scholarly journals Optimal control of a parabolic distributed parameter system using a fully exponentially convergent barycentric shifted gegenbauer integral pseudospectral method

2018 ◽  
Vol 14 (2) ◽  
pp. 473-496 ◽  
Author(s):  
Kareem T. Elgindy ◽  
Keyword(s):  
Optimal Control ◽  
Pseudospectral Method ◽  
Distributed Parameter ◽  
Distributed Parameter System ◽  
Parameter System

Optimale Steuerung eines Systems mit verteilten Parametern am Beispiel eines Tiefofens / Optimal control of a distributed parameter system applied to a metallurgical Furnace

1974 ◽  
Vol 22 (11) ◽  
Author(s):  
D. Franke
Keyword(s):  
Optimal Control ◽  
Distributed Parameter ◽  
Distributed Parameter System ◽  
Wird Eine ◽  
Parameter System ◽  
Metallurgical Furnace ◽  
Mathematisches Modell

Der Beitrag behandelt am Beispiel eines Tiefofens die Anwendung der Optimierungstheorie für Systeme mit verteilten Parametern. Als mathematisches Modell wird die Wärmeleitungsdifferentialgleichung zugrunde gelegt.Die Minimierung eines quadratischen Güte-Index bei beschränkter Stellgröße führt nach A. G. Butkovskiy auf eine nichtlineare Integralgleichung für die optimale Steuerfunktion. Zur Lösung dieser Integralgleichung wird eine hybride Rechenschaltung vorgestellt. Anhand eines Zahlenbeispiels werden Rechnerergebnisse mitgeteilt und diskutiert.

Optimal Control of a Distributed Parameter, Time-Lagged River Aeration System

1975 ◽  
Vol 97 (2) ◽  
pp. 164-171 ◽  
Author(s):  
M. K. O¨zgo¨ren ◽  
R. W. Longman ◽  
C. A. Cooper
Keyword(s):  
Optimal Control ◽  
Feedback Control ◽  
Open Loop ◽  
Optimal Feedback Control ◽  
Distributed Parameter ◽  
Control Law ◽  
Optimal Controls ◽  
Distributed Parameter System ◽  
Parameter System ◽  
Characteristic Lines

The control of artificial in-stream aeration of polluted rivers with multiple waste effluent sources is treated. The optimal feedback control law for this distributed parameter system is determined by solving the partial differential equations along characteristic lines. In this process the double integral cost functional of the distributed parameter system is reduced to a single integral cost. Because certain measurements are time consuming, the feedback control law is obtained in the presence of observation delay in some but not all of the system variables. The open loop optimal control is then found, showing explicity the effect of changes in any of the effluent sources on the aeration strategy. It is shown that the optimal strategy for a distribution of sources can be written as an affine transformation upon the optimal controls for sources of unit strength.

Switching Analysis for Constrained Bilinear Distributed Parameter System With Applications

1969 ◽  
Vol 91 (2) ◽  
pp. 277-283 ◽  
Author(s):  
D. L. Briggs ◽  
C. N. Shen
Keyword(s):  
Optimal Control ◽  
Boundary Control ◽  
Initial Conditions ◽  
Control Program ◽  
Necessary Condition ◽  
Stress Constraint ◽  
Distributed Parameter ◽  
Distributed Parameter System ◽  
Parameter System ◽  
State Equations

A distributed parameter thermal and stress model is developed for a nuclear rocket. The resultant equations for the optimal control problem are a pair of coupled, bilinear, partial differential equations. The thermal stress constraint forms an inequality which is a function of both the state and the control. The initial conditions are steady state, and the terminal condition is that the coolant flow obtain a fixed, higher level. The distributed parameter system is discretized in the space dimension to give an arbitrary order set of ordinary differential, state equations. It is shown how a result based on the Weierstrass necessary condition and derived by Berkovitz from the calculus of variations using a slack variable technique may be applied. This condition is shown to require the optimal control to be “boundary control” with no switching. The optimal control program must make the inequality constraint an equality at some location throughout the transient. Based on the result that boundary control is the optimal control, an algorithm is developed to compute the optimal control program. The algorithm was programmed on a digital computer and numerical results are given for the optimal flow program and the resultant stress distributions for various cases.

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