Design of finite-dimensional controllers for infinite-dimensional systems by approximation. (English) Zbl 0813.93032
Summary: Several difficulties in controller design for infinite-dimensional systems arise from using an approximation for the state of the system. In this paper it is demonstrated that the graph topology is an appropriate framework in which to discuss convergence of approximations used for controller design. It is also shown that Galerkin type approximations to large class of problems possess the required convergence properties and can be used to design controllers which will perform as desired when implemented on the original infinite-dimensional system. An \({\mathcal H}_ \infty\)-controller design problem is used to illustrate this approach.
MSC:
93B50 | Synthesis problems |
93B51 | Design techniques (robust design, computer-aided design, etc.) |
93C05 | Linear systems in control theory |
93D15 | Stabilization of systems by feedback |
93C25 | Control/observation systems in abstract spaces |
93C15 | Control/observation systems governed by ordinary differential equations |
65L60 | Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations |