Optimal Tracking Flight Control via the Chebyshev Polynomials

• Main Authors: I-Shiou Chen, 陳一修
• Other Authors: Jin-Cherng Chiou
• Format: Others
• Language: en_US
• Published: 1994
• Online Access: http://ndltd.ncl.edu.tw/handle/71895619750827858219

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.