Closed loop control of guided missiles using neural networks

An optimal guidance law for a missile flight is one which determines appropriate controls to produce a flight path such that some mission objective will be achieved in the most efficient manner. Optimal Control Theory is often used to accomplish this task. One must bear in mind, however, that the usefulness of optimal control is sharply divided between two distinct classes of dynamical systems, namely, linear systems and nonlinear systems. For linear systems, the theory is complete in the sense that given a quadratic cost, a closed-loop feedback guidance law may be determined. For nonlinear systems, generally the best one can do is to determine an open-loop guidance law numerically using a software package such as MISER (1). (Some notable exceptions exist where a complete analytical synthesis of the closed-loop control may be obtained for nonlinear systems, e.g., in (2).); Although open-loop optimal guidance laws for nonlinear systems can now be computed quite efficiently with the advances of sophisticated numerical techniques along with high-speed digital computers, the highly-nonlinear and complex dynamics of missiles precludes the possibility of on-line implementation of open-loop optimal control. It has always been realized that if optimal closed-loop solutions could be obtained for comprehensive nonlinear systems such as missiles, then guidance laws based on such results would be superior to any other guidance laws available today. This superiority is due to, among other things, the elimination of some of the restrictive, and in many cases unrealistic assumptions made in the derivation of most current guidance laws in use such as, for instance, "tail-chase", unbounded control, simplified dynamics and/or aerodynamics, and non-maneuvering target, to name a few.; In this study, an optimal closed-loop control law is obtained off-line by means of a Neural Network which is then used as an on-line controller for a generic missile. In the nonlinear case, the missile/target scenario is set up as a mathematical model using realistic dynamics. Then, given a Performance Index, the open-loop control is obtained by solving the problem using the optimal control software MISER for a number of different initial configurations. These open-loop solutions are then used to "teach" a neural network via backpropagation. Through simulation, it is then demonstrated how well the neural network performs as a feedback controller. The miss distance as well as the value of the Performance Index are used as measures of performance to be compared under the original open-loop control and the neural network closed-loop control. This problem is further extended to include a time lag in the missile dynamics. The effect of this time delay in the overall performance of the optimal controller is then examined.