Finite-horizon covariance control of state-affine nonlinear systems with application to proton beamline calibration

In this paper, we address the problem of finite-horizon distribution steering of state-affine nonlinear systems using open-loop control. The terminal distribution is constrained by an isotropy constraint which enforces uniformity in all directions. With the nonlinear dynamics and the isotropy constraint, a constrained nonlinear optimization problem is formulated. To solve this nonlinear problem, this paper proposes a sequential linearized algorithm that generates feasible iterates. The main advantage of the proposed algorithm is that it requires no a priori knowledge of the global Lipschtiz property of the gradients of the cost and constraint functions. The performance of the proposed algorithm is demonstrated by a beamline calibration problem in proton therapy.