Kalman Filter-Based Optimization for Linear Model Predictive Control

Abstract

This paper proposes a novel optimization strategy for Linear Model Predictive Control (MPC) of linear discrete-time systems, in which the classical quadratic programming (QP) or Newton-based update step is replaced by a Kalman Filter (KF) gain update. The control input sequence is treated as the state vector of a fictitious dynamical system, and the reference tracking error over the prediction horizon serves as the innovation signal. The Hessian inversion required in the Newton method is replaced by the Joseph-form covariance update, leading to a computationally lightweight and numerically robust algorithm. A formal analogy between the classical penalty parameter λ and the KF tuning parameters q and r is established, showing that λ ≈ r/q, which provides intuitive insight into controller tuning. The steady-state Kalman gain can be computed offline via a Riccati iteration, reducing online computation to a single matrix-vector product per time step. The proposed method is validated through simulation on a second-order open-loop unstable discrete-time LTI system under multi-step and sinusoidal reference signals.