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

Area of Science:

• Control Systems Engineering
• Optimization Theory
• Linear System Analysis

Background:

• Distributed control systems face challenges with interdependencies and uncertainties.
• Model Predictive Control (MPC) is effective but computationally intensive for large-scale systems.
• Robustness to disturbances and maintaining constraints are critical for reliable operation.

Purpose of the Study:

• To develop a robust distributed MPC strategy for linear systems with additive uncertainties and global constraints.
• To enhance tracking capabilities for time-varying targets in real-time optimization.
• To ensure robust constraint satisfaction under bounded disturbances.

Main Methods:

• Integration of a steady-state target optimizer using an offset cost function.
• Application of constraint tightening for enhanced robustness.
• Singular Value Decomposition (SVD) for decomposing the optimization problem into independent subsystems.
• Implementation of a distributed dual gradient algorithm with proven convergence.

Main Results:

• The SVD method decomposes the complex MPC problem into manageable subsystems.
• The distributed dual gradient algorithm efficiently computes control for each subsystem.
• Recursive feasibility and tracking ability of the SVD-RDMPC strategy are mathematically ensured.
• The system can be steered to a neighborhood of the closest steady setpoint.

Conclusions:

• The proposed SVD-RDMPC strategy effectively handles linear systems with uncertainties and constraints.
• The method demonstrates robust performance in simulations for building temperature and load frequency control.
• This approach offers a computationally efficient and robust solution for complex distributed control problems.