Multi-objective Nonlinear Model Predictive Control: Lexicographic Method

The design of most process control is essentially a dynamic multi-objective optimization problem (Meadowcroft et al., 1992), sometimes with nonlinear characters, and in which both economic benefit and social benefit should be considered. Commonly speaking, there are contradictory objectives such as quantity of products, quality of products, safety of manufacturing, cost of manufacturing, environment protection and so on. Since the different relative importance of these objectives cannot be ignored in the process of the controller design, we should manage the different priority of each objective correctly and exactly. Therefore, multivariable process control could be formulated as a complicated dynamic multi-objective optimization problem. Traditionally, a multi-objective control problem could be transformed into a single-objective dynamic optimization with the quadratic objective function, where the weights denote the different relative importance of different objectives. This method is easy to understand, but the value of the weight coefficients usually could be only decided by try-and-error method, based on engineering experiences, repeating simulations and other information, while there is no accurate theoretical analysis of these weight coefficients yet. So it can be seen that, the design process of the traditional method is complicated and time-consuming indeed. Especially, when the situation of manufacturing changes (such as sudden load increasing of a power supplier and so on), it is very hard for operators to renew the weights rapidly. Therefore, a new framework of multi-objective controller is desired, it should be driven by the relative importance of different objectives, which reflect the practical requirement of control problems, and it also should be convenient to redesign for engineers and operators, when the values or priorities of the objectives are changed. Using lexicographic method, which also called completely stratified method, Meadowcroft et al. proposed a priority-driven framework of controller: Modular Multivariable Controller (MMC), and analyzed its steady-state properties (Meadowcroft et al., 1992). It sorts objectives sequentially according to their relative importance, and then satisfies them as many as possible in the corresponding control modules by the order as Fig. 1., where one module handles with only one objective. Later, because of its advantages, researchers have extended MMC to the dynamic optimization of linear systems with model predictive control (MPC) and other controllers in past years (Ocampo-Martinez et al., 2008, Wu et al., 2000). 7