Feedback Optimal Control of Low-thrust Orbit Transfer in Central Gravity Field

Abstract

Low-thrust trajectories with variable radial thrust is studiedin this paper. The problem is tackled by solving the Hamilton-Jacobi-Bellman equation via State Dependent Riccati Equation(STDE) technique devised for nonlinear systems. Insteadof solving the two-point boundary value problem in which theclassical optimal control is stated, this technique allows us toderive closed-loop solutions. The idea of the work consistsin factorizing the original nonlinear dynamical system intoa quasi-linear state dependent system of ordinary differentialequations. The generating function technique is then appliedto this new dynamical system, the feedback optimal control issolved. We circumvent in this way the problem of expandingthe vector field and truncating higher-order terms because noremainders are lost in the undertaken approach. This techniquecan be applied to any planet-to-planet transfer; it has beenapplied here to the Earth-Mars low-thrust transfer.