Assessment and Future Directions of Nonlinear Model Predictive ...

594 A.N. Venkat, J.B. Rawlings, and S.J. WrightIn this work, a cooperation-based control strategy that facilitates the integrationof the various subsystem-based MPCs is described. The interactionsamong the subsystems are assumed to be stable; system re-design is recommendedotherwise. The proposed cooperation-based distributed MPC algorithmis iterative in nature. At convergence, the distributed MPC algorithm achievesoptimal (centralized) control performance. In addition, the control algorithmcan be terminated at any intermediate iterate without compromising feasibilityor closed-loop stability of the resulting distributed controller. The proposedmethod also serves to equip the practitioner with a low-risk strategy to explorethe benefits achievable with centralized control by implementing cooperatingMPC controllers instead. In many situations, the structure of the system andnature of the interconnections establishes a natural, distributed hierarchy formodeling and control. A distributed control framework also fosters implementationof a cooperation-based strategy for several interacting processes that arenot owned by the same organization.3 Modeling for Integrating MPCsConsider a plant comprised of M interconnected subsystems. The notation{1,M} is used to represent the sequence of integers 1, 2,...M.Decentralized models. Let the decentralized (local) model for each subsystembe represented by a discrete, linear time invariant (LTI) model of the formx ii(k +1)=A iix ii(k)+B iiu i(k),y ii(k) =C iix ii(k), ∀ i ∈{1,M},(1a)(1b)in which k is discrete time, and we assume (A ii ,B ii ,C ii ) is a minimal realizationfor each (u i ,y i ) input-output pair.In the decentralized modeling framework, it is assumed that the subsystemsubsysteminteractions have a negligible effect on system variables. Frequently,components of the networked system are tightly coupled due to material/energyand/or information flow between them. In such cases, the “decentralized” assumptionleads to a loss in achievable control performance.Interaction models (IM). Consider any subsystem i ∈{1,M}. The effect ofany interacting subsystem j ≠ i on subsystem i is represented through a discreteLTI model of the formx ij(k +1)=A ijx ij(k)+B iju j(k)y ij(k) =C ijx ij(k), ∀ i, j ∈{1,M},j ≠ i(2a)(2b)in which (A ij ,B ij ,C ij ) denotes a minimal realization for each (u j≠i ,y i )interactinginput-local output pair. The subsystem output is given by y i (k) = M y ij∑(k).j=1