16 research outputs found
Nonlinear Uncertainty Control with Iterative Covariance Steering
This paper considers the problem of steering the state distribution of a
nonlinear stochastic system from an initial Gaussian to a terminal distribution
with a specified mean and covariance, subject to probabilistic path
constraints. An algorithm is developed to solve this problem by iteratively
solving an approximate linearized problem as a convex program. This method,
which we call iterative covariance steering (iCS), is numerically demonstrated
by controlling a double integrator with quadratic drag force subject to
additive Brownian noise while satisfying probabilistic path constraints
Greedy Finite-Horizon Covariance Steering for Discrete-Time Stochastic Nonlinear Systems Based on the Unscented Transform
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. In principle, the latter
problem can be formulated as a density tracking problem, which seeks for a
feedback policy that will keep the probability density function of the state of
the system close, in terms of an appropriate metric, to the goal density. The
solution to the latter infinite-dimensional problem can be, however, a complex
and computationally expensive task. Instead, we propose a more tractable and
intuitive approach which relies on a greedy control policy. The latter control
policy is comprised of the first elements of the control policies that solve a
sequence of corresponding linearized covariance steering problems. Each of
these covariance steering problems relies only on information available about
the state mean and state covariance at the current stage and can be formulated
as 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