カートポール振り上げと安定化の到達可能性保証
Reachability Guarantees for Cart-Pole Swing-Up and Stabilization
エネルギー制御とLQRを切り替える制御器で、カートポールの振り上げから直立安定化までの収束を理論的に保証し、数値シミュレーションで検証した論文。
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分類: eess.SY, cs.RO, cs.SY, math.OC
原文アブストラクト
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 design exploits the phase-space geometry of the conservative pendulum: the upright equilibrium lies on the homoclinic orbit, and an energy-shaping law drives the energy error to zero, steering the pendulum onto this orbit; convergence follows from LaSalle's invariance principle. An augmented Lyapunov function additionally regulates the steady-state cart velocity to zero, and we prove almost-global convergence of the resulting closed-loop system. A local LQR with a certified ellipsoidal region of attraction stabilizes the upright equilibrium, and we verify numerically that the swing-up phase delivers the state into this region, formalizing the handoff. Numerical simulations corroborate the theoretical analysis.
