Gradient method applied to optimal control problems under inequality state variable constraints
Optimal control problems under inequality constraints imposed upon position, velocity, acceleration etc. have been studied for many years. The optimal control theories developed so far can be applied to such problems in the same way as to other problems without inequality constraints except that the auxiliary parameters change discontinuously at intersections of the state variable trajectory and the boundary of constraint domain. Such a discontinuous change of auxiliary parameters is called parameter jumping. It makes it very difficult to derive the optimal solution accurately because the number and location of intersections and the amount of discontinuous change are unknown. Dyer's gradient method was previously modified to analyze a bang-bang problem including singular control. This method is extended to a free final time optimal control problem under inequality constraints. Slack functions are introduced to deal with inequality constraints and the real time variable is expressed as a product of pseudo-time variable and time coefficient parameter. The parameter value is adjusted by gradient method. Two numerical examples are presented to demonstrate effectiveness of the proposed method.
- OSTI ID:
- 5149057
- Journal Information:
- Electr. Eng. Jpn. (Engl. Transl.); (United States), Vol. 104:6; Other Information: Translated from Denki Gakki Zasshi; 104-C: No. 10, 239-246(Oct 1984)
- Country of Publication:
- United States
- Language:
- English
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