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Back-stepping active disturbance rejection control design for integrated missile guidance and control system via reduced-order ESO
Abstract
This paper proposes a novel composite integrated guidance and control (IGC) law for missile intercepting against unknown maneuvering target with multiple uncertainties and control constraint. First, by using back-stepping technique, the proposed IGC law design is separated into guidance loop and control loop. The unknown target maneuvers and variations of aerodynamics parameters in guidance and control loop are viewed as uncertainties, which are estimated and compensated by designed model-assisted reduced-order extended state observer (ESO). Second, based on the principle of active disturbance rejection control (ADRC), enhanced feedback linearization (FL) based control law is implemented for the IGC model using the estimates generated by reduced-order ESO. In addition, performance analysis and comparisons between ESO and reduced-order ESO are examined. Nonlinear tracking differentiator is employed to construct the derivative of virtual control command in the control loop. Third, the closed-loop stability for the considered system is established. Finally, the effectiveness of the proposed IGC law in enhanced interception performance such as smooth interception course, improved robustness against multiple uncertainties as well as reduced control consumption during initial phase are demonstrated through simulations.
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Increasing ESO gains may improve estimation accuracy but also amplifies noises, leading to the peaking phenomenon or even system instability.
“Although increasing the ESO gains may improve the estimation accuracy, it would also amplify noises, leading to the so-called peaking phenomenon [45,46], or even system instability.”
From Compensation Function Observer-Based Backstepping Sliding-Mode Control of Uncertain Electro-Hydraulic Servo System (2024) · cites this paper as [45]
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“Second, since the order of the proposed ESO is identical to one, the peaking performance during the transient state can be substantially eliminated [18].”
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“Secondly, since the order of the proposed ESO is identical to one, the peaking performance during transient state can be totally eliminated [24].”
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“In[67],thetheoreticalanalysisandcomparison betweenthereducedESOandconventionalESOiscarriedout.”
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“During the last decades, the integrated guidance and control has received increasing attention in the missile technology [1,2].”
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“The ESO has also been used in the design of controllers for a helicopter [36], fixed-wing airplane [37], spacecraft [38], and missile [39].”
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“By adopting the active disturbance rejection control principle together with the reduced-order extended state observer for uncertainty estimation, the simultaneous design of the guidance and control was designed in [3].”
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Probe motion compound control for autonomous aerial refueling docking
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Force estimation and failure detection based on disturbance observer for an ear surgical device
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Modified reduced order observer based linear active disturbance rejection control for TITO systems
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Comfort braking control for brake-by-wire vehicles
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“Inequality (34) means that V(t) is eventually restricted by ς/a, ie, all signals in the closed loop are in the compact set Ω = { (e, y,ηT) , |||V ≤ ς a } ,∀t ≥ t0.”
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“Author of [35] proposed a backstepping controller for integrated missile control system via reduced-order ESO, which had fewer tuning parameter than the conventional second-order ESO.”
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Spatial Path-Following Control of Underactuated AUV With Multiple Uncertainties and Input Saturation
Guo, C. G., Han, Y., Yu, H., & Qin, J. (2019) · IEEE Access · doi:10.1109/access.2019.2928897 · Cited by 22
“REDUCED-ORDER ESOs Compared with the traditional ESO, the reduced-order ESO yields faster response with the same bandwidth as that in [12].”
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“Fortunately, it is still feasible to obtain the required states by constructing a suitable state observer, which does not affect the controller design (Han, 2009; Reichhartinger, Spurgeon, & Weyrer, 2016; Shao & Wang, 2015; Yao, Jiao, & Ma, 2014).”
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Anti-Disturbance Control for Tethered Aircraft System With Deferred Output Constraints
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“Up until now, various control methods have been employed to design IGC law, such as sliding mode control (SMC) (Hou and Duan, 2008; Guo et al., 2018), backstepping control (Shao and Wang, 2015) and dynamic surface control (DSC) (Hou et al., 2013; Wang et al., 2016b, 2016c; Zhang and Wu, 2016).”
BackgroundMethodOn-ground lateral direction control for an unswept flying-wing UAV
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Integrated guidance and control design of the suicide UCAV for terminal attack
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“The back-stepping method has been utilized widely because of its unique advantages in nonlinear systems, such as missile guidance and control systems [24], underwater vehicle systems [25].”
