Show simple item record

Computation of maximal output admissible sets for linear systems with polynomial constraints

dc.contributor.authorCotorruelo, Andres
dc.contributor.authorGarone, Emanuele
dc.contributor.authorKolmanovsky, Ilya V.
dc.contributor.authorRamirez, Daniel R.
dc.contributor.authorLimon, Daniel
dc.date.accessioned2023-04-04T17:40:17Z
dc.date.available2024-04-04 13:40:15en
dc.date.available2023-04-04T17:40:17Z
dc.date.issued2023-03
dc.identifier.citationCotorruelo, Andres; Garone, Emanuele; Kolmanovsky, Ilya V.; Ramirez, Daniel R.; Limon, Daniel (2023). "Computation of maximal output admissible sets for linear systems with polynomial constraints." Advanced Control for Applications: Engineering and Industrial Systems 5(1): n/a-n/a.
dc.identifier.issn2578-0727
dc.identifier.issn2578-0727
dc.identifier.urihttps://hdl.handle.net/2027.42/176041
dc.description.abstractIn this technical note we study the computation of the Maximal Output Admissible Set for linear systems subject to polynomial constraints. The computation of an inner approximation of the Maximal Output Admissible Sets requires the determination of constraint redundancy. We use a procedure to determine polynomial constraint redundancy based on a consequence of Putinar’s Positivstellensatz. Further, we present a modification of the algorithm to compute the Maximal Output Admissible Set with improved performance. Lastly, demonstrate the potential for practical applications in two case studies of spacecraft rendezvous and control of an electromagnetic actuator.
dc.publisherSpringer
dc.publisherWiley Periodicals, Inc.
dc.subject.otherconstrained control
dc.subject.othermaximal output admissible set
dc.subject.othernonlinear systems
dc.subject.otherredundant constraints
dc.subject.othersum of squares
dc.titleComputation of maximal output admissible sets for linear systems with polynomial constraints
dc.typeArticle
dc.rights.robotsIndexNoFollow
dc.subject.hlbsecondlevelIndustrial and Operations Engineering
dc.subject.hlbtoplevelEngineering
dc.description.peerreviewedPeer Reviewed
dc.description.bitstreamurlhttp://deepblue.lib.umich.edu/bitstream/2027.42/176041/1/adc2119_am.pdf
dc.description.bitstreamurlhttp://deepblue.lib.umich.edu/bitstream/2027.42/176041/2/adc2119.pdf
dc.identifier.doi10.1002/adc2.119
dc.identifier.sourceAdvanced Control for Applications: Engineering and Industrial Systems
dc.identifier.citedreferencePutinar M. Positive polynomials on compact semi-algebraic sets. Ind Univ Math J. 1993; 42 ( 3 ): 969 - 984.
dc.identifier.citedreferenceKolmanovsky I, Gilbert EG. Multimode regulators for systems with state & control constraints and disturbance inputs. Control Using Logic-Based Switching. Springer; 1997: 104 - 117.
dc.identifier.citedreferenceMayne D. Nonlinear model predictive control: challenges and opportunities. Nonlinear Model Predict Control. 2000; 26: 23 - 44.
dc.identifier.citedreferenceTian Y, Kolmanovsky I. Reduced order and prioritized reference governors for limit protection in aircraft gas turbine engines. Proceedings of the AIAA Guidance, Navigation, and Control Conference; 2014: 1149.
dc.identifier.citedreferenceSimon D, Härkegård O, Löfberg J. Angle of attack and load factor limiting in fighter aircraft using command governors. Proceedings of the AIAA Guidance, Navigation, and Control Conference; 2017: 1257.
dc.identifier.citedreferenceZinnecker A, Serrani A, Bolender M, Doman D. Combined reference governor and anti-windup design for constrained hypersonic vehicles models. Proceedings of the AIAA Guidance, Navigation, and Control Conference; 2009: 6283.
dc.identifier.citedreferenceYucelen T, Johnson E. Command governor-based adaptive control. Proceedings of the AIAA Guidance, Navigation, and Control Conference; 2012: 4618.
dc.identifier.citedreferenceMagree D, Yucelen T, Johnson E. Command governor-based adaptive control of an autonomous helicopter. Proceedings of the AIAA Guidance, Navigation, and Control Conference; 2012: 4830.
dc.identifier.citedreferenceWilcher K, Yucelen T. On performance improvement of gain-scheduled model reference adaptive control Laws. AIAA Scitech 2020 Forum; 2020:1118.
dc.identifier.citedreferenceDillsaver M, Cesnik C, Kolmanovsky I. Gust load alleviation control for very flexible aircraft. Proceedings of the AIAA Atmospheric Flight Mechanics Conference; 2011:6368.
dc.identifier.citedreferenceGruber J, Ramirez D, Alamo T, Camacho E. Min–max MPC based on an upper bound of the worst case cost with guaranteed stability. Application to a pilot plant. J Process Control. 2011; 21 ( 1 ): 194 - 204.
dc.identifier.citedreferenceBemporad A. Reference governor for constrained nonlinear systems. IEEE Trans Automat Contr. 1998; 43 ( 3 ): 415 - 419.
dc.identifier.citedreferenceCaron R, McDonald J, Ponic C. A degenerate extreme point strategy for the classification of linear constraints as redundant or necessary. J Optim Theory Appl. 1989; 62 ( 2 ): 225 - 237.
