Synthesis and SOS-based Stability Verification of a Neural-Network-Based Controller for a Two-wheeled Inverted Pendulum

TL;DR

This paper demonstrates a novel SOS-based method for verifying the stability of neural-network controllers for a two-wheeled inverted pendulum, showing successful stabilization and improved performance over traditional controllers.

Contribution

It introduces a new SOS-based stability verification procedure for neural-network controllers applied to a complex inverted pendulum system.

Findings

Verified local asymptotic stability of the NNC

Achieved a meaningful region of attraction estimate

Demonstrated improved control performance experimentally

Abstract

This work newly establishes the feasibility and practical value of a sum of squares (SOS)-based stability verification procedure for applied control problems utilizing neural-network-based controllers (NNCs). It successfully verifies closed-loop stability properties of a NNC synthesized using a generalizable procedure to imitate a robust, tube-based model predictive controller (MPC) for a two-wheeled inverted pendulum demonstrator system. This is achieved by first developing a state estimator and control-oriented model for the two-wheeled inverted pendulum. Next, this control-oriented model is used to synthesize a baseline linear-quadratic regulator (LQR) and a robust, tube-based MPC, which is computationally too demanding for real-time execution on the demonstrator system's embedded hardware. The generalizable synthesis procedure generates an NNC imitating the robust, tube-based MPC. Via an SOS-based stability verification procedure, a certificate of local asymptotic stability and a relevant inner estimate of the region of attraction (RoA) are obtained for the closed-loop system incorporating this NNC. Finally, experimental results on the physical two-wheeled inverted pendulum demonstrate that the NNC both stabilizes the system, and improves the control performance compared to the baseline LQR in both regulation and reference-tracking tasks.