Parametric Integrated Perturbation Analysis - Sequential Quadratic Programming Approach for Minimum-Time Model Predictive Control

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 twodimensional model of a hypersonic vehicle.