Youla-REN: Learning Nonlinear Feedback Policies with Robust Stability Guarantees
This addresses the challenge of designing stable controllers in robotics or control systems, offering a novel parameterization that simplifies learning, though it appears incremental as it builds on existing neural network architectures.
The paper tackles the problem of learning nonlinear feedback controllers for uncertain systems with guaranteed stability, proposing a framework that ensures all policies are globally exponentially stable and can be generalized to unseen data.
This paper presents a parameterization of nonlinear controllers for uncertain systems building on a recently developed neural network architecture, called the recurrent equilibrium network (REN), and a nonlinear version of the Youla parameterization. The proposed framework has "built-in" guarantees of stability, i.e., all policies in the search space result in a contracting (globally exponentially stable) closed-loop system. Thus, it requires very mild assumptions on the choice of cost function and the stability property can be generalized to unseen data. Another useful feature of this approach is that policies are parameterized directly without any constraints, which simplifies learning by a broad range of policy-learning methods based on unconstrained optimization (e.g. stochastic gradient descent). We illustrate the proposed approach with a variety of simulation examples.