Perturbation guidance laws for perfect information interceptors withsymmetrical nonlinearities

The nonlinearities in a dynamic system are assumed to be cubic and "small," i.e., all proportional to a single scalar small parameter e. The optimal digital nonlinear feedback control law in the case of perfect state knowledge, but with dynamic noise input, is carried through the first power of e. The control law involves cubic as well as linear terms in the state and depends on the prior covariance of the process noise. The theory is applied to a constant-speed coplanar model of a saturated interception and the numerical investigation shows a considerable advantage of the present nonlinear control law over the linear law (e = 0) as applied to the same system.