Maximal monotonicity is explored as a generalization of the linear theory of passivity, aiming at an algorithmic input/output analysis of physical models. The theory is developed for maximal monotone one-port circuits, formed by the series and parallel interconnection of basic elements. These circuits generalize passive LTI transfer functions. Periodic input signals are shown to be mapped to periodic output signals, and these input-output behaviors can be efficiently computed using a maximal monotone splitting algorithm, which decomposes the computation according to the circuit topology. A new splitting algorithm is presented, which applies to any monotone circuit defined as a port interconnection of monotone elements.The research leading to these results has received funding from the European Research Council under the Advanced ERC Grant Agreement Switchlet n. 670645.
FEBRUARY 2023 « IEEE CONTROL SYSTEMS 91 Q. What would be your main advice to a prospective Ph.D. student in control?Pieter: Take your time to learn new things. I think it is really easy for a new Ph.D. student to fall into the trap of focusing only on their immediate project and neglect wider learning. So personally, I like to schedule some time every week to make sure I am learning some new mathematics or reading some papers.Q. Thank you for your comments.
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