Greedy Finite-Horizon Covariance Steering for Discrete-Time Stochastic Nonlinear Systems Based on the Unscented Transform

Covariance Over Time	Sampled Trajectories

In this work, we consider the problem of steering the first two moments of the uncertain state of a discrete-time nonlinear stochastic system to prescribed goal quantities at a given final time. We propose a tractable and intuitive approach which relies on a greedy control policy which is comprised of the first elements of the control policies that solve a sequence of corresponding linearized covariance steering problems. Each of the latter problems is associated with a tractable (finite-dimensional) convex program. At each stage, the information on the state statistics is updated by computing approximations of the predicted state mean and covariance of the resulting closed-loop nonlinear system at the next stage by utilizing the (scaled) unscented transform. Numerical simulations that illustrate the key ideas of our approach are also presented.

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