An Inverse Optimal Control Problem and Its Application to the Choice of Performance Index for Economic Stabilization Policy

The specification of a performance criterion is one of the basic requirements for the formal analysis of quantitative decision processes. A procedure of quantitatively selecting the performance index for economic stabilization policy by solving the so-called inverse optimal control problem is developed. When a closed-loop system with a known control policy is given, the inverse optimal control problem is to determine performance indices for which the given control rule is optimal. A sufficient condition is developed for the solution of the inverse problem for long-run economic stabilization policy, and an explicit solution is obtained for short-run economic stabilization policy by considering a special case where the performance index does not penalize the costs of implementing control policies. The solution of the inverse problem is found to be not unique in general, which implies that the optimal control policies are fairly robust against different performance indices. Also, it is found that the solution of the inverse problem for a linear regulator holds true for the linear tracking problem, which makes the analysis much simpler. A procedure is developed for the selection of the performance index along with the optimal feedback control policy by which the economic system is to reveal the desired characteristics. The procedure demonstrates the determination of the steady states as policy goals, the computation of the feedback control policy, and the construction of a performance index, through a small econometric model.