Free Final Time Adaptive Mesh Covariance Steering via Sequential Convex Programming
This addresses the challenge of controlling stochastic systems with multiplicative noise for robotics or aerospace applications, representing an incremental improvement in covariance steering methods.
The paper tackles the problem of covariance steering for nonlinear stochastic systems with free final time by developing a sequential convex programming framework that simultaneously optimizes control policies and temporal grids, achieving improved covariance accuracy through adaptive time allocation.
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.