Multi-objective optimal control : a direct approach

Vasile, Massimiliano; Baù, Giulio and Celletti, Alessandra and Galeş, Cătălin Bogdan and Gronchi, Giovanni Federico, eds. (2019) Multi-objective optimal control : a direct approach. In: Satellite Dynamics and Space Missions. Springer INdAM Series . Springer, Cham, Switzerland, pp. 257-289. ISBN 9783030206338

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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.