M.Sc Student M.Sc Thesis Goldan Orly Ballistic Target Interception Using an Agile Interceptor Department of Mechanical Engineering PROFESSOR EMERITUS Shaul Gutman

Abstract

During the past few decades proportional navigation has become the major guidance law for target interception. However, it was designed to act under the assumptions of an ideal target and missile dynamics, constant speeds and initial conditions that are close to collision course.   An advanced guidance method, that would be presented here, is based on differential game theory, and proposes the classical methods as a special case of a more “realistic” environment. In particular, a conflict between a missile and a target is modeled as a zero sum differential game with the guaranteed miss distance as a cost. While the missile is trying to minimize the cost, the purpose of the target is to maximize it, and so, the optimal strategies of both the target and missile will be a solution of a saddle point inequality.

The guidance law produces the missile’s lateral acceleration in a closed loop form.  In order to get a good response of the missile to this command, there is a need for an inner additional control loop: the “autopilot”.

Fortunately, for an important class of linear games with bounded control magnitudes, the miss distance can be calculated explicitly, and we can use it’s formula as a design criterion.

However, in order to keep the linearity assumption valid, we have to make sure that no saturation will take place.

The problem gets more complex when we consider the fact that usually dynamical systems models include uncertainties. Also, a missile is designed to operate in different flight conditions, and so we extend the design objective to include robust guidance.

Finally, keeping in mind that, according to this guidance law, the miss distance is mostly influenced by the last moment missile’s behavior,  we suggest the option: “Agility against Stability” conflict.  We refer to a method known as “gain scheduling”, which basically fits the case for uncertainties, resulting from the change in the values of the parameter during the flight and the change of the conditions. In this method the time scale is divided into a number of intervals, and it is assumed that the parameters are known as constants for each one of them, so that different gains will be designed for them. Similarly, we suggest to make the system as stable as possible during most of the flight, and near collision (at the last moment)  to schedule  the autopilot to get a very low dumping ratio.