Feedback design for multi-agent systems: A saddle point approach

In this paper we propose a dynamic state feedback controller for an input affine nonlinear system that asymptotically stabilizes a point in the output space that is implicitly given as the solution to a convex optimization problem. The construction of the feedback law is based on saddle point flows for convex optimization problems and a backstepping technique. An explicit solution of the optimization problem is not needed for the controller design. We show how the design approach can be applied to multi-agent systems, yielding a decentralized controller. For a particular example, we extend the controller to the output feedback case.