Structure of Viability Kernels for Some Linear Differential Games

A convenient form of necessary and sufficient conditions of viability for differential games with linear dynamics is proposed. These conditions are utilized to construct maximal viable subsets of state constraints, viability kernels, in two illustrative two-dimensional examples. These examples demonstrate the relative simplicity of the structure of the viability kernels. It was found that the boundaries of the viability kernels consist of segments of the boundary of the state constraint and of lines defined by the first integrals of the governing equations as the players use extremal constant controls. It is conjectured that such a structure holds in high dimensional cases too. Keywords Linear differential games

• Type: Journal
• Year: 2010
• Where: JOTA
• Authors: N. D. Botkin, E. A. Ryazantseva
• Keywords: JOTA 2010, Maximal Viable Subsets, State Constraint, Viability Kernels