2022/01/26 by Shahriar Talebi, Mehran Mesbahi, Talebi, Shahriar +1 · 2 citations
Computer Science · Engineering · Physics and Astronomy · #Differential Geometry (math.DG) #FOS: Electrical engineering #FOS: Mathematics #Model Reduction and Neural Networks #Optimization and Control (math.OC) #Stability and Control of Uncertain Systems #Stochastic Gradient Optimization Techniques #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2201.11157
openalex publication_date 2022/01/26 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28
In this paper, we study linearly constrained policy optimization over the manifold of Schur stabilizing controllers, equipped with a Riemannian metric that emerges naturally in the context of optimal control problems. We provide extrinsic analysis of a generic constrained smooth cost function, that subsequently facilitates subsuming any such constrained problem into this framework. By studying the second order geometry of this manifold, we provide a Newton-type algorithm that does not rely on the exponential mapping nor a retraction, while ensuring local convergence guarantees. The algorithm hinges instead upon the developed stability certificate and the linear structure of the constraints. We then apply our methodology to two well-known constrained optimal control problems. Finally, several numerical examples showcase the performance of the proposed algorithm.