Free time optimal control problems with time delays
| Autor: | Helmut Maurer, P. Falugi, Richard B. Vinter, Andrea Boccia |
|---|---|
| Přispěvatelé: | Department of Electrical and Electronic Engineering [London] (DEEE), Imperial College London, Dipartimento di Matematica Pura e Applicata [Padova], Università degli Studi di Padova = University of Padua (Unipd), European Project: 264735,EC:FP7:PEOPLE,FP7-PEOPLE-2010-ITN,SADCO(2011), Department of Electrical and Electronic Engineering [London] ( DEEE ), Universita degli Studi di Padova, European Project : 264735,EC:FP7:PEOPLE,FP7-PEOPLE-2010-ITN,SADCO ( 2011 ) |
| Jazyk: | angličtina |
| Rok vydání: | 2013 |
| Předmět: |
[ MATH.MATH-OC ] Mathematics [math]/Optimization and Control [math.OC]
0209 industrial biotechnology Mathematical optimization Transversality Differential equation Computation 010102 general mathematics Parameterized complexity Perturbation (astronomy) Rule-based system 02 engineering and technology Optimal control 01 natural sciences 020901 industrial engineering & automation Maximum principle [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC] 0101 mathematics Mathematics |
| Zdroj: | 52nd IEEE Control and Decision Conference (CDC) 52nd IEEE Control and Decision Conference (CDC), 2013, Florence, Italy. pp.520-525, ⟨10.1109/CDC.2013.6759934⟩ 52nd IEEE Control and Decision Conference (CDC), 2013, Florence, Italy. pp.520-525, 2013, Proceedings of the IEEE 52nd Annual Conference on Decision and Control (CDC). 〈10.1109/CDC.2013.6759934〉 CDC |
| DOI: | 10.1109/CDC.2013.6759934⟩ |
| Popis: | International audience; Solutions to optimal control problems for retarded systems, on a fixed time interval, satisfy a form of the Maximum Principle, in which the co-state equation is an advanced differential equation. In this paper we present an extension of this well-known necessary condition of optimality, to cover situations in which the data is non-smooth, and the final time is free. The fact that the end-time is a choice variable is accommodated by an extra transversality condition. A traditional approach to deriving this extra condition is to reduce the free end-time problem to a fixed end-time problem by a parameterized change of the time variable. This approach is problematic for time delay problems because it introduces a parameter dependent time-delay that is not readily amenable to analysis; to avoid this difficulty we instead base our analysis on direct perturbation of the end-time. Formulae are derived for the gradient of the minimum cost as a function of the end-time. It is shown how these formulae can be exploited to construct two-stage algorithms for the computation of solutions to optimal retarded control problems with free-time, in which a sequence of fixed time problems are solved by means of Guinn's transformation, and the end-time is adjusted according to a rule based on the earlier derived gradient formulae for the minimum cost function. Numerical examples are presented. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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