Abstract
Input saturation is one of the common phenomena in many practical systems, and it is main obstacles that limits the systems performance. In this paper, the adaptive neural network (NN) control problem has been discussed for a family of uncertain nonstrict-feedback systems with input saturation. The innovations are summarized as follows: (1) the auxiliary systems and the NN state observer are developed to eliminate the influence of input saturation and estimate unmeasurable states; (2) in order to against the drawback of “explosion of complexity" for the traditional backstepping control technique (BCT), the dynamic surface control technique is used to reduce the excessive computation burden; (3) the proposed NN control approach for nonstrict-feedback systems only utilize the property of radial basis function-neural networks (RBF-NNs), instead of the restrictive assumption. Furthermore, unknown smooth functions are approximated by RBF-NNs in nonlinear systems. By employing the BCT, an adaptive output-feedback controller has been constructed. Meanwhile, all signals in closed-loop system are semi-globally uniformly ultimate bounded. An explicit function with the saturation error and designed parameters is obtained, which indicates the tracking error can be tuned through the saturation error and designed parameters. Finally, the superiority of the proposed control technique is validated by two examples.
Similar content being viewed by others
References
Cao P, Yang Z, Sun L, Liang Y, Yang M, Guan R (2019) Image captioning with bidirectional semantic attention-based guiding of long short-term memory. Neural Process Lett 50(1):103–119
Singh AK, Pal BC (2018) Decentralized nonlinear control for power systems using normal forms and detailed models. IEEE Trans Power Syst 33(2):1160–1172
Wang T, Gao H, Qiu J (2016) A combined fault-tolerant and predictive control for network-based industrial processes. IEEE Trans Ind Electron 63(4):2529–2536
Chen CLP, Ren C, Du T (2016) Fuzzy observed-based adaptive consensus tracking control for second-order multiagent systems with heterogeneous nonlinear dynamics. IEEE Trans Fuzzy Syst 24(4):906–915
Niu B, Li H, Qin T, Karimi HR (2018) Adaptive NN dynamic surface controller design for nonlinear pure-feedback switched systems with time-delays and quantized input. IEEE Trans Syst Man Cybern Syst 48(10):1676–1688
Zhou Q, Li H, Wu C, Wang L, Ahn CK (2017) Adaptive fuzzy control of nonlinear systems with unmodeled dynamics and input saturation using small-gain approach. IEEE Trans Syst Man Cybern Syst 47(8):1979–1989
Yu J, Shi P, Lin C, Yu H (2020) Adaptive neural command filtering control for nonlinear MIMO systems with saturation input and unknown control direction. IEEE Trans Cybern 50(6):2536–2545
Li Y, Tong S (2017) Adaptive fuzzy output-feedback stabilization control for a class of switched nonstrict-feedback nonlinear systems. IEEE Trans Cybern 47(4):1007–1016
Tong S, Li Y, Liu Y (2021) Observer-based adaptive neural networks control for large-scale interconnected systems with nonconstant control gains. IEEE Trans Neural Netw Learn Syst 32(4):1575–1585
Li Y, Tong S, Li T (2015) Composite adaptive fuzzy output feedback control design for uncertain nonlinear strict-feedback systems with input saturation. IEEE Trans Cybern 45(10):2299–2308
Du P, Pan Y, Li H, Lam H (2020) Nonsingular finite-time event-triggered fuzzy control for large-scale nonlinear systems. IEEE Trans Fuzzy Syst. https://doi.org/10.1109/TFUZZ.2020.2992632
Pan Y, Du P, Xue H, Lam H (2020) Singularity-free fixed-time fuzzy control for robotic systems with user-defined performance. IEEE Trans Fuzzy Syst. https://doi.org/10.1109/TFUZZ.2020.2999746
Liang H, Liu G, Zhang H, Huang T (2020) Neural-network-based event-triggered adaptive control of nonaffine nonlinear multiagent systems with dynamic uncertainties. IEEE Trans Neural Netw Learn Syst. https://doi.org/10.1109/TNNLS.2020.3003950
