Optimal Mass Transport over the Euler Equation
This work addresses angular stabilization in spacecraft with stochastic uncertainties, but it is incremental as it applies existing optimal mass transport theory to a specific bilinear drift case.
The paper tackles the problem of optimally steering the probability distribution of a rigid body's angular velocity, governed by the Euler equation, to achieve angular stabilization with stochastic initial and terminal states, and provides analytical and numerical results for the optimal controller synthesis.
We consider the finite horizon optimal steering of the joint state probability distribution subject to the angular velocity dynamics governed by the Euler equation. The problem and its solution amounts to controlling the spin of a rigid body via feedback, and is of practical importance, for example, in angular stabilization of a spacecraft with stochastic initial and terminal states. We clarify how this problem is an instance of the optimal mass transport (OMT) problem with bilinear prior drift. We deduce both static and dynamic versions of the Eulerian OMT, and provide analytical and numerical results for the synthesis of the optimal controller.