Adaptive Learning-based Model Predictive Control for Uncertain Interconnected Systems: A Set Membership Identification Approach
Ahmed Aboudonia, John Lygeros
TL;DR
The paper tackles robust control of large-scale interconnected systems with uncertain interconnections by casting the problem as discrete-time linear dynamics with unknown coupling strengths $a_{ij}$. It introduces an online two-phase framework: a learning phase that uses distributed set-membership identification to shrink the uncertainty set $\mathcal{W}_i$, and an adaptation phase where a rigid-tube based MPC computes optimal trajectories while updating ingredients such as the prestabilizing gain $K_i(t)$ and tightened constraint sets. The authors prove recursive feasibility and input-to-state stability, and demonstrate a favorable trade-off between performance and computation in simulations against robust, adaptive, and learning-based MPC schemes. The results suggest practical applicability to networks like microgrids or vehicle platoons, where online learning of couplings can safely improve control performance within a scalable distributed architecture.
Abstract
We propose a novel adaptive learning-based model predictive control (MPC) scheme for interconnected systems which can be decomposed into several smaller dynamically coupled subsystems with uncertain coupling. The proposed scheme is mainly divided into two main online phases; a learning phase and an adaptation phase. Set membership identification is used in the learning phase to learn an uncertainty set that contains the coupling strength using online data. In the adaptation phase, rigid tube-based robust MPC is used to compute the optimal predicted states and inputs. Besides computing the optimal trajectories, the MPC ingredients are adapted in the adaptation phase taking the learnt uncertainty set into account. These MPC ingredients include the prestabilizing controller, the rigid tube, the tightened constraints and the terminal ingredients. The recursive feasibility of the proposed scheme as well as the stability of the corresponding closed-loop system are discussed. The developed scheme is compared in simulations to existing schemes including robust, adaptive and learning-based MPC.