Kanellakopoulos I, Kokotovic PV, Morse AS (1991) Systematic design of adaptive controllers for feedback linearizable systems. In: ACC 1991, IEEE, pp 649–654
Zhou Z, Tong D, Chen Q, Zhou W (2021) Adaptive NN control for nonlinear systems with uncertainty based on dynamic surface control. Neurocomputing 421:161–172
Jia Y (2003) Alternative proofs for improved LMI representations for the analysis and the design of continuous-time systems with polytopic type uncertainty: a predictive approach. IEEE Trans Autom Control 48(8):1413–1416
Xu C, Tong D, Chen Q, Zhou W (2020) Asynchronous control of T-S fuzzy chaotic systems via a unified model using the hidden Markov model subject to strict dissipativity. Optim Contr Appl Met 41(2):587–604
Chen B, Liu X, Lin C (2018) Observer and adaptive fuzzy control design for nonlinear strict-feedback systems with unknown virtual control coefficients. IEEE Trans Fuzzy Syst 26(3):1732–1743
Xu C, Tong D, Chen Q, Zhou W, Shi P (2021) Exponential stability of Markovian jumping systems via adaptive sliding mode control. IEEE Trans Syst Man Cybern Syst 51(2):1249–1258
Liu Y, Guo BZ, Park JH, Lee S (2018) Event-based reliable dissipative filtering for T-S fuzzy systems with asynchronous constraints. IEEE Trans Fuzzy Syst 26(4):2089–2098
Xu Q, Li X (2020) HONN-based adaptive ILC for pure-feedback nonaffine discrete-time systems with unknown control directions. IEEE Trans Neural Netw Learn Syst 31(1):212–224
Swaroop D, Hedrick JK, Yip PP, Gerdes JC (2000) Dynamic surface control for a class of nonlinear systems. IEEE Trans Autom Control 45(10):1893–1899
Cui B, Xia Y, Liu K, Shen G (2020) Finite-time tracking control for a class of uncertain strict-feedback nonlinear systems with state constraints: A smooth control approach. IEEE Trans Neural Netw Learn Syst 31(11):4920–4932
Tong S, Sui S, Li Y (2015) Fuzzy adaptive output feedback control of MIMO nonlinear systems with partial tracking errors constrained. IEEE Trans Fuzzy Syst 23(4):729–742
Li Y, Shao X, Tong S (2019) Adaptive fuzzy prescribed performance control of nontriangular structure nonlinear systems. IEEE Trans Cybern 28(10):2416–2426
Jia F, Wang X, Zhou X (2019) Robust adaptive prescribed performance control for a class of nonlinear pure-feedback systems. Int J Robust Nonlinear Control 29(12):3971–3987
Li Y, Sun K, Tong S (2019) Observer-based adaptive fuzzy fault-tolerant optimal control for SISO nonlinear systems. IEEE Trans Cybern 49(2):649–661
Lu D, Tong D, Chen Q, Zhou W, Zhou J, Shen S (2021) Exponential synchronization of stochastic neural networks with time-varying delays and Lévy noises via event-triggered control. Neural Process Lett. https://doi.org/10.1007/s11063.021.10509.7
Tong Y, Tong D, Chen Q, Zhou W (2020) Finite-time state estimation for nonlinear systems based on event-triggered mechanism. Circ Syst Signal Process 39(7):3737–3757
Wang M, Wang Z, Dong H, Han QL (2021) A novel framework for backstepping-based control of discrete-time strict-feedback nonlinear systems with multiplicative noises. IEEE Trans Autom Control 66(4):1484–1496
Jia Y (2000) Robust control with decoupling performance for steering and traction of 4WS vehicles under velocity-varying motion. IEEE Trans Control Syst Technol 8(3):554–569
Chen Q, Tong D, Zhou W, Xu Y, Mou J (2021) Exponential stability using sliding mode control for stochastic neutral-type systems. Circ Syst Signal Process 40:2006–2024
Tong D, Xu C, Chen Q, Zhou W, Xu Y (2020) Sliding mode control for nonlinear stochastic systems with Markovian jumping parameters and mode-dependent time-varying delays. Nonlinear Dyn 100(2):1343–1358
Tong D, Rao P, Chen Q, Ogorzalek M, Li X (2018) Exponential synchronization and phase locking of a multilayer Kuramoto-oscillator system with a pacemaker. Neurocomputing 308:129–137
Tong S, Li Y, Sui S (2016) Adaptive fuzzy tracking control design for SISO uncertain nonstrict feedback nonlinear systems. IEEE Trans Fuzzy Syst 24(6):1441–1454
