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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