Top

Intelligent Industrial Systems

Published in:

01-10-2015 | Original Paper

Flatness-Based Adaptive Fuzzy Control of Autonomous Submarines

Authors: G. Rigatos, P. Siano

Published in: Intelligent Industrial Systems | Issue 3/2015

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

The paper proposes adaptive fuzzy control based on differential flatness theory for autonomous submarines. It is proven that the dynamic model of the submarine, having as state variables the vessel’s depth and its pitch angle, is a differentially flat one. This means that all its state variables and its control inputs can be written as differential functions of the flat output and its derivatives. By exploiting differential flatness properties the system’s dynamic model is written in the multivariable linear canonical (Brunovsky) form, for which the design of a state feedback controller becomes possible. After this transformation, the new control inputs of the system contain unknown nonlinear parts, which are identified with the use of neurofuzzy approximators. The learning procedure for these estimators is determined by the requirement the first derivative of the closed-loop’s Lyapunov function to be a negative one. Moreover, the Lyapunov stability analysis shows that H-infinity tracking performance is succeeded for the feedback control loop and this assures improved robustness to the aforementioned model uncertainty as well as to external perturbations. The efficiency of the proposed adaptive fuzzy control scheme is confirmed through simulation experiments.

previous article A New Nonlinear H-infinity Feedback Control Approach to the Problem of Autonomous Robot Navigation

next article A Modified Genetic Algorithm for Optimal Allocation of Capacitor Banks in MV Distribution Networks

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

Available only for authorised users

Do, K.D., Pan, J.: Global tracking control of underactuated ships with nonzero off-diagonal terms in their system matrices. Automatica 41, 87–95 (2005). ElsevierMATHMathSciNet

Sira-Ramirez, H., Aguilar-Ibanez, C.: On the control of the hovercraft system. Dyn. Control 10, 151–163 (2000). SpringerMATHMathSciNetCrossRef

Refsnes, J.B., Sorensen, A.J., Petersen, K.Y.: Model-based output feedback control of slender-body underactuated AUVs: theory and experiments. IEEE Trans. Control Syst. Technol. 16(5), 930–946 (2008)CrossRef

Fischer, N., Hughes, D., Walters, P., Swartz, E.M., Dixon, W.E.: Nonlinear RISE-based control of an autonomous underwater vehicle. IEEE Trans. Robot. 30(4), 845–852 (2014)CrossRef

He, B., Wang, B.R., Yan, T.H., Han, Y.Y.: A distributed parallel motion control for the multithruster autonomous underwater vehicle. Mech Based Des Struct Mach 41(2), 236–257 (2013). Taylor and FrancisCrossRef

Arslan, M.S., Fukushima, N., Hagiwara, J.: Nonlinear optimal control of an AUV and its actuator failure compensation. In: 10th International Conference on Control, Automation, Robotics and Vision, Hanoi, Vietnam (2008)

Fishcer, N., Bhasin, S., Dixon, W.E.: Nonlinear control of an autonomous underwater vehicle: a RISE-based approach. In: 2011 American Control Conference, San Francisco (2011)

Petersen, K.Y., Egeland, O.: Time-varying exponential stabilization of the position and attitude of an underactuated autonomous unerwater vehicle. IEEE Trans. Autom. Control 44(1), 112–115 (1999)CrossRef

Rigatos, G.G.: Sensor fusion-based dynamic positioning of ships using extended Kalman and particle filtering. Robot. Camb. Univ. Press 31(3), 389–403 (2013)MathSciNet

10.

Soltun, R.A., Ashrafiuon, H., Muske, K.R.: ODE-based obstacle avoidance and trajectory planning for unmanned surface vessels. Robotica 29, 691–703 (2010)CrossRef

11.

Lapierre, L., Saetanto, D.: Nonlinear path-following control of an AUV. Ocean Eng. 34, 1734–1744 (2007). ElsevierCrossRef

12.

Lapierre, L.: Robust diving control of an AUV. Ocean Eng. 36, 92–104 (2009). ElsevierCrossRef

13.

Moreira, L., Gueda Soares, C.: H2 and H1 design for diving and course control of an autonomous underwater vehicle in presence of waves. IEEE J. Ocean. Eng. 33(2), 69–88 (2008)CrossRef

14.

