Close Search Advanced
Journals
Resources
About Us
Open Access

An Efficient Method for Multiobjective Optimal Control and Optimal Control Subject to Integral Constraints

An Efficient Method for Multiobjective Optimal Control and Optimal Control Subject to Integral Constraints
Preview
Add to basket

Year:    2010

Journal of Computational Mathematics, Vol. 28 (2010), Iss. 4 : pp. 517–551

Abstract

We introduce a new and efficient numerical method for multicriterion optimal control and single criterion optimal control under integral constraints. The approach is based on extending the state space to include information on a "budget" remaining to satisfy each constraint; the augmented Hamilton-Jacobi-Bellman PDE is then solved numerically. The efficiency of our approach hinges on the causality in that PDE, i.e., the monotonicity of characteristic curves in one of the newly added dimensions. A semi-Lagrangian "marching" method is used to approximate the discontinuous viscosity solution efficiently. We compare this to a recently introduced "weighted sum" based algorithm for the same problem [25]. We illustrate our method using examples from flight path planning and robotic navigation in the presence of friendly and adversarial observers.

Submit Article

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.1003-m0015

Journal of Computational Mathematics, Vol. 28 (2010), Iss. 4 : pp. 517–551

Published online:    2010-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    35

Keywords:    Optimal control Multiobjective optimization Pareto front Vector dynamic programming Hamilton-Jacobi equation Discontinuous viscosity solution Semi-Lagrangian discretization.

  1. Multiobjective Optimization Based on Expensive Robotic Experiments under Heteroscedastic Noise

    Ariizumi, Ryo | Tesch, Matthew | Kato, Kenta | Choset, Howie | Matsuno, Fumitoshi

    IEEE Transactions on Robotics, Vol. 33 (2017), Iss. 2 P.468

    https://doi.org/10.1109/TRO.2016.2632739 [Citations: 25]

  2. Multiobjective Optimization Based on Response Surface Methodology with Consideration of Input Dependent Noise

    ARIIZUMI, Ryo | TESCH, Matthew | CHOSET, Howie | MATSUNO, Fumitoshi

    Transactions of the Society of Instrument and Control Engineers, Vol. 50 (2014), Iss. 11 P.792

    https://doi.org/10.9746/sicetr.50.792 [Citations: 0]

  3. Optimal Path-Planning With Random Breakdowns

    Gee, Marissa | Vladimirsky, Alexander

    IEEE Control Systems Letters, Vol. 6 (2022), Iss. P.1658

    https://doi.org/10.1109/LCSYS.2021.3130193 [Citations: 5]

  4. Quantifying and Managing Uncertainty in Piecewise-Deterministic Markov Processes

    Cartee, Elliot | Farah, Antonio | Nellis, April | Van Hook, Jacob | Vladimirsky, Alexander

    SIAM/ASA Journal on Uncertainty Quantification, Vol. 11 (2023), Iss. 3 P.814

    https://doi.org/10.1137/20M1357275 [Citations: 5]

  5. Multi-objective optimization of dynamic systems and problem of the Pareto front control

    Romanova, I. K.

    XLIII ACADEMIC SPACE CONFERENCE: dedicated to the memory of academician S.P. Korolev and other outstanding Russian scientists – Pioneers of space exploration, (2019), P.110016

    https://doi.org/10.1063/1.5133250 [Citations: 7]

  6. Multistep Look-Ahead Policy Iteration for Optimal Control of Discrete-Time Nonlinear Systems With Isoperimetric Constraints

    Li, Tao | Wei, Qinglai | Wang, Fei-Yue

    IEEE Transactions on Systems, Man, and Cybernetics: Systems, Vol. 54 (2024), Iss. 3 P.1414

    https://doi.org/10.1109/TSMC.2023.3327492 [Citations: 0]

  7. Rates of Convergence for the Continuum Limit of Nondominated Sorting

    Cook, Brendan | Calder, Jeff

    SIAM Journal on Mathematical Analysis, Vol. 54 (2022), Iss. 1 P.872

    https://doi.org/10.1137/20M1344901 [Citations: 3]

  8. Equivalent Extensions of Hamilton–Jacobi–Bellman Equations on Hypersurfaces

    Martin, Lindsay | Tsai, Yen-Hsi Richard

    Journal of Scientific Computing, Vol. 84 (2020), Iss. 3

    https://doi.org/10.1007/s10915-020-01292-z [Citations: 5]

  9. Dynamic Congestion and Tolls with Mobile Source Emission

    Friesz, Terry L. | Han, Ke | Liu, Hongcheng | Yao, Tao

    Procedia - Social and Behavioral Sciences, Vol. 80 (2013), Iss. P.818

    https://doi.org/10.1016/j.sbspro.2013.05.044 [Citations: 16]

