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Original Articles

Time-optimal control of a self-propelled particle in a spatiotemporal flow field

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Pages 623-634 | Received 19 Mar 2015, Accepted 26 Aug 2015, Published online: 01 Dec 2015

References

  • Akulenko, L.D. (2008). The time-optimal transfer of a perturbed dynamical object to a given position. Journal of Applied Mathematics and Mechanics, 72(2), 136–143.
  • Akulenko, L.D. (2011). Time-optimal steering of an object moving in a viscous medium to a desired phase state. Journal of Applied Mathematics and Mechanics, 75(5), 534–538.
  • Akulenko, L.D., & Koshelev, A.P. (2007). Time-optimal steering of a point mass to a specified position with the required velocity. Journal of Applied Mathematics and Mechanics, 71(2), 200–207.
  • Akulenko, L.D., & Shmatkov, A.M (2002). Time-optimal steering of a point mass onto the surface of a sphere at zero velocity. Journal of Applied Mathematics and Mechanics, 66(1), 9–21.
  • Athans, M., & Falb, P.L. (2007). Optimal control, an introduction to the theory and its applications. New York, NY: Dover Publications.
  • Bakolas, E. (2014). Optimal guidance of the isotropic rocket in the presence of wind. Journal of Optimization Theory and Applications, 162(3), 954–974.
  • Bakolas, E., & Tsiotras, P. (2010). The Zermelo Voronoi diagram: A dynamic partition problem. Automatica, 46(12), 2059–2067.
  • Bakolas, E., & Tsiotras, P. (2013). Optimal partitioning for spatiotemporal coverage in a drift field. Automatica, 49(7), 2064–2073.
  • Bao, D., Robles, C., & Shen, Z. (2004). Zermelo navigation on Riemannian manifolds. Journal of Differential Geometry, 66, 377–435.
  • Betts, J.T. (2010). Practical methods for optimal control and estimation using nonlinear programming. Philadelphia, PA: SIAM.
  • Brockett, R.W. (1970). Finite dimensional linear systems. New York, NY: John Wiley & Sons, Inc.
  • Bryson, A.E. Jr, & Ho, Y.C. (1969). Applied optimal control. Waltham, MA: Blaisdell.
  • Carathéodory, C. (1999). Calculus of variations and partial differential equations of first order (3rd ed.). Washington, DC: American Mathematical Society.
  • Conti, R. (1965). Contributions to linear control theory. Journal of Differential Equations, 1(4), 427–445.
  • Halkin, H. (1964). A generalization of LaSalle's “Bang-Bang” principle. Journal of SIAM Control, 2(2), 199–202.
  • Hermes, H., & LaSalle, J.P. (1969). Functional analysis and time optimal control. New York, NY: Academic Press.
  • Jurdjevic, V. (1997). Geometric control theory. New York, NY: Cambridge University Press.
  • Krasovskii, N.N. (1957). On the theory of optimal regulation. Automation and Remote Control, 18, 1005–1016.
  • Kurzweil, J. (1963). On the linear theory of optimal control systems. Časopis pro pěstování matematiky, 1(4), 110–117.
  • LaSalle, J.P. (1960). The time optimal control problem. In Contributions to the theory of nonlinear oscillations (Vol. 5, pp. 1–24). Princeton, NJ: Princeton University Press.
  • Lee, E.B., & Markus, L. (1986). Foundations of optimal control theory. Malabar, FL: Krieger Publishing Company.
  • Neustadt, L.W. (1963). The existence of optimal controls in the absence of convexity conditions. Journal of Mathematical Analysis and Applications, 1(4), 110–117.
  • Olech, C. (1966). Extremal solutions of a control system. Journal of Differential Equations, 2, 74–101.
  • Osher, S., & Sethian, J.A. (1988). Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton–Jacobi formulations. Journal of Computational Physics, 79, 12–49.
  • Pontryagin, L.S., Boltyanskii, V.G., Gamkrelidze, R.V., & Mishchenko, E.F. (1962). The mathematical theory of optimal processes. New York, NY: Interscience.
  • Rhoads, B., Mezić, I., & Poje, A. (2010). Minimum time feedback control of autonomous underwater vehicles. Proceedings of 49th IEEE Conference on Decision and Control (pp. 5828–5834). Atlanta, GA: IEEE.
  • Serres, U. (2006). On the curvature of two-dimensional optimal control systems and Zermelo's navigation problem. Journal of Mathematical Sciences, 135(4), 3224–3243.
  • Serres, U. (2009). On Zermelo-like problems: Gause Bonnet inequality and E. Hopf theorem. Journal of Dynamical and Control Systems, 15(1), 99–131.
  • Sethian, J. (1996). Level set methods and fast marching methods. Cambridge: Cambridge University Press.
  • Trélat, E. (2012). Optimal control and applications to aerospace: Some results and challenges. Journal of Optimization Theory and Applications, 154(3), 713–758.
  • Tsai, Y., Cheng, L., Osher, S., & Zhao, H. (2003). Fast sweeping algorithms for a class of Hamilton–Jacobi equations. SIAM Journal on Numerical Analysis, 41(2), 673–694.
  • Tsitsiklis, J. (1995). Efficient algorithms for globally optimal trajectories. IEEE Transactions on Automatic Control, 40(9), 1528–1538.
  • Venkatraman, A., & Bhat, S. (2006). Optimal planar turns under acceleration constraints. Proceedings of 45th IEEE Conference on Decision and Control (pp. 235–240). San Diego, CA: IEEE.
  • Zermelo, E. (1931). Über das Navigationsproblem bei ruhender oder vernderlicher Windverteilung [On navigation in the air as a problem in the calculus of variations]. Zeitschrift für Angewandte Mathematik und Mechanik, 11(2), 114–124.

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