Reliable Computing Experiment in the Study of Generalized Controllability of Linear Functional Differential Systems

Abstract

The basis of the constructive (computer-assisted) study of linear problems in the theory of FDE is a special technique of approximate description of the set of solutions to the linear FDE under study in combination with a guaranteed explicit error bound for the approximation. This technique is used in parallel with special theorems, conditions of which can be verified with use of the reliable computing experiment due to the modern mathematical packages (e.g., Maple, Mathematica). Presently the theoretical ground and a technology of the reliable computing experiment are worked out 1–4 as applied to studying linear boundary value problems of FDEs for the unique solvability, linear functional differential control systems for controllability, linear FDEs with delay and periodic parameters for stability. Notice that sometimes, when known traditional sufficient conditions for a property under consideration (say, the unique solvability of a boundary value problem) are inapplicable, the computer-assisted study can give the only chance to obtain the result.