Constrained LQR problems in elliptic distributed control systems with point observations - Convergence results Academic Article

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 Lp 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. 1997 Springer-Verlag New York Inc.

authors

• Zhou, Jianxin

published proceedings

• APPLIED MATHEMATICS AND OPTIMIZATION

author list (cited authors)

• Ding, Z., & Zhou, J.

citation count

• 2

complete list of authors

• Ding, Z||Zhou, J

publication date

• January 1997

publisher

• Springer Nature  Publisher

published in

• Applied Mathematics and Optimization  Journal

keywords

• Bem
• Distributed Boundary Control
• Lqr
• Point Observation
• Potential Theory
• Singularity Decomposition
• Strong Convergence
• Uniform Convergence
• Variational Inequality

Digital Object Identifier (DOI)

• 10.1007/bf02683342

URI

• https://hdl.handle.net/1969.1/181182

start page

• 173

end page

• 201

volume

• 36

issue

• 2

URL

• http://dx.doi.org/10.1007/bf02683342