Synthesis of Stabilizing Recurrent Equilibrium Network Controllers
This work addresses the problem of ensuring stability in nonlinear control systems for applications like robotics or autonomous systems, representing an incremental advance in controller synthesis methods.
The authors developed a parameterization for nonlinear dynamic controllers using recurrent equilibrium networks that guarantees exponential stability for partially observed dynamical systems with sector bounded nonlinearities, and demonstrated their method's effectiveness through simulated examples of controlling nonlinear plants.
We propose a parameterization of a nonlinear dynamic controller based on the recurrent equilibrium network, a generalization of the recurrent neural network. We derive constraints on the parameterization under which the controller guarantees exponential stability of a partially observed dynamical system with sector bounded nonlinearities. Finally, we present a method to synthesize this controller using projected policy gradient methods to maximize a reward function with arbitrary structure. The projection step involves the solution of convex optimization problems. We demonstrate the proposed method with simulated examples of controlling nonlinear plants, including plants modeled with neural networks.