Control Contraction Metrics on Finsler Manifolds
For nonlinear control systems, this work extends CCMs to a more general geometric framework, but the improvement is incremental as it builds on existing CCM theory.
This paper generalizes Control Contraction Metrics (CCMs) to Finsler manifolds, enabling non-Riemannian metrics, and provides open-loop and sampled-data controllers that avoid real-time computation of globally shortest paths.
Control Contraction Metrics (CCMs) provide a nonlinear controller design involving an offline search for a Riemannian metric and an online search for a shortest path between the current and desired trajectories. In this paper, we generalize CCMs to Finsler geometry, allowing the use of non-Riemannian metrics. We provide open loop and sampled data controllers. The sampled data control construction presented here does not require real time computation of globally shortest paths, simplifying computation.