A modified-secant iterative method for solving the Hamilton–Jacobi–Bellman–Isaac equations in non-linear optimal control

In this study, a gradient-free iterative secant method approach for solving the Hamilton–Jacobi–Bellman–Isaacs equations arising in the optimal control of affine non-linear systems is discussed. Local convergence of the method is established under fairly mild assumptions, and some examples are solved to demonstrate the utility of the method. However, the results presented here are preliminary, and it will need several experimentations to establish the computational efficiency of the method.