A gradient algorithm for optimal control problems with model-reality differences
In this paper, we propose a computational approach to solve a model-based optimal control problem. Our aim is to obtain the optimal so- lution of the nonlinear optimal control problem. Since the structures of both problems are different, only solving the model-based optimal control problem will not...
| Main Authors: | , , |
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| Format: | Article |
| Published: |
American Institute of Mathematical Sciences
2015
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| Subjects: | |
| Online Access: | http://dx.doi.org/10.3934/naco.2015.5.251 http://dx.doi.org/10.3934/naco.2015.5.251 http://eprints.uthm.edu.my/8111/1/dr_kek_sie_long.pdf |
| Summary: | In this paper, we propose a computational approach to solve a
model-based optimal control problem. Our aim is to obtain the optimal so-
lution of the nonlinear optimal control problem. Since the structures of both
problems are different, only solving the model-based optimal control problem
will not give the optimal solution of the nonlinear optimal control problem.
In our approach, the adjusted parameters are added into the model used so
as the differences between the real plant and the model can be measured.
On this basis, an expanded optimal control problem is introduced, where system optimization and parameter estimation are integrated interactively. The
Hamiltonian function, which adjoins the cost function, the state equation and
the additional constraints, is defined. By applying the calculus of variation, a
set of the necessary optimality conditions, which defines modified model-based
optimal control problem, parameter estimation problem and computation of
modifiers, is then derived. To obtain the optimal solution, the modified model-
based optimal control problem is converted in a nonlinear programming prob-
lem through the canonical formulation, where the gradient formulation can be
made. During the iterative procedure, the control sequences are generated as
the admissible control law of the model used, together with the corresponding
state sequences. Consequently, the optimal solution is updated repeatedly by
the adjusted parameters. At the end of iteration, the converged solution ap-
proaches to the correct optimal solution of the original optimal control problem
in spite of model-reality differences. For illustration, two examples are studied
and the results show the effciency of the approach proposed. |
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