Ellipsoidal methods in solving reachability and control synthesis problems for time-lag systems

This report deals with reachability and control synthesis problems for linear controlled time-lag systems. Their feature is infinite-dimensional nature of described processes. There are considered various value functionals used in describing the reachability and solvability sets for the linear controlled time-lag system. The appropriate Hamilton–Jacobi–Bellman type equations are derived. Exhaustive internal ellipsoidal approximations of reach sets in finite- and infinite-dimensional spaces, external ellipsoidal approximations of reach sets in finite-dimensional space are derived. A regularization of the control synthesis problem is considered. The on-line calculation scheme of ellipsoidal synthesis constructing is described using the approximation of the origin system with the method of lines.