Finite-Time State-Dependent Coefficient Method for Optimal Control of Nonlinear Systems

The paper exams the solution of a nonlinear optimal control problem over a finite time interval based on the state-dependent coefficients technique. A widely used solution method via the state-dependent Riccati equation (SDRE) requires the backward integration of the state-dependent differential Riccati equation (SDDRE). At the same time, there is a difficulty in implementation due to the unavailability of information about the system state at future time. One of the ways to overcome the state information problem during backward integration is based on an approximate solution through the hypothesis of “frozen” coefficients and a state-dependent Lyapunov differential equation. However, this approximate solution may be less accurate, for example, compared to the method of approximating sequence of Riccati equations (ASRE). In this paper, an algorithm for the SDRE controller design is proposed through backward integration together with the solution of the auxiliary backward optimal control problem. The effectiveness of the method is shown by an example of the problem of assessing systemic risk.