Optimal attitude control of a rigid body
The control of satellite motion is studied under the condition that the cost functional measuring the overall angular velocity is minimized. The author uses the Jurdjevic's geometric method quoted in the bibliography. This technique can be considered as classical calculus of variations applied to optimal control problems without constraints, but it can be also formulated for control problems on arbitrary manifolds and presented in coordinate-free language. The evolution state is modelled by a differential equation in the space of nonlinear states using the angular velocities \(\omega_k\) of rotations around the principal axes of the body. The Pontryagin's maximum principle allows to determine optimal trajectories and integral curves at a certain time -- an invariant Hamiltonian vector field. The optimal angular velocities \(\omega_k^*(t)\) can then be found by means of Poisson brackets applied to a system of differential equations. The unknown optimal torques can be determined by using the Euler's equations. Finally, the author presents eight particular cases together with numerical results.
scientific article; zbMATH DE number 897234