The optimal event-based control of parachute opening problem I: Theory

We propose an event-based controller associated with an optimized strategy of parachute air drop. In a rescue mission or combat, it is important to minimize the drop interval to ensure a fast and accurate landing while a safe landing speed must be guaranteed. Opening the parachute timely is viewed as an optimal event-based control problem. The idea of optimal event-based control design is to identify the key event of the hybrid dynamics where a supervisor triggers the event-based controller at a right time. Perfect timing is given by a particular nonlinear optimization problem. To this end, we propose a method that takes a couple of steps to simplify the optimization via the tools of integration, penalty function and steepest descent algorithm. The method can be used to a range of applications: such as diaster rescue, combat, and space device recycling.