E. J. P. Georg Schmidt

Modelling, Stabilization, and Control of Flow in Networks of Open Channels

In this paper we present a model for the controlled flow of a fluid through a network of channels using a coupled System of St Venant equations. We generalize in a variety of ways recent results of Coron, d’Andrea-Novel and Bastin concerning the stabilizability around equilibrium of the flow through a single channel to serially connected channels and finally to networks of channels. The work presented here is entirely based on the theory of quasilinear hyperbolic Systems. We also consider open-loop optimal control problems and provide numerical schemes both for the simulation and the control of such Systems.

Invariance theory for infinite dimensional linear control systems

AbstractIn this paper we characterize the situation wherein a subspaceS of a separable Hilbert state space is holdable under the abstract linear autonomous control system

On the total—and strict total—Positivity of the kernels associated with parabolic initial boundary value problems

\dot x = Ax + Bu

On the Linearised Dynamics of Linked Mechanical Structures

, whereA is the infinitesimal generator of aC0-semigroup of operators and whereB is a bounded linear operator mapping a Hilbert space Ω intoX. WhenS⊥∩D(A*) is dense inS⊥, it is shown that a necessary (but insufficient) condition for holdability is (1):

Boundary control of a vibrating plate with internal damping

A[S \cap D\left( A \right)] \subset \bar S + B\Omega

Phase Transitions in a Relaxation Model of Mixed Type with Periodic Boundary Condition

. A stronger condition than (1) is shown to be sufficient for a type of approximate holdability. In the finite dimensional setting, (1) reduces to (A, B)-invariance, which is known to be equivalent to the existence of a (bounded) linear feedback control law which achieves holdability inS. We prove that this equivalence holds in infinite dimensions as well, whenA is bounded and the linear spacesS, BΩ andS+ BΩ are closed.In the unbounded case, our results are illustrated by the shift semigroup and by the heat equation on an infinite rod with distributed controls. In the bounded case, our example is an integro-differential control system.