Summary: | In this paper, the testing of linear models with different parameter values is conducted for
solving the optimal control problem of a second-order dynamical system. The purpose of this
testing is to provide the solution with the same structure but different parameter values in the
model used. For doing so, the adjusted parameters are added to each model in order to measure
the differences between the model used and the plant dynamics. On this basis, an expanded
optimal control problem, which combines system optimization and parameter estimation, is
introduced. Then, the Hamiltonian function is defined and a set of the necessary conditions is
derived. Consequently, a modified model-based optimal control problem has resulted. Follow
from this, an equivalent optimization problem without constraints is formulated. During the
calculation procedure, the conjugate gradient algorithm is employed to solve the optimization
problem, in turn, to update the adjusted parameters repeatedly for obtaining the optimal
solution of the model used. Within a given tolerance, the iterative solution of the model used
approximates the correct optimal solution of the original linear optimal control problem despite
model-reality differences. The results obtained show the applicability of models with the same
structures and different parameter values for solving the original linear optimal control problem.
In conclusion, the efficiency of the approach proposed is highly verified.
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