Iterative Design of Suboptimal Feedback Control for Bilinear Parabolic PDE Systems
C. Xu and E. Schuster
American Control Conference
St. Louis, Missouri, USA, June 10-12, 2009
Abstract
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Optimal control of infinite dimensional systems
is one of the central problems in the control of distributed
parameter systems. With the development of high performance
computers, numerical methods for optimal control design have
regained attention and achieved significant progress, mostly
in the form of open-loop solutions. We consider in this work
an optimal control problem for a bilinear parabolic partial
differential equation (PDE) system. Based on the optimality
conditions derived from Pontryaginís maximum principle
for a reduced-order model, and stated as a two-boundaryvalue
problem, we propose an iterative scheme for suboptimal
closed-loop control design. In each iteration step, we take
advantage of linear synthesis methods to construct a sequence
of controllers. The convergence of the controller sequence is
proved in appropriate functional spaces. When compared with
previous iterative schemes, the proposed scheme avoids repeated
numerical computation of the Riccati equation and therefore
reduces significantly the number of ODEs that must be solved
at each iteration step. A numerical simulation study shows the
effectiveness of this new approach.