Optimized discrete-time state dependent Riccati equation regulator

The state dependent Riccati equation was originally developed for the continuous time systems. In the paper the optimality of a discrete time version of the state dependent Riccati equation is considered. The derivation of the optimal control strategy is based on the Hamiltonian optimal solution for the nonlinear optimal control problem. The new form of the discrete state dependent Riccati equation with a correction tensor is derived. The prediction of the future trajectory is used in the derivation.