Optimal Control of a Passive Particle Advected by a Lamb–Oseen (Viscous) Vortex
This work concerns the optimal control of a passive particle in viscous flows. This is relevant since, while there are many studies on optimal control in inviscid flows, there is little to no work in this context for viscous flows, and viscosity cannot always be neglected. Furthermore, in many tasks...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-05-01
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| Series: | Computation |
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| Online Access: | https://www.mdpi.com/2079-3197/10/6/87 |
| _version_ | 1797488626450300928 |
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| author | Gil Marques Sílvio Gama Fernando Lobo Pereira |
| author_facet | Gil Marques Sílvio Gama Fernando Lobo Pereira |
| author_sort | Gil Marques |
| collection | DOAJ |
| description | This work concerns the optimal control of a passive particle in viscous flows. This is relevant since, while there are many studies on optimal control in inviscid flows, there is little to no work in this context for viscous flows, and viscosity cannot always be neglected. Furthermore, in many tasks, there is a need to reduce the energy spent; thus, energy-optimal solutions to problems are important. The aim of this work is to investigate how to optimally move a passive particle advected by a Lamb–Oseen (viscous) vortex between two given points in space in a given time interval while minimising the energy spent on this process. We take a control acting only on the radial component of the motion, and, by using the Pontryagin’s Maximum Principle, we find an explicit time-dependent extremal. We also analyse how the energy cost changes with the viscosity of the flow.The problem is transformed into a parameter search problem with two parameters related to the radial and angular coordinates of the initial point. The energy cost of the process increases with viscosity as long as the passive particle maintains the number of full turns it makes around the vortex. However, the energy cost increases if the increase in viscosity forces the particle to make fewer full revolutions around the vortex. |
| first_indexed | 2024-03-10T00:04:58Z |
| format | Article |
| id | doaj.art-1925eab6164f406ca19b83c634ad7010 |
| institution | Directory Open Access Journal |
| issn | 2079-3197 |
| language | English |
| last_indexed | 2024-03-10T00:04:58Z |
| publishDate | 2022-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Computation |
| spelling | doaj.art-1925eab6164f406ca19b83c634ad70102023-11-23T16:09:33ZengMDPI AGComputation2079-31972022-05-011068710.3390/computation10060087Optimal Control of a Passive Particle Advected by a Lamb–Oseen (Viscous) VortexGil Marques0Sílvio Gama1Fernando Lobo Pereira2CMUP—Department of Mathematics, FCUP, University of Porto, 4169-007 Porto, PortugalCMUP—Department of Mathematics, FCUP, University of Porto, 4169-007 Porto, PortugalSYSTEC—Department of Electrical and Computer Engineering, FEUP, University of Porto, 4200-465 Porto, PortugalThis work concerns the optimal control of a passive particle in viscous flows. This is relevant since, while there are many studies on optimal control in inviscid flows, there is little to no work in this context for viscous flows, and viscosity cannot always be neglected. Furthermore, in many tasks, there is a need to reduce the energy spent; thus, energy-optimal solutions to problems are important. The aim of this work is to investigate how to optimally move a passive particle advected by a Lamb–Oseen (viscous) vortex between two given points in space in a given time interval while minimising the energy spent on this process. We take a control acting only on the radial component of the motion, and, by using the Pontryagin’s Maximum Principle, we find an explicit time-dependent extremal. We also analyse how the energy cost changes with the viscosity of the flow.The problem is transformed into a parameter search problem with two parameters related to the radial and angular coordinates of the initial point. The energy cost of the process increases with viscosity as long as the passive particle maintains the number of full turns it makes around the vortex. However, the energy cost increases if the increase in viscosity forces the particle to make fewer full revolutions around the vortex.https://www.mdpi.com/2079-3197/10/6/87optimal controlPontryagin’s Maximum Principlevortex methodsLamb–Oseen vortexdynamical systems |
| spellingShingle | Gil Marques Sílvio Gama Fernando Lobo Pereira Optimal Control of a Passive Particle Advected by a Lamb–Oseen (Viscous) Vortex Computation optimal control Pontryagin’s Maximum Principle vortex methods Lamb–Oseen vortex dynamical systems |
| title | Optimal Control of a Passive Particle Advected by a Lamb–Oseen (Viscous) Vortex |
| title_full | Optimal Control of a Passive Particle Advected by a Lamb–Oseen (Viscous) Vortex |
| title_fullStr | Optimal Control of a Passive Particle Advected by a Lamb–Oseen (Viscous) Vortex |
| title_full_unstemmed | Optimal Control of a Passive Particle Advected by a Lamb–Oseen (Viscous) Vortex |
| title_short | Optimal Control of a Passive Particle Advected by a Lamb–Oseen (Viscous) Vortex |
| title_sort | optimal control of a passive particle advected by a lamb oseen viscous vortex |
| topic | optimal control Pontryagin’s Maximum Principle vortex methods Lamb–Oseen vortex dynamical systems |
| url | https://www.mdpi.com/2079-3197/10/6/87 |
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