Optimal control problems of parabolic-hyperbolic systems with integral time delays

2012 ◽  
Author(s):  
Adam Kowalewski
Keyword(s):  
Optimal Control ◽  
Time Delays ◽  
Optimal Control Problems ◽  
Hyperbolic Systems ◽  
Control Problems ◽  
Integral Time

High-order relaxation approaches for adjoint-based optimal control problems governed by nonlinear hyperbolic systems of conservation laws

2016 ◽  
Vol 24 (1) ◽  
Author(s):  
Elimboto M. Yohana ◽  
Mapundi K. Banda
Keyword(s):  
Optimal Control ◽  
Conservation Laws ◽  
Optimal Control Problems ◽  
Initial Conditions ◽  
Hyperbolic Systems ◽  
Control Problems ◽  
Computational Investigation ◽  
Backward Problem ◽  
Systems Of Conservation Laws ◽  
The Cost

AbstractA computational investigation of optimal control problems which are constrained by hyperbolic systems of conservation laws is presented. The general framework is to employ the adjoint-based optimization to minimize the cost functional of matching-type between the optimal and the target solution. Extension of the numerical schemes to second-order accuracy for systems for the forward and backward problem are applied. In addition a comparative study of two relaxation approaches as solvers for hyperbolic systems is undertaken. In particular optimal control of the 1-D Riemann problem of Euler equations of gas dynamics is studied. The initial values are used as control parameters. The numerical flow obtained by optimal initial conditions matches accurately with observations.

scholarly journals Optimal control problems with time delays: Two case studies in biomedicine

2018 ◽  
Vol 15 (5) ◽  
pp. 1137-1154 ◽  
Author(s):  
Laurenz Göllmann ◽  
◽  
Helmut Maurer ◽  
Keyword(s):  
Optimal Control ◽  
Case Studies ◽  
Time Delays ◽  
Optimal Control Problems ◽  
Control Problems

Computation of Approximately Optimal Control Signals for Systems With Time Delays

1974 ◽  
Vol 96 (3) ◽  
pp. 269-276
Author(s):  
L. B. Horwitz
Keyword(s):  
Optimal Control ◽  
Time Delays ◽  
Computational Algorithm ◽  
Optimal Control Problems ◽  
Control Signal ◽  
Control Problems ◽  
Piecewise Constant ◽  
Switching Times ◽  
Control Signals ◽  
Approximate Nature

A computational algorithm is presented for a class of optimal control problems involving time delays. The approach is to restrict the control signal to a class of piecewise constant time functions with a prescribed number of switching times, compute the optimal member of this class, and then repeat with a larger number of switching times. By allowing the number of switching times to increase beyond bound a sequence of restricted optimal control signals is developed whose limit approaches the unrestricted optimal control signal. In practice the computations are terminated after a finite number of repeats, thus leading to the approximate nature of the solution. The results of two examples are included to illustrate the technique.

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