This Small Business Innovation Research Phase I project aims to develop an efficient algorithm for approximately computing nonlinear H( control laws. The design of a nonlinear H( control law is reduced to solving two Hamilton-Jacobi-lsaacs (HJI) equations, an extension of the algebraic Ricatti equation. Due to their nonlinear nature, it is almost impossible to obtain the closed-form solution of the HJI equations. An innovative algorithm and data structure is proposed to find a numerical solution of the HJI equations. Assuming the solution of the HJI equation in the Taylor series form, this algorithm will obtain the coefficients of the Taylor series by iteratively solving an algebraic Ricatti equation and a sequence of linear algebraic equations. American GNC Corporation's approach is the first-ever effort for providing a systematic procedure to approximately solve the HJI equations. This procedure can be easily implemented in routine computer languages and software packages. Their approach may be the only feasible method for making the nonlinear H( control a practical design tool and can find a wide range of applications for controlling highly uncertain nonlinear systems such as high performance missile and/or aircraft systems, high accuracy robot manipulators, and large maneuvering spacecraft. The effectiveness of the proposed approach will be illustrated by a high performance missile autopilot design experiment in a real-time control/simulation environment.
