Higher-order neighboring-optimal guidance for continuous-thrust orbit transfer

This paper presents an application of a recently-developed technique for designing finite-time optimal feedback controllers for analytic, nonlinear systems to the problem of continuous-thrust, minimum-fuel orbit transfer. The cost-to-go function and the Hamiltonian are represented using higher-order polynomial series expansions involving the perturbations of the states and terminal-constraint Lagrange multipliers. The differential equations for the time-dependent coefficients (gains) of various orders of the expansion of the cost-to-go are obtained from the Hamilton-Jacobi-Bellman equation. The gain differential equations, with known terminal boundary conditions, are solved using backward integration. The stored gains are utilized in a higher-order neighboring-optimal feedback control law. Sensitivities of the feedback solutions as well as the cost-to-go are evaluated with respect to perturbations in the known initial states. Error analysis is also performed with respect to the order of feedback control by using the open-loop solutions to the respective problems for comparison. It is shown that for small perturbations, highly accurate guidance solutions can be achieved by using a third-order feedback control law.

Higher-order neighboring-optimal guidance for continuous-thrust orbit transfer Conference Paper