Controller Synthesis through Riemannian Optimization

Abstract

This dissertation studies controller synthesis for both open-loop and closed-loop systems through the usage of Riemannian optimization. In the closed-loop setting, the space of dynamic output-feedback controllers is formulated as a Riemannian orbit manifold, enabling fast and intrinsic optimization without reliance on extrinsic parameterizations. We establish topological characterizations of this space and provide convergence rate guarantees for the resulting algorithms. For open-loop control, we develop an intrinsic successive convexification framework that optimizes trajectories directly on the manifold of states and inputs, leading to improved numerical behavior in applications such as attitude guidance. This work demonstrates how exploiting the intrinsic manifold structure of control problems yields fast theoretically principled algorithms across open- and closed-loop control paradigms.