Reachability Guarantees for Cart-Pole Swing-Up and Stabilization

• URL: http://arxiv.org/abs/2606.28627v1
• Date: Fri, 26 Jun 2026 22:03:21 GMT
• Title: Reachability Guarantees for Cart-Pole Swing-Up and Stabilization
• Abstract summary: We present a reachability analysis of a switched energy-based/LQR controller that certifies convergence to the upright equilibrium.<n>We also propose an augmented Lyapunov function to regulate the steady-state cart velocity to zero, for which we establish almost-global convergence.<n>For the controller handoff, a switching region is designed to lie strictly within the LQR region of attraction, formally certifying the swing-up-to-stabilization transition.
• Score: 0.7310043452300737
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The cart-pole swing-up is a canonical benchmark for nonlinear control of underactuated systems, yet an end-to-end guarantee linking the global swing-up maneuver to the local stabilizer is seldom formalized. We present a reachability analysis of a switched energy-based/LQR controller that certifies convergence to the upright equilibrium from a compact set of initial conditions. The swing-up law is derived from an energy-error Lyapunov function; canceling the autonomous conservative term yields a strictly sign-definite Lyapunov derivative, and convergence follows from LaSalle's invariance principle. We also propose an augmented Lyapunov function to regulate the steady-state cart velocity to zero, for which we establish almost-global convergence. For the controller handoff, a switching region is designed to lie strictly within the LQR region of attraction, formally certifying the swing-up-to-stabilization transition. Numerical simulations corroborate the theoretical analysis.

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