| With the further research of the aerospace, marine, aviation and guidance technology, optimal control problem has become an important issue. Particularly, linear optimal control is one branch of modern control theory which has been used with great success in fields such as economics, engineering disciplines and so on.In this thesis, an optimal Homotopy Analysis Method(optimal HAM) is applied to solve the linear Optimal Control Problems(OCPs), which have a quadratic performance index. This approach contains two convergence-control parameters which depend on the control system and is computationally rather efficient. A squared residual error for the system is defined, which can be used to find the unknown optimal convergence-control parameters by using Liao’s Mathematica package BVPh(version 2.0). According to the characteristics of the system, different calculation results of one or two convergence-control parameters are achieved and their advantages and disadvantages are compared. Besides, the results of comparisons among the proposed method, the homotopy perturbation method(HPM), the Adomian decomposition method(ADM), the differential transform method(DTM) and the homotopy analysis method(HAM) provide verification for the validity of the proposed approach. Moreover, numerical results are presented by several examples involving scalar and 2nd-order systems to clarify the efficiency and high accuracy of the proposed approach.The contribution of this thesis is to introduce a new method based on optimal HAM and PMP for solving the linear optimal control problems(OCPs).Using the Pontryagin’s Maximum Principle(PMP), the linear OCPs can be expressed as a two point boundary value problem(TPBVP). Besides, a squared residual error for the system is defined, and the unknown optimal convergence-control parameters are achieved by using Mathematica package BVPh(version 2.0) which was reset the parameters according to the linear optimal control problems. |
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