Kehan Long

I am currently a PhD candidate in Mathematics and Contextual Robotics Institute at University of California, San-Diego. I work at the Existential Robotics Laboratory. I am fortunate to be advised by Prof. Nikolay Atanasov and Prof. Melvin Leok. I also work closely with Prof. Jorge Cortés.

My academic journey began at the University of Illinois,Urbana-Champaign, where I obtained a B.S. degree in Applied Mathematics, complemented by a minor in Computer Engineering.

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Research Interests

My research interests lie at the intersection of robotics, machine learning, and control theory, with an emphasis on safe autonomy. My work focuses on developing safety and stability verification methodologies for robotic control systems amid model and environmental uncertainties. My goal is to devise scalable and robust approaches for operating autonomous systems within highly dynamic and uncertain settings, while providing safety and stability guarantees.

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Selected Publications

Distributionally Robust Policy and Lyapunov-Certificate Learning

This article presents novel methods for synthesizing distributionally robust stabilizing neural controllers and certificates for control systems under model uncertainty. A key challenge in designing controllers with stability guarantees for uncertain systems is the accurate determination of and adaptation to shifts in model parametric uncertainty during online deployment. We tackle this with a novel distributionally robust formulation of the Lyapunov derivative chance constraint ensuring a monotonic decrease of the Lyapunov certificate. To avoid the computational complexity involved in dealing with the space of probability measures, we identify a sufficient condition in the form of deterministic convex constraints that ensures the Lyapunov derivative constraint is satisfied. We integrate this condition into a loss function for training a neural network-based controller and show that, for the resulting closed-loop system, the global asymptotic stability of its equilibrium can be certified with high confidence, even with Out-of-Distribution (OoD) model uncertainties. To demonstrate the efficacy and efficiency of the proposed methodology, we compare it with an uncertainty-agnostic baseline approach and several reinforcement learning approaches in two control problems in simulation.

Distributionally Robust Lyapunov Function Search Under Uncertainty

This paper devises methods for proving Lyapunov stability of dynamical systems subject to disturbances with an unknown distribution. We assume only a finite set of disturbance samples is available and that the true online disturbance realization may be drawn from a different distribution than the given samples. We formulate an optimization problem to search for a sum-of-squares (SOS) Lyapunov function and introduce a distributionally robust version of the Lyapunov function derivative constraint. We show that this constraint may be reformulated as several SOS constraints for polynomial systems. For general and higher dimensional systems, we provide a distributionally robust chance-constrained formulation for neural network Lyapunov function search.

Safe and Stable Control Synthesis for Uncertain System Models via Distributionally Robust Optimization

This paper considers enforcing safety and stability of dynamical systems in the presence of model uncertainty. We assume that only a finite set of model parametric uncertainty samples is available and formulate a distributionally robust chance-constrained program (DRCCP) for control synthesis with CBF safety and CLF stability guarantees. To facilitate efficient computation of control inputs during online execution, we present a reformulation of the DRCCP as a second-order cone program (SOCP).

Safe Control Synthesis With Uncertain Dynamics and Constraints

This paper explores the synthesis of safe controls for dynamical systems with either probabilistic or worst-case uncertainty in both the dynamics model and the safety constraints (environments). We formulate novel probabilistic and robust (worst-case) control Lyapunov function (CLF) and control barrier function (CBF) constraints that take into account the effect of uncertainty in either case. We show that either the probabilistic or the robust (worst-case) formulation leads to a second-order cone program (SOCP), which enables efficient safe stabilizing control synthesis in real-time.

Learning Barrier Functions with Memory for Robust Safe Navigation

This paper investigates safe navigation in unknown environments, using on-board range sensing to construct control barrier functions online. To represent different objects in the environment, we use the distance measurements to train neural network approximations of the signed distance functions incrementally with replay memory. This allows us to formulate a novel robust control barrier safety constraint which takes into account the error in the estimated distance fields and its gradient. Our formulation leads to a second-order cone program, enabling safe and stable control synthesis in a prior unknown environments.

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