| Summary: | 碩士 === 國立交通大學 === 控制工程系 === 82 === A polynomial approximation involving the Chebyshev technique
for solving the nonlinear optimal control problems or two-point
boundary value problems (TPBVP) has been developed. The main
cha- racteristic of the technique is basd on the assumption
that the state and control variables can be expanded in the
Chebyshev ser- ies. Consequently, the differential equation and
integral involv- ed in the system dynamics, performance index,
and boundary condi- tion of the TPBVP can be converted into a
set of algebraic equat- ions and greatly simplifying the
optimal control problems. Never- theless, the Chebyshev
approach for the TPBVP has presented a ma- jor difficulty when
the nonlinear optimal control problems have been converted into
a set of nonlinear algebraic equation. Mainly , this difficulty
comes from the determination of the starting v- alues of the
Lagrangian multiplier when iterative numerical tech- niques
(such as Newton method) are applied. Therefore, an improv- ed
algorithm that overcomes this difficulty is presented in this
thesis. Finally, the proposed technique and improved numerical
a- lgorithm have been applied to optimal tracking flight
control pr- oblems.
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