By Murat Arcak, Chris Meissen, Andrew Packard
ISBN-10: 3319299271
ISBN-13: 9783319299273
ISBN-10: 331929928X
ISBN-13: 9783319299280
This e-book addresses an immense challenge for today’s large-scale networked structures: certification of the necessary balance and function homes utilizing analytical and computational versions. at the foundation of illustrative case stories, it demonstrates the applicability of theoretical how to organic networks, car fleets, and net congestion keep watch over. instead of take on the community as an entire —an procedure that seriously limits the power of current how you can deal with huge numbers of actual elements— the e-book develops a compositional process that derives network-level promises from key structural homes of the elements and their interactions. The foundational instrument during this strategy is the confirmed dissipativity idea, that is reviewed within the first bankruptcy and supplemented with sleek computational ideas. The ebook blends this idea with the authors’ fresh study efforts at a degree that's obtainable to graduate scholars and working towards engineers accustomed to in basic terms the main uncomplicated nonlinear platforms recommendations. Code linked to the numerical examples should be downloaded at extras.springer.com, permitting readers to breed the examples and turn into conversant in the appropriate software.
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Additional resources for Networks of Dissipative Systems: Compositional Certification of Stability, Performance, and Safety
Sample text
Y N ) M I ≤0 ⇒ M I T X(Y¯1 , . . 1 Reduction for Stability Certification where 57 1 Y¯i = |Oi | Yj. 7) j∈Oi The theorem follows from this implication by setting Yi = pi X i . 7) to p¯ i X i . 6) implies RT M I T X(Y1 , . . , Y N ) M I X(Y1 , . . 1), is identical to M I T R 0 0 R T M I ≤ 0. 9) It follows from the definition of X(Y1 , . . 7) that R 0 0 R T X(Y1 , . . , Y N ) R 0 0 R = X(Y R(1) , . . 10) where R(i) denotes the index to which i gets permuted by the automorphism R. Thus, T M M ≤ 0.
2. Fig. 4). The storage functions Si (vi , v¯ i ) = 1 (vi − v¯ i )2 , i = 1, . . 23) where we have used f i (¯vi , u¯ i ) = −¯vi + vi0 + u¯ i = 0 in the second equation. The zl subsystems are integrators with input wl and output h l (zl ) = (zl − z 0 )1/3 . The storage functions 3 1 (zl − z 0 )4/3 − (zl − z 0 )(¯zl − z 0 )1/3 + (¯zl − z 0 )4/3 , l = 1, . . 26) where w¯ l = 0. 13) to ensure dissipativity with the L 2 reachability supply rate. 17). 17) for each l. To reduce the dimension of the problem we recall that the skew symmetric coupling of the subsystems suggests equal weights pi .
Duality and network theory in passivity-based cooperative control. Automatica 50(8), 2051–2061 (2014) 4. : Rate control in communication networks: shadow prices, proportional fairness and stability. J. Oper. Res. Soc. 49, 237–252 (1998) 5. : A unifying passivity framework for network flow control. IEEE Trans. Autom. Control 49(2), 162–174 (2004) 6. : The Mathematics of Internet Congestion Control. Birkhauser, Boston (2004) 7. : Mathematical Biology, I: an Introduction, 3rd edn. 1 Compositional Performance Certification Consider the interconnection in Fig.