Rapid distributed model predictive control design using singular value decomposition for linear systems

• SVD distribution model predictive control (DMPC) with quick convergence is proposed.
• The large scale system is decomposed into several independent subsystems.
• The optimal inputs can be separately designed without any interaction problems.
• System stability and convergence of SVD-DMPC is proven.
• SVD-DMPC outperforms Jacobi based DMPC.

The issue of model predictive control design of distribution systems using a popular singular value decomposition (SVD) technique is addressed. Namely, projection to a set of conjugate structure is dealt with in this paper. The structure of the resulting predictive model is decomposed into small sets of subsystems. The optimal inputs can be separately designed at each subsystem in parallel without any interaction problems. The optimal inputs can be directly obtained and the communication among the subsystems can be significantly reduced. In addition, the design of distribution model predictive control (DMPC) with constraints using the SVD framework is also presented. The unconstraint inputs are checked in parallel in the conjugate space. Without solving the QP problem of each subsystem, the suboptimal solution can be quickly obtained by selecting the bigger singular values and discarding the small singular values in the singular value space. The convergence condition of the proposed algorithm is also proved. Two case studies are used to illustrate the distribution control systems using the suggested approach. Comparisons between the centralized model predictive control method and the proposed DMPC method are carried out to show the advantages of the newly proposed method.