# Direct adaptive control of unknown nonlinear systems using a new neuro-fuzzy method together with a novel approach of parameter hopping

Dimitris Theodoridis; Yiannis Boutalis; Manolis Christodoulou

Kybernetika (2009)

- Volume: 45, Issue: 3, page 349-386
- ISSN: 0023-5954

## Access Full Article

top## Abstract

top## How to cite

topTheodoridis, Dimitris, Boutalis, Yiannis, and Christodoulou, Manolis. "Direct adaptive control of unknown nonlinear systems using a new neuro-fuzzy method together with a novel approach of parameter hopping." Kybernetika 45.3 (2009): 349-386. <http://eudml.org/doc/37671>.

@article{Theodoridis2009,

abstract = {The direct adaptive regulation for affine in the control nonlinear dynamical systems possessing unknown nonlinearities, is considered in this paper. The method is based on a new Neuro-Fuzzy Dynamical System definition, which uses the concept of Fuzzy Dynamical Systems (FDS) operating in conjunction with High Order Neural Network Functions (F-HONNFs). Since the plant is considered unknown, we first propose its approximation by a special form of a fuzzy dynamical system (FDS) and in the sequel the fuzzy rules are approximated by appropriate HONNFs. The fuzzy-recurrent high order neural networks (F-RHONN) are used as models of the unknown plant, practically transforming the original unknown system into a F-RHONN model which is of known structure, but contains a number of unknown constant value parameters. The proposed scheme does not require a-priori experts' information on the number and type of input variable membership functions making it less vulnerable to initial design assumptions, is extremely fast and, hence, can be applied in several difficult and very demanding real-time engineering applications. When the F-RHONN model matches the unknown plant, we provide a comprehensive and rigorous analysis of the stability properties of the closed loop system. Convergence of the state to zero plus boundedness of all other signals in the closed loop is guaranteed without the need of parameter (weights) convergence, which is assured only if a sufficiency-of-excitation condition is satisfied. The existence of the control signal is always assured by introducing a novel method of parameter hopping and incorporating it in weight updating law. Simulations illustrate the approximation superiority of the proposed scheme in comparison to other well established approaches. The applicability of the method is also tested on well known simulated nonlinear plants where it is shown that by following the proposed procedure one can obtain asymptotic regulation. Comparison is also made to simple RHONN controllers, showing that our approach is superior to the case of simple RHONN's.},

author = {Theodoridis, Dimitris, Boutalis, Yiannis, Christodoulou, Manolis},

journal = {Kybernetika},

keywords = {Neuro-Fuzzy systems; direct adaptive control; parameter hopping; neuro-fuzzy systems; direct adaptive control; parameter hopping},

language = {eng},

number = {3},

pages = {349-386},

publisher = {Institute of Information Theory and Automation AS CR},

title = {Direct adaptive control of unknown nonlinear systems using a new neuro-fuzzy method together with a novel approach of parameter hopping},

url = {http://eudml.org/doc/37671},

volume = {45},

year = {2009},

}

TY - JOUR

AU - Theodoridis, Dimitris

AU - Boutalis, Yiannis

AU - Christodoulou, Manolis

TI - Direct adaptive control of unknown nonlinear systems using a new neuro-fuzzy method together with a novel approach of parameter hopping

JO - Kybernetika

PY - 2009

PB - Institute of Information Theory and Automation AS CR

VL - 45

IS - 3

SP - 349

EP - 386

AB - The direct adaptive regulation for affine in the control nonlinear dynamical systems possessing unknown nonlinearities, is considered in this paper. The method is based on a new Neuro-Fuzzy Dynamical System definition, which uses the concept of Fuzzy Dynamical Systems (FDS) operating in conjunction with High Order Neural Network Functions (F-HONNFs). Since the plant is considered unknown, we first propose its approximation by a special form of a fuzzy dynamical system (FDS) and in the sequel the fuzzy rules are approximated by appropriate HONNFs. The fuzzy-recurrent high order neural networks (F-RHONN) are used as models of the unknown plant, practically transforming the original unknown system into a F-RHONN model which is of known structure, but contains a number of unknown constant value parameters. The proposed scheme does not require a-priori experts' information on the number and type of input variable membership functions making it less vulnerable to initial design assumptions, is extremely fast and, hence, can be applied in several difficult and very demanding real-time engineering applications. When the F-RHONN model matches the unknown plant, we provide a comprehensive and rigorous analysis of the stability properties of the closed loop system. Convergence of the state to zero plus boundedness of all other signals in the closed loop is guaranteed without the need of parameter (weights) convergence, which is assured only if a sufficiency-of-excitation condition is satisfied. The existence of the control signal is always assured by introducing a novel method of parameter hopping and incorporating it in weight updating law. Simulations illustrate the approximation superiority of the proposed scheme in comparison to other well established approaches. The applicability of the method is also tested on well known simulated nonlinear plants where it is shown that by following the proposed procedure one can obtain asymptotic regulation. Comparison is also made to simple RHONN controllers, showing that our approach is superior to the case of simple RHONN's.

