Acta mathematica scientia, Series B >
ASYMPTOTIC SOLUTION OF SINGULARLY PERTURBED HYBRID DYNAMICAL SYSTEMS
Received date: 2014-12-06
Revised date: 2016-04-25
Online published: 2016-10-25
Supported by
This project is supported by the National Natural Science Foundation of China (11471118, 11401385 and 11371140), Natural Science Foundation of Hebei Province (A2015407063) and Doctoral Foundation of Hebei Normal University of Science and Technology(2013YB008).
In this paper, we consider a class of optimal control problem for the singularly perturbed hybrid dynamical systems. By means of variational method, we obtain the necessary conditions of the hybrid dynamical systems. Meanwhile, the existence of solution for the hybrid dynamical system is proved by the sewing method and the uniformly valid asymptotic expansion of the optimal trajectory is constructed by the boundary function method. Finally, an example is presented to illustrate the result.
Key words： optimal control; hybrid dynamical system; singular perturbation
Limeng WU , Juan ZHANG , Mingkang NI , Haibo LU . ASYMPTOTIC SOLUTION OF SINGULARLY PERTURBED HYBRID DYNAMICAL SYSTEMS[J]. Acta mathematica scientia, Series B, 2016 , 36(5) : 1457 -1466 . DOI: 10.1016/S0252-9602(16)30081-9
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