Nonlinear Predictive Optimization for Deploying Space Tethered Satellite via Discrete-Time Fractional-Order Sliding Mode

This article develops a discrete-time fractional-order sliding mode control scheme to deploy space tethered satellite, with the nonlinear predictive optimization of underactuated dynamics. Firstly, by the discrete-time Euler-Lagrangian mechanics, the discrete-time dynamical equations are derived for the tether deployment, and some preliminaries of discrete-time fractional-order calculus are prepared. Secondly, a model predictive control (MPC)-based hybrid sliding manifold is designed based on the discrete-time fractional-order sliding mode and nonsingular terminal sliding mode. These two sliding modes correspond to the actuated and underactuated states of tethered system, whose nonlinear coupling is explicitly regulated by MPC optimization. Then, an MPC-based discrete-time fractional-order sliding mode control is raised to drive system states onto the hybrid sliding manifold, by solving the online optimization problem of the contractive MPC scheme. Furthermore, a compensation analysis of input saturation is presented to deal with the adverse impact of saturated tension, and realize a more stable early deployment. Finally, numerical simulations and comparisons of tether deployment are performed, to verify the effectiveness and superiority of the proposed scheme.