  10. Time-Dependent Surveillance-Evasion Games

    Cartee, Elliot | Lai, Lexiao | Song, Qianli | Vladimirsky, Alexander

    2019 IEEE 58th Conference on Decision and Control (CDC), (2019), P.7128

    https://doi.org/10.1109/CDC40024.2019.9029329 [Citations: 3]

  11. A direct verification argument for the Hamilton–Jacobi equation continuum limit of nondominated sorting

    Calder, Jeff

    Nonlinear Analysis: Theory, Methods & Applications, Vol. 141 (2016), Iss. P.88

    https://doi.org/10.1016/j.na.2016.03.023 [Citations: 3]

  12. Approximation of the pareto optimal set for multiobjective optimal control problems using viability kernels

    Guigue, Alexis

    ESAIM: Control, Optimisation and Calculus of Variations, Vol. 20 (2014), Iss. 1 P.95

    https://doi.org/10.1051/cocv/2013056 [Citations: 5]

  13. Threshold-awareness in adaptive cancer therapy

    Wang, MingYi | Scott, Jacob G. | Vladimirsky, Alexander | Mustonen, Ville

    PLOS Computational Biology, Vol. 20 (2024), Iss. 6 P.e1012165

    https://doi.org/10.1371/journal.pcbi.1012165 [Citations: 0]

  14. Dynamic Multiobjective Control for Continuous-Time Systems Using Reinforcement Learning

    Lopez, Victor G. | Lewis, Frank L.

    IEEE Transactions on Automatic Control, Vol. 64 (2019), Iss. 7 P.2869

    https://doi.org/10.1109/TAC.2018.2869462 [Citations: 33]

  15. A continuum limit for non-dominated sorting

    Calder, Jeff | Esedoglu, Selim | Hero, Alfred O.

    2014 Information Theory and Applications Workshop (ITA), (2014), P.1

    https://doi.org/10.1109/ITA.2014.6804207 [Citations: 3]

  16. Multi-objective infinite horizon optimal control problems: characterization of the Pareto fronts and Pareto solutions

    Chorobura, Ana Paula

    Computational and Applied Mathematics, Vol. 40 (2021), Iss. 8

    https://doi.org/10.1007/s40314-021-01633-0 [Citations: 1]

  17. Direction-dependent optimal path planning for autonomous vehicles

    Shum, Alex | Morris, Kirsten | Khajepour, Amir

    Robotics and Autonomous Systems, Vol. 70 (2015), Iss. P.202

    https://doi.org/10.1016/j.robot.2015.02.003 [Citations: 30]

  18. Optimizing adaptive cancer therapy: dynamic programming and evolutionary game theory

    Gluzman, Mark | Scott, Jacob G. | Vladimirsky, Alexander

    Proceedings of the Royal Society B: Biological Sciences, Vol. 287 (2020), Iss. 1925 P.20192454

    https://doi.org/10.1098/rspb.2019.2454 [Citations: 46]

  19. Minimum time heading control of underpowered vehicles in time-varying ocean currents

    Rhoads, Blane | Mezić, Igor | Poje, Andrew C.

    Ocean Engineering, Vol. 66 (2013), Iss. P.12

    https://doi.org/10.1016/j.oceaneng.2013.03.012 [Citations: 29]

  20. Stochastic Optimal Control of a Sailboat

    Miles, Cole | Vladimirsky, Alexander

    IEEE Control Systems Letters, Vol. 6 (2022), Iss. P.2048

    https://doi.org/10.1109/LCSYS.2021.3136438 [Citations: 2]

  21. Expensive multiobjective optimization for robotics with consideration of heteroscedastic noise

    Ariizumi, Ryo | Tesch, Matthew | Choset, Howie | Matsuno, Fumitoshi

    2014 IEEE/RSJ International Conference on Intelligent Robots and Systems, (2014), P.2230

    https://doi.org/10.1109/IROS.2014.6942863 [Citations: 5]

  22. Optimal Trajectories of Curvature Constrained Motion in the Hamilton–Jacobi Formulation

    Takei, Ryo | Tsai, Richard

    Journal of Scientific Computing, Vol. 54 (2013), Iss. 2-3 P.622

    https://doi.org/10.1007/s10915-012-9671-y [Citations: 30]

  23. Corner Cases, Singularities, and Dynamic Factoring

    Qi, Dongping | Vladimirsky, Alexander

    Journal of Scientific Computing, Vol. 79 (2019), Iss. 3 P.1456

    https://doi.org/10.1007/s10915-019-00905-6 [Citations: 3]