Solving Constrained Optimal Control Problems Using State-Dependent Factorization and Chebyshev Polynomials

Gomroki M. M., Topputo F., Bernelli-Zazzera F., TEKİNALP O.

JOURNAL OF GUIDANCE CONTROL AND DYNAMICS, vol.41, no.3, pp.618-631, 2018 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 41 Issue: 3
  • Publication Date: 2018
  • Doi Number: 10.2514/1.g002392
  • Journal Name: JOURNAL OF GUIDANCE CONTROL AND DYNAMICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.618-631
  • Middle East Technical University Affiliated: Yes

Abstract

The present work introduces a method to solve constrained nonlinear optimal control problems using state-dependent coefficient factorization and Chebyshev polynomials. A recursive approximation technique known as approximating sequence of Riccati equations is used to replace the nonlinear problem by a sequence of linear-quadratic and time-varying approximating problems. The state variables are approximated and expanded in Chebyshev polynomials. Then, the control variables are written as a function of state variables and their derivatives. The constrained nonlinear optimal control problem is then converted to quadratic programming problem, and a constrained optimization problem is solved. Different final state conditions (unspecified, partly specified, and fully specified) are handled, and the effectiveness of the proposed method is demonstrated by solving sample problems.