American Institute of Mathematical Sciences

Advanced
2011, 2011(Special): 1467-1476. doi: 10.3934/proc.2011.2011.1467

Inverse problems for linear ill-posed differential-algebraic equations with uncertain parameters

Sergiy Zhuk 1,

1. 

INRIA Paris-Rocquencourt, Rocquencourt, B.P. 105 - 78153 Le Chesnay Cedex, France

Received  July 2010 Revised  August 2010 Published  October 2011

This paper describes a minimax state estimation approach for linear differential-algebraic equations (DAEs) with uncertain parameters. The approach addresses continuous-time DAEs with non-stationary rectangular matrices and uncertain bounded deterministic input. An observation’s noise is supposed to be random with zero mean and unknown bounded correlation function. Main result is a Generalized Kalman Duality (GKD) principle, describing a dual control problem. Main consequence of the GKD is an optimal minimax state estimation algorithm for DAEs with non-stationary rectangular matrices. An algorithm is illustrated by a numerical example for 2D timevarying DAE with a singular matrix pencil.
Keywords: Euler- Lagrange equations, Differential-algebraic equations, Descriptor systems, Minimax, State estimation.
Mathematics Subject Classification: Primary: 34K32,49N45x; Secondary: 49N30.
Citation: Sergiy Zhuk. Inverse problems for linear ill-posed differential-algebraic equations with uncertain parameters. Conference Publications, 2011, 2011 (Special) : 1467-1476. doi: 10.3934/proc.2011.2011.1467
[1]

Vu Hoang Linh, Volker Mehrmann. Spectral analysis for linear differential-algebraic equations. Conference Publications, 2011, 2011 (Special) : 991-1000. doi: 10.3934/proc.2011.2011.991
[2]

Yingjie Bi, Siyu Liu, Yong Li. Periodic solutions of differential-algebraic equations. Discrete & Continuous Dynamical Systems - B, 2020, 25 (4) : 1383-1395. doi: 10.3934/dcdsb.2019232
[3]

Jason R. Scott, Stephen Campbell. Auxiliary signal design for failure detection in differential-algebraic equations. Numerical Algebra, Control & Optimization, 2014, 4 (2) : 151-179. doi: 10.3934/naco.2014.4.151
[4]

Roderick V.N. Melnik, Ningning Song, Per Sandholdt. Dynamics of torque-speed profiles for electric vehicles and nonlinear models based on differential-algebraic equations. Conference Publications, 2003, 2003 (Special) : 610-617. doi: 10.3934/proc.2003.2003.610
[5]

Ferenc Hartung. Parameter estimation by quasilinearization in differential equations with state-dependent delays. Discrete & Continuous Dynamical Systems - B, 2013, 18 (6) : 1611-1631. doi: 10.3934/dcdsb.2013.18.1611
[6]

Jan Sieber. Finding periodic orbits in state-dependent delay differential equations as roots of algebraic equations. Discrete & Continuous Dynamical Systems - A, 2012, 32 (8) : 2607-2651. doi: 10.3934/dcds.2012.32.2607
[7]

Agnieszka B. Malinowska, Delfim F. M. Torres. Euler-Lagrange equations for composition functionals in calculus of variations on time scales. Discrete & Continuous Dynamical Systems - A, 2011, 29 (2) : 577-593. doi: 10.3934/dcds.2011.29.577
[8]

Elena K. Kostousova. State estimation for linear impulsive differential systems through polyhedral techniques. Conference Publications, 2009, 2009 (Special) : 466-475. doi: 10.3934/proc.2009.2009.466
[9]

La-Su Mai, Kaijun Zhang. Asymptotic stability of steady state solutions for the relativistic Euler-Poisson equations. Discrete & Continuous Dynamical Systems - A, 2016, 36 (2) : 981-1004. doi: 10.3934/dcds.2016.36.981
[10]

Timoteo Carletti. The lagrange inversion formula on non--Archimedean fields, non--analytical form of differential and finite difference equations. Discrete & Continuous Dynamical Systems - A, 2003, 9 (4) : 835-858. doi: 10.3934/dcds.2003.9.835
[11]

Janosch Rieger. The Euler scheme for state constrained ordinary differential inclusions. Discrete & Continuous Dynamical Systems - B, 2016, 21 (8) : 2729-2744. doi: 10.3934/dcdsb.2016070
[12]

M. Sumon Hossain, M. Monir Uddin. Iterative methods for solving large sparse Lyapunov equations and application to model reduction of index 1 differential-algebraic-equations. Numerical Algebra, Control & Optimization, 2019, 9 (2) : 173-186. doi: 10.3934/naco.2019013
[13]

Bahareh Akhtari, Esmail Babolian, Andreas Neuenkirch. An Euler scheme for stochastic delay differential equations on unbounded domains: Pathwise convergence. Discrete & Continuous Dynamical Systems - B, 2015, 20 (1) : 23-38. doi: 10.3934/dcdsb.2015.20.23
[14]

Weiyin Fei, Liangjian Hu, Xuerong Mao, Dengfeng Xia. Advances in the truncated Euler–Maruyama method for stochastic differential delay equations. Communications on Pure & Applied Analysis, 2020, 19 (4) : 2081-2100. doi: 10.3934/cpaa.2020092
[15]

Marissa Condon, Alfredo Deaño, Arieh Iserles. On systems of differential equations with extrinsic oscillation. Discrete & Continuous Dynamical Systems - A, 2010, 28 (4) : 1345-1367. doi: 10.3934/dcds.2010.28.1345
[16]

Jaume Llibre, Claudia Valls. Algebraic limit cycles for quadratic polynomial differential systems. Discrete & Continuous Dynamical Systems - B, 2018, 23 (6) : 2475-2485. doi: 10.3934/dcdsb.2018070
[17]

Hermen Jan Hupkes, Emmanuelle Augeraud-Véron. Well-posedness of initial value problems for functional differential and algebraic equations of mixed type. Discrete & Continuous Dynamical Systems - A, 2011, 30 (3) : 737-765. doi: 10.3934/dcds.2011.30.737
[18]

Ovide Arino, Eva Sánchez. A saddle point theorem for functional state-dependent delay differential equations. Discrete & Continuous Dynamical Systems - A, 2005, 12 (4) : 687-722. doi: 10.3934/dcds.2005.12.687
[19]

Tibor Krisztin. A local unstable manifold for differential equations with state-dependent delay. Discrete & Continuous Dynamical Systems - A, 2003, 9 (4) : 993-1028. doi: 10.3934/dcds.2003.9.993
[20]

Eugen Stumpf. Local stability analysis of differential equations with state-dependent delay. Discrete & Continuous Dynamical Systems - A, 2016, 36 (6) : 3445-3461. doi: 10.3934/dcds.2016.36.3445

 Impact Factor: 

Tools

Metrics

  • PDF downloads (13)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2020 American Institute of Mathematical Sciences