TITLE:
Application of Conjugate Gradient Approach for Nonlinear Optimal Control Problem with Model-Reality Differences
AUTHORS:
Sie Long Kek, Wah June Leong, Sy Yi Sim, Kok Lay Teo
KEYWORDS:
Nonlinear Optimal Control, Conjugate Gradient Approach, Iterative Solution, Adjusted Parameters, Model-Reality Differences
JOURNAL NAME:
Applied Mathematics,
Vol.9 No.8,
August
29,
2018
ABSTRACT:
In this paper, an efficient computational algorithm is proposed to solve the
nonlinear optimal control problem. In our approach, the linear quadratic optimal
control model, which is adding the adjusted parameters into the model
used, is employed. The aim of applying this model is to take into account the
differences between the real plant and the model used during the calculation
procedure. In doing so, an expanded optimal control problem is introduced
such that system optimization and parameter estimation are mutually interactive.
Accordingly, the optimality conditions are derived after the Hamiltonian
function is defined. Specifically, the modified model-based optimal control
problem is resulted. Here, the conjugate gradient approach is used to
solve the modified model-based optimal control problem, where the optimal
solution of the model used is calculated repeatedly, in turn, to update the adjusted
parameters on each iteration step. When the convergence is achieved,
the iterative solution approaches to the correct solution of the original optimal
control problem, in spite of model-reality differences. For illustration, an
economic growth problem is solved by using the algorithm proposed. The
results obtained demonstrate the efficiency of the algorithm proposed. In
conclusion, the applicability of the algorithm proposed is highly recommended.