dc.identifier.citedreferencePaulraj S, Chellappan C, Natesan T. A heuristic approach for identification of redundant constraints in linear programming models. Int J Comput Math. 2006; 83 ( 8–9 ): 675 - 683.
dc.identifier.citedreferencePaulraj S, Sumathi P. A comparative study of redundant constraints identification methods in linear programming problems. Math Probl Eng. 2010; 2010:1748-1763.
dc.identifier.citedreferenceGilbert E, Kolmanovsky I. Nonlinear tracking control in the presence of state and control constraints: a generalized reference governor. Automatica. 2002; 38 ( 12 ): 2063 - 2073.
dc.identifier.citedreferenceBochnak J, Coste M, Roy MF. Real Algebraic Geometry. Vol 36. Springer Science & Business Media; 2013.
dc.identifier.citedreferenceGilbert EG, Kolmanovsky I. Fast reference governors for systems with state and control constraints and disturbance inputs. Int J Robust Nonlinear Control IFAC-Affiliat J. 1999; 9 ( 15 ): 1117 - 1141.
dc.identifier.citedreferencePowers V, Wörmann T. An algorithm for sums of squares of real polynomials. J Pure Appl Algebra. 1998; 127 ( 1 ): 99 - 104.
dc.identifier.citedreferenceTütüncü RH, Toh KC, Todd MJ. Solving semidefinite-quadratic-linear programs using SDPT3. Math Program. 2003; 95 ( 2 ): 189 - 217.
dc.identifier.citedreferenceLöfberg J. YALMIP: a toolbox for modeling and optimization in MATLAB. Proceedings of the CACSD Conference; 2004; Taipei, Taiwan.
dc.identifier.citedreferenceKalabić U, Kolmanovsky I, Gilbert E. Reference governors for linear systems with nonlinear constraints. Proceedings of the 2011 50th IEEE Conference on Decision and Control and European Control Conference; 2011:2680-2686; IEEE.
dc.identifier.citedreferenceApS M. MOSEK optimizer API for C 8.1.0.83; 2021.
dc.identifier.citedreferenceHong J, Cummings I, Washabaugh P, Bernstein D. Stabilization of a mass and spring system with electromagnetic actuation. Proceedings of the 1997 IEEE International Conference on Control Applications; 1997: 189 - 194; IEEE.
dc.identifier.citedreferenceMiller RH, Kolmanovsky I, Gilbert EG, Washabaugh PD. Control of constrained nonlinear systems: a case study. IEEE Control Syst Mag. 2000; 20 ( 1 ): 23 - 32.
dc.identifier.citedreferenceTelgen J. Identifying redundant constraints and implicit equalities in systems of linear constraints. Manag Sci. 1983; 29 ( 10 ): 1209 - 1222.
dc.identifier.citedreferenceHenrion D, Korda M. Convex computation of the region of attraction of polynomial control systems. IEEE Trans Automat Contr. 2013; 59 ( 2 ): 297 - 312.
dc.identifier.citedreferencePandita R, Chakraborty A, Seiler P, Balas G. Reachability and region of attraction analysis applied to GTM dynamic flight envelope assessment. Proceedings of the AIAA Guidance, Navigation, and Control Conference; 2009: 6258.
dc.identifier.citedreferenceZhang L, Wang C, Chen L. Stability and stabilization of a class of multimode linear discrete-time systems with polytopic uncertainties. IEEE Trans Ind Electron. 2009; 56 ( 9 ): 3684 - 3692.
dc.identifier.citedreferenceCotorruelo A, Limon D, Garone E. Output admissible sets and reference governors: saturations are not constraints! IEEE Trans Automat Contr. 2019; 65 ( 3 ): 1192 - 1196.
dc.identifier.citedreferenceYu S, Maier C, Chen H, Allgöwer F. Tube MPC scheme based on robust control invariant set with application to Lipschitz nonlinear systems. Syst Control Lett. 2013; 62 ( 2 ): 194 - 200.
dc.identifier.citedreferenceBlanchini F, Miani S. Set-Theoretic Methods in Control. Springer; 2008.
dc.identifier.citedreferenceGilbert EG, Tan KT. Linear systems with state and control constraints: the theory and application of maximal output admissible sets. IEEE Trans Automat Contr. 1991; 36 ( 9 ): 1008 - 1020.
dc.identifier.citedreferenceGilbert EG, Kolmanovsky I, Tan KT. Nonlinear control of discrete-time linear systems with state and control constraints: a reference governor with global convergence properties. Proceedings of 1994 33rd IEEE Conference on Decision and Control; 1994: 144 - 149; IEEE.
dc.identifier.citedreferenceGarone E, Di Cairano S, Kolmanovsky I. Reference and command governors for systems with constraints: a survey on theory and applications. Automatica. 2017; 75: 306 - 328.
dc.working.doiNOen
dc.owningcollnameInterdisciplinary and Peer-Reviewed


Files in this item

Show simple item record

Remediation of Harmful Language

The University of Michigan Library aims to describe library materials in a way that respects the people and communities who create, use, and are represented in our collections. Report harmful or offensive language in catalog records, finding aids, or elsewhere in our collections anonymously through our metadata feedback form. More information at Remediation of Harmful Language.

Accessibility

If you are unable to use this file in its current format, please select the Contact Us link and we can modify it to make it more accessible to you.