Controllability Of Infinite-dimensional Linear Systems Research Articles

On strong controllability of infinite-dimensional linear systems

If an infinite-dimensional linear system is strongly controllable (i.e., every state can be reached from any state in finite time), then it is strongly controllable in uniform finite time.

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.

Controllability, observability and duality in infinite dimensional linear systems with multiple norm-bounded controllers

Controllability of infinite-dimensional linear systems with multiple independent controllers, each of which is norm-bounded, is studied. Necessary and sufficient conditions for systems to be such are presented. Both the usual (cooperative) and the game (non-cooperative) controllability are examined. The problem of sending an initial state to some target sets is investigated. Applications to differential delay linear systems and simple distributed parameter systems are given. For the cooperative mode, a duality theory is introduced for the constrained infinite dimensional case.

On weak and strong reachability and controllability of infinite-dimensional linear systems

The notions of reachability and controllability generalize to infinite-dimensional systems in two different ways. We show that the strong notions are equivalent to finite-time reachability and controllability. For discrete systems in Hilbert space, we get simple relations generalizing the Kalman conditions. In the case of a continuous system in Hilbert space, weak reachability is equivalent to the weak reachability of a related discrete system via the Cayley transform.

On the controllability of infinite-dimensional linear systems

Two types of controllability, namely weak controllability and strong controllability, are defined for general linear systems. Both types of controllability are useful in control theory. If the system is finite-dimensional, the two types of controllability are equivalent to each other and to the standard concept of complete state-controllability.