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 -