Comparative Analysis of Control Strategies for Linear Systems with Noise: Optimal Horizon Selection for MPC

This paper addresses the unresolved problem of optimal prediction horizon selection for Model Predictive Control (MPC) in linear systems with noise, comparing it with Linear Quadratic Regulator (LQR), Kalman-filtered LQR, and Sliding Mode Control (SMC). A Lyapunov-based framework quantifies the trade-off between output variance and computational cost, proving that N = 10 minimizes the variance (0.092202) under Gaussian noise. An adaptive horizon strategy enhances robustness by 5%, and new stability proofs for correlated noise are provided. Simulations confirm MPC’s superior noise suppression, outperforming LQR (7.488106), Kalman+LQR (8.393631), and SMC (0.475674). Applications in autonomous driving, CO2 conversion, IoT, audio, drones, medical, and aerospace systems demonstrate a broad impact.