**Acknowledgements**

ture predicted control or state variables computed locally, so that any local regulator can predict the interaction effects over the considered prediction horizon. With reference to the simple case of Figure 6, the MPC regulators *R*1and *R*2are designed to control the subsystems *S*1 and*S*2, respectively. If the information was exchange among the local regulators (*R*1and *R*2) concerns the predicted evolution of the system states (*x*1and*x*2), any local regulator

In any case, it is apparent that the performance of the closed-loop system depends on the decisions that all the agents take. Hence, cooperation and communication policies become

With respect to available results in this direction, several DMPC methods have been pro‐ posed in the literature that deal with the coordination of separate MPCs. These communi‐ cate in order to obtain optimal input trajectories in a distributed manner see [145, 146, 152] for reviews of results in this area. Some distributed MPC formulations are available in the

However, all of the above results are based on the assumption of continuous sampling of the entire plant state vector and assuming no delays and perfect communication between sub‐ systems. In practice, individual subsystems exchange information over a communication network, especially wireless communication network, where the data is transmitted in dis‐ crete packets. These packets may be lost during communication. Moreover, the communica‐ tion media is a resource that is usually accessed in a mutually exclusive manner by neighborhood agents. This means that the throughput capacity of such networks is limited. Thus, how to improve the global performance of each subsystem with the limited network

Previous work on MPC design for systems subject to asynchronous or delayed measure‐ ments has primarily focused on centralized MPC design [158], [159] and little attention has been given to the design of DMPC. In [160], the issue of delays in the communica‐ tion between distributed controllers was addressed. The authors of [161] consider the design of distributed MPC schemes for nonlinear systems in a more common setting. That is, measurements of the state are not available continuously but asynchronously and

Recently, there has been much interest in model predictive control which allows research‐ ers to address problems like feasibility, stability and performance in a rigorous manner. We first give a review of discrete-time model predictive control of constrained dynamic systems, both linear and nonlinear. The min-max approach for handling uncertainties are illustrated, then the LMIs methods are showed, and the advantages and disadvantages of

communication or limited available information is a valuable problem.

needs only to know the dynamics of the subsystem directly controlled (*S*1and*S*2).

very important issues.

104 Advances in Discrete Time Systems

literatures [153-157].

with delays.

**9. Conclusions**

**8.3. DMPC over network information exchange**

The work of Yuanqing Xia was supported by the National Basic Research Program of China (973 Program) (2012CB720000), the National Natural Science Foundation of China (60974011), Program for New Century Excellent Talents in University of China (NCET-08-0047), the Ph.D. Programs Foundation of Ministry of Education of China (20091101110023, 20111101110012), and Program for Changjiang Scholars and Innovative Research Team in University, and Beijing Municipal Natural Science Foundation (4102053,4101001). The work of Magdi S. Mahmoud is supported by the research group project no. RG1105-1 from DSR-KFUPM.
