A General Lattice Representation for Explicit Model Predictive Control

Model predictive control (MPC) is one of the most successful techniques to control multi-variable constraint systems. The MPC uses a mathematical model to predict the future effects of control inputs to system behaviors. The optimal control policy is obtained by solving an optimization problem that minimizes/maximizes a performance objective subject to inputs and outputs constraints over a future time horizon (Morari & Lee, 1999, Mayne et al., 2000, Dua et al, 2008). The MPC control laws are open-loop optimal with respect to the corresponding objective function. However, the conventional MPC may require intensive online computation due to the repetitive solutions of an optimization problem. This limits its applications to large and slowly varying systems. In addition, the MPC control strategy is hard to validate, especially for safety critical system (Grancharova & Johansen, 2005, Pistikopoulos, et al. 2001, Alessio & Bemporad 2009). In 2002, Bemporad, Morari, Dua & Pistikopolous introduced the concept of explicit MPC (eMPC). The eMPC reformulates the online optimization in a MPC into a mutli-parametric linear/quadratic program (mpLP/mpQP). The optimal control action is calculated off-line as a continuous piecewise-affine (PWA) function of the state and reference vectors (Saffer et al, 2004, Bemporad et al. 2002a, 2002b). The eMPC has several advantages: i) The online computational time can be reduced to the microsecond-millisecond range. It makes the eMPC attractive for fast systems; ii) The MPC functionality is achieved in an easily verifiable way. The eMPC control policies can be validated before real online operations; iii) The eMPC solutions can be implemented with low-cost hardware (Johansen et al., 2007, Wen & Ma, 2008a, 2008b). The eMPC is then promising to be used in embedded systems, small/medium process systems, where the control systems should not be more expensive than the process systems. The eMPC found successful applications in many areas, e.g. AC-DC converters (Beccuti et al. 2009), autonomous vehicle steering, air separation unit (Grancharova et al. 2004), active valve train, hybrid separation, air condition (Pistikopoulos, et al. 2001), biomedical systems and drug delivery systems (Dua et al, 2004), scheduling (Ryu, & Pistikopoulos, 2007), spacecraft attitude control (Hegrenas et al, 2000)and crude distillation unit (Pannocchia et al, 2007). The eMPC is essentially a strategy of trading time for space. A continuous PWA control map is calculated offline, and stored in memory for online usage (Pannocchia et al, 2007). The 10