Distributed Model Predictive Control Based on Dynamic Games

Model predictive control (MPC) is widely recognized as a high performance, yet practical, control technology. This model-based control strategy solves at each sample a discrete-time optimal control problem over a finite horizon, producing a control input sequence. An attractive attribute of MPC technology is its ability to systematically account for system constraints. The theory of MPC for linear systems is well developed; all aspects such as stability, robustness,feasibility and optimality have been extensively discussed in the literature (see, e.g., (Bemporad & Morari, 1999; Kouvaritakis & Cannon, 2001; Maciejowski, 2002; Mayne et al., 2000)). The effectiveness of MPC depends on model accuracy and the availability of fast computational resources. These requirements limit the application base for MPC. Even though, applications abound in process industries (Camacho & Bordons, 2004), manufacturing (Braun et al., 2003), supply chains (Perea-Lopez et al., 2003), among others, are becoming more widespread. Two common paradigms for solving system-wide MPC calculations are centralised and decentralised strategies. Centralised strategies may arise from the desire to operate the system in an optimal fashion, whereas decentralised MPC control structures can result from the incremental roll-out of the system development. An effective centralised MPC can be difficult, if not impossible to implement in large-scale systems (Kumar & Daoutidis, 2002; Lu, 2003). In decentralised strategies, the system-wide MPC problem is decomposed into subproblems by taking advantage of the system structure, and then, these subproblems are solved independently. In general, decentralised schemes approximate the interactions between subsystems and treat inputs in other subsystems as external disturbances. This assumption leads to a poor systemperformance (Sandell Jr et al., 1978; Šiljak, 1996). Therefore, there is a need for a cross-functional integration between the decentralised controllers, in which a coordination level performs steady-state target calculation for decentralised controller (Aguilera & Marchetti, 1998; Aske et al., 2008; Cheng et al., 2007; 2008; Zhu & Henson, 2002). Several distributed MPC formulations are available in the literature. A distributed MPC framework was proposed by Dumbar and Murray (Dunbar & Murray, 2006) for the class 4