Comparative Study of Linear Quadratic Regulator, Linear and Robust Model Predictive Control, and a Neural Network-based Controller : Application to SIGI, a two-wheeled inverted pendulum

Sammanfattning

This master’s thesis investigates and compares control strategies for the stabilisation and reference tracking of a two-wheeled inverted pendulum robot. The study focuses on three model-based approaches: linear quadratic regulator (LQR), linear model predictive control (MPC), and constraint tightening MPC (CTMPC), alongside a data-driven neural network-based controller (NNC) designed for realtime implementation. The evaluation is divided into simulation and experimental phases. The simulation phase consists of two parts: trajectory simulations under nominal initial conditions and estimation of the region of attraction (RoA) using a Monte Carlo approach. To this end, we employ a certified terminal set computed directly from the nonlinear dynamics, which guarantees invariance for the closed-loop system and allows stopping simulations once the set is reached. Validation on hardware is carried out for the LQR and NNC controllers through stabilisation and reference tracking tasks, while MPC and CTMPC are not feasible for real-time implementation on the embedded platform. This limitation motivates the adoption of the NNC, which approximates the behaviour of CTMPC while remaining suitable for deployment on hardware. In simulation, all controllers perform comparably under nominal conditions. The estimated RoA is identical for the model-based controllers, whereas the NNC exhibits a smaller RoA. In hardware experiments under uncertainties, however, the NNC outperforms the LQR, benefiting from being trained on the robust CTMPC policy. The study demonstrates that while conventional model-based controllers achieve strong nominal performance, robustness to uncertainties can be improved through robust formulations and their learned approximations. The NNC offers a computationally efficient way to imitate CTMPC control behaviour on embedded hardware, enabling improved performance over the LQR under real-world conditions without requiring online optimisation.