Optimal input design for parameter estimation of nonlinear systems: case study of an unstable delta wing

ABSTRACT A closed-loop optimal experimental design for online parameter identification approach is developed for nonlinear dynamic systems. The goal of the observer and the nonlinear model predictive control theories is here to perform online computation of the optimal time-varying input and to estimate the unknown model parameters online. The main contribution consists in combining Lyapunov stability theory with an existing closed-loop identification approach, in order to maximise the information content in the experiment and meanwhile to asymptotically stabilise the closed-loop system. To illustrate the proposed approach, the case of an open-loop unstable aerodynamic mechanical system is discussed. The simulation results show that the proposed algorithm allows to estimate all unknown parameters, which was not possible according to previous work, while keeping the closed-loop system stable.

[1]  Stabilization of Feedback Linearized Nonlinear Processes under Bounded Perturbations , 1989, 1989 American Control Conference.

[2]  D.G. Dudley,et al.  Dynamic system identification experiment design and data analysis , 1979, Proceedings of the IEEE.

[3]  Günter Wozny,et al.  Experimental evaluation of an approach to online redesign of experiments for parameter determination , 2013 .

[4]  Victor M. Zavala,et al.  The advanced-step NMPC controller: Optimality, stability and robustness , 2009, Autom..

[5]  Sandro Macchietto,et al.  Model-based design of experiments for parameter precision: State of the art , 2008 .

[6]  Pascal Dufour,et al.  Observer and model predictive control for on-line parameter identification in nonlinear systems , 2013 .

[7]  Nicolas Boizot,et al.  An adaptive high-gain observer for nonlinear systems , 2010, Autom..

[8]  T. Westerlund,et al.  Remarks on "Asymptotic behavior of the extended Kalman filter as a parameter estimator for linear systems" , 1980 .

[9]  J. Gauthier,et al.  A simple observer for nonlinear systems applications to bioreactors , 1992 .

[10]  H. Hammouri,et al.  Observer synthesis for state-affine systems , 1990, 29th IEEE Conference on Decision and Control.

[11]  Henry Cox,et al.  On the estimation of state variables and parameters for noisy dynamic systems , 1964 .

[12]  Hassan Hammouri,et al.  Observer Design for MIMO Non-Uniformly Observable Systems , 2012, IEEE Transactions on Automatic Control.

[13]  Alex Simpkins,et al.  System Identification: Theory for the User, 2nd Edition (Ljung, L.; 1999) [On the Shelf] , 2012, IEEE Robotics & Automation Magazine.

[14]  Christophe Prieur,et al.  Dynamic boundary stabilization of linear and quasi-linear hyperbolic systems , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[15]  David Angeli,et al.  Fundamentals of economic model predictive control , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[16]  Hassan Hammouri,et al.  Optimal input design for online identification: a coupled observer-MPC approach , 2008 .

[17]  A. H. Nayfeh,et al.  Analytical study of the subsonic wing-rock phenomenon for slender delta wings , 1989 .

[18]  Mario Zanon,et al.  Indefinite linear MPC and approximated economic MPC for nonlinear systems , 2014 .

[19]  Lorenz T. Biegler,et al.  Lyapunov stability of economically oriented NMPC for cyclic processes , 2011 .

[20]  Tung-Sang Ng,et al.  Optimal experiment design for linear systems with input-output constraints , 1977, Autom..

[21]  Panagiotis D. Christofides,et al.  Economic model predictive control of nonlinear process systems using empirical models , 2015 .

[22]  Helen Durand,et al.  A tutorial review of economic model predictive control methods , 2014 .

[23]  Lennart Ljung,et al.  System Identification: Theory for the User , 1987 .

[24]  Biao Huang,et al.  Receding horizon experiment design with application in SOFC parameter estimation , 2010 .

[25]  Hassan Hammouri,et al.  Observer Design for Uniformly Observable Systems With Sampled Measurements , 2013, IEEE Transactions on Automatic Control.

[26]  Gildas Besançon,et al.  An Immersion-Based Observer Design for Rank-Observable Nonlinear Systems , 2007, IEEE Transactions on Automatic Control.

[27]  Petru-Daniel Morosan,et al.  Closed loop optimal experiment design for on-line parameter estimation , 2014, 2014 European Control Conference (ECC).

[28]  T. Basar,et al.  H∞-0ptimal Control and Related Minimax Design Problems: A Dynamic Game Approach , 1996, IEEE Trans. Autom. Control..

[29]  N. Ananthkrishnan,et al.  Parameter estimation of unstable, limit cycling systems using adaptive feedback linearization : example of delta wing roll dynamics , 2005 .

[30]  E. Stear,et al.  The simultaneous on-line estimation of parameters and states in linear systems , 1976 .

[31]  David Angeli,et al.  On Average Performance and Stability of Economic Model Predictive Control , 2012, IEEE Transactions on Automatic Control.

[32]  Biao Huang,et al.  Constrained receding‐horizon experiment design and parameter estimation in the presence of poor initial conditions , 2011 .

[33]  G. Bornard,et al.  Regularly persistent observers for bilinear systems , 1989 .

[34]  L. Keviczky.  "Design of Experiments" for the Identification of Linear Dynamic Systems , 1975 .

[35]  Hassan Hammouri,et al.  Application of nonlinear observers to fault detection and isolation , 1999 .

[36]  Eric Walter,et al.  Identification of Parametric Models: from Experimental Data , 1997 .

[37]  J. Willems.  A general stability criterion for non-linear time-varying feedback systems† , 1970 .