PySCP: A Multiple-Phase Optimal Control Software Using Sequential Convex Programming

Abstract

Optimal control problems are common in aerospace engineering. A Python software program called PySCP is described for solving multiple-phase optimal control problems using sequential convex programming methods. By constructing a series of approximated second-order cone programming subproblems, PySCP approaches to the solution of the original optimal control problem in an iterative way. The key components of the software are described in detail, including convexification, discretization, and the adaptive trust region method. The convexification of the first-order differential dynamic equation is implemented using successive linearization. Six discretization methods, including zero-order hold, first-order hold, Runge-Kutta, and three hp pseudospectral collocation methods, are implemented so that different types of optimal control problems can be tackled efficiently. Adaptive trust region method is employed, and robust convergence is achieved. Both free-final-time problem and fixed-final-time problem can be solved by the software. The application of the software is demonstrated on three optimal control problems with varying complexity. PySCP provides researchers a useful toolkit to solve a wide variety of optimal control problems using sequential convex programming.