Optimal incentive control for two-level dynamical constrained problems: a solution method through sensitivity analysis

Incentive control of hierarchical bilevel planning problems cannot be seen as usual optimal control problems since the upper-level decision maker, who wants to control the dynamical evolution of the system, has no direct means of action on the system´s decision variables, which are in the hands of the lower-level decision maker. However, he can ultimately trigger changes in the lower-level strategies through indirect actions called incentives. This two-level interaction between actors, with different control variables and different objective functions, can be seen as a dynamical constrained Stackelberg game. A thorough description and formulation of the problem characterized by a multi-objective dynamical constrained optimization and a hierarchical framework is given. An algorithm intending to solve this problem using sensitivity analysis, and an example from a regional planning context illustrating the concept of control for the upper-level actor are included