scholarly journals Memory-efficient Implementation of Riccati Approach for Time-Dependent Optimal Control Problems in ODEs

PAMM ◽  
2005 ◽  
Vol 5 (1) ◽  
pp. 695-696
Author(s):  
Julia Sternberg ◽  
Andreas Griewank
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Efficient Implementation ◽  
Time Dependent ◽  
Control Problems ◽  
Memory Efficient

scholarly journals Robust Iterative Solution of a Class of Time-Dependent Optimal Control Problems

PAMM ◽  
2012 ◽  
Vol 12 (1) ◽  
pp. 3-6 ◽  
Author(s):  
John W. Pearson ◽  
Martin Stoll ◽  
Andrew J. Wathen
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Iterative Solution ◽  
Time Dependent ◽  
Control Problems

Superconvergence of Finite Element Methods for Optimal Control Problems Governed by Parabolic Equations with Time-Dependent Coefficients

2013 ◽  
Vol 3 (3) ◽  
pp. 209-227
Author(s):  
Yuelong Tang ◽  
Yanping Chen
Keyword(s):  
Optimal Control ◽  
Finite Element ◽  
Optimal Control Problems ◽  
Finite Element Approximation ◽  
Euler Method ◽  
Time Dependent ◽  
Control Problems ◽  
Element Approximation ◽  
Time Discretisation ◽  
Backward Euler

AbstractIn this article, a fully discrete finite element approximation is investigated for constrained parabolic optimal control problems with time-dependent coefficients. The spatial discretisation invokes finite elements, and the time discretisation a nonstandard backward Euler method. On introducing some appropriate intermediate variables and noting properties of the L2 projection and the elliptic projection, we derive the superconvergence for the control, the state and the adjoint state. Finally, we discuss some numerical experiments that illustrate our theoretical results.

scholarly journals A New Approach to Solving Stochastic Optimal Control Problems

Mathematics ◽  
2019 ◽  
Vol 7 (12) ◽  
pp. 1207 ◽  
Author(s):  
Pablo T. Rodriguez-Gonzalez ◽  
Vicente Rico-Ramirez ◽  
Ramiro Rico-Martinez ◽  
Urmila M. Diwekar
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Objective Function ◽  
Stochastic Optimal Control ◽  
Optimal Control Problems ◽  
Biodiesel Production ◽  
Time Dependent ◽  
Control Problems ◽  
Model Calculations ◽  
New Approach

A conventional approach to solving stochastic optimal control problems with time-dependent uncertainties involves the use of the stochastic maximum principle (SMP) technique. For large-scale problems, however, such an algorithm frequently leads to convergence complexities when solving the two-point boundary value problem resulting from the optimality conditions. An alternative approach consists of using continuous random variables to capture uncertainty through sampling-based methods embedded within an optimization strategy for the decision variables; such a technique may also fail due to the computational intensity involved in excessive model calculations for evaluating the objective function and its derivatives for each sample. This paper presents a new approach to solving stochastic optimal control problems with time-dependent uncertainties based on BONUS (Better Optimization algorithm for Nonlinear Uncertain Systems). The BONUS has been used successfully for non-linear programming problems with static uncertainties, but we show here that its scope can be extended to the case of optimal control problems with time-dependent uncertainties. A batch reactor for biodiesel production was used as a case study to illustrate the proposed approach. Results for a maximum profit problem indicate that the optimal objective function and the optimal profiles were better than those obtained by the maximum principle.

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