Adaptive tracking control for a class of stochastic non-linear systems with input saturation constraint using multi-dimensional Taylor network
- Author(s): Yu-Qun Han 1, 2
-
-
View affiliations
-
Affiliations:
1:
School of Mathematics and Physics, Qingdao University of Science and Technology , Qingdao 266061 , People's Republic of China ;
2: Key Laboratory of Measurement and Control of Complex Systems of Engineering , Ministry of Education , Nanjing 210096 , People's Republic of China
-
Affiliations:
1:
School of Mathematics and Physics, Qingdao University of Science and Technology , Qingdao 266061 , People's Republic of China ;
- Source:
Volume 14, Issue 9,
11
June
2020,
p.
1193 – 1199
DOI: 10.1049/iet-cta.2019.0934 , Print ISSN 1751-8644, Online ISSN 1751-8652
The randomness and input saturation increase computational complexity and impede the tracking performance of stochastic non-linear systems, therefore, it is necessary to build a simple but effective controller. Based on this, a multi-dimensional Taylor network (MTN) is first applied to a class of stochastic non-linear systems with input saturation constraint in this study. Aiming to solve the tracking control problem, a novel MTN-based controller is proposed via backstepping, and the proposed control scheme has some advantages such as simple structure, good real-time performance and easy realisation. With the help of the hyperbolic tangent function approximating the symmetric saturation non-linearity, an adaptive MTN tracking control scheme is constructively designed via backstepping technique. The simulation results are given to illustrate the validity and accuracy of the model of the proposed approach.
Inspec keywords: nonlinear control systems; adaptive control; control system synthesis; function approximation; closed loop systems; tracking; linear systems; control nonlinearities
Other keywords: simple but effective controller; tracking performance; multidimensional Taylor network; novel MTN-based controller; tracking control problem; symmetric saturation nonlinearity; input saturation constraint; nonlinear systems; adaptive tracking control; input saturation increase computational complexity; good real-time performance; adaptive MTN tracking control scheme
Subjects: Linear control systems; Stability in control theory; Control system analysis and synthesis methods; Nonlinear control systems; Interpolation and function approximation (numerical analysis); Self-adjusting control systems
References
-
-
1)
-
1. Mao, X.R.: ‘Lasalle-type theorems for stochastic differential delay equations’, J. Math. Anal. Appl., 1999, 236, (2), pp. 350–369.
-
-
2)
-
35. Chen, M., Ge, S.S., Ren, B.: ‘Adaptive tracking control of uncertain MIMO nonlinear systems with input constraints’, Automatica, 2011, 47, (3), pp. 452–465.
-
-
3)
-
33. Li, Y.M., Tong, S.C., Li, T.S.: ‘Composite adaptive fuzzy output feedback control design for uncertain nonlinear strict-feedback systems with input saturation’, IEEE Trans. Cybern., 2015, 45, (10), pp. 2299–2308.
-
-
4)
-
42. Khas Minskii, R.Z.: ‘Stochastic stability of differential equations’ (Sijthoff & Noordhoff, Rockville, MD, 1980).
-
-
5)
-
12. Xie, X.J., Tian, J.: ‘Adaptive state-feedback stabilization of high-order stochastic systems with nonlinear parameterization’, Automatica, 2009, 45, (1), pp. 126–133.
-
-
6)
-
39. Sui, S., Li, Y.M., Tong, S.C.: ‘Adaptive fuzzy control design and applications of uncertain stochastic nonlinear systems with input saturation’, Neurocomputing, 2015, 156, pp. 42–51.
-
-
7)
-
36. Sui, S., Tong, S., Li, Y.: ‘Observer-based fuzzy adaptive prescribed performance tracking control for nonlinear stochastic systems with input saturation’, Neurocomputing, 2015, 158, pp. 100–108.
-
-
8)
-
11. Bian, T., Jiang, Y., Jiang, Z.P.: ‘Adaptive dynamic programming for stochastic systems with state and control dependent noise’, IEEE Trans. Autom. Control, 2016, 61, (12), pp. 4170–4175.
-
-
9)
-
31. Yan, H.S., Han, Y.Q.: ‘Decentralized adaptive multi-dimensional Taylor network tracking control for a class of large-scale stochastic nonlinear systems’, Int. J. Adapt. Control Signal Process., 2019, 33, (4), pp. 664–683.
-
-
10)
-
37. Wang, H., Chen, B., Liu, X., et al: ‘Adaptive neural tracking control for stochastic nonlinear strict-feedback systems with unknown input saturation’, Inf. Sci., 2014, 269, pp. 300–315.
-
-
11)
-
30. Han, Y.Q., Yan, H.S.: ‘Observer-based multi-dimensional Taylor network decentralised adaptive tracking control of large-scale stochastic nonlinear systems’, Int. J. Control, 2018, doi: 10.1080/00207179.2018.1521994.
