In this paper, the problem of anti-disturbance control is studied for non-linear systems with stochastic multiple disturbances. The multiple disturbances include two types: one is the stochastic harmonic disturbance and the other non-harmonic noise generated by a linear stochastic exogenous system. An adaptive stochastic disturbance observer (ASDO) is constructed to estimate both the two aforementioned disturbances. Combining the disturbance estimation with a conventional state feedback control law, a composite anti-disturbance control scheme is constructed such that the closed-loop system is stochastically stable, and different types of disturbances may be attenuated and rejected. By using the Lyapunov function method and linear matrix inequalities technique, sufficient conditions for the stochastic stability of the closed-loop system are established. Moreover, an adaptive stochastic extended state observer (ASESO) is proposed for the output feedback case. Finally, an application example is provided to demonstrate the effectiveness of the proposed method.
AnHLiuJWangCet al. (2016) Disturbance observer-based anti-windup control for air-breathing hypersonic vehicles. IEEE Transactions on Industrial Electronics99: 1. https://doi.org/10.1109/TIE.2016.2516498
2.
ChenW-H (2003) Nonlinear disturbance observer-enhanced dynamic inversion control of missiles. Journal of Guidance, Control, and Dynamics26(1): 161–166. https://doi.org/10.2514/2.5027
3.
ChenW-H (2004) Disturbance observer based control for nonlinear systems. IEEE/ASME Transactions on Mechatronics9(4): 706–710. https://doi.org/10.1109/TMECH.2004.839034
4.
ChenW-HOhnishiKGuoL (2015) Advances in disturbance/uncertainty estimation and attenuation [Guest editors’ introduction]. IEEE Transactions on Industrial Electronics62(9): 5758–5762. https://doi.org/10.1109/TIE.2015.2453347
5.
ChenW-HYangJGuoLet al. (2016) Disturbance-observer-based control and related methods – an overview. IEEE Transactions on Industrial Electronics63(2): 1083–1095. https://doi.org/10.1109/TIE.2015.2478397
GuoLChenWH (2005) Disturbance attenuation and rejection for systems with nonlinearity via DOBC approach. International Journal of Robust and Nonlinear Control15(3): 109–125. https://doi.org/10.1002/rnc.978
LiYSunHZongGet al. (2016) Composite anti-disturbance resilient control for Markovian jump nonlinear systems with partly unknown transition probabilities and multiple disturbances. International Journal of Robust and Nonlinear Control18(October2014): 557–569. https://doi.org/10.1002/rnc.3682
MaoXYuanC (2006) Stochastic Differential Equations with Markovian Switching. London: Imperial College Press.
17.
StoorvogelASaberiA (2015) Necessary and sufficient conditions for global external stochastic stabilisation of linear systems with input saturation. IEEE Transactions on Automatic Control9286(c): 1–1. https://doi.org/10.1109/TAC.2015.2471676
18.
SuJLiBChenWH (2015a) On existence, optimality and asymptotic stability of the Kalman filter with partially observed inputs. Automatica53: 149–154.
19.
SuJLiBChenWH (2015b) Simultaneous state and input estimation with partial information on the inputs. Systems Science & Control Engineering3(1): 445–452.
20.
SunHGuoL (2014) Composite adaptive disturbance observer based control and back-stepping method for nonlinear system with multiple mismatched disturbances. Journal of the Franklin Institute351(2): 1027–1041. https://doi.org/10.1016/j.jfranklin.2013.10.002
TaoGKokotovicPV (1992) Adaptive control of plants with unknown dead-zones. IEEE Transactions on Automatic Control39(1): 59–68.
23.
TianMTaoG (1997) Adaptive dead-zone compensation for output-feedback canonical systems. International Journal of Control67(5): 791–812.
24.
Van ParysBPGKuhnDGoulartPJet al. (2014) Distributionally robust control of constrained stochastic systems. IEEE Transactions on Automatic Control61(2): 430–442. https://doi.org/10.1109/tac.2015.2444134
25.
WangZPanY (2017) Robust adaptive fault tolerant control for a class of nonlinear systems with dynamic uncertainties. Optik – International Journal for Light and Electron Optics131: 941–952. https://doi.org/10.1016/j.ijleo.2016.11.209
26.
WangZYuanJCheD (2017) Adaptive attitude takeover control for space non-cooperative targets with stochastic actuator faults. Optik – International Journal for Light and Electron Optics137: 279–290. https://doi.org/10.1016/j.ijleo.2017.02.071
27.
WangZYuanJPanYet al. (2017) Adaptive neural control for high order Markovian jump nonlinear systems with unmodeled dynamics and dead zone inputs. Neurocomputing247: 62–72. https://doi.org/10.1016/j.neucom.2017.03.041
28.
WangZZhangBYuanJet al. (2017) Robust adaptive fault tolerant control for a class of linearly parameterized uncertain nonlinear systems: an integrated method. Transactions of the Institute of Measurement and Control131: 014233121769614. https://doi.org/10.1177/0142331217696142
29.
WeiKang (1995) Nonlinear H/sub ∞/ control and its application to rigid spacecraft. IEEE Transactions on Automatic Control40(7): 1281–1285. https://doi.org/10.1109/9.400476
30.
WeiXChenN (2014) Composite hierarchical anti-disturbance control for nonlinear systems with DOBC and fuzzy control. International Journal of Robust and Nonlinear Control24(2): 362–373. https://doi.org/10.1002/rnc.2891
31.
WeiXChenNLiW (2013) Composite adaptive disturbance observer-based control for a class of nonlinear systems with multisource disturbance. International Journal of Adaptive Control and Signal Processing27(3): 199–208. https://doi.org/10.1002/acs.2290
WenCZhouJWangW (2009) Decentralized adaptive backstepping stabilization of interconnected systems with dynamic input and output interactions. Automatica45(1): 55–67. https://doi.org/10.1016/j.automatica.2008.06.018
34.
YangJDingZChenWet al. (2016) Output-based disturbance rejection control for non-linear uncertain systems with unknown frequency disturbances using an observer backstepping approach. IET Control Theory & Applications10(9): 1052–1060. https://doi.org/10.1049/iet-cta.2015.1160
YaoXGuoL (2014) Composite disturbance-observer-based output feedback control and passive control for Markovian jump systems with multiple disturbances. IET Control Theory and Applications8(10): 873–881.
37.
ZhangJLiuXXiaYet al. (2016) Disturbance observer based integral sliding mode control for systems with mismatched disturbances. IEEE Transactions on Industrial Electronics0046(c): 1–1. https://doi.org/10.1109/TIE.2016.2583999
38.
ZhangTPGeSS (2008) Adaptive dynamic surface control of nonlinear systems with unknown dead zone in pure feedback form. Automatica44(7): 1895–1903. https://doi.org/10.1016/j.automatica.2007.11.025
ZongGLiYHouLet al. (2016) Disturbance-observer-based-control and L 2−L ∞ resilient control for Markovian jump non-linear systems with multiple disturbances and its application to single robot arm system. IET Control Theory & Applications10(2): 226–233. https://doi.org/10.1049/iet-cta.2015.0430.
