arXiv subjects

Lorenzo Fici

Publications and source records attributed to Lorenzo Fici.

2 recordsLinked to original sources

arXiv2026

Implicit Predecessor-Based Region of Attraction Estimation and Robust Invariance Analysis for a Two-Wheeled Inverted Pendulum

Estimating the region of attraction (RoA) of nonlinear systems is fundamental for assessing closed-loop stability and ensuring safe operation. While Lyapunov-based approaches provide certified stability guarantees, they often yield conservative inner approximations of the RoA. This paper combines a certified Lyapunov-based positively invariant set with a predecessor-based implicit representation to compute a significantly less conservative inner approximation of the RoA while preserving formal stability guarantees. In addition, the robust positive invariance of the initial certified Lyapunov-based invariant set is analyzed under bounded additive input disturbances, providing formal robustness guarantees. The proposed methodology is demonstrated on a nonlinear two-wheeled inverted pendulum stabilized by a saturated linear quadratic regulator. The resulting RoA approximation is compared with the initial Lyapunov-certified invariant set and validated through Monte Carlo simulations and hardware experiments, showing a substantially enlarged certified operating region that matches the empirical closed-loop behavior. These results demonstrate the practical applicability of combining certified Lyapunov analysis with predecessor-based set propagation for RoA approximation and robustness assessment of nonlinear systems.

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arXiv2026

Region of Attraction Estimation for Linear Quadratic Regulator, Linear and Robust Model Predictive Control on a Two-Wheeled Inverted Pendulum

Nonlinear underactuated systems such as two-wheeled inverted pendulums (TWIPs) exhibit a limited region of attraction (RoA), which defines the set of initial conditions from which the closed-loop system converges to the equilibrium. The RoA of nonlinear and constrained systems is generally nonconvex and analytically intractable, requiring numerical or approximate estimation methods. This work investigates the estimation of the RoA for a TWIP stabilized under three model-based control strategies: saturated linear quadratic regulator (LQR), linear model predictive control (MPC), and constraint tightening MPC (CTMPC). We first derive a Lyapunov-based invariant set that provides a certified inner approximation of the RoA. Since this analytical bound is highly conservative, a Monte Carlo-based estimation procedure is then employed to obtain a more representative approximation of the RoA, capturing how the controllers behave beyond the analytically guaranteed region. The proposed methodology combines analytical guarantees with data-driven estimation, providing both a formally certified inner bound and an empirical characterization of the RoA, offering a practical way to evaluate controller performance without relying solely on conservative analytical bounds or purely empirical simulation.

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