Analysis of General Ideal Proportional Navigation Guidance Laws

In this work, the capture region of the general ideal proportional navigation guidance law is analyzed with the following constraints: i the target's input acceleration is subject to independent or magnitude saturation, and ii the missile's input acceleration is subject to magnitude saturation. In addition to the case of unbounded maneuverability of missile with or without knowing the target acceleration, the necessary and sufficient condition for a bounded maneuvering missile that captures a nonmaneuvering target is also derived. Furthermore, the conditions that result in zero impact velocity are discovered and discussed in some of the cases. The capture regions that cannot be obtained analytically are determined numerically by a powerful classifier, the least square support vector machines. To have the capture region ready for least square support vector machines, all the state variables are transformed into modified polar variables and non-dimensionalized to reduce the number of independent variables. In order to make the implementation possible in real time, an approximation of the Gaussian radial basis function is adopted to obtain the corresponding nonlinear feature mapping function. Through numerous numerical experiments, the proposed technique is found to be adequate for storing the capture region in an onboard fire control computer.