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Alternative passive maps in the Brayton-Moser framework: Implications on control and optimization
In the recent years, passivity theory has gained renewed attention because of
its advantages and practicality in modeling of multi-domain systems and
constructive control techniques. Unlike Lyapunov theory, passivity theory takes
a behavioral approach in its control design methodologies. Hence, it provides
solutions, which not only achieve the control objectives, but are also easily
interpretable in the standard engineering parlance. The fundamental idea in
passivity based control (PBC) methodologies is to find a controller that
renders the closed-loop system passive. It is well known that, the PBC
methodologies that rely on power-conjugate port-variables do not work for
control objectives that require bounded power and unbounded energy. This is
commonly known as the dissipation obstacle. One possible alternative that has
been well explored, in the case of finite dimensional systems, is Brayton-Moser
formulation. However, designing controllers in this framework leads to various
difficulties, such as, solving for partial differential equations and finding
storage functions satisfying a gradient structure.Comment: Thesi