Chance constrained nonlinear model predictive control for multiple systems with shared resources

Abstract

This paper proposes chance constrained nonlinear model predictive control (CCNMPC) for multiple interconnected systems sharing limited resources under uncertainty. Each subsystem with uncertainties has its local objectives and constraints and is coupled to the other subsystems through the shared resource. The shared resource limitation is satisfied by a global chance constraint which is decomposed into individual local chance constraints via the Bonferroni inequality, enabling a distributed solution approach. The chance constrained problem is then transformed into a sequence of smooth deterministic problems through the inner–outer approximation method, in which the smoothing parameter is shown to act as an implicit constraint-tightening mechanism that recovers the classical Gaussian tube-MPC back-off in the zero-smoothing limit. Within this framework, we prove probabilistic one-step recursive feasibility under unbounded disturbances. The resulting distributed nonconvex problem is solved using an adapted Augmented Lagrangian based Alternating Direction Inexact Newton (ALADIN) algorithm. The framework is validated on a shared battery energy storage system serving multiple microgrids with non-Gaussian demand forecast errors over a 24-h horizon: the empirical violation rates remain below the prescribed 5% threshold and the terminal invariance condition is satisfied with substantial margin throughout.