| Autor: |
Ghassemi, Hussein, Maleki, Mohammad, Allame, Masoud |
| Předmět: |
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| Zdroj: |
Optimal Control - Applications & Methods; May2021, Vol. 42 Issue 3, p717-743, 27p |
| Abstrakt: |
A modified pseudospectral (PS) method is presented based on direct Legendre interpolation for unconstrained optimal control problems (OCP). The conditions for the convergence of the proposed PS method are provided and it is proved that the method possesses the spectral accuracy for solutions in appropriate Sobolev spaces. Different from existing convergence results in the literature, in this new analysis neither special cases of the problem nor relaxing the discretized dynamics is considered. Moreover, the proof does not use necessary conditions of optimal control. An iterative procedure is then proposed for nonlinear OCPs. The nonlinear problem is first replaced with a sequence of linear‐quadratic OCPs by utilizing the quasilinearization technique. Then, this sequence of problems are successively solved using the modified PS method. In some nonlinear OCPs where the resulting nonlinear programming problem is dense, the PS method becomes computationally intractable. In such a this problems, the iterative PS method reduces the computational complexity and saves work. In addition, a new efficient costate estimation procedure is derived by employing the necessary optimality conditions. This new costate estimation method is flexible in that it allows us to define three different schemes based on the structure of the problem. Several examples of varying complexity are included to demonstrate the efficiency and accuracy of the proposed methods. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
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