Inverse identification of inputs of a random utility based model using optimal control

• A methodology for inverse identification of the inputs to the RUBMRIO model has been developed in this work.
• The RUBMRIO model was shown to be a nonlinear discrete time dynamical system.
• It was then proved that the aforementioned dynamical system is input-to-state stable.
• A method based on optimal control was developed to solve for the inputs given the desired output levels.
• It is shown that the proposed inverse identification methodology solves for the inputs up to an acceptable accuracy level.

The random utility based multiregional input–output (RUBMRIO) model is used by several integrated land use and transportation models (ILUTMs) to forecast commodity flows in a region and for spatial allocation of production activities. It makes use of multiregional input–output models which are based on random utility theory. In this work, we use optimal control techniques to find optimal final demand and transportation costs of a RUBMRIO model, that would lead to a desired level of commodity flow and production costs.At first, the RUBMRIO model is formulated as a discrete time dynamical system. It is shown, using Lyapunov argument, that the fixed point of the dynamical system is input-to-state stable (ISS). Then, a discrete time optimal control problem is formulated with states as commodity flows and production costs, and the final demand and transportation costs as control inputs. An optimization problem is then solved to obtain control inputs that would lead to desired commodity flows and production costs.Further, the proposed methodology is applied to a numerical example. It is shown that the optimal control based method can achieve user specified commodity flows and production costs up to an acceptable accuracy level.