text: 1,47,1240845694421721089,92182169,Ian Manchester,New paper (with Ray Wang and Roland Toth) introducing virtual control contraction metrics: <LINK> Extends CCM to a wider class of problems. Generalises both local (gain scheduling) and global (exact linearisation) LPV control with stronger theoretical guarantees,https://arxiv.org/abs/2003.08513,"This paper proposes a novel approach to nonlinear state-feedback control design that has three main advantages: (i) it ensures exponential stability and $ \mathcal{L}_2 $-gain performance with respect to a user-defined set of reference trajectories, and (ii) it provides constructive conditions based on convex optimization and a path-integral-based control realization, and (iii) it is less restrictive than previous similar approaches. In the proposed approach, first a virtual representation of the nonlinear dynamics is constructed for which a behavioral (parameter-varying) embedding is generated. Then, by introducing a virtual control contraction metric, a convex control synthesis formulation is derived. Finally, a control realization with a virtual reference generator is computed, which is guaranteed to achieve exponential stability and $ \mathcal{L}_2 $-gain performance for all trajectories of the targeted reference behavior. Connections with the linear-parameter-varying (LPV) theory are also explored showing that the proposed methodology is a generalization of LPV state-feedback control in two aspects. First, it is a unified generalization of the two distinct categories of LPV control approaches: global and local methods. Second, it provides rigorous stability and performance guarantees when applied to the true nonlinear system, while such properties are not guaranteed for tracking control using LPV approaches. ","Virtual Control Contraction Metrics: Convex Nonlinear Feedback Design