Towards Robust Data-Driven Control Synthesis for Nonlinear Systems with Actuation Uncertainty
This work provides a starting point for addressing model uncertainty in nonlinear control theory, which is a significant challenge for ensuring model-based controllers transfer to real-world systems.
This paper addresses robust control synthesis for nonlinear systems with actuation uncertainty by developing a data-driven approach using Control Certificate Functions (CCFs). The result is a convex optimization-based controller that provides data-dependent guarantees for properties like stability and safety, validated through simulations with an inverted pendulum.
Modern nonlinear control theory seeks to endow systems with properties such as stability and safety, and has been deployed successfully across various domains. Despite this success, model uncertainty remains a significant challenge in ensuring that model-based controllers transfer to real world systems. This paper develops a data-driven approach to robust control synthesis in the presence of model uncertainty using Control Certificate Functions (CCFs), resulting in a convex optimization based controller for achieving properties like stability and safety. An important benefit of our framework is nuanced data-dependent guarantees, which in principle can yield sample-efficient data collection approaches that need not fully determine the input-to-state relationship. This work serves as a starting point for addressing important questions at the intersection of nonlinear control theory and non-parametric learning, both theoretical and in application. We validate the proposed method in simulation with an inverted pendulum in multiple experimental configurations.