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A minimum-time Model Predictive Control (MPC) problem is considered. By employing a time scaling transformation and cost regularization, it is shown that this problem becomes amenable to the application of parametric Integrated Perturbation Analysis - Sequential Quadratic Programming (IPA-SQP). The IPA-SQP framework exploits neighboring extremal optimal control and sequential quadratic programming based updates to efficiently and rapidly compute approximations to solutions in receding horizon optimal control. An interesting feature of the minimum-time MPC problem is that, after reformulation, the optimization needs to be performed simultaneously with respect to the control sequence and a constant parameter (terminal time) over the prediction horizon. Two examples are considered. The first example is for a double integrator with a control constraint. The second example is based on a two-dimensional model of a hypersonic vehicle.

A Model Predictive Control (MPC) framework is developed for control of spacecraft rendezvous and docking to a non-rotating/non-tumbling platform. The approach is based on combining conventional linear quadratic MPC with dynamically reconfigurable and changing in real-time constraints, that approximate the original constraints. An explicit solution is constructed in the form of a piecewise affine control law, and its complexity is evaluated.