Title:
|
Fixed-time safe tracking control of uncertain high-order nonlinear pure-feedback systems via unified transformation functions (English) |
Author:
|
Guo, Chaoqun |
Author:
|
Hu, Jiangping |
Author:
|
Hao, Jiasheng |
Author:
|
Čelikovský, Sergej |
Author:
|
Hu, Xiaoming |
Language:
|
English |
Journal:
|
Kybernetika |
ISSN:
|
0023-5954 (print) |
ISSN:
|
1805-949X (online) |
Volume:
|
59 |
Issue:
|
3 |
Year:
|
2023 |
Pages:
|
342-364 |
Summary lang:
|
English |
. |
Category:
|
math |
. |
Summary:
|
In this paper, a fixed-time safe control problem is investigated for an uncertain high-order nonlinear pure-feedback system with state constraints. A new nonlinear transformation function is firstly proposed to handle both the constrained and unconstrained cases in a unified way. Further, a radial basis function neural network is constructed to approximate the unknown dynamics in the system and a fixed-time dynamic surface control (FDSC) technique is developed to facilitate the fixed-time control design for the uncertain high-order pure-feedback system. Combined with the proposed unified transformation function and the FDSC technique, an adaptive fixed-time control strategy is proposed to guarantee the fixed-time tracking. The novel original results of the paper allow to design the independent unified flexible fixed-time control strategy taking into account the actual possible constraints, either present or missing. Numerical examples are presented to demonstrate the proposed fixed-time tracking control strategy. (English) |
Keyword:
|
fixed-time safe control |
Keyword:
|
nonlinear pure-feedback systems |
Keyword:
|
state constrains |
Keyword:
|
dynamic surface control |
Keyword:
|
unified transformation function |
MSC:
|
70K20 |
MSC:
|
93D15 |
DOI:
|
10.14736/kyb-2023-3-0342 |
. |
Date available:
|
2023-07-12T07:15:33Z |
Last updated:
|
2023-07-12 |
Stable URL:
|
http://hdl.handle.net/10338.dmlcz/151720 |
. |
Reference:
|
[1] Andrieu, V., Praly, L., Astolfi, A.: Homogeneous approximation, recursive observer design, and output feedback..SIAM J. Control Optim. 47 (2009), 1814-1850. MR 2421331, |
Reference:
|
[2] Bhat, S., Bernstein, D.: Geometric homogeneity with applications to finite-time stability..Math. Control Signals Syst. 17 (2005), 101-127. Zbl 1110.34033, MR 2150956, |
Reference:
|
[3] Cao, Y., Wen, C., Song, Y.: A unified event-triggered control approach for uncertain pure-feedback systems with or without state constraints..IEEE Trans. Cybernet. 51 (2021), 1262-1271. |
Reference:
|
[4] Čelikovský, S., Anderle, M., Vyhlídal, T.: Virtual nonholonomic constraints to damp the varying length pendulum swing..In: IEEE Conference on Decision and Control (CDC) 2021, pp. 3893-3900. |
Reference:
|
[5] Čelikovský, S., Aranda-Bricaire, E.: Constructive nonsmooth stabilization of triangular systems..Syst. Control Lett. 36 (1999), 21-37. MR 1750623, |
Reference:
|
[6] Chen, B., Hu, J., Zhao, Y., Ghosh, B. K.: Finite-time velocity-free rendezvous control of multiple AUV systems with intermittent communication..IEEE Trans. Syst. Man Cybernet. Syst. 52 (2022), 6618-6629. |
Reference:
|
[7] Cui, E., Jing, Y., Gao, X.: Full state constraints control of switched complex networks based on time-varying barrier Lyapunov functions..IET Control Theory Appl. 14 (2020), 2419-2428. MR 4417972, |
Reference:
|
[8] Fang, L., Ding, S., Park, J. H., Ma, L.: Adaptive fuzzy output-feedback control design for a class of p-norm stochastic nonlinear systems with output constraints..IEEE Trans. Circuits Syst. I, Reg. Papers 68 (2021), 2626-2638. MR 4290703, |
Reference:
|
[9] Filippov, A. F.: Differential equations with discontinuous right-hand sides..J. Math. Anal. Appl. 154 (1998), 99-128. MR 0114016 |
Reference:
|
[10] Gómez-Gutiérrez, D., Vázquez, C. R., Čelikovský, S., Sánchez-Torres, J. D., Ruiz-León, J.: On finite-time and fixed-time consensus algorithms for dynamic networks switching among disconnected digraphs..Int. J. Control 93 (2020), 2120-2134. MR 4134400, |
Reference:
|
[11] Guiochet, J., Machin, M., Waeselynck, H.: Safety-critical advanced robots: A survey..Robotics Autonomous Systems 94 (2017), 43-52. |
Reference:
|
