SVD-Based Robust Distributed MPC for Tracking Systems Coupled in Dynamics With Global Constraints

This article presents a novel singular value decomposition (SVD)-based robust distributed model predictive control (SVD-RDMPC) strategy for linear systems with additive uncertainties. The system is globally constrained and consists of multiple interrelated subsystems with bounded disturbances, each of whom has local constraints on states and inputs. First, we integrate the steady-state target optimizer into the MPC problem through the offset cost function to formulate a modified single optimization problem for tracking changing targets from real-time optimization. Then, the concept of constraint tightening is utilized to enhance the robustness and ensure robust constraint satisfaction in the presence of interferences. On this basis, the SVD method is introduced to decompose the new optimization problem into several independent subsystems on the orthogonal projection space, and a distributed dual gradient algorithm with convergence proved is implemented to obtain the control of each nominal subsystem. The recursive feasibility is then ensured and the tracking ability of the strategy is analyzed. It is verified that for a target, the system can be steered to a neighborhood of the closest possible steady setpoint. At last, the effectiveness of the raised SVD-RDMPC strategy is established in two simulations on building temperature control and load frequency control.