Zhang, Jiabo; Ding, Feng; Shi, Yang Self-tuning control based on multi-innovation stochastic gradient parameter estimation. (English) Zbl 1154.93040 Syst. Control Lett. 58, No. 1, 69-75 (2009). Summary: This paper uses the Multi-Innovation Stochastic Gradient (MISG) algorithm to estimate the parameters of discrete-time systems, and presents an MISG based self-tuning control scheme. Furthermore, we prove that the parameter estimation error converges to zero under persistent excitation, and the parameter estimation based control algorithm can asymptotically achieve virtually optimal control, and ensure that the closed-loop systems are stable and globally convergent. A simulation example is included. Cited in 66 Documents MSC: 93E10 Estimation and detection in stochastic control theory 93E12 Identification in stochastic control theory 93C40 Adaptive control/observation systems 93E25 Computational methods in stochastic control (MSC2010) Keywords:recursive identification; parameter estimation; adaptive control; self-tuning control; stochastic gradient; multi-innovation identification methods × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Åström, K. J.; Wittenmak, B., On self-tuning regulators, Automatica, 9, 2, 185-199 (1973) · Zbl 0249.93049 [2] Goodwin, G. C.; Sin, K. S., Adaptive Filtering Prediction and Control (1984), Prentice-hall: Prentice-hall Englewood Cliffs, NJ · Zbl 0653.93001 [3] Ding, F.; Chen, T.; Iwai, Z., Adaptive digital control of Hammerstein nonlinear systems with limited output sampling, SIAM Journal on Control and Optimization, 45, 6, 2257-2276 (2007) · Zbl 1126.93034 [4] Ding, F.; Chen, T., Least squares based self-tuning control of dual-rate systems, International Journal of Adaptive Control and Signal Processing, 18, 8, 697-714 (2004) · Zbl 1055.93044 [5] Delyon, B., General results on the convergence of stochastic algorithms, IEEE Transactions on Automatic Control, 41, 9, 1245-1255 (1996) · Zbl 0867.93075 [6] Fang, H.; Chen, H. F., Stability and instability of limit points for stochastic approximation algorithms, IEEE Transactions on Automatic Control, 45, 3, 413-420 (2000) · Zbl 0970.62050 [7] Buche, R.; Kushner, H. J., Stochastic approximation and user adaptation in a competitive resource sharing system, IEEE Transactions on Automatic Control, 45, 5, 844-853 (2000) · Zbl 0967.90022 [8] Greblicki, W., Stochastic approximation in nonparametric identification of Hammerstein systems, IEEE Transactions on Automatic Control, 47, 11, 1800-1810 (2002) · Zbl 1364.93829 [9] Caines, P.; Laforune, S., Adaptive control with recursive identification for stochastic linear systems, IEEE Transactions on Automatic Control, 29, 4, 312-321 (1984) · Zbl 0538.93071 [10] Radenkovi, M. S.; Stankovi, S., Strong consistency of parameter estimates in direct self-tuning control algorithms based on stochastic approximation, Automatica, 26, 3, 533-544 (1990) · Zbl 0705.93053 [11] Radenkovic, M. S.; Michel, A. N., Almost sure rate of convergence of the parameter estimates in stochastic approximation algorithm, IEEE Transactions on Automatic Control, 45, 6, 1161-1166 (2000) · Zbl 0981.93078 [12] Ding, F.; Chen, T., Performance analysis of multi-innovation gradient type identification methods, Automatica, 43, 1, 1-14 (2007) · Zbl 1140.93488 [13] Ding, F.; Chen, H. B.; Li, M., Multi-innovation least squares identification methods based on the auxiliary model for MISO systems, Applied Mathematics and Computation, 187, 2, 658-668 (2007) · Zbl 1114.93101 [14] J.B. Zhang, F. Ding, Y. Shi, Multi-innovation gradient parameter estimation based adaptive control for discrete-time Systems, in: Proceedings of the IEEE International Conference on Automation and Logistics, Jinan, China, August 18-21, 2007, pp. 399-404; J.B. Zhang, F. Ding, Y. Shi, Multi-innovation gradient parameter estimation based adaptive control for discrete-time Systems, in: Proceedings of the IEEE International Conference on Automation and Logistics, Jinan, China, August 18-21, 2007, pp. 399-404 [15] Ding, F.; Chen, T., Identification of Hammerstein nonlinear ARMAX systems, Automatica, 41, 9, 1479-1489 (2005) · Zbl 1086.93063 [16] Ding, F.; Liu, P. X.; Yang, H. Z., Parameter identification and intersample output estimation for dual-rate systems, IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans, 38, 4, 966-975 (2008) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.