Optimal control of a rectilinear motion of a rocket

Abstract

In this work, we have modelled the problem of maximizing the velocity of a rocket moving with a rectilinear motion by a linear optimal control problem, where the control represents the action of the pilot on the rocket. In order to solve the obtained model, we applied both analytical and numerical methods. The analytical solution is calculated using the Pontryagin maximum principle while the approximate solution of the problem is found using the shooting method as well as two techniques of discretization: the technique using the Cauchy formula and the one using the Euler formula. In order to compare the different methods, we developed an implementation with MATLAB and presented some simulation results.

Optimal control of COVID-19

“…Indirect method to solve optimal control problems are based on the Pontryagin's maximum principle to compute the optimal solution. Therefor, these methods require the state system with initial value [4], and necessary conditions [4,5,7], to find the solution of a given optimal control problem, by convering it into a boundary value problem.…”

“…It is a fast, high-precision method that does not require assumptions about the control structure. The shooting method consists in three main steps [7,8]:…”

“…This work is structured as follows: after a brief introduction, in section 2, we defined the model used and explained the importance of each of its compartments. Section 3 is devoted to the theoretical resolution of the modeled problem, using the Pontryagin maximum principle [4][5][6][7][8]. The numerical resolution is evoked in section 4, we solved the considered problem with two numerical methods, namely the direct method (Euler discretization ) and an indirect method (shooting method).…”

Direct method to solve linear-quadratic optimal control problems

“…The theory of optimal control is a branch of mathematics which consists in finding the best control which guides a given system, such as a car, a space shuttle, or a chemical reaction, on which we have an action, from an initial state to a final one. The optimal control theory can be applied in various fields: aeronautics and aerospace [1,2,3,6,12,18], mechanics [8,10], agriculture [13,14], etc.…”

“…In [2], the Cauchy discretization technique is combined with an interior-point method to efficiently solve the linear optimal control problem modelling a rectilinear motion of a rocket and in [19], the Cauchy discretization technique is combined with the hybrid direction algorithm developed in [5] to solve the linear optimal control problem.…”