M.Sc Thesis

M.Sc StudentOshra Belapolsky
SubjectMiss Distance as a Function of Trajectory Shaping in the
Terminal Phase for Tactical Missiles using Linear
Quadratic Differential Games
DepartmentDepartment of Aerospace Engineering
Supervisor Full Professors Ben-Asher Yoseph
Full Thesis textFull thesis text - English Version


A large part of modern guidance techniques is based on the theory of linear quadratic (LQ) optimal control and on LQ differential games (LQDG). The interception of a maneuvering target is formulated as a zero-sum pursuit-evasion game. The nonlinear phenomenon of bounded lateral acceleration is modeled by adding quadratic penalty terms on the, assumed to be unbounded, controls to the square of the miss distance, the natural cost function of the game. The clear advantage of the linear quadratic formulation is a continuous and smooth linear control strategy. The flexibility to include in the cost function a running cost on the state variables, in addition to the weights on the terminal variables, is another advantage of the LQDG formulation. By augmenting the cost function with this additional cost we achieve predetermined terminal conditions like interception angle and avoid physically prohibited bounds, more important we can introduce some "trajectory shaping". In this research the effect of the trajectory shaping in the terminal phase is presented and analyzed for a maneuvering evader and non zero initial conditions. We investigate the influence of the hand over errors dominated by the initial heading error on the stability of the solution in equilibrium. We use different methods, such as Lyapunov stability theorem, Routh-Hurwitz and root-locus to analyze the instability and find an envelope of initial conditions which can be handled satisfactorily by this guidance scheme. Recently, an increasing attention has been paid to the degenerate ("non-classical") formulation of optimal control problems. There are two main advantages for this formulation the first is the availability of analytical solution to the Lyapunov equation, and the second is the stability of this formulation. In this research we examine the miss distance and the required maneuver achieved by this formulation. We analyze the degenerate problem formulation as a possible solution for the instability of the standard LQDG with trajectory shaping caused by a large initial heading error.