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Nonlinear observer design for state and disturbance estimation

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Title: Nonlinear observer design for state and disturbance estimation
Authors: Kravaris, Costas1 kravaris@chemeng.upatras.gr, Sotiropoulos, Vassilios1, Georgiou, Costas1, Kazantzis, Nikolaos2 nikolas@wpi.edu, Xiao, MingQing3 mxiao@math.siu.edu, Krener, Arthur J.4 ajkrener@ucdavis.edu
Source: Systems & Control Letters. Nov2007, Vol. 56 Issue 11/12, p730-735. 6p.
Subjects: Nonlinear assignment problems, Assignment problems (Programming), Nonlinear boundary value problems, Analytic functions
Abstract: Abstract: A new systematic framework for nonlinear observer design that allows the concurrent estimation of the process state variables together with key unknown process or sensor disturbances is proposed. The nonlinear observer design problem is addressed within a similar methodological framework as the one introduced in [N. Kazantzis, C. Kravaris, Nonlinear observer design using Lyapunov''s auxiliary theorem, Systems Control Lett. 34 (1998) 241; A.J. Krener, M. Xiao, Nonlinear observer design in the Siegel domain, SIAM J. Control Optim. 41 (2002) 932.] for state estimation purposes only. From a mathematical standpoint, the problem under consideration is addressed through a system of first-order singular PDEs for which a rather general set of solvability conditions is derived. A nonlinear observer is then designed with a state-dependent gain that is computed from the solution of the system of singular PDEs. Under the aforementioned conditions, both state and disturbance estimation errors converge to zero with assignable rates. The convergence properties of the proposed nonlinear observer are tested through simulation studies in an illustrative example involving a biological reactor. [Copyright &y& Elsevier]
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Database: Engineering Source
Description
Abstract:Abstract: A new systematic framework for nonlinear observer design that allows the concurrent estimation of the process state variables together with key unknown process or sensor disturbances is proposed. The nonlinear observer design problem is addressed within a similar methodological framework as the one introduced in [N. Kazantzis, C. Kravaris, Nonlinear observer design using Lyapunov''s auxiliary theorem, Systems Control Lett. 34 (1998) 241; A.J. Krener, M. Xiao, Nonlinear observer design in the Siegel domain, SIAM J. Control Optim. 41 (2002) 932.] for state estimation purposes only. From a mathematical standpoint, the problem under consideration is addressed through a system of first-order singular PDEs for which a rather general set of solvability conditions is derived. A nonlinear observer is then designed with a state-dependent gain that is computed from the solution of the system of singular PDEs. Under the aforementioned conditions, both state and disturbance estimation errors converge to zero with assignable rates. The convergence properties of the proposed nonlinear observer are tested through simulation studies in an illustrative example involving a biological reactor. [Copyright &y& Elsevier]
ISSN:01676911
DOI:10.1016/j.sysconle.2007.05.001