Closed-loop soft-constrained time-optimal control of flexible space structures

We propose numerically efficient solutions for the open- and closed-loop time-optimal soft-constrained control of a linear system representing a large flexible space structure. The open-loop solution is expressed in terms of the controllability Grammian matrix, for which we have obtained a closed-form expression for the undamped system. The qualitative dependence of the control on the initial state and the existence of many solutions satisfying the necessary conditions are shown. A nominal closed-loop control policy is subsequently formulated, but it is shown to be numerically expensive due to the nonuniqueness of extremal solutions. A continuation-based algorithm is proposed to alleviate the computational problem. Finally, the open- and closedloop controls are shown to exhibit a saturation property reminiscent of the hard-constrained problem.