Wu C, Liu J, Xiong Y, Wu L (2018) Observer-based adaptive fault-tolerant tracking control of nonlinear nonstrict-feedback systems. IEEE Trans Neural Netw Learn Syst 29(7):3022–3033
Pérez-Arancibia NO, Tsao TC, Gibson JS (2010) Saturation-induced instability and its avoidance in adaptive control of hard disk drives. IEEE Trans Control Syst Technol 18(2):368–382
Li Z, Li T, Feng G, Zhao R, Shan Q (2020) Neural network-based adaptive control for pure-feedback stochastic nonlinear systems with time-varying delays and dead-zone input. IEEE Trans Syst Man Cybern Syst 50(12):5317–5329
Wang L, Chen CP (2021) Reduced-order observer-based dynamic event-triggered adaptive NN control for stochastic nonlinear systems subject to unknown input saturation. IEEE Trans Neural Netw Learn Syst 32(4):1678–1690
Li P, Yang G (2011) An adaptive fuzzy design for fault-tolerant control of mimo nonlinear uncertain systems. J Control Theory App 9(2):244–250
Chen B, Lin C, Liu X, Liu K (2015) Adaptive fuzzy tracking control for a class of MIMO nonlinear systems in nonstrict-feedback form. IEEE Trans Cybern 45(12):2744–2755
Wang H, Liu X, Liu K, Karimi HR (2015) Approximation-based adaptive fuzzy tracking control for a class of nonstrict-feedback stochastic nonlinear time-delay systems. IEEE Trans Fuzzy Syst 23(5):1746–1760
Wang H, Chen B, Liu K, Liu X, Lin C (2014) Adaptive neural tracking control for a class of nonstrict-feedback stochastic nonlinear systems with unknown backlash-like hysteresis. IEEE Trans Neural Netw Learn Syst 25(5):947–958
Tong D, Xu C, Chen Q, Zhou W (2020) Sliding mode control of a class of nonlinear systems. J Franklin Inst 357(3):1560–1581
Huang HC, Chiang CH (2016) An evolutionary radial basis function neural network with robust genetic-based immunecomputing for online tracking control of autonomous robots. Neural Process Lett 44(1):19–35
He W, Sun Y, Yan Z, Yang C, Li Z, Kaynak O (2020) Disturbance observer-based neural network control of cooperative multiple manipulators with input saturation. IEEE Trans Neural Netw Learn Syst 31(5):1735–1746
Keighobadi J, Hosseini-Pishrobat M, Faraji J (2020) Adaptive neural dynamic surface control of mechanical systems using integral terminal sliding mode. Neurocomputing 379:141–151
Tong D, Zhang L, Zhou W, Zhou J, Xu Y (2016) Asymptotical synchronization for delayed stochastic neural networks with uncertainty via adaptive control. Int J Control Autom 14(3):706–712
Wang J, Tian L (2019) Stability of inertial neural network with time-varying delays via sampled-data control. Neural Process Lett 50(2):1123–1138
Liu Z, Lai G, Zhang Y, Chen CLP (2015) Adaptive neural output feedback control of output-constrained nonlinear systems with unknown output nonlinearity. IEEE Trans Neural Netw Learn Syst 26(8):1789–1802
Yao B, Tomizuka M (1997) Adaptive robust control of SISO nonlinear systems in a semi-strict feedback form. Automatica 33(5):893–900
Zhou Q, Li H, Wang L, Lu R (2018) Prescribed performance observer-based adaptive fuzzy control for nonstrict-feedback stochastic nonlinear systems. IEEE Trans Syst Man Cybern Syst 48(10):1747–1758
Li Y, Yang G (2016) Fuzzy adaptive output feedback fault-tolerant tracking control of a class of uncertain nonlinear systems with nonaffine nonlinear faults. IEEE Trans Fuzzy Syst 24(1):223–234
Author information
Authors and Affiliations
Corresponding authors
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
This work is partially supported by National Natural Science Foundation of China (61673257), the Natural Science Foundation of Shanghai (20ZR1422400), the China Postdoctoral Science Foundation (2019M661322).
Rights and permissions
About this article
Cite this article
Liu, X., Tong, D., Chen, Q. et al. Observer-Based Adaptive NN Tracking Control for Nonstrict-Feedback Systems with Input Saturation. Neural Process Lett 53, 3757–3781 (2021). https://doi.org/10.1007/s11063-021-10575-x
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11063-021-10575-x