A series solution method for the solution of the Hamilton Jacobi Isaacs equation and its applications to aerospace systems

A novel application of the series solution approach for terminally constrained nonlinear optimal control problems is proposed for solving the time dependent Hamilton-Jacobi-Isaacs (HJI) equation. The HJI equation appears in nonlinear pursuit-evasion games and designing H control laws. As the first innovative application of the proposed methodology to solving the HJI equation, this paper considers the example of nonlinear differential games in orbits. The HJI equation is solved in order to construct nonlinear feedback strategies for finite time pursuit and evasion scenarios involving space assets. A soft terminal constraint is used to penalize terminal error. The second novel application presented in the paper is associated with finite-time H control formulation for hard constrained optimal control problems with disturbances. The short-period pitch dynamics of a missile is considered to show the efficacy of the method. The applied algorithm yields third-order feedback laws for both the problems. Several numerical examples are illustrated and compared with their respective open-loop solutions.

A series solution method for the solution of the Hamilton Jacobi Isaacs equation and its applications to aerospace systems Conference Paper