Constrained LQR problems in elliptic distributed control systems with point observations—convergence results

Constrained LQR problems in elliptic distributed control systems with point... In this paper constrained LQR problems in distributed control systems governed by the elliptic equation with point observations are studied. A variational inequality approach coupled with potential theory in a Banach space setting is adopted. First the admissible control set is extended to be bounded by two functions, and feedback characterization of the optimal control in terms of the optimal state is derived; then two numerical algorithms proposed in (5) are modified, and the strong convergence and uniform convergence in Banach space are proved. This verifies that the numerical algorithm is insensitive to the partition number of the boundary. Since our control variables are truncated below and above by two functions in L p and in our numerical computation only the layer density not the control variable is assumed to be piecewise smooth, uniform convergence guarantees a better convergence. Finally numerical computation for an example is carried out and confirms the analysis. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

Constrained LQR problems in elliptic distributed control systems with point observations—convergence results

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Publisher
Springer-Verlag
Copyright
Copyright © 1997 by Springer-Verlag New York Inc.
Subject
Mathematics; Systems Theory, Control; Calculus of Variations and Optimal Control; Optimization; Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Methods
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/BF02683342
Publisher site
See Article on Publisher Site

Abstract

In this paper constrained LQR problems in distributed control systems governed by the elliptic equation with point observations are studied. A variational inequality approach coupled with potential theory in a Banach space setting is adopted. First the admissible control set is extended to be bounded by two functions, and feedback characterization of the optimal control in terms of the optimal state is derived; then two numerical algorithms proposed in (5) are modified, and the strong convergence and uniform convergence in Banach space are proved. This verifies that the numerical algorithm is insensitive to the partition number of the boundary. Since our control variables are truncated below and above by two functions in L p and in our numerical computation only the layer density not the control variable is assumed to be piecewise smooth, uniform convergence guarantees a better convergence. Finally numerical computation for an example is carried out and confirms the analysis.

Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Sep 1, 1997

References

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