Stochastic Model Predictive Control for Linear Systems using Probabilistic Reachable Sets
For control engineers, it offers a method to handle probabilistic constraints in linear systems with unbounded disturbances, though it is an incremental extension of robust MPC techniques.
The paper proposes a stochastic MPC algorithm for linear systems with unbounded disturbances and probabilistic constraints, using probabilistic reachable sets for constraint tightening. It guarantees closed-loop chance constraint satisfaction under unimodal disturbances and provides an asymptotic average performance bound, demonstrated with examples.
In this paper we propose a stochastic model predictive control (MPC) algorithm for linear discrete-time systems affected by possibly unbounded additive disturbances and subject to probabilistic constraints. Constraints are treated in analogy to robust MPC using a constraint tightening based on the concept of probabilistic reachable sets, which is shown to provide closed-loop fulfillment of chance constraints under a unimodality assumption on the disturbance distribution. A control scheme reverting to a backup solution from a previous time step in case of infeasibility is proposed, for which an asymptotic average performance bound is derived. Two examples illustrate the approach, highlighting closed-loop chance constraint satisfaction and the benefits of the proposed controller in the presence of unmodeled disturbances.