D-optimal design for parameter estimation in discrete-time nonlinear dynamic systems

An optimal input design method for parameter estimation in a discrete-time nonlinear system is presented in the paper to improve the observability and identification precision of model parameters. Determinant of the information matrix is used as the criterion function which is generally a nonconvex function about the input signals to be designed. To avoid the locally optimizing problem, a randomized design method is proposed by which a globally optimizing test plan other than input signals may be obtained. Then the randomized design can be approximated by a nonrandomized design about optimal inputs. An iterative algorithm integrated with dynamic programming is given and verified by a numerical example on experimental design for self-calibration tests of ISP system.

[1]  D. E. Goldberg,et al.  Genetic Algorithms in Search , 1989 .

[2]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[3]  A. A. Zhigli︠a︡vskiĭ,et al.  Theory of Global Random Search , 1991 .

[4]  Jianbin Qiu,et al.  A New Design of Delay-Dependent Robust ${\cal H}_{\bm \infty}$ Filtering for Discrete-Time T--S Fuzzy Systems With Time-Varying Delay , 2009, IEEE Transactions on Fuzzy Systems.

[5]  H. Szu,et al.  Nonconvex optimization by fast simulated annealing , 1987, Proceedings of the IEEE.

[6]  Huijun Gao,et al.  Novel Robust Stability Criteria for Stochastic Hopfield Neural Networks With Time Delays , 2009, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[7]  Jun Hu,et al.  Robust Sliding Mode Control for Discrete Stochastic Systems With Mixed Time Delays, Randomly Occurring Uncertainties, and Randomly Occurring Nonlinearities , 2012, IEEE Transactions on Industrial Electronics.

[8]  Jun Hu,et al.  Probability-guaranteed H∞ finite-horizon filtering for a class of nonlinear time-varying systems with sensor saturations , 2012, Syst. Control. Lett..

[9]  Goldberg,et al.  Genetic algorithms , 1993, Robust Control Systems with Genetic Algorithms.

[10]  Yeung Sam Hung,et al.  Distributed H∞-consensus filtering in sensor networks with multiple missing measurements: The finite-horizon case , 2010, Autom..

[11]  Raman K. Mehra,et al.  Optimal input signals for parameter estimation in dynamic systems--Survey and new results , 1974 .

[12]  Huijun Gao,et al.  Distributed Filtering for a Class of Time-Varying Systems Over Sensor Networks With Quantization Errors and Successive Packet Dropouts , 2012, IEEE Transactions on Signal Processing.

[13]  Louis J. Lintereur.  Optimal test trajectories for calibrating inertial systems , 1996 .

[14]  Yongduan Song,et al.  A Novel Approach to Filter Design for T–S Fuzzy Discrete-Time Systems With Time-Varying Delay , 2012, IEEE Transactions on Fuzzy Systems.

[15]  Zidong Wang,et al.  H∞ filtering for nonlinear discrete-time stochastic systems with randomly varying sensor delays , 2009, Autom..

[16]  Eugene A. Morelli,et al.  Optimal Input Design for Aircraft Parameter Estimation using Dynamic Programming Principles , 1990 .

[17]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[18]  Elder M. Hemerly,et al.  Aircraft Parameter Estimation Experiment Design Considering Measurement Colored Residuals , 2006 .

[19]  Huijun Gao,et al.  Robust $H_{\infty}$ Filtering for a Class of Nonlinear Networked Systems With Multiple Stochastic Communication Delays and Packet Dropouts , 2010, IEEE Transactions on Signal Processing.

[20]  Art Lew,et al.  Dynamic Programming: A Computational Tool , 2006 .

[21]  W. J. Studden,et al.  Theory Of Optimal Experiments , 1972 .

[22]  Jianbin Qiu,et al.  Model Approximation for Discrete-Time State-Delay Systems in the T–S Fuzzy Framework , 2011, IEEE Transactions on Fuzzy Systems.