Liceaga-Castro, E., van der Molen, G.M.: Submarine H1 depth control under wave disturbances. IEEE Trans. Control Syst. Technol. 3(3), 338–346 (1995)CrossRef

15.

Sira-Ramirez, H.: Dynamic second-order sliding-mode control of the hovercraft vessel. IEEE Trans. Control Syst. Technol. 10(6), 860–865 (2002)CrossRef

16.

Lee, K.W., Singh, S.N.: Multi-input submarine control via L2 adaptive feedback despite uncertainties. J. Syst. Control Eng. 228(5), 330–347 (2014). Sage Publications

17.

Pan, C.Z., Lai, X.Z., Yang, S.X., Wu, M.: An efficient neural network approach to tracking control of an autonomous surface vehicle with unknown dynamics. Expert Syst. Appl. 40, 1629–1635 (2013)CrossRef

18.

Zhang, L.J., Qi, X., Peng, Y.J.: Adaptive output feedback control based on DFRNN for AUV. Ocean Eng. 36, 716–722 (2009). ElsevierCrossRef

19.

Rigatos, G.G., Tzafestas, S.G.: Adaptive fuzzy control for the ship steering problem. J. Mechatron. 16(6), 479–489 (2006). ElsevierCrossRef

20.

Li, H.X., Tong, S.: A hybrid adaptive fuzzy control for a class of nonlinear MIMO systems. IEEE Trans. Fuzzy Syst. 11(1), 24–35 (2003)CrossRef

21.

Song, T., Bin, C., Wang, Y.: Fuzzy adaptive output feedback control for MIMO nonlinear systems. Fuzzy Sets Syst. 156, 285–299 (2005). ElsevierCrossRef

22.

Chen, C.S.: Dynamic structure adaptive neural fuzzy control for MIMO uncertain nonlinear systems. Inf. Sci. 179, 2676–2688 (2009). ElsevierMATHCrossRef

23.

Tong, S., Li, Y.: Observer-based adaptive control for strict feedback nonlinear systems. Fuzzy Sets Syst. 160, 1749–1764 (2009)MATHMathSciNetCrossRef

24.

Chen, C.H., Lin, C.M., Chen, T.Y.: Intelligent adaptive control for MIMO uncertain nonlinear systems. Expert Syst. Appl. 35, 865–877 (2008)CrossRef

25.

Qi, R., Tao, G., Tan, C., Yao, X.: Adaptive control of discrete-time state-space TS fuzzy systems with general relative degree. Fuzzy Sets Syst. 217, 2240 (2013). ElsevierMathSciNetCrossRef

26.

Yang, Y., Zhou, C., Jia, X.: Robust adaptive fuzzy control and its application to ship roll stabilization. Inf. Sci. 142(1–4), 177–194 (2002). ElsevierMATHCrossRef

27.

Yousef, H.A., Hamdy, M., Shafiq, M.: Flatness-based adaptive fuzzy output tracking excitation control for power system generators. J. Frankl. Inst. 350(8), 2334–2353 (2013). ElsevierMATHMathSciNetCrossRef

28.

Rigatos, G.: Nonlinear Control and Filtering Approaches Using Differential Flatness Theory: Applications to Electromechanical Systems. Springer, New York (2015)CrossRef

29.

Rigatos, G.: Modelling and Control for Intelligent Industrial Systems: Adaptive Algorithms in Robotics and Industrial Engineering. Springer, New York (2011)CrossRef

30.

Rigatos, G.: Advanced Models of Neural Networks: Nonlinear Dynamics and Stochasticity of Biological Neurons. Springer, Berlin (2013)

31.

Rudolph, J.: Flatness Based Control of Distributed Parameter Systems, Examples and Computer Exercises from Various Technological Domains. Shaker, Aachen (2003)

32.

Sira-Ramirez, H., Agrawal, S.: Differentially Flat Systems. Marcel Dekker, New York (2004)MATH

33.

Lévine, J.: On necessary and sufficient conditions for differential flatness. Appl. Algebra Eng. Commun. Comput. 22(1), 47–90 (2011). SpringerMATHCrossRef

34.

