Global solution of multi-objective optimal control problems with multi agent collaborative search and direct finite elements transcription

Abstract

This version is available at https://strathprints.strath.ac.uk/59172/ Strathprints is designed to allow users to access the research output of the University of Strathclyde. Unless otherwise explicitly stated on the manuscript, Copyright © and Moral Rights for the papers on this site are retained by the individual authors and/or other copyright owners. Please check the manuscript for details of any other licences that may have been applied. You may not engage in further distribution of the material for any profitmaking activities or any commercial gain. You may freely distribute both the url (https://strathprints.strath.ac.uk/) and the content of this paper for research or private study, educational, or not-for-profit purposes without prior permission or charge.Any correspondence concerning this service should be sent to the Strathprints administrator: strathprints@strath.ac.ukThe Strathprints institutional repository (https://strathprints.strath.ac.uk) is a digital archive of University of Strathclyde research outputs. It has been developed to disseminate open access research outputs, expose data about those outputs, and enable the management and persistent access to Strathclyde's intellectual output. Abstract-This paper addresses the solution of optimal control problems with multiple and possibly conflicting objective functions. The solution strategy is based on the integration of Direct Finite Elements in Time (DFET) transcription into the Multi Agent Collaborative Search (MACS) framework. Multi Agent Collaborative Search is a memetic algorithm in which a population of agents performs a set of individual and social actions looking for the Pareto front. Direct Finite Elements in Time transcribe an optimal control problem into a constrained Non-linear Programming Problem (NLP) by collocating states and controls on spectral bases. MACS operates directly on the NLP problem and generates nearly-feasible trial solutions which are then submitted to a NLP solver. If the NLP solver converges to a feasible solution, an updated solution for the control parameters is returned to MACS, along with the corresponding value of the objective functions. Both the updated guess and the objective function values will be used by MACS to generate new trial solutions and converge, as uniformly as possible, to the Pareto front. To demonstrate the applicability of this strategy, the paper presents the solution of the multi-objective extensions of two well-known space related optimal control problems: the Goddard Rocket problem, and the maximum energy orbit rise problem.

Multi-Objective Optimal Control of Re-entry and Abort Scenarios

“…Thus, the optimal control problem in Eq. (15) was transcribed into the non-linear programming (NLP) problem (20), which in compact form reads as: min…”

“…In [1,20,21] the typical Lagrange interpolation basis was used. When solving the minimum time trajectory injection problem, which has a bang-bang solution, a high order polynomial representation of the controls resulted in highly oscillating results across the discontinuity, exceeding the upper or lower bound even if the computed nodal solution was correct.…”

“…Problem (22) is solved with MACS [2, 27] a memetic multi-objective optimisation algorithm that combines a stochastic agent-based search with a local (gradient in this case) refinement of the solutions [7,20,21]. The agent-step solves the following two-level problem: Fig.…”

“…In [1,20,21] the ascent problem was proposed as a simple test case to validate the DFET transcription method. The dynamics in (32) below are a simplification of the problem described by (1) because it deals with the ascent of a point mass in a plane subject only to a constant gravitational acceleration in an inertial frame, and controlled by the changing the angle u of a constant thrust vector.…”

Direct Transcription of Optimal Control Problems with Finite Elements on Bernstein Basis

“…In the past decade, direct transcription with FET on spectral bases has been successfully used to solve a range of difficult problems: from the design of low-thrust multi-gravity assist trajectories to Mercury [5] and the Sun [6], to the design of weak stability boundary transfers to the Moon, low-thrust transfers in the restricted three body problem and optimal landing trajectories to the Moon [2]. More recently they have been used to perform multi-objective optimal control of spacecraft [7,8], ascent trajectories of launchers [9], or abort trajectories of reusable launch vehicles [10].…”