Optimal midcourse guidance of an air-to-air missile via SVM and RVM

Abstract

Midcourse phase of a medium-range missile guidance is actually a two point boundary value problem (TPBVP) that is too time-consuming to be implemented on an ordinary on-board computer. To solve this problem, one alternative choice is to use the approximation capability of a professional regression model, possessing a high level of generalization potential. In this way, it is necessary to obtain a set of optimal trajectories for various initial and terminal conditions via an off-line numerical method. These trajectories contain valuable information about inherent relationship of the missile states and related optimal commands. This database can be then employed for the training phase of a regression model chosen for estimation of the optimal commands. In this paper, we utilize two professional and known sparse kernel machines, the support vector machine (SVM) and the relevance vector machine (RVM), in their regression mode, to evaluate the ability and benefits of this approach. These two models provide a sparse representation of their input space and benefit from effective ideas which keep them away from the overfitting problem. Several experiments with different terminal conditions are conducted which demonstrate the ability of developed models to guide the missile with satisfactory accuracy during the midcourse phase. Moreover, investigating the parameters of the developed models exhibits that with the same level of accuracy, the RVM-based approach leads to a much sparser model. Such a property is really interesting for real-time applications, since the complexity of the suboptimal commands estimation process reduces by decreasing the number of the model parameters.