American Institute of Mathematical Sciences

Advanced
  • Previous Article
    A unified model for state feedback of discrete event systems I: framework and maximal permissive state feedback
  • JIMO Home
  • This Issue
  • Next Article
    Optimal portfolios under a value-at-risk constraint with applications to inventory control in supply chains
January  2008, 4(1): 95-105. doi: 10.3934/jimo.2008.4.95

Computational aspects of the optimal transit path problem

Louis Caccetta 1, , Ian Loosen 1, and  Volker Rehbock 1,

1. 

Western Australian Centre of Excellence in Industrial Optimisation, Department of Mathematics and Statistics, Curtin University of Technology, Bentley, WA, 6102, Australia, Australia

Received  September 2006 Revised  January 2007 Published  January 2008

We consider a class of path design problems which arise when an object needs to traverse between two points through a specified region. The path must optimise a prescribed criterion such as risk, reliability or cost and satisfy a number of constraints such as total travel time. Problems of this type readily arise in the defence, transport and communication industries. We specifically look at the problem of determining an optimal (in terms of minimizing the overall probability of detection) transit path for a submarine moving through a field of sonar sensors, subject to a total time constraint. A computational strategy along with results are presented.
Keywords: transit path., discretization, optimisation, Optimal Control.
Mathematics Subject Classification: Primary: 49J15, 49N90; Secondary: 90B1.
Citation: Louis Caccetta, Ian Loosen, Volker Rehbock. Computational aspects of the optimal transit path problem. Journal of Industrial & Management Optimization, 2008, 4 (1) : 95-105. doi: 10.3934/jimo.2008.4.95
[1]

Paolo Rinaldi, Heinz Schättler. Minimization of the base transit time in semiconductor devices using optimal control. Conference Publications, 2003, 2003 (Special) : 742-751. doi: 10.3934/proc.2003.2003.742
[2]

Max Gunzburger, Sung-Dae Yang, Wenxiang Zhu. Analysis and discretization of an optimal control problem for the forced Fisher equation. Discrete & Continuous Dynamical Systems - B, 2007, 8 (3) : 569-587. doi: 10.3934/dcdsb.2007.8.569
[3]

Shanjian Tang, Fu Zhang. Path-dependent optimal stochastic control and viscosity solution of associated Bellman equations. Discrete & Continuous Dynamical Systems - A, 2015, 35 (11) : 5521-5553. doi: 10.3934/dcds.2015.35.5521
[4]

Matthias Gerdts, Martin Kunkel. Convergence analysis of Euler discretization of control-state constrained optimal control problems with controls of bounded variation. Journal of Industrial & Management Optimization, 2014, 10 (1) : 311-336. doi: 10.3934/jimo.2014.10.311
[5]

Tiffany A. Jones, Lou Caccetta, Volker Rehbock. Optimisation modelling of cancer growth. Discrete & Continuous Dynamical Systems - B, 2017, 22 (1) : 115-123. doi: 10.3934/dcdsb.2017006
[6]

Thalya Burden, Jon Ernstberger, K. Renee Fister. Optimal control applied to immunotherapy. Discrete & Continuous Dynamical Systems - B, 2004, 4 (1) : 135-146. doi: 10.3934/dcdsb.2004.4.135
[7]

Ellina Grigorieva, Evgenii Khailov. Optimal control of pollution stock. Conference Publications, 2011, 2011 (Special) : 578-588. doi: 10.3934/proc.2011.2011.578
[8]

Hang-Chin Lai, Jin-Chirng Lee, Shuh-Jye Chern. A variational problem and optimal control. Journal of Industrial & Management Optimization, 2011, 7 (4) : 967-975. doi: 10.3934/jimo.2011.7.967
[9]

Hassan Belhadj, Mohamed Fihri, Samir Khallouq, Nabila Nagid. Optimal number of Schur subdomains: Application to semi-implicit finite volume discretization of semilinear reaction diffusion problem. Discrete & Continuous Dynamical Systems - S, 2018, 11 (1) : 21-34. doi: 10.3934/dcdss.2018002
[10]

Qun Lin, Ryan Loxton, Kok Lay Teo. The control parameterization method for nonlinear optimal control: A survey. Journal of Industrial & Management Optimization, 2014, 10 (1) : 275-309. doi: 10.3934/jimo.2014.10.275
[11]

Cristiana J. Silva, Helmut Maurer, Delfim F. M. Torres. Optimal control of a Tuberculosis model with state and control delays. Mathematical Biosciences & Engineering, 2017, 14 (1) : 321-337. doi: 10.3934/mbe.2017021
[12]

Jorge San Martín, Takéo Takahashi, Marius Tucsnak. An optimal control approach to ciliary locomotion. Mathematical Control & Related Fields, 2016, 6 (2) : 293-334. doi: 10.3934/mcrf.2016005
[13]

C.Z. Wu, K. L. Teo. Global impulsive optimal control computation. Journal of Industrial & Management Optimization, 2006, 2 (4) : 435-450. doi: 10.3934/jimo.2006.2.435
[14]

Robert J. Kipka, Yuri S. Ledyaev. Optimal control of differential inclusions on manifolds. Discrete & Continuous Dynamical Systems - A, 2015, 35 (9) : 4455-4475. doi: 10.3934/dcds.2015.35.4455
[15]

Filipe Rodrigues, Cristiana J. Silva, Delfim F. M. Torres, Helmut Maurer. Optimal control of a delayed HIV model. Discrete & Continuous Dynamical Systems - B, 2018, 23 (1) : 443-458. doi: 10.3934/dcdsb.2018030
[16]

Antonio Fernández, Pedro L. García. Regular discretizations in optimal control theory. Journal of Geometric Mechanics, 2013, 5 (4) : 415-432. doi: 10.3934/jgm.2013.5.415
[17]

Bavo Langerock. Optimal control problems with variable endpoints. Conference Publications, 2003, 2003 (Special) : 507-516. doi: 10.3934/proc.2003.2003.507
[18]

Alberto Bressan, Yunho Hong. Optimal control problems on stratified domains. Networks & Heterogeneous Media, 2007, 2 (2) : 313-331. doi: 10.3934/nhm.2007.2.313
[19]

François Gay-Balmaz, Tudor S. Ratiu. Clebsch optimal control formulation in mechanics. Journal of Geometric Mechanics, 2011, 3 (1) : 41-79. doi: 10.3934/jgm.2011.3.41
[20]

M'hamed Kesri. Structural stability of optimal control problems. Communications on Pure & Applied Analysis, 2005, 4 (4) : 743-756. doi: 10.3934/cpaa.2005.4.743

2018 Impact Factor: 1.025

Tools

Metrics

  • PDF downloads (5)
  • HTML views (0)
  • Cited by (2)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences