We consider covariance control problems for nonlinear stochastic systems. Our objective is to find an optimal control strategy to steer the state from an initial distribution to a terminal one with specified mean and covariance. This problem is considerably more complicated than previous studies on covariance control for linear systems. We leverage a widely used technique -differential dynamic programming -in nonlinear optimal control to achieve our goal. In particular, we adopt the stochastic differential dynamic programming framework to handle the stochastic dynamics. Additionally, to enforce the terminal statistical constraints, we construct a Lagrangian and apply a primal-dual type algorithm. Several examples are presented to demonstrate the effectiveness of our framework.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.