Viscosity Solution of Bellman-Isaacs Equation Arising in Non-linear Uncertain Object Control

The problem of optimal control for a class of non-linear objects with uncontrolled bounded disturbances is formulated in the sense of a differential game. In case of problems with quadratic quality functional, the problem of optimal control search is reduced to finding of solution of Hamilton-Jacobi-Isaacs equation. Solutions of this equation at the rate of functioning of the object are searched by means of special algorithmic procedures obtained with the use of viscosity solution theory. The obtained results may be used for solving of theoretical and applied problems of mathematics, mechanics, physics, biology, chemistry, engineering, control and navigation. This work (research grant No 14-01-0112) was supported by The National Research University Higher School of Economics’ Acad. Fund Program.