An improved iterative computational approach to the solution of the Hamilton–Jacobi equation in optimal control problems of affine nonlinear systems with application

2020 ◽  
Vol 51 (14) ◽  
pp. 2625-2634
Author(s):  
M. D. S. Aliyu
Keyword(s):  
Optimal Control ◽  
Nonlinear Systems ◽  
Jacobi Equation ◽  
Optimal Control Problems ◽  
Computational Approach ◽  
Control Problems ◽  
Affine Nonlinear Systems ◽  
Hamilton Jacobi Equation

On the Formulation of Adaptive Optimal Control Problems

1965 ◽  
Vol 87 (1) ◽  
pp. 125-134 ◽  
Author(s):  
A. E. Pearson ◽  
P. E. Sarachik
Keyword(s):  
Optimal Control ◽  
Nonlinear Systems ◽  
Optimal Control Problem ◽  
Optimal Control Problems ◽  
Performance Criteria ◽  
Control Problems ◽  
Operator Representation ◽  
Adaptive Optimal Control ◽  
Output Time ◽  
Input Time

The paper relates to an approach introduced by Kulikowski for adaptive optimal control of nonlinear systems. In this approach, the plant dynamics are represented symbolically by an operator which transforms or maps input time functions into corresponding output time functions. The contributions of the paper arise mainly from the physical considerations associated with such an operator representation, specifically the memory of the plant, and the influence of these considerations upon the formulation. It is shown that the optimal control problem may be formulated in various ways for a given plant and given performance criteria depending upon how the memory of the plant is taken into account.

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