Generalized observer design of index one for descriptor systems with unknown inputs

• Autorzy: Kumar Abhinav , Gupta Mahendra Kumar

Identyfikatory

DOI

10.24425/acs.2023.145115

• Języki publikacji: EN

Abstrakty

EN

Generalized observers are proposed to relax the existing conditions required to design Luenberger observers for rectangular linear descriptor systems with unknown inputs. The current work is focused on designing index one generalized observers, which can be naturally extended to higher indexes. Sufficient conditions in terms of system operators for the existence of generalized observers are given and proved. Orthogonal transformations are used to derive the results. A physical model is presented to show the usefulness of the proposed theory.

Słowa kluczowe

EN

descriptor systems; DAEs; unknown inputs; state estimation; generalized; observer; index

• Wydawca: Polish Academy of Sciences, Committee of Automatic Control and Robotics
• Czasopismo: Archives of Control Sciences
• Rocznik: 2023
• Tom: Vol. 33, No. 1
• Strony: 83--99
• Opis fizyczny: Bibliogr. 21 poz., rys., wzory

Twórcy

autor

Kumar Abhinav

• Department of Mathematics, National Institute of Technology Jamshedpur, Jharkhand, India

autor

Gupta Mahendra Kumar

• School of Basic Sciences, Indian Institute of Technology Bhubaneswar, Argul, Khordha, Odisha, 752050 - India

Bibliografia

• [1] V.K. Mishra, N.K. Tomar, and M.K. Gupta: Regularization and index reduction for linear differential-algebraic systems. Computational and Applied Mathematics, 37(4), (2018), 4587-4598. DOI: 10.1007/S40314-018-0589-3.
• [2] G.-R. Duan: Analysis and design of descriptor linear systems. Part of the book series: Advances in Mechanics and Mathematics, 23 Springer, 2010.
• [3] A. Kumar and P. Daoutidis: Control of nonlinear differential algebraic equation systems with applications to chemical processes. CRC Press, Boca Raton, 1999. DOI: 10.1201/9781003072218.
• [4] R.K. Mandela, L. Sridhar, and R. Rengaswamy: Introducing DAE systems in undergraduate and graduate chemical engineering curriculum. Chemical Engineering Education, 44(1), (2010), 73-80.
• [5] R. Riaza: Differential-algebraic Systems: Analytical Aspects and Circuit Applications. World Scientific, Singapore, 2008.
• [6] M.K. Gupta, N.K. Tomar, and M. Darouach: Unknown inputs observer design for descriptor systems with monotone nonlinearities. International Journal of Robust Nonlinear Control, 28(17), (2018), 5481-5494. DOI: 10.1002/rnc.4331.
• [7] L. Moysis, M.K. Gupta, V. Mishra, M. Marwan, and C. Volos: Observer design for rectangular descriptor systems with incremental quadratic constraints and nonlinear outputs - Application to secure communications. International Journal of Robust Nonlinear Control, 30(18), (2020), 8139-8158. DOI: 10.1002/rnc.5233.
• [8] P. Kunkel and V. Mehrmann: Analysis of over- and underdetermined nonlinear differential-algebraic systems with application to nonlinear control problems. Mathematics of Control, Signals and Systems, 14(3), (2001), 233-256. DOI: 10.1007/PL00009884.
• [9] M.K. Gupta, N.K. Tomar, and S. Bhaumik: Full- and reduced-order observer design for rectangular descriptor systems with unknown inputs. Journal of the Franklin Institute, 352(3), (2015), 1250-1264. DOI: 10.1016/j.jfranklin.2015.01.003.
• [10] S.L. Campbell: Singular Systems of Differential Equations. Pitman, London, 1980.
• [11] L. Moysis, M. Tripathi, M.K. Gupta, M. Marwan, and C. Volos: Adaptive observer design for systems with incremental quadratic constraints and nonlinear outputs-application to chaos synchronization. Archives of Control Sciences, 32(1), (2022) 105-121. DOI: 10.24425/acs.2022.140867.
• [12] M. Darouach and M. Boutayeb: Design of observers for descriptor systems. IEEE Transactions on Automatic Control, 40(7), (1995), 1323-1327. DOI: 10.1109/9.400467.
• [13] M. Hou and P.C. Müller: Observer design for descriptor systems. IEEE Transactions on Automatic Control, 44(1), (1999), 164-169. DOI: 10.1109/9.739112.
• [14] J. Ren and Q. Zhang: PD observer design for descriptor system: An LMI approach. International Journal of Control, Automation and Systems, 8(4), (2010), 735-740. DOI: 10.1007/s12555-010-0404-4.
• [15] M.K. Gupta, N.K. Tomar, D. Sharma, and J. Jaiswal: PD observer design for descriptor systems with unknown inputs: Application to infinite bus system. In 5th IEEE International Conference on Recent Advances and Innovations in Engineering, IEEE, Jaipur, (2020), 1-5.
• [16] A.-G. Wu, G.-R. Duan, and W. Liu: Proportional multiple-integral observer design for continuous-time descriptor linear systems. Asian Journal of Control, 14(2), (2012), 476-488. DOI: 10.1002/asjc.295.
• [17] D. Koenig: Unknown input proportional multiple-integral observer design for linear descriptor systems: Application to state and fault estimation. IEEE Transactions on Automatic Control, 50(2), (2005), 212-217. DOI: 10.1109/TAC.2004.841889.
• [18] M. Darouach, M. Zasadzinski, and M. Hayar: Reduced-order observer design for descriptor systems with unknown inputs. IEEE Transactions on Automatic Control, 41(7), (1996), 1068-1072. DOI: 10.1109/9.508918.
• [19] M.K. Gupta, N.K. Tomar, and S. Bhaumik: On detectability and observer design for rectangular linear descriptor system. International Journal of Dynamics and Control, 4(4), (2016), 438-446. DOI: 10.1007/s40435-014-0146-x.
• [20] J. Jaiswal, M.K. Gupta, and N.K. Tomar: Necessary and sufficient conditions for ODE observer design of descriptor systems. Systems & Control Letters, 151 (2021), 104916. DOI: 10.1016/j.sysconle.2021.104916.
• [21] K.S. Bobinyec: Observer construction for systems of differential algebraic equations using completions. North Carolina State University, 2013.

Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023)