Volume 19, Issue 6 (2019)                   Modares Mechanical Engineering 2019, 19(6): 1375-1384 | Back to browse issues page

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Roshanravan S, Shamaghdari S. Tracking Controller Design for Polynomial Nonlinear Systems Using Sum of Squares Optimization and Input to State Stability. Modares Mechanical Engineering. 2019; 19 (6) :1375-1384
URL: http://journals.modares.ac.ir/article-15-20812-en.html
1- Control Department, Electrical Engineering Faculty, Iran University of Science & Technology, Tehran, Iran
2- Control Department, Electrical Engineering Faculty, Iran University of Science & Technology, Tehran, Iran , shamaghdari@iust.ac.ir
Abstract:   (974 Views)
This paper presents a new method to design stabilizing and tracking control laws for a class of nonlinear systems whose state space description is in the form of polynomial functions. This method employs the nonlinear model directly in the controller design process without the need for local about an operating point. The approach is based on the sum of squares (SOS) decomposition of multivariate polynomials which is transformed into a convex optimization problem. It is shown that the design problem can be formulated as a sum of squares optimization problem. This method can guarantee of the nonlinear system with less conservatism than based Also, a sum of squares technique is used to evaluate the stability of closed loop system state with respect to exogenous input. The nonlinear dynamic model of air vehicles can usually be expressed by polynomial nonlinear equations. Therefore, the proposed method can be applied to design an air vehicle autopilot. The hardware in the loop (HIL) simulation is an important test for evaluation of the aerospace control system before flight test. The HIL results using designed controller for a supersonic air vehicle are presented. The results from HIL is compared to the software simulation that the appropriate consistency of results shows the efficiency of the proposed method in the air vehicle autopilot control loop.
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Received: 2018/05/13 | Accepted: 2018/12/23 | Published: 2019/06/1

