© The Institution of Engineering and Technology
An indirect adaptive fuzzy prescribed performance control scheme is developed for a class of uncertain multi-input and multi-output feedback linearisable non-linear systems with unknown control direction and external disturbances. The properties of symmetric matrix and hyperbolic tangent function are exploited and the predefined tracking performance boundary is used to design the adaptive fuzzy prescribed performance controller, which can avoid the possible singularity problem and calculating the inverse of matrix. A robust controller equipped with a Nussbaum-type function is constructed to compensate for the lumped errors and solve the unknown control direction problem. The proposed scheme guarantees that all the signals in the resulting closed-loop system are bounded and that the tracking errors converge to a small residual set with the prescribed performance bounds. Simulation results are used to demonstrate the effectiveness of the proposed approach.
References
-
-
1)
-
38. Bechlioulis, C.P., Rovithakis, G.A.: ‘Prescribed performance adaptive control for multi-input multi-output affine in the control nonlinear systems’, IEEE Trans. Autom. Control, 2010, 55, (5), pp. 1220–1226.
-
2)
-
23. Zheng, W.: ‘Positioning control for an unmanned airship using sliding mode control based on fuzzy approximation’, Proc. Inst. Mech. Eng. G J. Aerosp. Eng., 2014, 228, (12), pp. 2627–2640.
-
3)
-
42. Na, J., Chen, Q., Ren, X., et al: ‘Adaptive prescribed performance motion control of servo mechanisms with friction compensation’, IEEE Trans. Ind. Electron., 2014, 61, (1), pp. 486–494.
-
4)
-
16. Tong, S., Li, C., Li, Y.: ‘Fuzzy adaptive observer backstepping control for MIMO nonlinear systems’, Fuzzy Sets Syst., 2009, 160, (19), pp. 2755–2775.
-
5)
-
21. Amer, A.F., Sallam, E.A., Elawady, W.M.: ‘Quasi sliding mode-based single input fuzzy self-tuning decoupled fuzzy pi control for robot manipulators with uncertainty’, Int. J. Robust Nonlinear Control, 2014, 22, pp. 2026–2054.
-
6)
-
44. Zhang, L., Tong, S., Li, Y.: ‘Prescribed performance adaptive fuzzy output-feedback control of uncertain nonlinear systems with unmodeled dynamics’, Nonlinear Dyn., 2014, 77, (4), pp. 1653–1665.
-
7)
-
49. Slotine, J., Li, W.: ‘Applied nonlinear control’ (Prentice-Hall, Englewood Cliffs, NJ, 1991).
-
8)
-
26. Nussbaum, R.: ‘Some remarks on a conjecture in parameter adaptive control’, Syst. Control Lett., 1983, 3, (5), pp. 243–246.
-
9)
-
35. Tong, S., Li, H.-X.: ‘Direct adaptive fuzzy output tracking control of nonlinear systems’, Fuzzy Sets Syst., 2002, 128, (1), pp. 107–115.
-
10)
-
17. Li, Y., Tong, S., Li, T.: ‘Hybrid fuzzy adaptive output feedback control design for MIMO time-varying delays uncertain nonlinear systems’, IEEE Trans. Fuzzy Syst., 2016, 24, (4), pp. 841–853.
-
11)
-
43. Li, Y., Tong, S.: ‘Prescribed performance adaptive fuzzy output-feedback dynamic surface control for nonlinear large-scale systems with time delays’, Inf. Sci., 2015, 292, pp. 125–142.
-
12)
-
32. Zhang, T., Ge, S.: ‘Adaptive neural control of MIMO nonlinear state time-varying delay systems with unknown dead-zones and gain signs’, Automatica, 2007, 43, (6), pp. 1021–1033.
-
13)
-
8. Shi, W.: ‘Observer-based fuzzy adaptive control for multi-input multi-output nonlinear systems with a nonsymmetric control gain matrix and unknown control direction’, Fuzzy Sets Syst., 2015, 263, pp. 1–26.
-
14)
-
18. Li, Y., Tong, S., Liu, Y., et al: ‘Adaptive fuzzy robust output feedback control of nonlinear systems with unknown dead zones based on a small-gain approach’, IEEE Trans. Fuzzy Syst., 2014, 22, (1), pp. 164–176.
-
15)
-
9. Shi, W.: ‘Adaptive fuzzy control for multi-input multi-output nonlinear systems with unknown dead-zone inputs’, Appl. Soft Comput., 2015, 30, pp. 36–47.
