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Technical Brief

Design and Analysis of Adaptive Control Systems Over Wireless Networks

[+] Author and Article Information
Ali Albattat

Department of Mechanical and Aerospace Engineering,
Missouri University of Science and Technology,
Rolla, MO 65409

Benjamin Gruenwald

Department of Mechanical Engineering,
University of South Florida,
Tampa, FL 33620

Tansel Yucelen

Department of Mechanical Engineering,
University of South Florida,
Engineering Building C 2209,
4202 East Fowler Avenue,
Tampa, FL 33620
e-mail: tyucelen@gmail.com

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received January 18, 2016; final manuscript received October 18, 2016; published online May 9, 2017. Assoc. Editor: Yongchun Fang.

J. Dyn. Sys., Meas., Control 139(7), 074501 (May 09, 2017) (8 pages) Paper No: DS-16-1037; doi: 10.1115/1.4035094 History: Received January 18, 2016; Revised October 18, 2016

In this paper, we study the design and analysis of adaptive control systems over wireless networks using event-triggering control theory. The proposed event-triggered adaptive control methodology schedules the data exchange dependent upon errors exceeding user-defined thresholds to reduce wireless network utilization and guarantees system stability and command following performance in the presence of system uncertainties. Specifically, we analyze stability and boundedness of the overall closed-loop dynamical system, characterize the effect of user-defined thresholds and adaptive controller design parameters to the system performance, and discuss conditions to make the resulting command following performance error sufficiently small. An illustrative numerical example is provided to demonstrate the efficacy of the proposed approach.

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References

Zhang, W. , Branicky, M. S. , and Phillips, S. M. , 2001, “ Stability of Networked Control Systems,” IEEE Control Syst. Mag., 21(1), pp. 84–99. [CrossRef]
Tipsuwan, Y. , and Chow, M.-Y. , 2003, “ Control Methodologies in Networked Control Systems,” Control Eng. Pract., 11(10), pp. 1099–1111. [CrossRef]
Hespanha, J. P. , Naghshtabrizi, P. , and Xu, Y. , 2007, “ A Survey of Recent Results in Networked Control Systems,” Proc. IEEE, 95(1), pp. 138–162. [CrossRef]
Wang, F.-Y. , and Liu, D. , 2008, Networked Control Systems, Springer, New York.
Bemporad, A. , Heemels, M. , and Johansson, M. , 2010, Networked Control Systems, Springer, New York.
Zhou, K. , and Doyle, J. C. , 1998, Essentials of Robust Control, Prentice Hall, Upper Saddle River, NJ.
Dullerud, G. , and Paganini, F. , 2000, Course in Robust Control Theory, Springer-Verlag, New York.
Ioannou, P. A. , and Sun, J. , 2012, Robust Adaptive Control, Courier Corporation, North Chelmsford, MA.
Narendra, K. S. , and Annaswamy, A. M. , 2012, Stable Adaptive Systems, Courier Corporation, North Chelmsford, MA.
Åström, K. J. , and Wittenmark, B. , 2013, Adaptive Control, Courier Corporation, North Chelmsford, MA.
Yucelen, T. , and Haddad, W. M. , 2012, “ A Robust Adaptive Control Architecture for Disturbance Rejection and Uncertainty Suppression With L∞ Transient and Steady-State Performance Guarantees,” Int. J. Adapt. Control Signal Process., 26(11), pp. 1024–1055. [CrossRef]
Yucelen, T. , and Johnson, E. , 2013, “ A New Command Governor Architecture for Transient Response Shaping,” Int. J. Adapt. Control Signal Process., 27(12), pp. 1065–1085. [CrossRef]
Sahoo, A. , Xu, H. , and Jagannathan, S. , 2013, “ Neural Network-Based Adaptive Event-Triggered Control of Nonlinear Continuous-Time Systems,” IEEE International Symposium on Intelligent Control (ISIC), Hyderabad, India, Aug. 28–30, pp. 35–40.
Sahoo, A., Xu, H., and Jagannathan, S., 2014, “ Neural Network Approximation-Based Event-Triggered Control of Uncertain Mimo Nonlinear Discrete Time Systems,” IEEE American Control Conference, June 4–6, pp. 2017–2022.
Wang, X. , and Hovakimyan, N. , 2010, “ L1 Adaptive Control of Event-Triggered Networked Systems,” IEEE American Control Conference (ACC), Baltimore, MD, June 30–July 2, pp. 2458–2463.
Wang, X. , Kharisov, E. , and Hovakimyan, N. , 2015, “ Real-Time Adaptive Control for Uncertain Networked Control Systems,” IEEE Trans. Autom. Control, 60(9), pp. 2500–2505. [CrossRef]
Yucelen, T. , and Calise, A. J. , 2011, “ Derivative-Free Model Reference Adaptive Control,” J. Guid., Control, Dyn., 34(4), pp. 933–950. [CrossRef]
Tabuada, P. , 2007, “ Event-Triggered Real-Time Scheduling of Stabilizing Control Tasks,” IEEE Trans. Autom. Control, 52(9), pp. 1680–1685. [CrossRef]
Mazo, M., Jr. , and Tabuada, P. , 2008, “ On Event-Triggered and Self-Triggered Control Over Sensor/Actuator Networks,” IEEE Conference on Decision and Control (CDC), Cancun, Mexico, Dec. 9–11, pp. 435–440.
Mazo, M., Jr. , Anta, A. , and Tabuada, P. , 2009, “ On Self-Triggered Control for Linear Systems: Guarantees and Complexity,” IEEE European Control Conference (ECC), Budapest, Hungary, Aug. 23–26, pp. 3767–3772.
Lunze, J. , and Lehmann, D. , 2010, “ A State-Feedback Approach to Event-Based Control,” Automatica, 46(1), pp. 211–215. [CrossRef]
Postoyan, R. , Anta, A. , Nesic, D. , and Tabuada, P. , 2011, “ A Unifying Lyapunov-Based Framework for the Event-Triggered Control of Nonlinear Systems,” IEEE Conference on Decision and Control and European Control Conference (CDC-ECC), Orlando, FL, Dec. 12–15, pp. 2559–2564.
Heemels, W. , Johansson, K. H. , and Tabuada, P. , 2012, “ An Introduction to Event-Triggered and Self-Triggered Control,” IEEE 51st Annual Conference on Decision and Control (CDC), Maui, HI, Dec. 10–13, pp. 3270–3285.
Li, H. , and Shi, Y. , 2014, “ Event-Triggered Robust Model Predictive Control of Continuous-Time Nonlinear Systems,” Automatica, 50(5), pp. 1507–1513. [CrossRef]
Shi, D. , Chen, T. , and Shi, L. , 2014, “ An Event-Triggered Approach to State Estimation With Multiple Point-and Set-Valued Measurements,” Automatica, 50(6), pp. 1641–1648. [CrossRef]
Lavretsky, E. , Gadient, R. , and Gregory, I. M. , 2010, “ Predictor-Based Model Reference Adaptive Control,” J. Guid. Control Dyn., 33(4), pp. 1195–1201. [CrossRef]
Muse, J. A. , and Calise, A. J. , 2010, “ H∞ Adaptive Flight Control of the Generic Transport Model,” AIAA Paper No. 2010-3323.
Stepanyan, V. , and Krishnakumar, K. , 2010, “ MRAC Revisited: Guaranteed Performance With Reference Model Modification,” IEEE American Control Conference (ACC), Baltimore, MD, June 30–July 2, pp. 93–98.
Stepanyan, V., and Krishnakumar, K., 2011, “ M-MRAC for Nonlinear Systems With Bounded Disturbances,” 50th IEEE Conference on Decision and Control and European Control Conference, (CDC-ECC), Orlando, FL, Dec. 12–15, pp. 5419–5424.
Gibson, T. E. , Annaswamy, A. M. , and Lavretsky, E. , 2012, “ Improved Transient Response in Adaptive Control Using Projection Algorithms and Closed Loop Reference Models,” AIAA Paper No. 2012-4775.
Yucelen, T. , De La Torre, G. , and Johnson, E. N. , 2014, “ Improving Transient Performance of Adaptive Control Architectures Using Frequency-Limited System Error Dynamics,” Int. J. Control, 87(11), pp. 2383–2397.
Gibson, T. E. , Annaswamy, A. M. , and Lavretsky, E. , 2012, “ Adaptive Systems With Closed-Loop Reference Models: Stability, Robustness and Transient Performance,” e-print arXiv: 1201.4897.
Lavretsky, E. , and Wise, K. , 2012, Robust and Adaptive Control: With Aerospace Applications, Springer, New York.
Pomet, J.-B. , and Praly, L. , 1992, “ Adaptive Nonlinear Regulation: Estimation From the Lyapunov Equation,” IEEE Trans. Autom. Control, 37(6), pp. 729–740. [CrossRef]
Haddad, W. M. , and Chellaboina, V. , 2008, Nonlinear Dynamical Systems and Control: A Lyapunov-Based Approach, Princeton University Press, Princeton, NJ.
Bernstein, D. S. , 2009, Matrix Mathematics: Theory, Facts, and Formulas, Princeton University Press, Princeton, NJ.
Khalil, H. K. , 1996, Nonlinear Systems, Prentice Hall, Upper Saddle River, NJ.

