Phantom Tracking Method

Rathia, Dinesh (2022) Phantom Tracking Method. Masters thesis, Indian Institute of Science Education and Research Kolkata.

Text (MS dissertation of Dinesh Rathia (17MS189)) 17MS189_Thesis_file.pdf - Submitted Version Restricted to Repository staff only Download (328kB)

Abstract

The work in this thesis consists of results in the theory of ordinary differential equations control theory of ordinary differential equations. In chapter-1, we explain controllability and stabilization. In chapter-2, we stated some definitions and results of control theory and ODE of linear systems and explained how gramiam can be used to completely stabilize the linear control system. In chapter-3, we provided the Lyapunov theorem, explained how its conditions are sufficient through an example, and introduced LaSalle’s invariance principle, stating its theorem and examples. In chapter-4, we explain on various examples the “phantom tracking” method based on an implicit Lyapunov-based approach. The phantom tracking method can be used to stabilize nonlinear control systems modeled by ordinary differential equations(ODE) or partial differential equations(PDE). We show how it can handle homogeneity issues or fast stabilization for ODE

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