Generic Homotopic Smoothing for Low-Thrust Optimal Control Problems with Power Constraints

This brief is devoted to the power-constrained low-thrust optimal control problem (OCP). First, a general model for a class of power constraints is proposed by defining a piecewise smooth function, which describes the discontinuities of the control system. Subsequently, a recursive smoothing function is proposed to smooth the generalized discontinuous terms leading to a family of smooth OCPs, whose solutions converge to the solution of the discontinuous power-constrained OCP. The distinguished feature is that the variations of the control bound, caused by the power constraints, are embedded into the smoothing function, and are retrieved gradually. Consequently, the constrained and unconstrained OCPs are seamlessly connected, allowing an easy start and convergence improvement of the continuation. Moreover, a homotopy is constructed to guarantee a smooth connection, providing a differential homotopy path-tracking process. Finally, by comparing with the existing methods, typical scenarios are simulated to demonstrate the convergence improvement and efficiency of the proposed generic homotopic smoothing method.