Free Final Time Adaptive Mesh Covariance Steering via Sequential Convex Programming

TL;DR

This paper introduces a sequential convex programming framework for covariance steering of nonlinear stochastic systems with free final time, utilizing adaptive mesh discretization and exact local linearization to improve accuracy under multiplicative noise.

Contribution

It develops a novel SCP method that adaptively optimizes control and time discretization for stochastic systems with multiplicative noise, maintaining diffusion structure for better covariance propagation.

Findings

Adaptive time discretization improves covariance accuracy.

Method effectively handles multiplicative noise in nonlinear systems.

Numerical results show superior performance over fixed discretization.

Abstract

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.