LA - eng

KW - Neuro-Fuzzy systems; direct adaptive control; parameter hopping; neuro-fuzzy systems; direct adaptive control; parameter hopping

UR - http://eudml.org/doc/37671

ER -

## References

top- A new Neuro FDS definition for indirect adaptive control of unknown nonlinear systems using a method of parameter hopping, IEEE Trans. Neural Networks, to appear 2009.
- Adaptively controlling nonlinear continuous time systems using multilayer neural networks, IEEE Trans. Automat. Control 39 (1994), 1306–1310. MR1283714
- Tracking design of uncertain nonlinear SISO systems: Adaptive fuzzy approach, IEEE Trans. Fuzzy Systems 4 (1996), 32–43.
- Radial basis function based adaptive fuzzy systems and their applications to system identification and prediction, Fuzzy Sets and Systems 83 (1996), 325–339. MR1417777
- Building optimal fuzzy dynamical systems description based on recurrent neural network approximation, In: Proc. Internat. Conference of Networked Distributed Systems for Intelligent Sensing and Control, Kalamata 2007.
- Fuzzy model identification based on cluster estimation, J. Intelligent and Fuzzy Systems 2 (1994), 267–284.
- Fuzzy neural networks for direct adaptive control, IEEE Trans. Industrial Electronics 50 (2003), 507–513.
- Adaptive neural/fuzzy control for interpolated nonlinear systems, IEEE Trans. Fuzzy Systems 10 (2002), 583–595.
- Stable indirect fuzzy adaptive control, Fuzzy Sets and Systems 137 (2003), 353–366. MR1987932
- Online adaptive fuzzy neural identification and control of a class of MIMO nonlinear systems, IEEE Trans. Fuzzy Systems 4 (2003), 462–477.
- Fuzzy chaos and recursive partitioning, In: Fuzzy Engineering (B. Kosko, ed.), Prentice-Hall, Englewood Cliffs, N. J. 1997.
- Multilayer feedforward networks are universal approximators, Neural Networks 2 (1989), 359–366.
- Hybrid adaptive fuzzy identification and control of nonlinear systems, IEEE Trans. Fuzzy Systems 10 (2002), 198–210.
- A robust direct adaptive controller, IEEE Trans. Automat. Control AC-31 (1986), 1033–1043.
- Robust adaptive control: A unified approach, Proc. IEEE 79 (1991), 1735–1768.
- Robust Adaptive Control, Prentice-Hall, Englewood Cliffs, N. J. 1996.
- Adaptive control tutorial, SIAM: Advances in Design and Control Series, 2006. MR2278287
- Nonlinear Control System, Third edition. Springer-Verlag, Berlin – Heigelberg – New York 1995.
- Feedback linearization of discrete time system, System Control Lett. 9 (1987), 411–416. MR0917706
- ANFIS: Adaptive-network-based fuzzy inference system, IEEE Trans. Systems Man Cybernet. 23 (1993), 665–684.
- An on-line self-constructing neural fuzzy inference network and its applications, IEEE Trans. Fuzzy Systems 6 (1998), 12–32.
- Singular Perturbation Methods in Control: Analysis and Design, Academic Press, New York 1986. MR0937051
- Structural properties of gradient recurrent high order neural networks, IEEE Trans. Circuits and Systems, Part II, Express Briefs 42 (1995), 592–603.
- Recurrent neural networks for approximation of fuzzy dynamical systems, Internat. J. Intelligent Control and Systems 1 (1996), 223–233. MR1451003
- Adaptive fuzzy control of a class of MIMO nonlinear systems, Fuzzy Sets and Systems 151 (2005), 59–77. MR2116146
- Identification and control of dynamic systems using recurrent fuzzy neural networks, IEEE Trans. Fuzzy Systems 8 (2000), 349–366.
- Control of Electrical Drives, Springer-Verlag, Berlin 1985.
- Observer-based direct adaptive fuzzy-neural control for nonaffine nonlinear systems, IEEE Trans. Neural Networks 16 (2005), 853–861.
- A new approach to rule learning based on fusion of fuzzy logic and neural networks, IEICE Trans. Fuzzy Systems E78-d (1995), 1509–1514.
