EIA: Control System Synthesis: Nonlinear Feedback

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This proposal is concerned with the issue of robustness in feedback control. It has two primary goals: To develop efficient numerical procedures for certain robust feedback system design problems, and to explore the merits of nonlinear feedback in robust control. Regarding the first goal, preliminary work indicates that certain control system design problems can be reduced to simpler optimization problems involving nonlinear programming with only a finite number of parameters. This would represent a dramatic improvement over currently available techniques. This possibility and also the important numerical details will be investigated. The second goal is aimed at understanding the types of control system design problems for which nonlinear feedback is substantially superior to linear feedback. In this context it has recently been demonstrated that for some design problems in which the plant model has unknown parameters, nonlinear control offers enormous advantage. However, for situations where the plant model has substantial unmodeled dynamics, nonlinear feedback is no better than linear feedback. These results indicate that for many control systems design problems, the precision to which the plant model is known determines the type of feedback best suited to control that plant. This principle will be investigated to determine its validity in specific control design problems.