Constrained stochastic controllability of infinite-dimensional linear systems

The main purpose of this article is to investigate the problem of (ε, δ)-stochastic controllability for linear systems of evolution type in infinite-dimensional spaces, wherein the controls are subjected to norm-bounded constrained sets. Some basic prerequisites of infinite-dimensional measures, in particular, Gaussian distributed type, are discussed. Corresponding to this measure, various properties of (ε, δ)-stochastic attainable sets in Hilbert spaces are studied. Necessary and sufficient conditions for (ε, δ)-stochastic controllability with respect to Hilbert space valued linear systems are obtained. Relationships with the deterministic counterpoint are noted. Pursuit game problems are also considered. Examples on systems governed by stochastic linear partial differential equations and stochastic differential delay equations are given for illustration.