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A robust output error identifier for continuous-time systems. (English) Zbl 1330.93069

Summary: This paper shows that the adaptive output error identifier for linear time-invariant continuous-time systems proposed by Bestser and Zeheb is robust vis-à-vis finite energy measurement noise. More precisely, it is proven that the map from the noise to the estimation error is \(\mathcal{L}_2\)–stable–provided a tuning parameter is chosen sufficiently large. A procedure to determine the required minimal value of this parameter is also given. If the noise is exponentially vanishing, asymptotic convergence to zero of the prediction error is achieved. Instrumental for the establishment of the results is a suitable decomposition of the error system equations that allows us to strengthen–to strict–the well-known passivity property of the identifier. The estimator neither requires fast adaptation, a dead-zone, nor the knowledge of an upperbound on the noise magnitude, which is an essential requirement to prove stability of standard output error identifiers. To robustify the estimator with respect to non-square integrable (but bounded) noises, a prediction error-dependent leakage term is added in the integral adaptation. \(\mathcal{L}_\infty\)-stability of the modified scheme is established under a technical assumption. A simulated example, which is unstable for the equation error identifier and the output error identifier of Bestser and Zeheb, is used to illustrate the noise insensitivity property of the new scheme.

MSC:

93B30 System identification
93D99 Stability of control systems
93C05 Linear systems in control theory
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References:

[1] Johansson, Identification of continuous-time models, IEEE Transactions on Signal Processing 42 (4) pp 887– (1994) · doi:10.1109/78.285652
[2] Goodwin, Adaptive Filtering Prediction and Control (1984) · Zbl 1250.93001
[3] Johansson, Multivariable systems identification via continued-fractions expansion, IEEE Transactions on Automatic Control 40 (3) pp 507– (1995) · Zbl 0831.93014 · doi:10.1109/9.376070
[4] Landau, Adaptive Control: The Model Reference Approach (1979) · Zbl 0475.93002
[5] Ren, Stochastic parallel model adaptation, IEEE Transactions on Automatic Control 37 (5) pp 566– (1992) · Zbl 0756.93082 · doi:10.1109/9.135490
[6] Garnett, Convergence of the signed output error adaptive identifier, IEEE Transactions on Automatic Control 39 (7) pp 1387– (1994) · Zbl 0826.93040 · doi:10.1109/9.299619
[7] Ding, System Identificaion-New Theory and Methods (2013)
[8] Narendra, Stable Adaptive Systems (1989)
[9] Ding, Combined parameter and output estimation of dual-rate systems using an auxiliary model, Automatica 40 (10) pp 1739– (2004) · Zbl 1162.93376 · doi:10.1016/j.automatica.2004.05.001
[10] Ding, Parameter estimation of dual-rate stochastic systems by using an output error method, IEEE Transactions on Automatic Control 50 (9) pp 1436– (2005) · Zbl 1365.93480 · doi:10.1109/TAC.2005.854654
[11] Ding, Identification of dual-rate systems based on finite impulse response models, International Journal of Adaptive Control and Signal Processing 18 (7) pp 589– (2004) · Zbl 1055.93018 · doi:10.1002/acs.820
[12] Ding, Least squares based self-tuning control of dual-rate systems, International Journal of Adaptive Control and Signal Processing 18 (8) pp 697– (2004) · Zbl 1055.93044 · doi:10.1002/acs.828
[13] Ding, Least-squares parameter estimation for systems with irregularly missing data, International Journal of Adaptive Control and Signal Processing 24 (7) pp 540– (2010) · Zbl 1200.93130
[14] Anderson, Stability of Adaptive Systems: Passivity and Averaging Analysis (1986)
[15] Tomizuka, On relaxation of SPR condition in parallel MRAS: continuous-time case, IEEE Transactions on Automatic Control 33 pp 976– (1988) · Zbl 0664.93046 · doi:10.1109/9.7259
[16] Bestser, Modified output error identification-elimination of the SPR condition, IEEE Transactions on Automatic Control 40 (1) pp 190– (1995) · Zbl 0925.93150 · doi:10.1109/9.362871
[17] Lawrence, Parameter drift instability in disturbance-free adaptive systems, IEEE Transactions on Automatic Control 38 (4) pp 584– (1993) · Zbl 0775.93121 · doi:10.1109/9.250526
[18] Carrillo F Baysse A Habadi A OEI algorithms for continuous-time systems operating in closed-loop Proceedings of the 15th IFAC Symposium on System Identification 2009 408 413
[19] Landau, An output error recursive algorithm for unbiased identification in closed-loop, Automatica 33 (5) pp 933– (1997) · Zbl 0910.93086 · doi:10.1016/S0005-1098(96)00223-3
[20] Wang L Ortega R Su H Liu X Zhu Y A robust output-error identifier for continuous-time systems Proceedings of the 11th IFAC International Workshop on Adaptation and Learning in Control and Signal Processing 2013 170 175
[21] Sastry, Adaptive Control; Stability, Convergence and Robustness (1989) · Zbl 0693.93046
[22] Zeheb, A sufficient condition for output feedback stabilization of uncertain systems, IEEE Transactions on Automatic Control 38 (8) pp 1055– (1986) · Zbl 0619.93052 · doi:10.1109/TAC.1986.1104174
[23] Vidyasagar, Input-Output Analysis of Large-Scale Interconnected Systems (1981) · Zbl 0454.93002 · doi:10.1007/BFb0044060
[24] Ortega, Robustness of discrete-time direct adaptive controllers, IEEE Transactions on Automatic Control 30 (12) pp 1178– (1985) · Zbl 0588.93040 · doi:10.1109/TAC.1985.1103890
[25] Barmish, New Tools for Robustness of Linear Systems (1994) · Zbl 1094.93517
[26] Dasgupta, Conditions for designing strictly positive real transfer functions for adaptive output error identification, IEEE Transactions on Circuits and Systems 34 (7) pp 731– (1987) · doi:10.1109/TCS.1987.1086198
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