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  1. Computational Mathematics and Mathematical Physics
  2. Computational Mathematics and Mathematical Physics : Volume 52
  3. Computational Mathematics and Mathematical Physics : Volume 52, Issue 10, October 2012
  4. Real-time computation of optimal control
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Computational Mathematics and Mathematical Physics : Volume 57
Computational Mathematics and Mathematical Physics : Volume 56
Computational Mathematics and Mathematical Physics : Volume 55
Computational Mathematics and Mathematical Physics : Volume 54
Computational Mathematics and Mathematical Physics : Volume 53
Computational Mathematics and Mathematical Physics : Volume 52
Computational Mathematics and Mathematical Physics : Volume 52, Issue 12, December 2012
Computational Mathematics and Mathematical Physics : Volume 52, Issue 11, November 2012
Computational Mathematics and Mathematical Physics : Volume 52, Issue 10, October 2012
Schoenberg’s polynomial B-splines of odd degrees: A brief review of application
Differential properties of the minimum function for diagonalizable quadratic problems
Real-time computation of optimal control
Runge-Kutta collocation methods for differential-algebraic equations of indices 2 and 3
Singular boundary value problem for the integrodifferential equation in an insurance model with stochastic premiums: Analysis and numerical solution
On the initial boundary value problem for a nonlinear nonhomogeneous equation of Sobolev type
Regularity of the solution and well-posedness of a mixed problem for an elliptic system with quadratic nonlinearity in gradients
Three-dimensional instability of flow in a flat channel between elastic plates
Splitting over physical processes as applied to the construction of a numerical method for solving the system of kinetic equations governing a hall thruster rarefied plasma jet
On the complexity of the dualization problem
Computational Mathematics and Mathematical Physics : Volume 52, Issue 9, September 2012
Computational Mathematics and Mathematical Physics : Volume 52, Issue 8, August 2012
Computational Mathematics and Mathematical Physics : Volume 52, Issue 7, July 2012
Computational Mathematics and Mathematical Physics : Volume 52, Issue 6, June 2012
Computational Mathematics and Mathematical Physics : Volume 52, Issue 5, May 2012
Computational Mathematics and Mathematical Physics : Volume 52, Issue 4, April 2012
Computational Mathematics and Mathematical Physics : Volume 52, Issue 3, March 2012
Computational Mathematics and Mathematical Physics : Volume 52, Issue 2, February 2012
Computational Mathematics and Mathematical Physics : Volume 52, Issue 1, January 2012
Computational Mathematics and Mathematical Physics : Volume 51
Computational Mathematics and Mathematical Physics : Volume 50
Computational Mathematics and Mathematical Physics : Volume 49
Computational Mathematics and Mathematical Physics : Volume 48
Computational Mathematics and Mathematical Physics : Volume 47
Computational Mathematics and Mathematical Physics : Volume 46

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Real-time computation of optimal control

Content Provider Springer Nature Link
Author Aleksandrov, V. M.
Copyright Year 2012
Abstract A new approach to the real-time implementation of time-optimal control for linear systems with a bounded control is proposed. The computational costs are separated between preliminary computations and computations in the course of the control process. The preliminary computations are independent of the particular initial condition and are based on the approximation of sets reachable in different times by a collection of hyperplanes. Methods for constructing hyperplanes and selecting a supporting hyperplane are described. Methods are proposed for approximately finding the normalized vector of initial conditions of the adjoint system, the driving time, and the switching times of the time-optimal control, and an iterative method for their refinement is developed. The computational complexity of the method is estimated. The computational algorithm is described, and simulation and numerical results are presented.
Starting Page 1351
Ending Page 1372
Page Count 22
File Format PDF
ISSN 09655425
Journal Computational Mathematics and Mathematical Physics
Volume Number 52
Issue Number 10
e-ISSN 15556662
Language English
Publisher Springer US
Publisher Date 2012-10-24
Publisher Place Boston
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword optimal control reachable set hyperplane real time adjoint system boundary point initial approximation variation iterative process computational costs Computational Mathematics and Numerical Analysis
Content Type Text
Resource Type Article
Subject Computational Mathematics
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