Costate estimation for dynamic systems of the second order |
| |
Authors: | Hao Wen DongPing Jin and HaiYan Hu |
| |
Affiliation: | (1) Institute of Vibration Engineering Research, MOE Key Lab of Structure Mechanics and Control for Aircraft, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China |
| |
Abstract: | The dynamics of a mechanical system in the Lagrange space yields a set of differential equations of the second order and involves
much less variables and constraints than that described in the state space. This paper presents a so-called Legendre pseudo-spectral
(PS) approach for directly estimating the costates of the Bolza problem of optimal control of a set of dynamic equations of
the second order. Under a set of closure conditions, it is proved that the Karush-Kuhn-Tucker (KKT) multipliers satisfy the
same conditions as those determined by collocating the costate equations of the second order. Hence, the KKT multipliers can
be used to estimate the costates of the Bolza problem via a simple linear mapping. The proposed approach can be used to check
the optimality of the direct solution for a trajectory optimization problem involving the dynamic equations of the second
order and to remove any conversion of the dynamic system from the second order to the first order. The new approach is demonstrated
via two classical benchmark problems.
Supported by the National Natural Science Foundation of China (Grant Nos. 10372039, 10672073), and the Innovation Fund for
Graduate Students of NUAA (Grant No. 4003-019016) |
| |
Keywords: | costate estimation second order pseudo-spectral method |
本文献已被 CNKI SpringerLink 等数据库收录! |
|