Regularity of feedback opertors for boundary control of thermal processes
- Virginia Polytechnic Institute, Blacksburg, VA (United States)
- Oregon State Univ., Corvallis, OR (United States)
This note is concerned with the regularity of functional gains for boundary control of thermal processes. Functional gains are kernel functions in integral representations of feedback operators computed by solving algebraic Riccati equations arising from infinite dimensional LQR control problems. In and, Burns and King showed that distributed parameter systems described by certain parabolic partial differential equations often have a special structure that smooths solutions of the corresponding Riccati equation. When this result is applied to problems with distributed controllers it can be established that the resulting feedback operator is also smooth. However, it is the continuity of the input operator that leads to a positive result in this case. When boundary control is applied, the input operator is unbounded and the analysis in fails. However, for 1D heat flow it is possible to recover because of the special nature of the problem. The problem is still not settled for the 2D and 3D heat equation. In this paper we present numerical evidence to suggest that the functional gains exist and have compact support near the boundary where the control is applied. Both properties are important in addressing sensor and actuator location problems and they have practical implications in the design of reduced order controllers for PDE systems.
- OSTI ID:
- 481979
- Report Number(s):
- CONF-960503-; CNN: Grant F 49620-93-1-0280; Grant DMS-9409506; TRN: 97:010560
- Resource Relation:
- Conference: 1. international conference on nonlinear problems in aviation and aerospace, Daytona Beach, FL (United States), 9-11 May 1996; Other Information: PBD: 1994; Related Information: Is Part Of First international conference on nonlinear problems in aviation & aerospace; Sivasundaram, S. [ed.]; PB: 729 p.
- Country of Publication:
- United States
- Language:
- English
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