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Numerical method for solving optimal control problems with phase constraints

The authors are supported by RFBR grant 17-07-00627

This paper was prepared at the occasion of The 10th International Conference on Optimization: Techniques and Applications (ICOTA 2016), Ulaanbaatar, Mongolia, July 23-26,2016, with its Associate Editors of Numerical Algebra, Control and Optimization (NACO) being Prof. Dr. Zhiyou Wu, School of Mathematical Sciences, Chongqing Normal University, Chongqing, China, Prof. Dr. Changjun Yu, Department of Mathematics and Statistics, Curtin University, Perth, Australia, and Shanghai University, China, and Prof. Gerhard-Wilhelm Weber, Middle East Technical University, Ankara, Turkey.
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  • The main idea of the method consists in successive solving auxiliary problems, which minimizes a special constructed Lagrange function, subject to linearized phase constraints. The linearly constrained auxiliary problems are more simple than the original ones because linear constraints can be easily processed. We shall discuss different aspects connected with approximating control problems and using the program system for solving them. We shall then pay attention to optimal control problems with constraints on inertia of control functions. For illustrations, four control problems will be solved using the proposed software.

    Mathematics Subject Classification: Primary: 49K15; Secondary: 97N80, 93C95.


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  • Figure 1.  The optimal control and trajectories for the problem 1

    Figure 2.  The optimal control and trajectories for the problem 2

    Figure 3.  The optimal control and trajectories for the problem 3

    Figure 4.  The optimal control and trajectories for the problem 4

    Table 1.  The results of solving test problem Non-inertial Robot Arm

    Software $N = 10$ $N = 50$ $N = 100$ $N = 500$
    MINOS9.278630 (0.2)9.145749 (3.5)9.141995 (110)9.141334 (305)
    SNOPT9.278630 (2.30)9.145749 (64)-(10)-(315)
    OPTCON9.278615 (20)9.147535 (37)9.152146 (87)9.148295 (309)
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