Scenario MPC for linear time-varying systems with individual chance constraints

This paper presents a practicable Scenario-Based Model Predictive Control (Scenario MPC) approach for linear, time-varying systems with additive disturbances. Robust MPC propagates uncertainty through the dynamics based on uncertainty sets and Stochastic MPC by multi-variable convolutions of probability distributions. The idea of Scenario MPC is to propagate the uncertainty by using sampled uncertainty scenarios. This approach is computationally efficient and (implicitly) accounts for the probabilistic distribution of disturbances. Moreover, there exists a mathematical connection between the violation rate of individual chance constraints over time and the required sample size. The theory builds on very recent results in scenario-based optimization for multi-stage stochastic decision problems. In many applications, Scenario MPC requires only a very small sample size (generally a few tens of samples). This fact is demonstrated for a large-scale example of supply chain management, for which Scenario MPC yields a good control performance.