Integrated guidance and control with partial state constraints and actuator faults
Liu, W., Wei, Y., Hou, M., & Duan, G. (2019) · Journal of the Franklin Institute · doi:10.1016/j.jfranklin.2019.04.008 · Cited by 19
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“As the key technology of active disturbance rejection control(ADRC), ESO has shown the accuracy of estimating systems’ total unknown disturbances in many studies (Huang & Xue, 2014; Shao & Wang, 2015; Zhao & Guo, 2015).”
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Active disturbance rejection controller for small fixed-wing UAVs with model uncertainty
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“Besides, Shao et al [11] developed an integrated missile guidance and control system via reduced-order ESO ADRC.”
MethodWhole-Process Predefined-Time Tracking Control for T–S Fuzzy Euler–Lagrange Systems
Zhang, J.-D., Han, T., Xiao, B., Liang, C., & Yan, H. (2024) · IEEE Transactions on Fuzzy Systems · doi:10.1109/tfuzz.2024.3440049 · Cited by 17
“Besides, extended state observer (ESO) is used in [13] and [14], which can be integrated into a controller to fast observe the disturbance and approximation error in the TSFEL systems, and introduced as a substitution for the term of a constant multiplied signum function in SM control, which can…”
BackgroundMethodThree-dimensional mobile docking control method of an underactuated autonomous underwater vehicle
Xie, T., Li, Y., Jiang, Y., Pang, S., & Xu, X. (2022) · Ocean Engineering · doi:10.1016/j.oceaneng.2022.112634 · Cited by 17
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“Many effective techniques including TLC, MLP and ESO, aims to handle a series of problems in trajectory tracking control rather than a specific unmodeled dynamics and timevarying external disturbances problems.”
InfluentialExtended disturbance observer based robust sliding mode control for active suspension system
Waghmare, D. B., Asutkar, V. G., & Patre, B. M. (2021) · International Journal of Dynamics and Control · doi:10.1007/s40435-021-00761-z · Cited by 16
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Robust Path-Following Control for AUV under Multiple Uncertainties and Input Saturation
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“In previous studies [41,42], the error between the estimated values of the ESOs and the actual values for lumped disturbances has been proven to be bounded.”
Sigmoid function based integral-derivative observer and application to autopilot design
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“Up to now, nearly all of the IGC methods explore the backstepping method (Chen et al., 2016; He et al., 2016; Kim et al., 2007; Shao and Wang, 2015) or dynamics surface control method (Hou et al., 2013; Wang et al., 2015; Wang et al., 2016; Song and Zhang, 2016; Zhang and Wu, 2016), which is…”
MethodAdaptive NN control of integrated guidance and control systems based on disturbance observer
Liang, X., Xu, B., Jia, K., & Liu, X. (2022) · Journal of the Franklin Institute · doi:10.1016/j.jfranklin.2022.11.040 · Cited by 14
Integrated guidance and control for underactuated fixed-trim moving mass flight vehicles
Cheng, Y., Liu, Z., Zhou, H., Gao, C., Li, J., & Zhang, Z. (2023) · Aerospace Science and Technology · doi:10.1016/j.ast.2023.108680 · Cited by 14
Dong, J., Sun, J.-G., Guo, Y., & Song, S. (2018) · International Journal of Control Automation and Systems · doi:10.1007/s12555-016-0784-1 · Cited by 14
Lai, C., Wang, W., Liu, Z., Liang, T., & Yan, S. (2018) · IEEE Access · doi:10.1109/access.2018.2871051 · Cited by 14
“Consider the physical limitations on the missile during the interception process, we give the following assumption according to [35].”
BackgroundZhao, L., Liu, X., Zhang, J., & Wang, T. (2021) · Control Engineering Practice · doi:10.1016/j.conengprac.2021.104754 · Cited by 14
An Improved ELOS Guidance Law for Path Following of Underactuated Unmanned Surface Vehicles
Wu, S., Ye, H., Liu, W., Yang, X., Liu, Z., & Zhang, H. (2024) · Sensors · doi:10.3390/s24165384 · Cited by 13
“The reduced-order ESO is originally investigated to estimate the lumped disturbances in [40].”
BackgroundIntelligent Guidance and Control Methods for Missile Swarm
Huang, H., Zhao, X. M., & Zhang, X. Y. (2022) · Computational Intelligence and Neuroscience · doi:10.1155/2022/8235148 · Cited by 13
“-erefore, it has also been applied in the design of integrated guidance and control [39, 40].”
Miao, J., Deng, K., Zhang, W., Gong, X., Lyu, J., & Ren, L. (2022) · Journal of Marine Science and Engineering · doi:10.3390/jmse10020238 · Cited by 13
“Moreover, compared with the c ventional ESO, th reduced-order ESO produces f ster transient r spons in the same bandwidth [42].”
