The Scenario Approach for Stochastic Model Predictive Control with Bounds on Closed-Loop Constraint Violations

TL;DR

This paper introduces a novel Scenario-Based Model Predictive Control method that reduces conservatism and computational complexity by leveraging the structure of the MPC problem and interpreting probabilistic constraints as average-in-time.

Contribution

It presents a new SCMPC approach that accounts for MPC structure and average-in-time constraints, significantly reducing scenario requirements and conservatism.

Findings

Reduces the number of scenarios needed for control.

Eliminates conservatism in probabilistic constraint satisfaction.

Maintains computational efficiency and flexibility.

Abstract

Many practical applications of control require that constraints on the inputs and states of the system be respected, while optimizing some performance criterion. In the presence of model uncertainties or disturbances, for many control applications it suffices to keep the state constraints at least for a prescribed share of the time, as e.g. in building climate control or load mitigation for wind turbines. For such systems, a new control method of Scenario-Based Model Predictive Control (SCMPC) is presented in this paper. It optimizes the control inputs over a finite horizon, subject to robust constraint satisfaction under a finite number of random scenarios of the uncertainty and/or disturbances. While previous approaches have shown to be conservative (i.e. to stay far below the specified rate of constraint violations), the new method is the first to account for the special structure of the MPC problem in order to significantly reduce the number of scenarios. In combination with a new framework for interpreting the probabilistic constraints as average-in-time, rather than pointwise-in-time, the conservatism is eliminated. The presented method retains the essential advantages of SCMPC, namely the reduced computational complexity and the handling of arbitrary probability distributions. It also allows for adopting sample-and-remove strategies, in order to trade performance against computational complexity.