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

  • Authors

    • Isamu Ohnishi Hiroshima University
    https://doi.org/10.14419/28v4a204
  • Model Predictive Control; LQR; Sliding Mode Control; Noise Robustness; Prediction Horizon

  • Abstract

    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.

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  • How to Cite

    Ohnishi, I. (2025). Comparative Analysis of Control Strategies for Linear Systems with Noise: Optimal Horizon Selection for MPC. International Journal of Advanced Mathematical Sciences, 11(2), 46-55. https://doi.org/10.14419/28v4a204