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SUMMARY:Lorenzo Clemente (University of Warsaw)
DTSTART:20250919T130000Z
DTEND:20250919T140000Z
DTSTAMP:20260423T021708Z
UID:ACPMS/57
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/ACPMS/57/">A
 lgorithmic analysis of control systems with affine input and polynomial st
 ate dynamics</a>\nby Lorenzo Clemente (University of Warsaw) as part of Al
 gebraic and Combinatorial Perspectives in the Mathematical Sciences\n\n\nA
 bstract\nWe provide simple algorithms for the formal analysis of determini
 stic continuous-time control systems whose dynamics is affine in the input
  and polynomial in the state (in short\, polynomial systems). We consider 
 the following semantic properties: input-output equivalence\, input indepe
 ndence\, linearity\, and analyticity. Our approach is based on Chen-Fliess
  series\, which provide a unique representation of the dynamics of such sy
 stems via their generating series (in noncommuting indeterminates). Our st
 arting point is Fliess' seminal work showing how the semantic properties a
 bove are mirrored by corresponding combinatorial properties on generating 
 series. Next\, we observe that the generating series of polynomial systems
  coincide with the class of shuffle-finite series\, a nonlinear generalisa
 tion of Schützenberger's rational series which we have recently studied i
 n the context of automata theory and enumerative combinatorics. We exploit
  and extend recent results in the algorithmic analysis of shufflef-finite 
 series to show that the semantic properties above are decidable for polyno
 mial systems.\n
LOCATION:https://researchseminars.org/talk/ACPMS/57/
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