In this episode I talk to Professor Paolo Rapisarda about a bunch of interesting theoretical (but very useful) aspects of control, including his work on behavioural systems theory, model reduction, Willems’ fundamental lemma, and data-driven control.
You can find the transcript at: https://docs.google.com/document/d/1xosQlyCazjngvrydEdlSX917p84v4GY8Maljp5J8MQY/edit?usp=sharing
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Paolo Rapisarda: https://www.southampton.ac.uk/people/5x2hb9/professor-paolo-rapisarda
Introduction
State maps for linear systems: https://eprints.soton.ac.uk/264646/1/State_maps.pdf
Harry Trentelman: https://research.rug.nl/en/persons/harry-trentelman
Jan Willems: https://homes.esat.kuleuven.be/~sistawww/smc/jwillems/
PhD thesis: https://research.rug.nl/en/publications/linear-differential-systems-2
Behavioural systems
Epic Jan Willems behavioural systems paper: https://skoge.folk.ntnu.no/prost/proceedings/cpc6-jan2002/willems.pdf
State maps
LTV paper:https://eprints.soton.ac.uk/457114/1/State_for_linear_discrete_time_varying_systems.pdf
Leibnitz rule: https://www.cuemath.com/calculus/leibniz-rule/
Dissipativity
Jan Willem’s paper: https://link.springer.com/article/10.1007/bf00276493
Jan Willem’s optimal control paper: https://ieeexplore.ieee.org/abstract/document/1099831
Quadratic differential forms: https://epubs.siam.org/doi/10.1137/S0363012996303062
Balancing
Siep Weiland: https://ieeexplore.ieee.org/author/37301202100
Keith Glover: https://www.eng.cam.ac.uk/profiles/kg103
H-infinity model order reduction: https://ieeexplore.ieee.org/document/701085
1980 Moore balancing paper: https://ieeexplore.ieee.org/document/1102568
Kalman decomposition: https://en.wikipedia.org/wiki/Kalman_decomposition
Arjan van der Schaft: https://scholar.google.nl/citations?user=BIPifjAAAAAJ&hl=en
Hamiltonian systems: https://www.unige.ch/~hairer/poly_geoint/week1.pdf
Port Hamiltonianity:https://www.annualreviews.org/content/journals/10.1146/annurev-control-081219-092250
Jacqueline Scherpen: https://research.rug.nl/en/persons/jacqueline-scherpen
Balancing of Port-Hamiltonian systems: https://research.rug.nl/files/2999949/2003ProcIFACWorkshopLHMNCLopezlena.pdf
Balancing for non-linear systems: https://research.rug.nl/files/3318296/1993ProcECCScherpen.pdf
Fundamental lemma
Ivan Markovski: https://scholar.google.com/citations?user=qSl_3FQAAAAJ&hl=en
Continuous-time work: https://www.sciencedirect.com/science/article/pii/S016769112400238X
Chebychev polynomials: https://mathworld.wolfram.com/ChebyshevPolynomialoftheFirstKind.html
Kanat Camblibel: https://scholar.google.com/citations?user=aeWjKPcAAAAJ&hl=en
Sufficient condition modification of Willems’s lemma: https://arxiv.org/abs/2405.18962
Experimental implementation: https://arxiv.org/abs/2407.12509
Data-driven control
Data-driven ILC:https://ieeexplore.ieee.org/abstract/document/10384133
DeePC: https://arxiv.org/abs/1811.05890
Jonathan Mayo-Maldonado: https://scholar.google.co.uk/citations?user=W-vnMBwAAAAJ&hl=en
Extra questions
Aizerman’s conjecture: https://en.wikipedia.org/wiki/Aizerman%27s_conjecture