Symbolic Regression of Control Lyapunov Functions
Please login to view abstract download link
Designing stabilizing controllers for nonlinear systems with guaranteed performance remains difficult in practice. Optimal control formulations are often computationally intractable, while the construction of Control Lyapunov Functions (CLFs) typically relies on problem-specific insight or restrictive assumptions. This work presents a symbolic regression framework for the automatic discovery of analytic CLFs and the synthesis of stabilizing feedback laws using Sontag’s universal formula. The approach produces explicit stability certificates while avoiding predefined function templates. Symbolic regression searches over a broad space of mathematical expressions and evaluates candidate CLFs using a fitness function that enforces Lyapunov stability conditions together with simple performance-related criteria. Once a valid CLF is identified, a stabilizing controller is obtained directly from the analytic expression, yielding a closed-loop system with provable asymptotic stability. The method does not require the system dynamics, controller, or Lyapunov function to be polynomial, nor does it assume a fixed functional structure. The proposed framework is evaluated on four nonlinear benchmark systems and compared with standard baseline controllers, including linear--quadratic regulation (LQR) and neural Lyapunov-based controllers. Across all examples, symbolic regression consistently identifies compact and interpretable CLFs that stabilize the system from a wide range of initial conditions. The resulting controllers achieve performance comparable to neural controllers and typically outperform LQR when operating outside the local linearization region. Compared to sum-of-squares (SOS) approaches, the proposed method avoids polynomial restrictions on the dynamics and Lyapunov function and does not rely on degree selection. This makes it applicable to systems with general nonlinearities, including transcendental terms. Overall, the results demonstrate that symbolic regression provides a practical and certifiable alternative for nonlinear control design, bridging the gap between analytical Lyapunov methods and data-driven control approaches.
