Stability and Convergence Analysis of a Distributed MPC Scheme Based on Communication and Iterative Calculation of Control Action

An analysis of the convergence properties of a distributed model predictive control (DMPC) algorithm is presented. An overview of the proposed DMPC algorithm is given and explicit solutions for the control problems are obtained for a simplified network of two controllers over two single-input single-output (SISO) systems. These solutions are used to analyze the convergence behavior of the iterative DMPC scheme. Stability condition of discrete linear systems is employed to derive the conditions required for convergence. Examples are then given to illustrate the findings, both numerically and graphically. The convergence analysis results show that the tuning of the DMPC algorithm can be adjusted to guarantee convergence at any control instant. However, convergence to an equilibrium DMPC solution through tuning adjustments does not necessarily imply stability of the DMPC network, which is shown to depend on the DMPC design, more specifically on the distribution and pairing of the controlled and manipulated variables.