Safe Nonlinear Control Using Robust Neural Lyapunov-Barrier Functions (2109.06697v2)

Abstract: Safety and stability are common requirements for robotic control systems; however, designing safe, stable controllers remains difficult for nonlinear and uncertain models. We develop a model-based learning approach to synthesize robust feedback controllers with safety and stability guarantees. We take inspiration from robust convex optimization and Lyapunov theory to define robust control Lyapunov barrier functions that generalize despite model uncertainty. We demonstrate our approach in simulation on problems including car trajectory tracking, nonlinear control with obstacle avoidance, satellite rendezvous with safety constraints, and flight control with a learned ground effect model. Simulation results show that our approach yields controllers that match or exceed the capabilities of robust MPC while reducing computational costs by an order of magnitude.

• The paper introduces robust control Lyapunov-barrier functions (rCLBFs) that guarantee safety and stability in uncertain nonlinear systems.
• It leverages a model-based learning strategy with robust convex optimization to synthesize near real-time feedback controllers.
• Simulations on vehicle trajectory, satellite rendezvous, and UAV control demonstrate competitive performance with reduced computational cost compared to robust MPC.

Safe Nonlinear Control Using Robust Neural Lyapunov-Barrier Functions

The paper presents a framework leveraging neural Lyapunov-barrier functions and robust convex optimization for synthesizing feedback controllers that ensure safety and stability in nonlinear control systems, despite uncertainties in model parameters. The author provides an approach that synthesizes robust feedback controllers using a model-based learning strategy inspired by robust convex optimization principles and Lyapunov theory. The key advancement in this research is the introduction of robust control Lyapunov-barrier functions (rCLBFs), which broaden the capability of control methods to handle parametric uncertainties within nonlinear systems.

The challenges addressed in this work pertain to synthesizing controllers that guarantee both safety and stability while overcoming uncertainties, which is a long-standing open issue in control systems design. By extending control Lyapunov and control barrier functions (CLFs and CBFs) into robust CLBFs, the authors provide theoretically sound guarantees for system stability and safety, even under conditions where typical robust model predictive control (MPC) methods may fail, particularly outside linear cases.

The framework's efficacy is demonstrated through simulations involving various complex control problems, such as vehicle trajectory tracking, satellite rendezvous with non-convex constraints, and UAV flight control with learned ground effects. Results have shown that robust CLBF approaches either match or exceed the performance capabilities of robust MPC while achieving substantial reductions in computational cost, enabling near real-time control which is otherwise challenging for robust MPC due to computational heaviness and reliance on linear model assumptions.

Implications and Future Work

The implications of this work span both theoretical and practical domains. Theoretically, introducing rCLBFs represents an advancement in the control systems field, offering tight safety and stability certification in uncertain environments. Practically, the reductions in computation time expand the applicability of advanced control methods, making them viable for real-time systems with significant dynamic complexity.

The paper sets the stage for future research in several directions. For instance, the capability to validate and verify these learned certificates across diverse environments remains a ripe area for development. Moreover, exploring scalable verification strategies, such as using neural network verification techniques, could offer valuable frameworks for ascertaining the reliability and robustness of such learned functions. Another promising direction is integrating these techniques within systems characterized by noisy sensor data and delayed control, which closely align with real-world scenarios.

Given these methods' potential to generalize beyond seen examples, further research can adaptively incorporate techniques to explore problem domains characterized by high-dimensional and uncertain state spaces. Examining the method's effectiveness across different types of robotic platforms in real-world conditions will provide valuable insights and enhancements for deploying robust and safe nonlinear controllers in practical settings.

In conclusion, this research offers significant contributions toward achieving safe and stable control solutions in complex, nonlinear, and uncertain environments, providing a pathway to more intelligent and responsive control systems. The methodological advancements presented through the use of neural Lyapunov-barrier functions coupled with robust optimization highlight the possibilities of expanding beyond conventional control paradigms to systems capable of adapting to and operating satisfactorily within unpredictable real-world environments.