Abstract
This chapter deals with joint state and parameter estimation for nonlinear continuous-time systems. Based on an appropriate LPV approximation, the problem is formulated in terms of a set adaptive observer design problem which can be efficiently solved. The resolution methodology avoids the exponential complexity obstruction often met in set-membership parameter estimation. The efficacy of the proposed set adaptive observers is demonstrated on several examples.
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References
Besanc¸on, G.: Nonlinear observers and applications. Lecture Notes in Control and Inforamtion Science. Springer Verlag, Berlin (2007)
Nijmeijer H., Fossen, T.I.: New Directions in Nonlinear Observer Design. Springer-Verlag, London (1999)
Lee, L.H.: Identification and Robust Control of Linear Parameter-Varying Systems. PhDthesis, University of California at Berkeley, Berkeley, California (1997)
Tan, W.: Applications of Linear Parameter-Varying Control Theory. PhD-thesis, Dept. of Mechanical Engineering, University of California at Berkeley (1997)
Hansen, R.E.: Global optimization using interval analysis. CRC, 2nd edition (2004)
Moore, R.E.: Interval analysis. Prentice-Hall, Englewood Cliffs, NJ (1966)
Smith, H.L.: Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative Systems. AMS, Providence (1995)
Bogoliubov, N.N., Mitropolskii, Yu.A.: Asymptotic methods in the theory of nonlinear oscillations. Gordon and Breach, New York (1961)
Sanders, J., Verhulst, F., Murdock, J.: Averaging Methods in Nonlinear Dynamical Systems. Springer, New York (2007)
Kletting, M., Verified Methods for State and Parameter Estimators for Nonlinear Uncertain Systems with Applications in Engineering. PhD-thesis, Institute of Measurement, Control, and Microtechnology, University of Ulm, Germany (2009)
Bokor, J., Balas, G.: Detection Filter Design for LPV Systems - a Geometric Approach. Automatica 40, 511–518 (2004)
Marcos, A., Balas, G.: Development of linear-parameter-varying models for aircraft. J. Guidance, Control, Dynamics 27(2), 218–228 (2004)
Shamma, J., Cloutier, J.: Gain-scheduled missile autopilot design using linear parameter varying transformations. J. Guidance, Control, Dynamics 16(2), 256–261 (1993)
Ra¨ıssi, T., Videau, G., Zolghadri, A.: Interval observers design for consistency checks of nonlinear continuous-time systems. Automatica 46(3), 518–527 (2010)
Jaulin, L.: Nonlinear bounded-error state estimation of continuous time systems. Automatica 38(6), 1079–1082 (2002)
Ra¨ıssi, T., Ramdani, N., Candau, Y.: Set membership state and parameter estimation for systems described by nonlinear differential equations. Automatica 40(10), 1771–1777 (2004)
Kieffer, K. Walter, E.: Guaranteed nonlinear state estimator for cooperative systems. Numerical Algorithms 37, 187–198 (2004)
Mu¨ller, M.: U¨ ber das fundamental theorem in der the orieder gewohnlichen differential gleichungen. Math. Z 26, 619–645 (1920)
Bernard, O., Gouz´e, J.L.: Closed loop observers bundle for uncertain biotechnological models. J. Process Control 14, 765–774 (2004)
Gouz´e, J.L., Rapaport, A., Hadj-Sadok, M.Z.: Interval observers for uncertain biological systems. Ecological Modeling 133, 46–56 (2000)
Moisan, M., Bernard, O., Gouz´e, J.L.: Near optimal interval observers bundle for uncertain bioreactors. Automatica 45(1), 291–295 (2009)
Jaulin, L., Walter, E.: Set inversion via interval analysis for nonlinear bounded-error estimation. Automatica 29(4), 1053–1064 (1993)
Johnson, T., Tucker, W.: Rigorous parameter reconstruction for differential equations with noisy data. Automatica 44(9), 2422–2426 (2008)
Efimov, D.: Dynamical adaptive synchronization, Int. J. Adaptive Control and Signal Processing 20(9), 491–507 (2006)
Xu, A., Zhang, Q.: Residual Generation for Fault Diagnosis in Linear Time-Varying Systems. IEEE Trans. Autom. Control 49(5), 767–772 (2004)
Zhang, Q.: Adaptive observer for multiple-input-multiple-output (MIMO) linear time varying systems. IEEE Trans. Autom. Control (47(3), 525–529 (2002)
Sontag, E.D., Wang, Y.: Notions of input to output stability. Systems and Control Letters 38, 235–248 (1999)
Efimov, D., Ra¨ıssi, T., Zolghadri, A.: Adaptive set observers design for nonlinear continuoustime systems: Application to fault detection and diagnosis. IEEE Trans. Autom. Control, revised.
Fradkov, A.L., Nikiforov, V.O., Andrievsky, B.R.: Adaptive observers for nonlinear nonpassifiable systems with application to signal transmission. Proc. 41th IEEE Conf. Decision and Control, 4706–4711, Las Vegas (2002)
Meslem, N., Ramdani, N., Candau, Y.: Interval Observers for Uncertain Nonlinear Systems. Application to bioreactors. Proc. 17th IFAC World Congress, 9667–9672, Seoul, (2008)
Efimov D.V., Fradkov A.L. Hybrid adaptive resonance control of vibration machines: the double mass case. Proc. 3rd IFAC Workshop Periodic Control Systems (PSYCO’07), Saint-Petersburg, (2007)
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Efimov, D., Raässi, T., Zolghadri, A. (2011). Robust State and Parameter Estimation for Nonlinear Continuous-Time Systems in a Set-Membership Context. In: Rauh, A., Auer, E. (eds) Modeling, Design, and Simulation of Systems with Uncertainties. Mathematical Engineering, vol 3. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15956-5_12
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DOI: https://doi.org/10.1007/978-3-642-15956-5_12
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