Fliess, M., Mounier, H.: Tracking control and \(\pi \)-freeness of infinite dimensional linear systems. In: Picci, G., Gilliam, D.S. (eds.) Dynamical Systems, Control, Coding and Computer Vision, vol. 258, pp. 41–68. Birkhauser, Berlin (1999)

35.

Rouchon, P.: Flatness-based control of oscillators. J. Appl. Math. Mech. 85(6), 411–421 (2005). WileyMATHMathSciNet

36.

Martin, Ph., Rouchon, P.: Syst‘emes plats: planification et suivi des trajectoires, Journees XUPS, Ecole des Mines de Paris, Centre Automatique et Syst‘emes, Mai (1999)

37.

Bououden, S., Boutat, D., Zheng, G., Barbot, J.P., Kratz, F.: A triangular canonical form for a class of 0-flat nonlinear systems. Int. J. Control 84(2), 261–269 (2011). Taylor and FrancisMATHMathSciNetCrossRef

38.

Laroche, B., Martin, P., Petit, N.: Commande par platitude: Equations différentielles ordinaires et aux derivées partielles. Ecole Nationale Superieure des Techniques Avancées, Paris (2007)

39.

Rigatos, G.: A differential flatness theory approach to observer-based adaptive fuzzy control of MIMO nonlinear dynamical systems. Nonlinear Dyn. 76(2), 1335–1354 (2014). SpringerMATHMathSciNetCrossRef

40.

Rigatos, G.G., Tzafestas, S.G.: Extended Kalman filtering for fuzzy modelling and multi-sensor fusion. Math. Comput. Model. Dyn. Syst. 13, 251–266 (2007). Taylor & FrancisMATHMathSciNetCrossRef

41.

Basseville, M., Nikiforov, I.: Detection of Abrupt Changes: Theory and Applications. Prentice-Hall, Englewood Cliffs (1993)

42.

Rigatos, G., Zhang, Q.: Fuzzy model validation using the local statistical approach. Fuzzy Sets Syst. 60(7), 882–904 (2009). ElsevierMathSciNetCrossRef

43.

Doyle, J.C., Glover, K., Khargonekar, P.P., Francis, B.A.: State-space solutions to standard H2 and H1 control problems. IEEE Trans. Autom. Control 34, 831–847 (1989)MATHMathSciNetCrossRef

44.

Kurylowicz, A., Jaworska, I., Tzafestas, S.G.: Robust stabilizing control : an overview. In: Tzafestas, S.G. (ed.) Applied Control: Current Trends and Modern Methodologies, pp. 289–324. Marcel Dekker, New York (1993)

45.

Lublin, L., Athans, M.: An experimental comparison of and designs for interferometer testbed, Lectures Notes in Control and Information Sciences: Feedback Control. In: Francis, B., Tannenbaum, A. (eds.) Nonlinear Systems and Complexity, pp. 150–172. Springer, Berlin (1995)

46.

Khalil, H.K.: Nonlinear Systems, 2nd edn. Prentice Hall, Upper Saddle River (1996)

47.

Isidori, A.: Nonlinear Control Systems, 3rd edn. Springer, New York (1995)MATHCrossRef

Title: Flatness-Based Adaptive Fuzzy Control of Autonomous Submarines
Authors: G. Rigatos
P. Siano
Publication date: 01-10-2015
Publisher: Springer Singapore
Published in: Intelligent Industrial Systems / Issue 3/2015
Print ISSN: 2363-6912
Electronic ISSN: 2199-854X
DOI: https://doi.org/10.1007/s40903-015-0025-6

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Other articles of this Issue 3/2015

Preface to Volume 1 Issue No. 3

A Modified Genetic Algorithm for Optimal Allocation of Capacitor Banks in MV Distribution Networks

A New Nonlinear H-infinity Feedback Control Approach to the Problem of Autonomous Robot Navigation

A Novel Operating Strategy for Customer-Side Energy Storages in Presence of Dynamic Electricity Prices

Energy Semantic Network for Building Energy Management

Multi-Agent System Design Principles for Resilient Coordination & Control of Future Power Systems