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In the recent years, passivity theory has gained renewed attention because ofits advantages and practicality in modeling of multi-domain systems andconstructive control techniques. Unlike Lyapunov theory, passivity theory takesa behavioral approach in its control design methodologies. Hence, it providessolutions, which not only achieve the control objectives, but are also easilyinterpretable in the standard engineering parlance. The fundamental idea inpassivity based control (PBC) methodologies is to find a controller thatrenders the closed-loop system passive. It is well known that, the PBCmethodologies that rely on power-conjugate port-variables do not work forcontrol objectives that require bounded power and unbounded energy. This iscommonly known as the dissipation obstacle. One possible alternative that hasbeen well explored, in the case of finite dimensional systems, is Brayton-Moserformulation. However, designing controllers in this framework leads to variousdifficulties, such as, solving for partial differential equations and findingstorage functions satisfying a gradient structure.

Alternative passive maps in the Brayton-Moser framework: Implications on control and optimization