Control Contraction Metrics: Convex and Intrinsic Criteria for Nonlinear Feedback Design
This work offers a new convex framework for nonlinear control design, addressing the challenge of global stabilization for control engineers.
The paper introduces control contraction metrics, providing convex and intrinsic conditions for exponential stabilizability of nonlinear control systems, with necessity and sufficiency for feedback linearizable systems. The method enables global stabilization with local optimality, demonstrated via sum-of-squares programming on an unstable polynomial system.
We introduce the concept of a control contraction metric, extending contraction analysis to constructive nonlinear control design. We derive sufficient conditions for exponential stabilizability of all trajectories of a nonlinear control system. The conditions have a simple geometrical interpretation, can be written as a convex feasibility problem, and are invariant under coordinate changes. We show that these conditions are necessary and sufficient for feedback linearizable systems, and also derive novel convex criteria for exponential stabilization of a nonlinear submanifold of state space. We illustrate the benefits of convexity by constructing a controller for an unstable polynomial system that combines local optimality and global stability, using a metric found via sum-of-squares programming.