Figures

Grahic Jump Location
Fig. 1

Event-triggered adaptive control system

Grahic Jump Location
Fig. 4

Event triggers in Figs. 3(a)3(d) and comparison with a conventional periodic strategy in terms of state and control transmission: (a) State and control event triggers for the cases presented in Figs. 3(a)3(d) and (b) comparison of the proposed event-triggered adaptive control approach in Figs. 3(a)3(d) with a conventional periodic strategy

Grahic Jump Location
Fig. 2

An example showing the effect of user-defined thresholds and the adaptive controller design parameters to the ultimate bound given by Eq. (28): (a) effect of γ∈[1,100] and L∈[0,10] to the ultimate bound given by Eq. (28) for ϵx=1 and ϵu=1, where the arrow indicates the direction γ is increased (dashed line denotes the case with γ = 100), (b) effect of ϵx∈[0,1.5] to the ultimate bound given by Eq. (28) for ϵu=1, L∈[0,10], and γ = 100, where the arrow indicates the direction ϵx is increased (dashed line denotes that case with ϵx=1), and (c) effect of ϵu∈[0,3] to the ultimate bound given by Eq. (28) for ϵx=1, L∈[0,10], and γ = 100, where the arrow indicates the direction ϵu is increased (dashed line denotes that case with ϵu=1)

Grahic Jump Location
Fig. 3

Command following performance for the proposed event-triggered adaptive control approach: (a) ϵx=0.1, ϵu=0.1, γ=2.5, and L = 0, (b) ϵx=0.1, ϵu=0.1, γ=2.5, and L=5I, (c) ϵx=0.1, ϵu=0.1, γ = 20, and L=5I, and (d) ϵx=0.1, ϵu=0.1, γ = 40, and L=5I

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