PDE Solution to SDRE

These files present a PDE solution to the state-dependent Riccati equation. The coding is done based on Method on Lines.

The state‐dependent Riccati equation (SDRE) is a nonlinear optimal controller derived from applying optimality conditions on a Hamiltonian equation. The SDRE is usually considered as an ordinary differential equation. This work considers it as a partial differential equation. The details could be found in the following article:

S.R. Nekoo, "A PDE breach to the SDRE," Asian Journal of Control, 22 (2), pp. 667-676, 2020.

There are two codes based on the two examples in the paper. The first one is a scalar and the second one is a second-order example. The PDE solution is based on the Method of Lines. Since the solution approach is based on the finite difference method, the codes are pretty time consuming and the simulation time is long.