[12] Guo, C., Hu, J.: Time base generator based practical predefined-time stabilization of high-order systems with unknown disturbance..IEEE Trans. Circuits Syst. II, Exp. Briefs (2023). |
Reference:
|
[13] Guo, C., Hu, J.: Fixed-time stabilization of high-order uncertain nonlinear systems: output feedback control design and settling time analysis..J. Syst. Sci. Complex (2023), To appear. MR 4439669 |
Reference:
|
[14] Hong, Y., Jiang, Z.: Finite-time stabilization of nonlinear systems with parametric and dynamic uncertainties..IEEE Trans. Automat. Control 51 (2006), 1950-1956. MR 2284421, |
Reference:
|
[15] Hu, C., Qin, W., Li, Z., He, B., Liu, G.: Consensus-based state estimation for multi-agent systems with constraint information..Kybernetika 53 (2017), 545-561. MR 3684685, |
Reference:
|
[16] Jin, X., Xu, J. X.: Iterative learning control for output-constrained systems with both parametric and nonparametric uncertainties..Automatica 49 (2013), 2508-2516. MR 3072644, |
Reference:
|
[17] Krstic, M., Kokotovic, P. V., Kanellakopoulos, I.: Nonlinear and Adaptive Control Design..John Wiley and Sons, Inc. 1995. |
Reference:
|
[18] Li, Y. X.: Barrier Lyapunov function-based adaptive asymptotic tracking of nonlinear systems with unknown virtual control coefficients..Automatica 121 (2020), 109181. MR 4131834, |
Reference:
|
[19] Li, J., Yang, Y., Hua, C., Guan, X.: Fixed-time backstepping control design for high-order strict-feedback non-linear systems via terminal sliding mode..IET Control Theory Appl. 11 (2017), 1184-1193. MR 3700336, |
Reference:
|
[20] Liu, B., Hou, M., Ni, J., Li, Y., Wu, Z.: Asymmetric integral barrier Lyapunov function-based adaptive tracking control considering full-state with input magnitude and rate constraint..J. Franklin Inst. 357 (2020), 9709-9732. MR 4148332, |
Reference:
|
[21] Liu, Y., Zhang, H., Sun, J., Wang, Y.: Adaptive fuzzy containment control for multiagent systems with state constraints using unified transformation functions..IEEE Trans. Fuzzy Syst. 30 (2022), 162-174. |
Reference:
|
[22] Liu, Y., Zhang, H., Wang, Y., Yu, S.: Fixed-time cooperative control for robotic manipulators with motion constraints using unified transformation function..Int. J. Robust Nonlinear Control 31 (2021), 6826-6844. MR 4335261, |
Reference:
|
[23] Ma, J., Hu, J.: Safe consensus control of cooperative-competitive multi-agent systems via differential privacy..Kybernetika 58 (2022), 426-439. MR 4494099, |
Reference:
|
[24] Ou, M., Sun, H., Zhang, Z., Li, L., Wang, X.: Fixed-time tracking control for nonholonomic mobile robot..Kybernetika 57 (2021), 220-235. MR 4273573, |
Reference:
|
[25] Polyakov, A.: Nonlinear feedback design for fixed-time stabilization of linear control systems..IEEE Trans. Automat. Control 57 (2012), 2106-2110. MR 2957184, |
Reference:
|
[26] Tang, Z., Ge, S. S., Tee, K. P., He, W.: Robust adaptive neural tracking control for a class of perturbed uncertain nonlinear systems with state constraints..IEEE Trans. Syst., Man, Cybern., Syst. 46 (2016), 1618-1629. MR 3191823, |
Reference:
|
[27] Tian, B., Lu, H., Zuo, Z.: Fixed-time stabilization of high-order integrator systems with mismatched disturbances..Nonlinear Dynam. 94 (2018), 2889-2899. |
Reference:
|
[28] Wu, Z., Guo, J., Liu, B., Ni, J., Bu, X.: Composite learning adaptive dynamic surface control for uncertain nonlinear strict-feedback systems with fixed-time parameter estimation under sufficient excitation..Int. J. Robust Nonlinear Control 31 (2021), 5865-5889. MR 4329718, |
Reference:
|
[29] Yang, H., Ye, D.: Adaptive fault-tolerant fixed-time tracking consensus control for high-order unknown nonlinear multi-agent systems with performance constraint..J. Franklin Inst. 357 (2020), 11448-11471. MR 4160619, |
Reference:
|
[30] Zhang, T., Xia, M., Yi, Y.: Adaptive neural dynamic surface control of strict-feedback nonlinear systems with full state constraints and unmodeled dynamics..Automatica 81 (2017), 232-239. MR 3654606, |
Reference:
|
[31] Zhao, K., Song, Y.: Removing the feasibility conditions imposed on tracking control designs for state-constrained strict-feedback systems..IEEE Trans. Automat. Control 64 (2019), 1265-1272. MR 3922092, |
. |