Numerical methods for the guidance and control of air-to-air missiles

This dissertation presents an indirect numerical solution method for the guidance and control problem of general air-to-air missiles. The system model is formulated as a non-linear two-person zero-sum differential game. The system equations of motion are consisted of eight relative kinematic variables to describe the dynamics of the pursuing missile and its evading target, both maneuvering freely in a real three-dimensional space. Control functions are subjected to state dependent constraints. The information structure is nonlinear and allows different types of noise. The quadratic payoff functional is to be minimized by the missile and maximized by its target.; The original problem is decomposed into three smaller albeit solvable problems; they are, namely, the open-loop perfect information differential game problem, the real-time state estimation problem, and the near-closed-loop up-dating problem. Jacobson and Mayne's second order Differential Dynamic Programming method is extended to the differential game problems with state dependent control constraints. The algorithm has fewer number of first order differential equations needed to be integrated per iterative cycle and does not require good initial guessing of unknown parameters. However, it suffers the difficulty of selecting proper control increments. The new Retrogressive Weighted Convergency Control Parameters algorithm is introduced. It utilizes the local and the accumulated control errors as weighting factors to automatically adjust the step sizes.; The real-time nonlinear state estimator algorithm is similar to the Extended Kalman Filter. It minimizes the variance of the error propagation matrix and uses the most recent measurement data only to compute the filter updates. The difference lies on the consideration of time lags between when the measurement data is available and when the filter update is calculated. This is a significant factor as the target tracking frequency becomes very high during the terminal guidance stage.; Numerical simulations are performed for several types of target interception problems. Many optimal pursuit and evasion tactics are found. And, the solution method shows very promising future toward the realization of differential game methodology for missile guidance problems.