References
1. Andrieu V, Praly L, Astolfi A. Asymptotic tracking of a reference trajectory by output-feedback for a class of non linear systems. Systems and Control Letters. 2009;58(9):652-663. [Link] [DOI:10.1016/j.sysconle.2009.04.008]
2. Wang Z, Lu R, Wang H. Finite-time trajectory tracking control of a class of nonlinear discrete-time systems. IEEE Transactions on Systems Man and Cybernetics Systems. 2017;47(7):1679-1687. [Link] [DOI:10.1109/TSMC.2017.2663523]
3. Gao YF, Sun XM, Wen Ch, Wang W. Adaptive tracking control for a class of stochastic uncertain nonlinear systems with input saturation. IEEE Transactions on Automatic Control. 2017;62(5):2498-2504. [Link] [DOI:10.1109/TAC.2016.2600340]
4. Yang H, Fan X, Shi P, Hua Ch. Nonlinear control for tracking and obstacle avoidance of a wheeled mobile robot with nonholonomic constraint. IEEE Transactions on Control Systems Technology. 2016;24(2):741-746. [Link]
5. Papachristodoulou A, Prajna S. On the construction of Lyapunov functions using the sum of squares decomposition. Proceedings of the 41st IEEE Conference on Decision and Control, 10-13 December, 2002, Las Vegas, Nevada, USA. Piscataway: IEEE; 2002. [Link] [DOI:10.1109/CDC.2002.1184414]
6. Prajna S, Papachristodoulou A, Wu F. Nonlinear control synthesis by sum of squares optimization: A Lyapunov-based approach. 5th Asian Control Conference, 20-23 July, 2004, Melbourne, Victoria, Australia. Piscataway: IEEE; 2004. [Link]
7. Zhi Y, Zhao G, Yu J. Robust static output feedback for a class of nonlinear uncertain systems. International Conference on Computational and Information Sciences, 21-23 October, 2011, Chengdu, China. Piscataway: IEEE; 2011. [Link] [DOI:10.1109/ICCIS.2011.244]
8. Zakeri H, Antsaklis PJ. Local passivity analysis of nonlinear systems: A sum-of-squares optimization approach. American Control Conference (ACC), 6-8 July, 2016, Boston, Massachusetts, USA. Piscataway: IEEE; 2016. [Link] [DOI:10.1109/ACC.2016.7524923]
9. Slotine JJE, Li W. Applied nonlinear control. Upper Saddle River: Prentice Hall; 1991. [Link]
10. Khalil HK. Noninear systems. 3rd Edition. Upper Saddle River: Prentice Hall; 2002. [Link]
11. Dashkovskiy SN, Efimov DV, Sontag ED. Input to state stability and allied system properties. Automation and Remote Control. 2011;72(8):1579-1614. [Link] [DOI:10.1134/S0005117911080017]
12. Kellett CM, Wirth FR. Nonlinear scaling of (i) ISS-Lyapunov functions. IEEE Transactions on Automatic Control. 2016;61(4):1087-1092. [Link] [DOI:10.1109/TAC.2015.2458471]
13. Sontag ED. Input to state stability: Basic concepts and results. In: Agrachev AA, Stephen Morse A, Sontag ED, Sussmann HJ, Utkin VI. Nonlinear and optimal control theory. Nistri P, Stefani G, editors. Berlin: Springer; 2008. [Link] [DOI:10.1007/978-3-540-77653-6_3]
14. Prajna S, Papachristodoulou A, Parrilo PA. Introducing SOSTOOLS: A general purpose sum of squares programming solver. Proceedings of the 41st IEEE Conference on Decision and Control, 10-13 December, 2002, Las Vegas, Nevada, USA. Piscataway: IEEE; 2002. [Link] [DOI:10.1109/CDC.2002.1184594]
15. Lofberg J. YALMIP: A toolbox for modeling and optimization in MATLAB. International Conference on Robotics and Automation, 2-4 September, 2004, New Orleans, Louisiana, USA. Piscataway: IEEE; 2004. [Link] [DOI:10.1109/CACSD.2004.1393890]
16. Lofberg J. Pre-and post-processing sum-of-squares programs in practice. IEEE Transactions on Automatic Control. 2009;54(5):1007-1011. [Link] [DOI:10.1109/TAC.2009.2017144]
17. Mattei G, Monaco S. Nonlinear autopilot design for an asymmetric missile using robust backstepping control. Journal of Guidance Control and Dynamics. 2014;37(5):1462-1476. [Link] [DOI:10.2514/1.G000434]
18. Haeussermann W. Developments in the field of automatic guidance and control of rockets. Journal of Guidance Control and Dynamics. 1981;4(3):225-239. [Link] [DOI:10.2514/3.19735]
19. Kada B, Ghazzawi Y. Robust PID controller design for an UAV flight control system. Proceedings of the World Congress on Engineering and Computer Science, Vol II, 19-21 October, 2011, San Francisco, USA. Hong Kong: Lecture Notes in Engineering and Computer Science; 2011. [Link]
20. Sato M. Filter design for LPV systems using quadratically parameter-dependent Lyapunov functions. Automatica. 2006;42(11):2017-2023. [Link] [DOI:10.1016/j.automatica.2006.07.001]
21. Shtessel YB, Shkolnikov IA, Levant A. Smooth second-order sliding modes: Missile guidance application. Automatica. 2007;43(8):1470-1476. [Link] [DOI:10.1016/j.automatica.2007.01.008]
22. Yan H, Wang X, Yu B, Ji H. Adaptive integrated guidance and control based on backstepping and input-to-state stability. Asian Journal of Control. 2014;16(2):602-608. [Link] [DOI:10.1002/asjc.682]
23. Li Z, Xia Y, Su CY, Deng J, Fu J, He W. Missile guidance law based on robust model predictive control using neural-network optimization. IEEE Transactions on Neural Networks and Learning Systems. 2015;26(8):1803-1809. [Link] [DOI:10.1109/TNNLS.2014.2345734]
24. Ran M, Wang Q, Hou D, Dong Ch. Backstepping design of missile guidance and control based on adaptive fuzzy sliding mode control. Chinese Journal of Aeronautics. 2014;27(3):634-642. [Link] [DOI:10.1016/j.cja.2014.04.007]
25. Eichblatt EJ. Test and evaluation of the tactical missile. Reston: American Institute of Aeronautics and Astronautics; 1989. [Link]
26. Parrilo PA. Structured semidefinite programs and semialgebraic geometry methods in robustness and optimization [Dissertation]. Pasadena: California Institute of Technology; 2000. [Link]
27. Boyd S, El Ghaoui L, Feron E, Balakrishnan V. Linear matrix inequalities in system and control theory. Philadelphia: SIAM; 1994. [Link] [DOI:10.1137/1.9781611970777]
28. Baillieul J, Samad T. Encyclopedia of systems and control. New York: Springer Publishing Company; 2015. [Link] [DOI:10.1007/978-1-4471-5058-9]
29. Sontag ED, Wang Y. New characterizations of input-to-state stability. IEEE Transactions on Automatic Control. 1996;41(9):1283-1294. [Link] [DOI:10.1109/9.536498]
30. Ichihara H. Sum of squares based input-to-state stability analysis of polynomial nonlinear systems. SICE Journal of Control Measurement and System Integration. 2012;5(4):218-225. [Link] [DOI:10.9746/jcmsi.5.218]
31. Nichols RA, Reichert RT, Rugh WJ. Gain scheduling for H-infinity controllers: A flight control example. IEEE Transactions on Control Systems Technology. 1993;1(2):69-79. [Link] [DOI:10.1109/87.238400]
32. Roshanravan S, Sobhani Gendeshmin B, Shamaghdari S. Design of an actuator fault-tolerant controller for an air vehicle with nonlinear dynamics. Proceedings of the Institution of Mechanical Engineers Part G Journal of Aerospace Engineering. 2018 Sep. [Link] [DOI:10.1177/0954410018801254]
33. Isermann R, Schaffnit J, Sinsel S. Hardware-in-the-loop simulation for the design and testing of engine-control systems. Control Engineering Practice. 1999;7(5):643-653. [Link] [DOI:10.1016/S0967-0661(98)00205-6]

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