-
16)
-
19. Li, Y., Tong, S.: ‘Command-filtered-based fuzzy adaptive control design for MIMO switched nonstrict-feedback nonlinear systems’, IEEE Trans. Fuzzy Syst., doi: 10.1109/tfuzz.2016.2574913.
-
17)
-
50. Wang, L.-X.: ‘Fuzzy systems are universal approximators’. 1992 IEEE Int. Conf. on Fuzzy Systems, San Diego, CA, USA, 1992, pp. 1163–1170.
-
18)
-
2. Yang, Y.N., Wu, J., Zheng, W: ‘Station-keeping attitude control for an autonomous airship using feedback linearization and sliding mode control’, Int. J. Innovat. Comput. Inf. Control, 2012, 8, (9), pp. 152–165.
-
19)
-
39. Kostarigka, A.K., Rovithakis, G.A.: ‘Prescribed performance output feedback/observer-free robust adaptive control of uncertain systems using neural networks’, IEEE Trans. Syst. Man Cybern. B Cybern., 2011, 41, (6), pp. 1483–1494.
-
20)
-
45. 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.
-
21)
-
5. Labiod, S., Boucherit, M.S., Guerra, T.M.: ‘Adaptive fuzzy control of a class of MIMO nonlinear systems’, Fuzzy Sets Syst., 2005, 151, (1), pp. 59–77.
-
22)
-
20. Yang, Y.N., Wu, J., Zheng, W.: ‘Trajectory tracking for an autonomous airship using fuzzy adaptive sliding mode control’, J. Zhejiang Univ. Sci, C, 2012, 13, (7), pp. 534–543.
-
23)
-
28. Ye, X., Jiang, J.: ‘Adaptive nonlinear design without a priori knowledge of control directions’, IEEE Trans. Autom. Control, 1998, 43, (11), pp. 1617–1621.
-
24)
-
30. Boulkroune, A., M'Saad, M., Farza, M.: ‘Adaptive fuzzy controller for multivariable nonlinear state time-varying delay systems subject to input nonlinearities’, Fuzzy Sets Syst., 2011, 164, (1), pp. 45–65.
-
25)
-
11. Tong, S., Sui, S., Li, Y.: ‘Fuzzy adaptive output feedback control of MIMO nonlinear systems with partial tracking errors constrained’, IEEE Trans. Fuzzy Syst., 2015, 23, (4), pp. 729–742.
-
26)
-
51. Ge, S.S., Tee, K.P.: ‘Approximation-based control of nonlinear MIMO time-delay systems’, Automatica, 2007, 43, (1), pp. 31–43.
-
27)
-
22. Zheng, W.: ‘Station-keeping control for a stratospheric airship platform via fuzzy adaptive backstepping approach’, Adv. Space Res., 2013, 15, pp. 1157–1167.
-
28)
-
34. Tong, S., Wang, T., Tang, J.T.: ‘Fuzzy adaptive output tracking control of nonlinear systems’, Fuzzy Sets Syst., 2000, 111, pp. 169–182.
-
29)
-
1. Chen, J.L., Chang, W.D.: ‘Feedback linearization control of a two-link robot using a multi-crossover genetic algorithm’, Expert Syst. Appl., 2009, 36, pp. 4154–4159.
-
30)
-
48. Horn, R., Johnson, C.R.: ‘Matrix analysis’ (Cambridge University Press, 1990).
-
31)
-
3. Bao, X.W., Zhuo, F., Tian, Y.: ‘Simplified feedback linearization control of three-phase photovoltaic inverter with an lcl filter’, IEEE Trans. Power Electron., 2013, 28, (6), pp. 2739–2752.
-
32)
-
25. Chen, B.-S., Lee, C.-H., Chang, Y.-C.: ‘h∞ tracking design of uncertain nonlinear siso systems: adaptive fuzzy approach’, IEEE Trans. Fuzzy Syst., 1996, 4, (1), pp. 32–43.
-
33)
-
47. Psomopoulou, E., Theodorakopoulos, A., Doulgeri, Z., et al: ‘Prescribed performance tracking of a variable stiffness actuated robot’, IEEE Trans. Control Syst. Technol., 2015, 23, (5), pp. 1914–1926.
-
34)
-
10. Liu, Y.-J., Tong, S.-C., Li, T.-S.: ‘Observer-based adaptive fuzzy tracking control for a class of uncertain nonlinear MIMO systems’, Fuzzy Sets Syst., 2011, 164, (1), pp. 25–44.
