Page 125 - Distributed model predictive control for plant-wide systems

Local Cost Optimization-based Distributed Model Predictive Control 99

each agent such as prediction horizon, control horizon, weighting matrices, and sample time,
etc. can all be designed and tuned separately, which is superior to the centralized control and
can significantly reduce the online computational burden and be simple to implement. Notice
that the proposed scheme is not limited to the Shell benchmark control problem and can be
used in a wide range of real-world complex control problem.

5.4 Conclusion

In this chapter, the DMPC methods based on local cost optimization and Nash optimality are
developed for large-scale linear systems. To avoid the prohibitively high online computational
demand, the MPC is implemented in a distributed scheme with the inexpensive controllers
within the network environment. These controllers can cooperate and communicate with each
other to achieve the objective of the whole system. Coupling effects among the agents are fully
taken into account in this scheme, which is superior to other traditional decentralized control
methods.
The main advantage of this scheme is that the online optimization of a large-scale system can
be converted to that of several small-scale systems, thus can significantly reduce the computa-
tional complexity while keeping satisfactory performance. Furthermore, the design parameters
for each subsystem-based controller such as the prediction horizon, control horizon, weight-
ing matrix, sample time, etc. can all be designed and tuned separately, which provides more
flexibility for the analysis and applications. And these methods maintain the control system
integrity under component or system failure and the reduction on the computational load.
The first part of the chapter presents the LCO-DMPC, including the closed-loop solution
and the stability conditions. This method provides acceptable regions of tuning parameters
for which the stability is guaranteed and the performances are satisfactory. Usually, the stable
regions are associated with big prediction horizon P and small weight R. The second part of
this chapter provides the Nash-optimization-based DMPC and investigates the performance
of the distributed control scheme. The nominal stability and the performance deviation on the
single-step horizon under the communication failure are analyzed. These will provide users
a better understanding to the developed algorithm and sensible guidance in applications. In
addition, some simulation examples are presented to verify the efficiency and practicality of
the distributed MPC algorithms.

Appendix
Appendix A. QP problem transformation

Making use of stacked vectors and definitions (5.28), the cost function (5.7) in the optimization
problem of the MPC controller C can be expressed in the equivalent form
i
d 2 2
̂
J = ‖Y (k + 1, P|k)− Y (k + 1, P|k)‖ + ‖ΔU (k, M|k)‖
i i i i
Q i R i
ˆ
The concatenated local output prediction Y (k + 1, P|k) is a function of the manipulated vari-
i
ables; therefore, in order to express J as a function of Δ U (k, M|k), an explicit expression for
i
i
such a prediction is needed.