Operations Research Transactions ›› 2013, Vol. 17 ›› Issue (4): 24-32.

• Original Articles • Previous Articles     Next Articles

Approximating viability kernel for control systems

CHEN Zheng1,*, GAO Yan2   

  1. 1. School of Sciences, Ningbo University of Technology, Ningbo 315016, Zhengjiang, China; 2. Management School, University of Shanghai for Science and Technology, Shanghai 200093, China
  • Online:2013-12-15 Published:2013-12-15

Abstract: The computation of the viability kernel is an important topic  in control theory community. In this paper, we propose a new algorithm that computes the viability kernel of a discrete-time system. Based on the theory of machine learning, the algorithm of approximating viability kernel is presented. We give some conditions that guarantee the convergence of the approximations towards the actual viable kernel. This method avoids the exponential growth of the computing time with the dimension of the control space. Finally, examples are given to illustrate this result.

Key words: discrete-time systems, viability kernel, machine learning

CLC Number: