Infinite-Horizon Optimal Control for Deploying a Tethered Sub-satellite

Abstract

An infinite-horizon optimal control problem for the deployment of a tethered subsatellite under complex nonlinear constraints is presented. The nonlinearities in the system model and the constraints of states and control are taken into consideration. Legendre-Gauss-Radau pseudo spectral method is described for solving the infinitehorizon optimal control problem numerically. By using a smooth, monotonic domain transformation technique, an infinite-horizon optimal control problem is approximated with a finite-horizon problem. The resulting problem in the finite interval is transcribed to a nonlinear programming problem. The proposed methods yield a series of approximations to the state on the entire horizon. The optimal control law can be determined via a nonlinear programming, without any iteration. A numerical example is included to demonstrate the high effectiveness and hard real-time of the proposed schemes.