Solving multicriteria optimal control problems with Reference Multifunctions

This paper presents the theoretical foundations of decision rule selection for dynamic multicriteria decision-making problems. Specifically, we will propose solution methods for the optimal control of complex systems governed by ordinary differential equations with vector-valued criteria. For this class of system we will define an extension of the Multiple Reference Points method, termed the Reference Multifunction approach. This preference structure is derived from time-varying reference values in the criteria space. They can be interpreted as evolving targets, criteria-space constraints, or varying regions of avoidance for admissible criteria-space trajectories. All the above define a time-dependent multifunction allowing us to find compromise controls by distance minimization to its selectors, in an adaptive way. The above approach can be applied in a multicriteria model predictive control framework.