-
-
12)
-
18. Tong, S.C., Xu, Y.Y., Li, Y.M.: ‘Adaptive fuzzy decentralised control for stochastic nonlinear large-scale systems in pure-feedback form’, Int. J. Syst. Sci., 2015, 46, (8), pp. 1510–1524.
-
-
13)
-
45. Li, Y.H., Fang, Y.M., Li, J.X., et al: ‘Adaptive backstepping control of hydraulic servo system with input saturation for rolling mill based on multi-model switching’. Proc. 32nd Chinese Control Conf., Xi'an, China, July 2013, pp. 3068–3072.
-
-
14)
-
43. Liu, Y.G., Zhang, J.F.: ‘Reduced-order observer-based control design for nonlinear stochastic systems’, Syst. Control Lett., 2004, 52, (2), pp. 123–135.
-
-
15)
-
3. Wu, Z.J., Xie, X.J., Shi, P., et al: ‘Backstepping controller design for a class of stochastic nonlinear systems with Markovian switching’, Automatica, 2009, 45, (4), pp. 997–1004.
-
-
16)
-
26. Zhang, J.J., Yan, H.S.: ‘MTN optimal control of MIMO non-affine nonlinear time-varying discrete systems for tracking only by output feedback’, J. Franklin Inst., 2019, 356, (8), pp. 4304–4334.
-
-
17)
-
40. Zhao, Z.H., Yu, J.P., Zhao, L., et al: ‘Adaptive fuzzy control for induction motors stochastic nonlinear systems with input saturation based on command filtering’, Inf. Sci., 2018, 463–464, pp. 186–195.
-
-
18)
-
23. Kang, A.M., Yan, H.S.: ‘Stability analysis and dynamic regulation of multi-dimensional Taylor network controller for SISO nonlinear systems with time-varying delay’, ISA Trans., 2018, 73, pp. 31–39.
-
-
19)
-
34. Zhou, Q., Shi, P., Tian, Y., et al: ‘Approximation-based adaptive tracking control for MIMO nonlinear systems with input saturation’, IEEE Trans. Cybern., 2015, 45, (10), pp. 2119–2128.
-
-
20)
-
19. Wang, H.Q., Liu, P.X., Niu, B.: ‘Robust fuzzy adaptive tracking control for nonaffine stochastic nonlinear switching systems’, IEEE Trans. Cybern., 2018, 48, (8), pp. 2462–2471.
-
-
21)
-
46. Wen, C.Y., Zhou, J., Liu, Z.T., et al: ‘Robust adaptive control of uncertain nonlinear systems in the presence of input saturation and external disturbance’, IEEE Trans. Autom. Control, 2011, 56, (7), pp. 1672–1678.
-
-
22)
-
48. Wang, H.Q., Chen, B., Lin, C.: ‘Adaptive neural tracking control for a class of stochastic nonlinear systems with unknown dead-zone’, Int. J. Innov. Comput., Inf. Control, 2013, 9, (8), pp. 3257–3269.
-
-
23)
-
21. Wang, H.Q., Liu, P.X., Shi, P.: ‘Observer-based fuzzy adaptive output-feedback control of stochastic nonlinear multiple time-delay systems’, IEEE Trans. Cybern., 2017, 47, (9), pp. 2568–2578.
-
-
24)
-
47. Wang, H.Q., Chen, B., Liu, X.P., et al: ‘Robust adaptive fuzzy tracking control for pure-feedback stochastic nonlinear systems with input constraints’, IEEE Trans. Cybern., 2013, 43, (6), pp. 2093–2104.
-
-
25)
-
25. Zhang, C., Yan, H.S.: ‘Identification and adaptive multi-dimensional Taylor network control of single-input single-output non-linear uncertain time-varying systems with noise disturbances’, IET Control Theory Appl., 2019, 13, (6), pp. 841–853.
-
-
26)
-
22. Yan, H.S., Kang, A.M.: ‘Asymptotic tracking and dynamic regulation of SISO non-linear system based on discrete multi-dimensional Taylor network’, IET Control Theory Applic., 2017, 11, (10), pp. 1619–1626.
-
-
27)
-
38. Sui, S., Tong, S., Li, Y.: ‘Adaptive fuzzy backstepping output feedback tracking control of MIMO stochastic pure-feedback nonlinear systems with input saturation’, Fuzzy Sets Syst., 2014, 254, pp. 26–46.
-
-
28)
-
24. Han, Y.Q., Zhu, S.L., Yang, S.G., et al: ‘Adaptive multi-dimensional Taylor network tracking control for a class of nonlinear systems’, Int. J. Control, 2019, doi: 10.1080/00207179.2019.1590649.
-
-
29)
-
17. Liu, Y.J., Lu, S.M., Tong, S.C., et al: ‘Adaptive control-based barrier Lyapunov functions for a class of stochastic nonlinear systems with full state constraints’, Automatica, 2018, 87, pp. 83–93.
