On the optimization of distributed parameter systems with boundary control: A counter example for the maximum principle

AIChE Journal ◽  
1974 ◽  
Vol 20 (6) ◽  
pp. 1124-1130 ◽  
Author(s):  
F. Gruyaert ◽  
C. M. Crowe
Keyword(s):  
Maximum Principle ◽  
Boundary Control ◽  
Distributed Parameter Systems ◽  
Distributed Parameter ◽  
The Maximum Principle ◽  
Counter Example

Dynamic Programming and a Distributed Parameter Maximum Principle

1968 ◽  
Vol 90 (2) ◽  
pp. 152-156 ◽  
Author(s):  
W. L. Brogan
Keyword(s):  
Dynamic Programming ◽  
Maximum Principle ◽  
Programming Approach ◽  
Distributed Parameter ◽  
Programming Technique ◽  
Nonhomogeneous Boundary Condition ◽  
The Maximum Principle ◽  
Dynamic Programming Approach ◽  
Nonhomogeneous Boundary ◽  
Definition Of

A proof of a distributed parameter maximum principle is given by using dynamic programming. An example problem involving a nonhomogeneous boundary condition is also treated by using the dynamic programming technique and by extending the definition of the differential operator. It is thus demonstrated that for linear systems the dynamic programming approach is just as powerful as the variational approach originally used to derive the maximum principle.

scholarly journals Necessary and Sufficient Conditions of Optimality for a Damped Hyperbolic Equation in One-Space Dimension

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Ismail Kucuk ◽  
Kenan Yildirim
Keyword(s):  
Maximum Principle ◽  
Space Dimension ◽  
Sufficient Conditions ◽  
Necessary Condition ◽  
Distributed Parameter ◽  
Hyperbolic Partial Differential Equation ◽  
The Maximum Principle ◽  
Convexity Assumptions ◽  
Necessary And Sufficient ◽  
One Space Dimension

The present paper deals with the necessary optimality condition for a class of distributed parameter systems in which the system is modeled in one-space dimension by a hyperbolic partial differential equation subject to the damping and mixed constraints on state and controls. Pontryagin maximum principle is derived to be a necessary condition for the controls of such systems to be optimal. With the aid of some convexity assumptions on the constraint functions, it is obtained that the maximum principle is also a sufficient condition for the optimality.

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