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State waypoint approach to continuous‐time nonlinear optimal control problems
Author(s) -
Honarvarmahjoobin Mohamadhadi,
Tazaki Yuichi,
Imura Junichi
Publication year - 2009
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.148
Subject(s) - waypoint , nonlinear system , optimization problem , state (computer science) , mathematical optimization , optimal control , computer science , control theory (sociology) , continuous optimization , simple (philosophy) , control (management) , mathematics , algorithm , multi swarm optimization , artificial intelligence , real time computing , philosophy , physics , epistemology , quantum mechanics
Abstract In this paper, we propose an optimal control technique for a class of continuous‐time nonlinear systems. The key idea of the proposed approach is to parametrize continuous state trajectories by sequences of a finite number of intermediate target states; namely, waypoint sequences. It is shown that the optimal control problem for transferring the state from one waypoint to the next is given an explicit‐form suboptimal solution, by means of linear approximation. Thus the original continuous‐time nonlinear control problem reduces to a finite‐dimensional optimization problem of waypoint sequences. Any efficient numerical optimization method, such as the interior‐reflection Newton method, can be applied to solve this optimization problem. Finally, we solve the optimal control problem for a simple nonlinear system example to illustrate the effectiveness of this approach. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society