Download Control of Switching Systems by Invariance Analysis: by Laurent Fribourg, Romain Soulat PDF

By Laurent Fribourg, Romain Soulat

This publication offers correct-by-design regulate strategies for switching structures, utilizing diverse tools of balance research. Switching platforms are more and more utilized in the electronics and mechanical industries; in strength electronics and the automobile undefined, for instance. this is often because of their flexibility and straightforwardness in properly controlling commercial mechanisms. by means of adopting acceptable regulate ideas, we will be able to steer a switching process to a area established at a wanted equilibrium element, whereas averting “unsafe” areas of parameter saturation.
The authors clarify a number of correct-by-design equipment for keep watch over synthesis, utilizing diverse tools of balance and invariance research. additionally they supply numerous functions of those how to commercial examples of energy electronics.


1. keep an eye on thought: uncomplicated Concepts.
2. Sampled Switched Systems.
3. safeguard Controllers.
4. balance Controllers.
5. program to Multilevel Converters.
6. different matters: Reachability, Sensitivity, Robustness and Nonlinearity.

About the Authors

Laurent Fribourg is head of the LSV (Laboratoire Spécification et Vérification) and medical Coordinator of the Institut Farman, Institut Fédératif de Recherche CNRS, which brings jointly the services of 5 laboratories from ENS Cachan, in France, within the fields of modeling, simulation and validation of advanced platforms. He has released over 70 articles in overseas journals and reviewed lawsuits of overseas meetings, within the area of the idea of formal equipment and their commercial applications.
Romain Soulat is within the 3rd yr of his doctorate on the LSV at ENS Cachan in France, lower than the supervision of Laurent Fribourg. he's engaged on the modeling and verification of hybrid platforms. particularly, his pursuits problem robustness in scheduling difficulties – in particular as a part of a collaborative undertaking with EADS Astrium at the verification of an element within the launcher for the long run Ariane 6 rocket. He has released five articles in reviewed complaints of overseas conferences.

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A finer precision ε would require a much smaller η and accordingly Aη with an overwhelming number of vertices. This tends to indicate that the indirect method (at least applied without further refinement) leads to prohibitively expensive computations for this example. 9. Discrete-time trajectory of three-cell converter starting at x0 = (5, 5, 5, 16) in S = [4, 7] × [4, 7] × [4, 7] × [15, 17] using the direct control method (from a)–d): x1 , x2 , x3 , x4 as a function of time). 10. Partial graph of an abstract safety controller of the three-cell Boost converter, with η = 15 .

We now give a decomposition procedure that generates a k-invariant decomposition of R as follows. It first calls sub-function Find_Pattern in order to get a k-pattern such that R is R-invariant. If Find_Pattern succeeds, then we are done. Otherwise, it divides R into 2n sub-boxes V1 , . . , V2n of equal size. If, for each Vi , Find_Pattern gets a k-pattern making it R-invariant, it is done. If, for some Vj , no such pattern exists, the procedure is recursively applied to Vj . It ends with success when a k-invariant decomposition of R is found, or failure when the maximal degree d of decomposition is reached.

The under-approximation process also helps the algorithm to terminate. The output S ∗ of the algorithm is then an invariant subset of S, but is no longer maximal. 1. 79). 2. 1. However, there is no guarantee of termination of the procedure because the state space is infinite. An interesting alternative approach is the “indirect approach”: it consists of making an abstraction of the system into a finite discrete system. 1 then always terminates, and allows us to synthesize a maximally safe abstract controller, from which a controller can be derived at the real level, at the price of a certain approximation.

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