- A new approach to fuzzy-neural system modelling, IEEE Trans. Fuzzy Systems 3 (1995), 190–197.
- A neural fuzzy control system with structure and parameter learning, Fuzzy Sets and Systems 70 (1995), 183–212. MR1332320
- Observer-based indirect adaptive fuzzy-neural tracking control for nonlinear SISO systems using VSS and ${H}_{1}$ approaches, Fuzzy Sets and Systems 143 (2004), 211–232. MR2052838
- Neuro-fuzzy rule generation: survey in soft computing framework, IEEE Trans. Neural Networks 11 (2000), 748–768.
- Minimum-phase nonlinear discretetime systems and feedback stabilization, In: Proc. IEEE Conference Decision Control, Los Angeles 1987, pp. 979–986.
- Model reference adaptive control with an augmented error signal, IEEE Trans. Automat. Control AC-19 (1974), 474–484. Zbl0288.93022
- An adaptive neuro-fuzzy tracking control for multi-input nonlinear dynamic systems, Automatica, to appear 2008. MR2531811
- Stable Adaptive Systems, Prentice-Hall, Englewood Cliffs, N. J. 1989.
- Identification and control of dynamical systems using neural networks, IEEE Trans. Neural Networks 1 (1990), 4–27.
- Direct adaptive controller for nonaffine nonlinear systems using self-structuring neural networks, IEEE Trans. Neural Networks 16 (2005), 414–422.
- Fuzzy Control, Addison Wesley Longman, 1998.
- Direct adaptive fuzzy control with a self-structuring algorithm, Fuzzy Sets and Systems 159 (2008), 871–899. MR2401936
- Stable adaptive tracking of uncertain systems using nonlinearly parameterized online approximators, Internat. J. Control 70 (1998), 363–384. MR1624485
- Adaptive control of unknown plants using dynamical neural networks, IEEE Trans. Systems Man Cybernet. 24 (1994), 400–412. MR1279490
- Direct adaptive regulation of unknown nonlinear dynamical systems via dynamic neural networks, IEEE Trans. Systems Man Cybernet. 25 (1995), 1578–1594.
- Performance of a neural adaptive tracking controller for multi-input nonlinear dynamical systems in the presence of additive and multiplicative external disturbances, IEEE Trans. Systems Man Cybernet. Part A 30 (2000), 720–730. MR1774160
- Adaptive control with recurrent high order neural networks (Theory and industrial applications), In: Advances in Industrial Control (M. A. Grimble and M. A. Johnson, eds.), Springer Verlag, London Limited 2000.
- Adaptive Control: Stability, Convergence, and Robustness, Prentice-Hall, Englewood Cliffs, N. J. 1989.
- Adaptive control of linearizable systems, IEEE Trans. Automat. Control 34 (1989), 1123–1131. MR1020925
- Applied Nonlinear Control, Prentice-Hall, Englewood Cliffs, N. J. 1991.
- Stable adaptive control using fuzzy systems and neural networks, IEEE Trans. Fuzzy Systems 4 (1996), 339–359.
- Indirect adaptive neuro-fuzzy control based on high order neural network function approximators, In: Proc. 16th Mediterranean Conference on Control and Automation – MED08, Ajaccio 2008, pp. 386–393.
- Adaptive Fuzzy Systems and Control, Prentice Hall, Englewood Cliffs, N. J. 1994.
- Direct adaptive fuzzy-neural control with state observer and supervisory controller for unknown nonlinear dynamical systems, IEEE Trans. Fuzzy Systems 10 (2002), 39–49.
- Dynamic fuzzy neural networks, A novel approach to function approximation. IEEE Trans. Systems, Man Cybernet, Part B 30 (2000), 358–364.
- Feedback control of chaotic systems, Dynamic and Control 4 (1994), 97–114. MR1260105
- Fuzzy neural identification by online clustering with application on crude oil blending, In: Internat. Conference on Fuzzy Systems, Vancouver 2006.

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.