A Hybrid Differential Dynamic Programming Algorithm for Constrained Optimal Control Problems. Part 1: Theory

2012 ◽  
Vol 154 (2) ◽  
pp. 382-417 ◽  
Author(s):  
Gregory Lantoine ◽  
Ryan P. Russell
Keyword(s):  
Optimal Control ◽  
Dynamic Programming ◽  
Optimal Control Problems ◽  
Dynamic Programming Algorithm ◽  
Programming Algorithm ◽  
Control Problems ◽  
Differential Dynamic Programming ◽  
Constrained Optimal Control

A Constraining Hyperplane Technique for State Variable Constrained Optimal Control Problems

1973 ◽  
Vol 95 (4) ◽  
pp. 380-389 ◽  
Author(s):  
K. Martensson
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Control Variable ◽  
Dynamic Programming Algorithm ◽  
Inequality Constraints ◽  
Programming Algorithm ◽  
Control Problems ◽  
State Control ◽  
Constrained Optimal Control ◽  
State Variable

A new approach to the numerical solution of optimal control problems with state-variable inequality constraints is presented. It is shown that the concept of constraining hyperplanes may be used to approximate the original problem with a problem where the constraints are of a mixed state-control variable type. The efficiency and the accuracy of the combination of constraining hyperplanes and a second-order differential dynamic programming algorithm are investigated on problems of different complexity, and comparisons are made with the slack-variable and the penalty-function techniques.

scholarly journals Optimal Control of Complex Systems Based on Improved Dual Heuristic Dynamic Programming Algorithm

2017 ◽  
Vol 2017 ◽  
pp. 1-11
Author(s):  
Hui Li ◽  
Yongsui Wen ◽  
Wenjie Sun
Keyword(s):  
Neural Network ◽  
Optimal Control ◽  
Dynamic Programming ◽  
Complex Systems ◽  
Bp Neural Network ◽  
Optimal Control Problems ◽  
Dynamic Programming Algorithm ◽  
Data Modeling ◽  
Control Problems ◽  
Heuristic Dynamic Programming

When applied to solving the data modeling and optimal control problems of complex systems, the dual heuristic dynamic programming (DHP) technique, which is based on the BP neural network algorithm (BP-DHP), has difficulty in prediction accuracy, slow convergence speed, poor stability, and so forth. In this paper, a dual DHP technique based on Extreme Learning Machine (ELM) algorithm (ELM-DHP) was proposed. Through constructing three kinds of network structures, the paper gives the detailed realization process of the DHP technique in the ELM. The controller designed upon the ELM-DHP algorithm controlled a molecular distillation system with complex features, such as multivariability, strong coupling, and nonlinearity. Finally, the effectiveness of the algorithm is verified by the simulation that compares DHP and HDP algorithms based on ELM and BP neural network. The algorithm can also be applied to solve the data modeling and optimal control problems of similar complex systems.

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