Modified SDRE Method for Finite-time Nonlinear Optimal Control Problem

the optimal control problem on a finite-time interval for a nonlinear system with state-dependent coefficients is considered in this paper. The most common method for such systems is the state-dependent Riccati equation (SDRE) method. Ehe implementation of SDRE in a finite-time interval requires the solution of the state-dependent Riccati differential equation (SDDRE). Since the initial conditions for the SDDRE are set at a final time moment, the numerical solution requires integration from right to left. The lack of information about the system state at future time points does not allow this integration to be performed. This complexity can be overcome through an approximate solution based on the state-dependent Lyapunov differential equation. However, this approximate solution may be less accurate, for example, compared to Riccati Sequence Approximate Method (ASRE). A modification of the SDRE method based on preliminary calculations of the system matrices by solving an auxiliary terminal control problem on the inverse time interval is presented. In such a situation, the backward integration of the auxiliary problem on the specified time interval will take place in direct time for the original problem. Two examples of the application of this method in nonlinear problems are shown.