The calculation of discriminating kernel based on viability kernel and reachability

Abstract

Abstract We discuss the calculation of discriminating kernel for the discrete-time dynamic game and continuous-time dynamic game (namely differential game) using the viability kernel and reachable set. For the discrete-time dynamic game, we give an approximation of the viability kernel by the maximal reachable set. Then, based on the relationship between viability and discriminating kernels, we propose an algorithm of the discriminating kernel. For the differential game, we compute an underapproximation of the viability kernel by the backward reachable set from a closed target. Then, we put forward an algorithm of the discriminating kernel using the relationship of the discriminating and viability kernels. This means that the victory domain can be computed because it is computed by the discriminating kernel. The novelty is that we give two algorithms of the discriminating kernel for a dynamic game that contains two control variables, not one control variable as in differential inclusion.

Keywords

• dynamic game
• viability kernel
• discriminating kernel
• nonsmooth analysis
• reachability