-
35)
-
14. Tong, S.C., Li, Y.M., Feng, G., et al: ‘Observer-based adaptive fuzzy backstepping dynamic surface control for a class of MIMO nonlinear systems’, IEEE Trans. Syst. Man. Cybern. B Cybern., 2011, 41, (4), pp. 1124–1135.
-
36)
-
12. Tong, S., Chen, B., Wang, Y.: ‘Fuzzy adaptive output feedback control for MIMO nonlinear systems’, Fuzzy Sets Syst., 2005, 156, (2), pp. 285–299.
-
37)
-
41. Bechlioulis, C.P., Doulgeri, Z., Rovithakis, G.A.: ‘Neuro-adaptive force/position control with prescribed performance and guaranteed contact maintenance’, IEEE Trans. Neural. Netw., 2010, 21, (12), pp. 1857–1868.
-
38)
-
33. Ge, S., Hong, F., Lee, T.H.: ‘Adaptive neural control of nonlinear time-delay systems with unknown virtual control coefficients’, IEEE Trans. Syst. Man Cybern. B (Cybern.), 2004, 34, (1), pp. 499–516.
-
39)
-
6. Boulkroune, A., Farza, M., M'Saad, M.: ‘Fuzzy approximation-based indirect adaptive controller for multi-input multi-output non-affine systems with unknown control direction’, IET Control Theory Applic., 2012, 6, (17), pp. 2619–2629.
-
40)
-
4. Haojian, X., Ioannou, P.A.: ‘Robust adaptive control for a class of MIMO nonlinear systems with guaranteed error bounds’, IEEE Trans. Autom. Control, 2003, 48, (5), pp. 728–742.
-
41)
-
37. Bechlioulis, C.P., Rovithakis, G.A.: ‘Adaptive control with guaranteed transient and steady state tracking error bounds for strict feedback systems’, Automatica, 2009, 45, (2), pp. 532–538.
-
42)
-
7. Shi, W.: ‘Adaptive fuzzy control for MIMO nonlinear systems with nonsymmetric control gain matrix and unknown control direction’, IEEE Trans. Fuzzy Syst., 2014, 22, (5), pp. 1288–1300.
-
43)
-
46. Bechlioulis, C.P., Theodorakopoulos, A., Rovithakis, G.A.: ‘Output feedback stabilization with prescribed performance for uncertain nonlinear systems in canonical form’. 52nd IEEE Conf. on Decision and Control, Florence, Italy, 2013, pp. 5084–5089.
-
44)
-
15. Li, Y., Tong, S., Li, T.: ‘Observer-based adaptive fuzzy tracking control of MIMO stochastic nonlinear systems with unknown control direction and unknown dead-zones’, IEEE Trans. Fuzzy Syst., 2015, 23, (4), pp. 1228–1241.
-
45)
-
29. Ge, S.S., Hong, F., Lee, T.H.: ‘Adaptive neural control of nonlinear time-delay systems with unknown virtual control coefficients’, IEEE Trans. Syst. Man Cybern. B Cybern., 2004, 34, (1), pp. 499–516.
-
46)
-
24. Zheng, W.: ‘Self-organizing fuzzy optimal control for under-actuated systems’, Proc. Inst. Mech. Eng. I J. Syst. Control Eng., 2014, 228, (8), pp. 578–590.
-
47)
-
27. Mudgett, D.R., Morse, A.S.: ‘Adaptive stabilization of linear systems with unknown high frequency gain’, IEEE Trans. Automat. Contr., 1985, 30, pp. 549–554.
-
48)
-
13. Tong, S., Li, Y.: ‘Adaptive fuzzy output feedback control of MIMO nonlinear systems with unknown dead-zone inputs’, IEEE Trans. Fuzzy Syst., 2013, 21, (1), pp. 134–146.
-
49)
-
31. Boulkroune, A., Tadjine, M., M'Saad, M., et al: ‘Fuzzy adaptive controller for MIMO nonlinear systems with known and unknown control direction’, Fuzzy Sets Syst., 2010, 161, (6), pp. 797–820.
-
50)
-
40. Kostarigka, A.K., Rovithakis, G.A.: ‘Adaptive dynamic output feedback neural network control of uncertain MIMO nonlinear systems with prescribed performance’, IEEE Trans. Neural. Netw. Learn. Syst., 2012, 23, (1), pp. 138–149.
-
51)
-
36. Bechlioulis, C.P., Rovithakis, G.A.: ‘Robust adaptive control of feedback linearizable MIMO nonlinear systems with prescribed performance’, IEEE Trans. Autom. Control, 2008, 53, (9), pp. 2090–2099.
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