Assessment and Future Directions of Nonlinear Model Predictive ...

Distributed Model Predictive Control of Large-Scale Systems 595Composite models (CM). For each subsystem, the combination of the decentralizedmodel and all the interaction models is termed the composite model(CM). The decentralized state vector x ii is augmented with states arising dueto the influence of external subsystems.[Let x i = x ′ i1,...,x ′ ii,...,x ′ ]′iM denote the CM states for subsystem i. Fornotational convenience, the CM for subsystem i is written asx i(k +1)=A ix i(k)+B iu i(k)+ ∑ j≠iW iju j(k) (3a)y i(k) =C ix i(k)(3b)in which C i =[C i1 ...C ii ...C iM ] and⎡⎤⎡ ⎤⎛ ⎞A i1 00. .. ..A i =A ii , B i =B ii, W ij =0.⎢. 0B⎣.. ⎥⎢ ⎥⎜ ij⎟⎦⎣⎦⎝⎠A iM ..The CM for the entire plant can be written as⎡ ⎤ ⎡⎤ ⎡ ⎤ ⎡⎤x 11A 11 x 11B 11 . .. . . ... x 1MA 1M x 1MB 1M⎡ ⎤u 1.(k+ 1)=. .. .(k)+.⎢⎥⎣ . ⎦ (k),x M1A M1 x M1B M1u M ⎢⎥ ⎢. .. ⎥ ⎢⎥ ⎢ . .⎣ . ⎦ ⎣⎦ ⎣ . ⎦ ⎣ .⎥⎦x MM A MM x MM B MM⎡ ⎤x 11.⎡ ⎤ ⎡⎤y 1C 11 ··· C 1Mx 1M⎢⎥⎣ . ⎦ (k) = ⎢. .⎣.⎥⎦.(k).y M C M1 ··· C MM x M1⎢⎥⎣ . ⎦x MMFor large, networked systems after identification of the significant interactionsfrom closed-loop operating data, we expect many of the interaction terms to bezero. In the decentralized modeling framework, all of the interaction terms areassumed zero.