Scalable synthesis of safety certificates from data with application to learning-based control

Abstract

The control of complex systems faces a tradeoff between high performance and safety guarantees, which in particular restricts the application of learning-based methods to safety-critical systems. A recently proposed framework to address this issue is the use of a safety controller, which guarantees to keep the system within a safe region of the state space. This paper introduces efficient techniques for the synthesis of a safe set and control law, which offer improved scalability properties by relying on approximations based on convex optimization problems. The first proposed method requires only an approximate linear system model and Lipschitz continuity of the unknown nonlinear dynamics. The second method extends the results by showing how a Gaussian process prior on the unknown system dynamics can be used in order to reduce conservatism of the resulting safe set. We demonstrate the results with numerical examples, including an autonomous convoy of vehicles.

A Survey on Learning-Based Model Predictive Control: Toward Path Tracking Control of Mobile Platforms

“…by relying on the approximations based on convex optimization problems [127]. linear and potentially larger-scale systems with security certification, a securit work is proposed to improve the learning-based and insecure control strategies.…”

“…Different sets are different in their dynamic allocation of local sets and provide different trade-offs between the required communication and the realized set size. The synthesis of a security set and control law offer improved scalability by relying on the approximations based on convex optimization problems [127]. For nonlinear and potentially larger-scale systems with security certification, a security framework is proposed to improve the learning-based and insecure control strategies.…”

A Review of Safe Online Learning for Nonlinear Control Systems

“…Further efficiencies could be made by selectively updating the most important parameters while using less critical parameters from the previous time step to update the dynamics model. Wabersich [101] uses a linear quadratic control Lyapunov function from sampled data points and convex optimisation within a safety framework. The sampled data is further enhanced by adopting the use of a GP model to provide a priori uncertainty.…”

Linear Model Predictive Safety Certification for Learning-Based Control

“…Closely related to the approach proposed in this paper, the concept of a safety framework for learning-based control emerged from robust reachability analysis, robust invariance, as well as classical Lyapunov-based methods [30], [11], [31], [32]. The concept consists of a safe set in the state space and a safety controller as originally proposed in [33] for the case of perfectly known system dynamics in the context of safety barrier functions.…”