Journal of Applied Mathematics
Volume 2013 (2013), Article ID 615060, 9 pages
Research Article

Computational Techniques for Model Predictive Control of Large-Scale Systems with Continuous-Valued and Discrete-Valued Inputs

School of Information Science, Japan Advanced Institute of Science and Technology, Ishikawa 923-1292, Japan

Received 9 November 2012; Accepted 5 February 2013

Academic Editor: Piyapong Niamsup

Copyright © 2013 Koichi Kobayashi and Kunihiko Hiraishi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We propose computational techniques for model predictive control of large-scale systems with both continuous-valued control inputs and discrete-valued control inputs, which are a class of hybrid systems. In the proposed method, we introduce the notion of virtual control inputs, which are obtained by relaxing discrete-valued control inputs to continuous variables. In online computation, first, we find continuous-valued control inputs and virtual control inputs minimizing a cost function. Next, using the obtained virtual control inputs, only discrete-valued control inputs at the current time are computed in each subsystem. In addition, we also discuss the effect of quantization errors. Finally, the effectiveness of the proposed method is shown by a numerical example. The proposed method enables us to reduce and decentralize the computation load.