Algebraic Decomposition of Model Predictive Control Problems.

Area of Science:

• Control Engineering
• Systems Science
• Applied Mathematics

Background:

• Model predictive control (MPC) is crucial for managing complex dynamical systems.
• Large-scale systems with linear inequality constraints present significant computational challenges.
• Existing MPC methods struggle with scalability for high-dimensional problems.

Purpose of the Study:

• To develop a decomposition technique for large-scale linear dynamical systems under MPC with inequality constraints.
• To reduce the computational burden associated with solving these control problems.
• To maintain system information, cost function, and constraints throughout the decomposition.

Main Methods:

• A novel decomposition method is proposed for large-scale linear dynamical systems.
• The method incorporates linear inequality constraints directly into the decomposition procedure.
• It generalizes matrix block diagonalization techniques to handle constraints simultaneously.

Main Results:

• The proposed decomposition transforms a large-scale MPC problem into independent, lower-dimensional MPC problems.
• This approach successfully preserves all system, cost function, and constraint information.
• Practical examples demonstrate a significant reduction in computational complexity and CPU time compared to traditional methods.

Conclusions:

• The decomposition technique offers an efficient solution for applying MPC to large-scale systems with inequality constraints.
• This method enhances the practical applicability of MPC in complex engineering scenarios.
• The reduced computational load makes advanced control strategies more feasible for real-time implementation.