-
-
30)
-
8. Pan, Z.G., Basar, T.: ‘Backstepping controller design for nonlinear stochastic systems under a risk-sensitive cost criterion’, SIAM J. Control Optim., 1999, 37, (3), pp. 957–995.
-
-
31)
-
28. Han, Y.Q., Yan, H.S.: ‘Adaptive multi-dimensional Taylor network tracking control for SISO uncertain stochastic non-linear systems’, IET Control Theory Applic., 2018, 12, (8), pp. 1107–1115.
-
-
32)
-
13. Li, H.Y., Shi, P., Yao, D.Y.: ‘Adaptive sliding-mode control of Markov jump nonlinear systems with actuator faults’, IEEE Trans. Autom. Control, 2017, 62, (4), pp. 1933–1939.
-
-
33)
-
41. Kushner, H.J.: ‘Stochastic stability and control’ (Academic Press, New York, 1967).
-
-
34)
-
15. Sun, Y.M., Chen, B., Lin, C., et al: ‘Adaptive neural control for a class of stochastic nonlinear systems by backstepping approach’, Inf. Sci., 2016, 369, pp. 748–764.
-
-
35)
-
5. Kanellakopoulos, I., Kokotovic, P.V., Morse, A. S.: ‘Systematic design of adaptive controllers for feedback linearizable systems’, IEEE Trans. Autom. Control, 1991, 36, (11), pp. 1241–1253.
-
-
36)
-
29. Han, Y.Q.: ‘Output-feedback adaptive tracking control of stochastic nonlinear systems using multi-dimensional Taylor network’, Int. J. Adapt. Control Signal Process., 2018, 32, (3), pp. 494–510.
-
-
37)
-
10. Xiong, K., Liu, L., Zhang, H.: ‘Adaptive robust extended Kalman filter for nonlinear stochastic systems’, IET Control Theory Applic., 2008, 2, (3), pp. 239–250.
-
-
38)
-
16. Niu, B., Wang, D., Alotaibi, N.D., et al: ‘Adaptive neural state-feedback tracking control of stochastic nonlinear switched systems: an average dwell-time method’, IEEE Trans. Neural Netw. Learn. Syst., 2019, 30, (4), pp. 1076–1087.
-
-
39)
-
20. Sui, S., Chen, C.L.P., Tong, S.: ‘Fuzzy adaptive finite-time control design for nontriangular stochastic nonlinear systems’, IEEE Trans. Fuzzy Syst., 2019, 27, (1), pp. 172–184.
-
-
40)
-
6. Pan, Z., Basar, T.: ‘Adaptive controller design for tracking and disturbance attenuation in parametric strict-feedback nonlinear systems’, IEEE Trans. Autom. Control, 1998, 43, (8), pp. 1066–1083.
-
-
41)
-
7. Deng, H., Krstić, M.: ‘Stochastic nonlinear stabilization-I: A backstepping design’, Syst. Control Lett., 1997, 32, (3), pp. 143–150.
-
-
42)
-
14. Wang, H.Q., Chen, B., Lin, C.: ‘Adaptive neural tracking control for a class of stochastic nonlinear systems’, Int. J. Robust Nonlinear Control, 2014, 24, (7), pp. 1262–1280.
-
-
43)
-
4. Xie, S.L., Xie, L.H.: ‘Decentralized stabilization of a class of interconnected stochastic nonlinear systems’, IEEE Trans. Autom. Control, 2000, 40, (1), pp. 132–137.
-
-
44)
-
27. Yan, H.S., Han, Y.Q., Sun, Q.M.: ‘Optimal output-feedback tracking of SISO stochastic nonlinear systems using multi-dimensional Taylor network’, Trans. Inst. Meas. Control, 2017, 40, (10), pp. 3049–3058.
-
-
45)
-
32. Yang, T., Meng, Z., Dimarogonas, D.V., et al: ‘Global consensus for discrete-time multi-agent systems with input saturation constraints’, Automatica, 2014, 50, (2), pp. 499–506.
-
-
46)
-
9. Liu, S.J., Zhang, J.F., Jiang, Z.P.: ‘Decentralized adaptive output-feedback stabilization for large-scale stochastic nonlinear systems’, Automatica, 2007, 43, (2), pp. 238–251.
-
-
47)
-
44. Du, Z.B., Chen, W.S., Jiao, L.C.: ‘Output-feedback adaptive dynamic surface control of stochastic non-linear systems using neural network’, IET Control Theory Applic., 2010, 4, (12), pp. 3012–3021.
-
-
48)
-
2. Lan, Q.X., Li, S.H.: ‘Global output-feedback stabilization for a class of stochastic nonlinear systems via sampled-data control’, Int. J. Robust Nonlinear Control, 2017, 27, (17), pp. 3643–3658.
-
-
1)