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.
Highlights
IntroductionIndirect methods stem from the calculus of variations [1, 2]; direct methods use a nonlinear programming optimization [3, 4]
Optimal control problems are solved with indirect or direct methods
The method implements an approximating sequence of time-varying linear quadratic regulators that converge to the solution of the original, nonlinear problem
Summary
Indirect methods stem from the calculus of variations [1, 2]; direct methods use a nonlinear programming optimization [3, 4] Both methods require the solution of a complex set of equations (Euler-Lagrange differential equations or Karush-Kuhn-Tucker algebraic equations) for which iterative numerical methods are used. This paper presents an approximate method to solve nonlinear optimal control problems This is a modification of the method known as “approximating sequence of Riccati equations” (ASRE) [5, 6]. The way the dynamics and objective function are factorized recalls the state-dependent Riccati equations (SDRE) method [7,8,9] These two methods possess some similarities, the way they solve the optimal control problem is different. These could be used as first guess solutions for either indirect or direct methods
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