Virtual Control Contraction Metrics: Convex Nonlinear Feedback Design via Behavioral Embedding

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This paper presents a systematic 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.