A dynamic programming approach to the maximum principle of distributed-parameter systems

1979 ◽  
Vol 27 (4) ◽  
pp. 583-601 ◽  
Author(s):  
S. Fond
Keyword(s):  
Dynamic Programming ◽  
Maximum Principle ◽  
Distributed Parameter Systems ◽  
Programming Approach ◽  
Distributed Parameter ◽  
The Maximum Principle ◽  
Dynamic Programming Approach

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.

On the dynamic programming approach to Pontriagin's maximum principle

1968 ◽  
Vol 5 (3) ◽  
pp. 679-692 ◽  
Author(s):  
Richard Morton
Keyword(s):  
Dynamic Programming ◽  
Maximum Principle ◽  
The State ◽  
Dynamic Programming Principle ◽  
Programming Approach ◽  
Bellman Function ◽  
State Variables ◽  
Dynamic Programming Approach ◽  
Minimum Value ◽  
Image Position

Suppose that the state variables x = (x1,…,xn)′ where the dot refers to derivatives with respect to time t, and u ∊ U is a vector of controls. The object is to transfer x to x1 by choosing the controls so that the functional takes on its minimum value J(x) called the Bellman function (although we shall define it in a different way). The Dynamic Programming Principle leads to the maximisation with respect to u of and equality is obtained upon maximisation.

On the dynamic programming approach to Pontriagin's maximum principle

1968 ◽  
Vol 5 (03) ◽  
pp. 679-692
Author(s):  
Richard Morton
Keyword(s):  
Dynamic Programming ◽  
Maximum Principle ◽  
The State ◽  
Dynamic Programming Principle ◽  
Programming Approach ◽  
Bellman Function ◽  
State Variables ◽  
Dynamic Programming Approach ◽  
Minimum Value ◽  
Image Position

Suppose that the state variables x = (x 1,…,x n )′ where the dot refers to derivatives with respect to time t, and u ∊ U is a vector of controls. The object is to transfer x to x 1 by choosing the controls so that the functional takes on its minimum value J(x) called the Bellman function (although we shall define it in a different way). The Dynamic Programming Principle leads to the maximisation with respect to u of and equality is obtained upon maximisation.

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