Approximate Solutions to Nonlinear Optimal Control Problems in Astrodynamics

Abstract

A method to solve nonlinear optimal control problems is proposed in this work. The method implements an approximating sequence of time-varying linear quadratic regulators that converge to the solution of the original, nonlinear problem. Each subproblem is solved by manipulating the state transition matrix of the state-costate dynamics. Hard, soft, and mixed boundary conditions are handled. The presented method is a modified version of an algorithm known as "approximating sequence of Riccati equations. " Sample problems in astrodynamics are treated to show the effectiveness of the method, whose limitations are also discussed.

A parallel numerical method for solving optimal control problems based on whale optimization algorithm

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Analytical Impulsive-to-Continuous Thrust Conversion in Linearized Relative Dynamics

“…The proposed control analytically guarantees final constraint satisfaction in the linearized dynamics. A solution for the envisioned problem can be retrieved in analytical closed-form for an energy optimal problem [22,23]. However, the obtained control functions are complicated, and require a numerical iterative procedure to obtain the upper bound of the required thrust and to impose that its maximum value is not exceeded.…”

The archived-based genetic programming for optimal design of linear/non-linear controllers

“…Furthermore, since most of the conventional optimal control methods are based on either the linear control law or some simplified assumptions (Çimen, 2011), adopting these methods to nonlinear systems requires the linearization or simplification of the nonlinear problem conditions (Aliyu et al, 2012; Kamalapurkar et al, 2018), which in turn leads to the estimation error. Thus, such conventional methods are not as efficient in solving nonlinear problems compared with their performance in terms of problems of linear systems (Bourdin and Trélat, 2017; Topputo and Bernelli-Zazzera, 2013).…”