On guaranteed-cost, closed-form guidance via simple linear differential games

The problem of transforming nonlinear control systems into linear controllable systems is considered. In particular, necessary and sufficient conditions are given for a class of control systems to be equivalent to a linear system in the Brunovsky controllable form. It involves differential geometric techniques and the use of Lie derivatives. The new state variables depend only on the original state variables, and the new control variables depend both on the original states and on the original control variables. Therefore, the transformation is also called exact linearization. It was recently proved that linear differential games of a simple class with terminal cost have a closed-form solution. The solution can be extended to problems of capture and avoidance. The authors combine the above in order to derive guaranteed-cost, closed-form guidance laws for nonlinear problems of pursuit or evasion