Feedback semigroups and cosine operators for boundary feedback parabolic and hyperbolic equations

Representation of Feedback Operators for Hyperbolic Systems

We consider the problem of obtaining integral representation of feedback operators for damped hyperbolic control systems. We show that for the wave equation with Kelvin-Voigt damping and non-compact input operator, the feedback gain operator is Hilbert-Schmidt. This result is then used to provide an explicit integral representation for the feedback operator in terms of functional gains. Numeric...

Representation Of Feedback Operators For Hyperbolic Systems

Zero dynamics modeling and boundary feedback design for parabolic systems

In this work the authors introduce a notion of zero dynamics for distributed parameter systems governed by linear parabolic equations on bounded domains with controls implemented through first order linear boundary conditions. This notion is motivated by classical root-locus constructs from finite dimensional linear systems theory. In particular, for scalar proportional output feedback this not...

Output-feedback Stabilization and Control Optimization for Parabolic Equations with Neumann Boundary Control

Both of feedback stabilization and optimal control problems are analyzed for a parabolic partial differential equation with Neumann boundary control. This PDE serves as a model of heat exchangers in a conducting rod. First, we explicitly construct an output-feedback operator which exponentially stabilizes the abstract control system representing the model. Second, we derive a controller which, ...

Explicit schemes for parabolic and hyperbolic equations

Standard explicit schemes for parabolic equations are not very convenient for computing practice due to the fact that they have strong restrictions on a time step. More promising explicit schemes are associated with explicit-implicit splitting of the problem operator (Saul’yev asymmetric schemes, explicit alternating direction (ADE) schemes, group explicit method). These schemes belong to the c...