Page 38 - Distributed model predictive control for plant-wide systems

12 Distributed Model Predictive Control for Plant-Wide Systems

predictive control communicates with other interacted local predictive control many times
in a single control period. And the time cost by communicating is very little, such that it
could be ignored as compared to the control period. Each local predictive control solves its
optimal control law based on the presumed control sequence. Then it transforms this con-
trol law to its interacted local predictive controllers. After that, each local predictive solves
the new optimal control law based on the optimal control law based on its neighbors’ opti-
mal control laws solved at the last previous iteration, and then repeats this process until the
iteration broken-down conditions are satisfied, e.g., [19, 29, 37, 48, 49].

The noniterative algorithms consume less communication resources than the iterative
algorithms, and have a fast computation speed in comparison to the iterative algorithms.
The iterative algorithms are able to achieve a better global performance than the noniterative
algorithms.
There are three kinds of DMPCs if we classify DMPCs by the cost function of each local
predictive control. And the DMPCs that accommodate the same kind of cost function for each
subsystem-based MPC can be solved either by the iterative algorithm or by the noniterative
algorithm. We briefly review these methods as motivations for the content to be presented later
in the book.

• Local cost optimization-based DMPC (LCO-DMPC): distributed algorithms where each
subsystem-based controller minimizes the cost function of its own subsystem were proposed
in [1–4]
N−1 ( )
∑ 2 2
2
J (k)= ‖x (k + N)‖ + ‖ x (k + s) ‖ + u (k + s) ‖ (1.1)
‖
i
i
‖ i
‖ i
P i ‖Q i ‖R i
s=0
When computing the optimal solution, each local controller exchanges state estimation
with the neighboring subsystems to improve the performance of the local subsystem. This
method is simple and very convenient for implementation. An extension of this stabilizing
DMPC with input constraint for nonlinear continuous systems is given in [51, 52], and a
stabilizing DMPC with input and state constraints is given in [50].
Also, an iterative algorithm for DMPC based on Nash optimality was developed in [1]. The
whole system will arrive at Nash equilibrium if the convergence condition of the algorithm
is satisfied.
• Cooperative distributed MPC (C-DMPC): to improve the global performance, distributed
algorithms, where each local controller minimizes a global cost function
∑
J (k)= J (k) (1.2)
j
i
j∈P
were proposed in [31, 37, 44, 48, 53]. In this method, each subsystem-based MPC
exchanges information with all other subsystems. And some iterative stabilizing designs
are proposed which take the advantages of the model of the whole system, and are used in
each subsystem-based MPC. This strategy may result in a better performance but consumes
much more communication resources, in comparison with the method described in (1.1).
• Networked DMPC with information constraints (N-DMPC): to balance the performance,
communication cost, and the complexity of the DMPC algorithm, a novel coordination strat-
egy was recently proposed in [19, 47, 54]. Here each subsystem-based controller minimizes