Energy compensation-based approach for solving the HJI equation in the nonlinear H∞ synthesis

The H∞ framework provides an efficient and systemic method for the design of controllers for both linear and nonlinear systems. In the nonlinear controller synthesis, however, the limitation of this method is usually associated with the existence of a solution to the Hamilton–Jacobi–Isaac (HJI) equation. In this paper, an innovative energy compensation-based approach to the solution of the HJI equations is presented and compared with the existing methods relying on Taylor series expansion. This new approach provides an efficient methodology that ensures the existence of a solution to the HJI equation. Numerical application to spacecraft attitude control is presented to validate the developments.