Ph.D Thesis

Ph.D StudentGoldan Orly
SubjectRobust Missile Guidance
DepartmentDepartment of Mechanical Engineering
Supervisor PROFESSOR EMERITUS Shaul Gutman
Full Thesis text - in Hebrew Full thesis text - Hebrew Version


During the past few decades proportional navigation (PN) has become the major guidance law for target interception. However, PN was originally proposed under the assumptions of a non maneuvering target, unconstrained missile abilities, constant speeds, initial conditions close to collision course, and noise free measurements. In order to study the PN performances against maneuvering targets, the classical adjoint method is commonly used. In the present research we extend the miss-distance calculation from the case were the target performs a step maneuver to the case were the target performs an arbitrary bounded maneuver. Moreover, using optimal control, our general approach enables us to go beyond planer engagement to a three dimensional conflict. In this case the miss-distance is a norm of a vector and instead of a single target we may have several bounded inputs. One of these inputs may be a bounded noise function. Thus it is possible to accumulate the influence of all inputs on the PN performances. An important practical question arises at this point: can the evader increase the miss-distance by increasing the duration of its maneuver without bound? It is shown that under mild conditions this is impossible. It is interesting to note that this issue is connected directly to the expoential stability of the adjoint system. Since this system is time variant, we apply the circle criterion to obtain stability conditions. As PN has not been developed to compensate for complicated target maneuvers, we proceed to an advanced guidance method, based on differential game theory. In this model we use a zero sum differential game with the miss-distance as a cost, and where both players have bounded controls. The optimal strategies of the players satisfy the saddle point inequality. Fortunately, for an important class of games with linear dynamics and bounded control magnitudes, the miss-distance can be calculated explicitly. Moreover, in some region of the state space, the optimal strategy pair is arbitrary, and outside this region the optimal strategy is bang-bang. Thus, in that particular region we choose a linear guidance law. We take advantage of the guaranteed cost property of the saddle point and extend the linear strategy all the way until termination. It is assured that once the initial conditions lie in the above mentioned region, the entire trajectory remains in an extended region up to termination. In this way, we can apply the adjoint method to calculate the worst miss-distance.