Performance Analysis of Stochastic Model Predictive Control with Direct and Indirect Feedback

Recursively feasible stochastic predictive control using an interpolating initial state constraint -- extended version

“…One exception is the implementation suggested in [7, Agl. 1], which provides an unnecessarily large probability of constraint satisfaction and thus results in a significant performance deterioration, compare also [30] for a detailed discussion of this effect. Furthermore, the proposed approach (λ k ∈ [0, 1]) outperforms the case distinction (λ k ∈ {0, 1}), which outperforms the indirect feedback (λ k = 0).…”

“…To ensure closed-loop chance constraint satisfaction under more general conditions, the indirect feedback SMPC was suggested in [8], where the feasible set is independent of the realized disturbances. Further extensions of this SMPC paradigm can be found in [6], [29] and a comparison to the case distinction SMPC is given in [30].…”

Stochastic Hybrid Model Predictive Control using Gaussian Processes for Systems with Piecewise Residual Dynamics

“…Since searching over the space of all possible control laws is generally infeasible, one usually defines a form of control law to optimize over. Here an "indirect" feedback control law [66] is considered which is defined as,…”

“…The term "indirect" comes from the fact that feedback of the state mean µ x k is not directly considered as is conventional [92] but rather consider the deviation of the true state from the mean. [64] compares the two approaches and shows how the indirect feedback law prevents over-conservatism that might result from using the direct feedback law. Remark 3.5.1.…”