Optimal guidance law based on inverse optimal problem and performance analysis

Based on the typical energy optimal guidance laws (TEOGL), the two characteristic roots (CR) of the TEOGL were extended from a limited points/lines area to all the possible positive-real-roots area and the inverse optimal guidance problem was proposed. The construction procedure of the weighting matrices in the performance index of the inverse optimal problem was discussed and the calculation equations of those weighting matrices and Riccati matrix were also present. As an example, the calculation procedure was demonstrated when the control weighting matrix was chosen as -n power of time-to-go. It is concluded that, for the eight pairs of different CR, although every possible pair of CR may have an optimal explanation, it can't guarantee a similar guidance performance with the TEOGL, except a pair of CR which is chosen to be close to the CR of the TEOGL.