Regular linear systems governed by a boundary controlled heat equation. (English) Zbl 1010.93052

Byrnes, C. I.; Gilliam, D. S.; Shubov, V. I.; Weiss, G.

J. Dyn. Control Syst. 8, No. 3, 341-370 (2002).

The systems are governed by the heat equation \[ {\partial y(t, x) \over \partial t} = \Delta y(t, x) \quad (0 \leq t < \infty, \;x \in \Omega) \] in a \(n\)-dimensional domain \(\Omega\) with various inputs and outputs; for instance, Type 1 input is Neumann boundary control on part of the boundary, Type 1 output is the trace of \(y(t, x)\) on part of the boundary. The object is to show that these systems are regular in the sense of G. Weiss (see references in the paper).

Reviewer: Hector O.Fattorini (Los Angeles)

MSC:

93C20	Control/observation systems governed by partial differential equations
35K20	Initial-boundary value problems for second-order parabolic equations
35K05	Heat equation
93C05	Linear systems in control theory

Keywords:

regular linear systems; boundary control; heat equation