Course by Shiva Shankar «Controllability and Vector Potential» (October 20–November 3, 2019, Steklov Mathematical Institute, 8 Gubkina, Moscow)
Kalman's fundamental notion of a controllable state space system, first
described in Moscow, has been generalised to higher order systems by Willems, and further to distributed systems de ned by partial di erential equations .
It turns out, that for systems de ned in several important spaces of distributions,
controllability is now identical to the notion of vector potential in physics, or of
vanishing homology in mathematics. These lectures will explain this relationship,
and a few of its consequences. It will also pose an important question: does a
controllable system, in any space of distributions, always admit a vector potential?
In other words, is Kalman's notion of a controllable system, suitably generalised,
nothing more or less than the possibility of describing the dynamics of the
system by means of a vector potential?
Financial support:
The visit of Shiva Shankar is supported by the Simons Foundation (grant No. 615793).
Program
Abstracts
Organizer
Shankar Shiva
Institutions
Steklov Mathematical Institute of Russian Academy of Sciences, Moscow |
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Course by Shiva Shankar «Controllability and Vector Potential», Moscow, October 20–November 3, 2019 |
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October 20–November 3, 2019 |
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The Controllability Question Sh. Shankar October 20–November 3, 2019, Moscow, Steklov Mathematical Institute, 8 Gubkina
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Necessary and Sufficient Conditions for Controllability Sh. Shankar October 20–November 3, 2019, Moscow, Steklov Mathematical Institute, 8 Gubkina
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The Controllable-Uncontrollable Decomposition Sh. Shankar October 20–November 3, 2019, Moscow, Steklov Mathematical Institute, 8 Gubkina
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Genericity Sh. Shankar October 20–November 3, 2019, Moscow, Steklov Mathematical Institute, 8 Gubkina
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Pathologies Sh. Shankar October 20–November 3, 2019, Moscow, Steklov Mathematical Institute, 8 Gubkina
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The Nullstellensatz for Systems of PDE Sh. Shankar October 20–November 3, 2019, Moscow, Steklov Mathematical Institute, 8 Gubkina
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