrator with drag and velocity-dependent diffusion validate free-final-time minimization through adaptive time allocation and improved covariance accuracy relative to frozen-diffusion linearizations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_14868 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Free Final Time Adaptive Mesh Covariance Steering via Sequential Convex Programming Pilipovsky, Joshua Optimization and Control Systems and Control In this paper we develop a sequential convex programming (SCP) framework for free-final-time covariance steering of nonlinear stochastic differential equations (SDEs) subject to both additive and multiplicative diffusion. We cast the free-final-time objective through a time-normalization and introduce per-interval time-dilation variables that induce an adaptive discretization mesh, enabling the simultaneous optimization of the control policy and the temporal grid. A central difficulty is that, under multiplicative noise, accurate covariance propagation within SCP requires retaining the first-order diffusion linearization and its coupling with time dilation. We therefore derive the exact local linear stochastic model (preserving the multiplicative structure) and introduce a tractable discretization that maintains the associated diffusion terms, after which each SCP subproblem is solved via conic/semidefinite covariance-steering relaxations with terminal moment constraints and state/control chance constraints. Numerical experiments on a nonlinear double-integrator with drag and velocity-dependent diffusion validate free-final-time minimization through adaptive time allocation and improved covariance accuracy relative to frozen-diffusion linearizations. |
| title | Free Final Time Adaptive Mesh Covariance Steering via Sequential Convex Programming |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2603.14868 |