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A relaxation theorem for partially observed stochastic control on Hilbert space

N.U. Ahmed (2007)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper, we present a result on relaxability of partially observed control problems for infinite dimensional stochastic systems in a Hilbert space. This is motivated by the fact that measure valued controls, also known as relaxed controls, are difficult to construct practically and so one must inquire if it is possible to approximate the solutions corresponding to measure valued controls by those corresponding to ordinary controls. Our main result is the relaxation theorem which states that...

Absolute stability results for well-posed infinite-dimensional systems with applications to low-gain integral control

Hartmut Logemann, Ruth F. Curtain (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We derive absolute stability results for well-posed infinite-dimensional systems which, in a sense, extend the well-known circle criterion to the case that the underlying linear system is the series interconnection of an exponentially stable well-posed infinite-dimensional system and an integrator and the nonlinearity ϕ satisfies a sector condition of the form (ϕ(u),ϕ(u) - au) ≤ 0 for some constant a>0. These results are used to prove convergence and stability properties of low-gain integral...

Adaptive compensators for perturbed positive real infinite-dimensional systems

Ruth Curtain, Michael Demetriou, Kazufumi Ito (2003)

International Journal of Applied Mathematics and Computer Science

The aim of this investigation is to construct an adaptive observer and an adaptive compensator for a class of infinite-dimensional plants having a known exogenous input and a structured perturbation with an unknown constant parameter, such as the case of static output feedback with an unknown gain. The adaptive observer uses the nominal dynamics of the unperturbed plant and an adaptation law based on the Lyapunov redesign method. We obtain conditions on the system to ensure uniform boundedness of...

Algebraic systems theory towards stabilization under parametrical and degree changes in the polynomial matrices of linear mathematical models.

Manuel de la Sen (1988)


This paper deals with the stabilization of the linear time-invariant finite dimensional control problem specified by the following linear spaces and subspaces on C: χ (state space) = χ* ⊕ χd, U (input space) = U1 ⊕ U2, Y (output space) = Y1 + Y2, together with the linear mappings: Qs = χ x U x [0,t} --> χ associated with the evolution equation of the C0-semigroup S(t) generated by the matrices, of real and complex entries A belonging to L(χ,χ) and B belonging to L(U,χ) of a given differential...

Circle criterion and boundary control systems in factor form: input-output approach

Piotr Grabowski, Frank Callier (2001)

International Journal of Applied Mathematics and Computer Science

A circle criterion is obtained for a SISO Lur’e feedback control system consist- ing of a nonlinear static sector-type controller and a linear boundary control system in factor form on an infinite-dimensional Hilbert state space H previ- ously introduced by the authors (Grabowski and Callier, 1999). It is assumed for the latter that (a) the observation functional is infinite-time admissible, (b) the factor control vector satisfies a compatibility condition, and (c) the trans- fer function belongs...

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