EIA: Robust Control of Systems with Parameter Uncertainty: An Operator Theoretic Approach

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The general problem of robust system control consists of constructing fixed feedback controllers for possibly unstable families of systems with parameter or modelling uncertainty in order to stabilize the given family and in order to meet certain performance specifications. This proposal is concerned with an operator theoretic and functional analytic approach to this problem for multivariable, distributed, and even possibly nonlinear plants. Specifically, techniques will be proposed to solve the H-Infinity-optimal weighted sensitivity problem for multivariate distributed systems, and methods will be developed for obtaining new qualitative and quantitive results for very general multivariable gain margin problems. Moreover, a nonlinear version of classical interpolation theory will be considered and it should have important consequences in adaptive and robust nonlinear control. It is expected that the proposed operator theoretic approach should help resolve some fundamental problems in robust design and illuminate a number of central theoretical issues in this area. In addition, specific algorithms will be developed to implement the methods on the computer. The general problem of robust system control consists of constructing fixed feedback controllers for possibly unstable families of systems with parameter or modelling uncertainty in order to stabilize the given family and in order to meet certain performance specifications. This proposal is concerned with an operator theoretic and functional analytic approach to this problem for multivariable, distributed, and even possibly nonlinear plants.