Analytical neighboring optimal guidance to finite horizon linear quadratic tracking problems

In this paper, a new approach to solving finite horizon linear quadratic tracking problems is proposed. An analytical means is derived based on the virtual motion camouflage concept, and pseudospectral discretization and differential inclusion techniques. The method avoids several disadvantages of classic approaches by avoiding backward propagation and satisfying the boundary conditions exactly. The solution requires only a single matrix inversion and a numerical example is provided to show the effectiveness of the algorithm.