Successive Radial Basis Function Approximation for Finite-Horizon Nonlinear <i>H_∞ </i> Control Problems

In this paper, a successive radial basis function (RBF) approximation approach is proposed to solve the Hamilton-Jacobi-Isaacs (HJI) partial differential equation (PDE) associated with finite-horizon nonlinear H∞ control problems. Unlike conventional discretization techniques such as finite difference or Galerkin methods, the successive radial basis function approximation strategy reformulates the nonlinear HJI PDE into a series of easily solvable initial value problems. By iteratively refining the solution through successive point sampling, numerical integration, and RBF interpolation, the method circumvents the need for exhaustive domain discretization. Numerical simulations confirm the effectiveness and accuracy of the proposed method in solving the finite-horizon nonlinear H∞ control problem.