Multi-objective optimal control: a direct approach

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

The chapter introduces an approach to solve optimal control problems with multiple conflicting objectives. The approach proposed in this chapter generates sets of Pareto optimal control laws that satisfy a set of boundary conditions and path constraints. The chapter starts by introducing basic concepts of multi-objective optimisation and optimal control theory and then presents a general formulation of multi-objective optimal control problems in scalar form using the Pascoletti-Serafini scalarisation method. From this scalar form the chapter derives the first order necessary conditions for local optimality and develops a direct transcription method by Finite Elements in Time (DFET) that turns the infinite dimensional multi-objective optimal control problem into a finite dimensional multi-objective nonlinear programming problem (MONLP). The transcription method is proven to be locally convergent under some assumptions on the nature of the optimal control problem. A memetic agent-based optimisation approach is then proposed to solve the MONLP problem and return a partial reconstruction of the globally optimal Pareto set. An illustrative example concludes the chapter.

Original languageEnglish
Title of host publicationSatellite Dynamics and Space Missions
EditorsGiulio Baù, Alessandra Celletti, Cătălin Bogdan Galeş, Giovanni Federico Gronchi
Place of PublicationCham, Switzerland
PublisherSpringer
Pages257-289
Number of pages33
ISBN (Print)9783030206321, 9783030206338
DOIs
Publication statusPublished - 19 Sep 2019

Publication series

NameSpringer INdAM Series
Volume34
ISSN (Print)2281-518X
ISSN (Electronic)2281-5198

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Keywords

  • finite elements
  • multi-objective optimisation
  • optimal control
  • trajectory optimisation

Cite this

Vasile, M. (2019). Multi-objective optimal control: a direct approach. In G. Baù, A. Celletti, C. B. Galeş, & G. F. Gronchi (Eds.), Satellite Dynamics and Space Missions (pp. 257-289). (Springer INdAM Series; Vol. 34). Cham, Switzerland: Springer. https://doi.org/10.1007/978-3-030-20633-8_6