Research Initiation: Development of the l1 - Based Design Methodology for Systems with Uncertainties

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This project is concerned with the development of multivariable feedback control systems design in the presence of disturbances, noise, and plant uncertainty. In particular, we will consider the l1 -based design methodology recently developed to optimally reject arbitrary, but bounded and persistent disturbances or noise. The objective is to develop the theory further to achieve performance robustness: stability and good performance in the presence of plant uncertainties. Better representation of disturbances will be achieved by introducing time-varying pre-filters, and hence the theory will be generalized for such problems. We will develop the theory to handle infinite dimensional systems (e.g. systems with delays). This will make the design methodology applicable to a larger class of problems such as systems governed by partial differential equations. Software based on numerically robust algorithms and state-space computations will be developed, and then the theory will be applied on some practical examples. This project will have a significant impact on the general design philosophy and the understanding of uncertain systems. The results will be readily applicable to many problems such as space applications, robotics, process control and others. Also, it will have an impact on related fields such as adaptive control.