A Class of Robust Stabilization Problems in Nonlinear Control

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ECS-9707927 Dayawansa It is proposed to study two related aspects of the robust stabilization of a parameterized family of nonlinear systems. The first aspect has to do with stabilization of a family when the parameters hover around a nominal value at which the linear approximation has a nontrivial unstable uncontrollable part. Such systems are referred to as undergoing C-bifurcation. Proposed research aims at developing analytical tools to systematically study dynamical behavior of a control system near a C-bifurcation point. Included among the sought after tools are ways to extract out a low dimensional subsystem which contains crucial information, definition of pertinent equivalence relations and group actions and ways to study them via properties of their linearization, classification, recognition and normal forms of low CO-dimensional C-bifurcation, and classification of robust stabilizability properties of such normal forms. The second aspect has to do with parameterized families where the parameters are time dependent, but in a way in which only partial knowledge is available a priori. To simplify matters parameter variation is assumed to be piecewise constant in time. Feedback control laws are sought to robustly stabilize the family. Proposed research will be carried out within the framework of differential geometric methods in nonlinear control theory. Basic tools will come from singularity theory and global differential topology.