Bifurcations; Linear complementarity problems; Piecewise linear equations; Topological equivalence; Bifurcation; Bifurcations theory; Control engineering; Nonsmooth bifurcations; Piecewise linear; Piecewise linear equation; Piecewise-linear; Control and Systems Engineering
Abstract :
[en] Many systems of interest to control engineering can be modeled by linear complementarity problems. We introduce a new notion of equivalence between linear complementarity problems that sets the basis to translate the powerful tools of smooth bifurcation theory to this class of models. Leveraging this notion of equivalence, we introduce new tools to analyze, classify, and design nonsmooth bifurcations in linear complementarity problems and their interconnection.
Disciplines :
Engineering, computing & technology: Multidisciplinary, general & others
Author, co-author :
Castaños, Fernando; Automatic Control Department, CDMX, Mexico
Miranda-Villatoro, Felix A.; Department of Engineering, University of Cambridge., Cambridge, United Kingdom
Franci, Alessio ; Université de Liège - ULiège > Département d'électricité, électronique et informatique (Institut Montefiore) > Brain-Inspired Computing ; Department of Mathematics, Universidad Nacional Autónoma de México, CDMX, Mexico
Language :
English
Title :
A notion of equivalence for linear complementarity problems Applications to the design of nonsmooth bifurcations
scite shows how a scientific paper has been cited by providing the context of the citation, a classification describing whether it supports, mentions, or contrasts the cited claim, and a label indicating in which section the citation was made.
Bibliography
Acary, V., Bonnefon, O., and Brogliato, B. (2011). Nonsmooth modeling and simulation for switched circuits. Lecture Notes in Electrical Engineering. Springer.
Arnold, V.I., Varchenko, A.N., and Gusein-Zade, S.M. (1985). Singularities of Differentiable Maps, volume 1. Birkhäuser.
Brogliato, B. (1999). Nonsmooth mechanics: models, dynamics and control. Springer-Verlag, London, second edition.
Castaños, F. and Franci, A. (2017). Implementing robust neuromodulation in neuromorphic circuits. Neurocomputing, 233, 3-13.
Castaños, F., Miranda-Villatoro, F., and Franci, A. (2019). A notion of equivalence for linear complementarity problems with application to the design of non-smooth bifurcations. ArXiv:1911.03774.
Clarke, F. (1990). Optimization and nonsmooth analysis. Society for Industrial and Applied Mathematics.
Cottle, R.W., Pang, J.S., and Stone, R.E. (2009). The Linear Complementarity Problem. Classics in Applied Mathematics. Society for Industrial and Applied Mathematics.
Danao, R.A. (1994). Q-matrices and boundedness of solutions to linear complementarity problems. Journal of Optimization Theory and Applications, 83(2), 321-332.
Di Bernardo, M., Budd, C.J., Champneys, A.R., Kowalczyk, P., Nordmark, A.B., Tost, G.O., and Piiroinen, P.T. (2008). Bifurcations in nonsmooth dynamical systems. SIAM review, 50(4), 629-701.
Garcia, C.B., Gould, F.J., and Turnbull, T.R. (1983). Relations between PL maps, complementary cones, and degree in linear complementarity problems. In Homotopy Methods and Global Convergence, 91-144. Plenum Publishing Corporation.
Golubitsky, M. and Schaeffer, D. (1985). Singularities and Groups in Bifurcation Theory, volume I of Applied Mathematical Sciences. Springer, New York.
Leenaerts, D.M. and Bokhoven, W.M.G. (1998). Piecewise linear modeling and analysis. Kluwer Academic. Springer, New York.
Leine, R.I. and Nijmeijer, H. (2004). Dynamics and bifurcations on non-smooth mechanical systems. Springer, Berlin.
Murty, K.G. (1988). Linear complementarity, linear and nonlinear programming. Helderman Verlag, Berlin.
Nagurney, A. (1999). Network economics: A variational inequality approach. Advances in Computational Economics. Springer-Science+Business Media.
Sikorski, R. (1969). Boolean Algebras. Springer-Verlag, Berlin, Germany.
van der Schaft, A.J. and Schumacher, J. (1998). Complementarity modeling of hybrid systems. IEEE Trans. Autom. Control, 43, 483 - 490.
Similar publications
Sorry the service is unavailable at the moment. Please try again later.
This website uses cookies to improve user experience. Read more
Save & Close
Accept all
Decline all
Show detailsHide details
Cookie declaration
About cookies
Strictly necessary
Performance
Strictly necessary cookies allow core website functionality such as user login and account management. The website cannot be used properly without strictly necessary cookies.
This cookie is used by Cookie-Script.com service to remember visitor cookie consent preferences. It is necessary for Cookie-Script.com cookie banner to work properly.
Performance cookies are used to see how visitors use the website, eg. analytics cookies. Those cookies cannot be used to directly identify a certain visitor.
Used to store the attribution information, the referrer initially used to visit the website
Cookies are small text files that are placed on your computer by websites that you visit. Websites use cookies to help users navigate efficiently and perform certain functions. Cookies that are required for the website to operate properly are allowed to be set without your permission. All other cookies need to be approved before they can be set in the browser.
You can change your consent to cookie usage at any time on our Privacy Policy page.
