Power series solution of the Hamilton-Jacobi-Bellman equation for DAE models with a discounted cost

This paper considers infinite horizon optimal feedback control of nonlinear models with discounted cost. The paper includes two extentions of existing results about optimal feedback control. First, it is proven that for real analytic state-space models, a time-invariant real analytic feedback solution exists, even when the cost function includes a discount factor, provided certain regularity conditions. Second, the result is generalized to nonlinear DAE models. The feedback solution is valid in a neighborhood of the origin. In both cases, explicit formulas for the series expansions of the cost function and control law are given.