The Optimal Event-based Control Of Parachute Opening Problem

We propose an event-based feedback controller associated with an optimized strategyof parachute air drop. In the course of parachute air drop, there exists controller designof event-based feedback, including conditions that followed, a fast and accurate landingwhile a safe landing speed must be guaranteed, and minimizing the drop interval, wedesign an event-based control system (that is, one kind of hybrid systems) containing thedesign theory of optimal control law. In order to solve this, we give the following scheme.Based on the Newton’s second Law and the basic aerodynamics, assuming the open-ing instant as the first event, landing as the second, we obtain the dynamical equationof parachute air drop, then give the transfer condition(the first event) and the boundarycondition(the second event). Here, the optimal design of controller is the solving processconcerning the given boundary condition and the optimized transfer moment.In detail, we take the numerical simulation based on Matlab, then obtain the optimalparameter by finite recursion. According to the simulation results, we get the optimalcontrol law that meets both the boundary condition and minimizing the drop interval.Consequently, we refine the optimal control of parachute air drop into an event-based optimal control law design, and we give the schemes to solve this kind of controlproblems. Moreover, the problem and solving method have certain universality, that is,which can be used in similar optimal control problems in multiple applications.