TY - CHAP

T1 - Multi-objective optimal control

T2 - a direct approach

AU - Vasile, Massimiliano

PY - 2019/9/19

Y1 - 2019/9/19

N2 - 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.

AB - 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.

KW - finite elements

KW - multi-objective optimisation

KW - optimal control

KW - trajectory optimisation

UR - http://www.scopus.com/inward/record.url?scp=85072803811&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-20633-8_6

DO - 10.1007/978-3-030-20633-8_6

M3 - Chapter

AN - SCOPUS:85072803811

SN - 9783030206321

SN - 9783030206338

T3 - Springer INdAM Series

SP - 257

EP - 289

BT - Satellite Dynamics and Space Missions

A2 - Baù, Giulio

A2 - Celletti, Alessandra

A2 - Galeş, Cătălin Bogdan

A2 - Gronchi, Giovanni Federico

PB - Springer

CY - Cham, Switzerland

ER -