LQG for Constrained Linear Systems: Indirect Feedback Stochastic MPC with Kalman Filtering

• DOI: 10.23919/ecc57647.2023.10178356
• Publication Date: 2023-08-01T18:00:50Z
• Authors: Simon Muntwiler; Kim P. Wabersich; Robert Miklos; Melanie N. Zeilinger
• Keywords: Initialization

We present an output feedback stochastic model predictive control (SMPC) approach for linear systems subject to Gaussian disturbances and measurement noise probabilistic constraints on system states inputs. The presented combines a Kalman filter state estimation with indirect SMPC, which is initialized predicted nominal state, while of the current estimate enters through objective SMPC problem. For this combination, we establish recursive feasibility problem due chosen initialization, closed-loop chance constraint satisfaction thanks appropriate tightening in also considering uncertainty. Additionally, show that specific design choices problem, unconstrained linear-quadratic-Gaussian (LQG) solution recovered if it feasible given initial condition considered constraints. demonstrate fact numerical example, resulting controller can provide non-conservative satisfaction.