Differential Games for Fractional-Order Systems: Hamilton–Jacobi–Bellman–Isaacs Equation and Optimal Feedback Strategies

The paper deals with a two-person zero-sum differential game for dynamical system described by equations the Caputo fractional derivatives of an order ??(0,1) and Bolza-type cost functional. A relationship between Cauchy problem corresponding Hamilton–Jacobi–Bellman–Isaacs equation coinvariant ? natural boundary condition is established. An emphasis given to construction optimal positional (feedback) strategies players. First, smooth case studied when considered assumed have sufficiently solution. After that, cope general non-smooth case, generalized minimax solution this involved.