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

We present an output feedback stochastic model predictive control (SMPC) approach for linear systems subject to Gaussian disturbances and measurement noise and probabilistic constraints on system states and inputs. The presented approach combines a linear Kalman filter for state estimation with an i...

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Bibliographic Details
Published inarXiv.org
Main Authors Muntwiler, Simon, Wabersich, Kim P, Miklos, Robert, Zeilinger, Melanie N
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 17.11.2023
Subjects
Closed loops
Computer Science - Systems and Control
Constraints
Control systems
Feasibility
Feedback control
Kalman filters
Linear systems
Mathematics - Optimization and Control
Noise measurement
Output feedback
Predictive control
State estimation
Stochastic models
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Summary:We present an output feedback stochastic model predictive control (SMPC) approach for linear systems subject to Gaussian disturbances and measurement noise and probabilistic constraints on system states and inputs. The presented approach combines a linear Kalman filter for state estimation with an indirect feedback SMPC, which is initialized with a predicted nominal state, while feedback of the current state estimate enters through the objective of the SMPC problem. For this combination, we establish recursive feasibility of the SMPC problem due to the chosen initialization, and closed-loop chance constraint satisfaction thanks to an appropriate tightening of the constraints in the SMPC problem also considering the state estimation uncertainty. Additionally, we show that for specific design choices in the SMPC problem, the unconstrained linear-quadratic-Gaussian (LQG) solution is recovered if it is feasible for a given initial condition and the considered constraints. We demonstrate this fact for a numerical example, and show that the resulting output feedback controller can provide non-conservative constraint satisfaction.
ISSN:2331-8422
DOI:10.48550/arxiv.2212.00351