BackgroundInfluentialQu, Y., & Cai, L. (2022) · ISA Transactions · doi:10.1016/j.isatra.2022.10.041 · Cited by 13
Li, Z., Dong, Q., Zhang, X., Zhang, H., & Zhang, F. (2022) · Aerospace · doi:10.3390/aerospace9110640 · Cited by 12
“There exist observer gains , 1,2, ,4 i i for the reduced-order ESO in Equations (22), (28), (34) and (40) that make the observer estimations , 1,2, ,4 i d i converge to the system-lumped disturbances , 1,2, ,4 i d i ; that is, 1 1 d d , 2 2 d d , 3 3 d d , and 4 4 d d [26].”
InfluentialLi, H., Liu, Z., Huang, J. H., An, X., & Chen, Y. (2025) · Ocean Engineering · doi:10.1016/j.oceaneng.2025.120456 · Cited by 12
“According (Xingling and Honglun, 2015) and (Liu et al., 2016), the reduced-order ESO applied to estimate 𝑔 is presented by where ̂𝑔 is the estimation of 𝑔 .”
Sliding mode control for continuous casting mold oscillatory system driven by servo motor
Shi, S., Kang, K., Li, J., & Fang, Y. (2017) · International Journal of Control Automation and Systems · doi:10.1007/s12555-016-0333-y · Cited by 12
Design and stability analysis of a generalized reduced-order active disturbance rejection controller
Wang, Y., Chen, Z., Sun, M., & Sun, Q. (2021) · Science China Technological Sciences · doi:10.1007/s11431-020-1803-4 · Cited by 12
Disturbance rejection control for the course keeping of the fully-submerged hydrofoil craft
Liu, S., Xu, C., & Wang, Y. (2016) · Chinese Control Conference (CCC) · doi:10.1109/chicc.2016.7553174 · Cited by 11
“Disturbance observer-based control (DOBC) provides an effective way for high precise control, which has been widely used in motor control [11][13][15], manipulator tracking [12], aircraft control[16][17], etc.”
BackgroundLiang, W., Zhang, W., Wang, D., Peng, K., & Yang, H. (2017) · Advances in Mechanical Engineering · doi:10.1177/1687814017733251 · Cited by 11
Cooperative Guidance Law Based on Super-Twisting Observer for Target Maneuvering
Gao, M., Yan, T., Han, B., Cheng, H., Fu, W., & Han, B. (2024) · Journal of Systems Engineering and Electronics · doi:10.23919/jsee.2024.000102 · Cited by 10
Li, G., Wu, Y., Liu, J., & Zhao, J. (2023) · Aerospace Science and Technology · doi:10.1016/j.ast.2023.108723 · Cited by 10
Pan, C., Wang, Y., Yang, S. X., Li, Z., & Xiao, J. (2024) · Machines · doi:10.3390/machines12100719 · Cited by 16
Metadata
- Authors
- Xingling, S., & Honglun, W.
- Affiliations
- Beihang University (CN)
- Corresponding author
- Honglun, Wang
- Venue
- ISA Transactions
- Publisher
- Elsevier BV
- Published
- 2015-07
- Volume
- 57
- Pages
- 10-22
- ISSN
- 0019-0578 (ISSN-L)
- OpenAlex
- W2008500509
- Cited by
- 196
- References
- 25
- Citations by year
- 2026: 8 · 2025: 10 · 2024: 20 · 2023: 20 · 2022: 16 · 2021: 14 · 2020: 19 · 2019: 27 · 2018: 25 · 2017: 21 · 2016: 13 · 2015: 2
- FWCI
- 29.52
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- ISA Transactions (publishedVersion)
- PubMed (publishedVersion)
- Funders
- National Natural Science Foundation of China (61175084/F030601)
- Program for Changjiang Scholars and Innovative Research Team in University (IRT 13004)
- Aeronautical Science Foundation of China (2014ZA51002)
- Topics
- Physical Sciences › Engineering › Aerospace Engineering › Guidance and Control Systems
- Physical Sciences › Engineering › Control and Systems Engineering › Adaptive Control of Nonlinear Systems
- Physical Sciences › Engineering › Aerospace Engineering › Aerospace Engineering and Control Systems
- Keywords
- integrated guidance and control, missile intercept, backstepping control, active disturbance rejection control, reduced-order extended state observer, feedback linearization, nonlinear tracking differentiator, input constraints, robustness to uncertainty, closed-loop stability
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