Direct adaptive neural control for affine nonlinear systems

Indrani Kar, Laxmidhar Behera

    Research output: Contribution to journalArticle

    31 Citations (Scopus)

    Abstract

    This paper presents a direct adaptive neural control scheme for a class of affine nonlinear systems which are exactly input–output linearizable by nonlinear state feedback. For single-input–single-output (SISO) systems of the form View the MathML source, the control problem is comprehensively solved when both f(x) and g(x) are unknown. In this case, the control input comprises two terms. One is an adaptive feedback linearization term and the other one is a sliding mode term. The weight update laws for two neural networks, which approximate f(x) and g(x), have been derived to make the closed loop system Lyapunov stable. It is also shown that a similar control approach can be applied for a class of multi-input–multi-output (MIMO) systems whose structure is formulated in this paper. Simulation results for both SISO- and MIMO-type nonlinear systems have been presented to validate the theoretical formulations.
    LanguageEnglish
    Pages756-764
    JournalApplied Soft Computing
    Volume9
    DOIs
    Publication statusPublished - 2009

    Fingerprint

    Nonlinear systems
    Nonlinear feedback
    Feedback linearization
    State feedback
    Closed loop systems
    Neural networks

    Keywords

    • Feedback linearization
    • Adaptive control
    • Neural network
    • Lyapunov stability

    Cite this

    Kar, Indrani ; Behera, Laxmidhar. / Direct adaptive neural control for affine nonlinear systems. In: Applied Soft Computing. 2009 ; Vol. 9. pp. 756-764.
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    abstract = "This paper presents a direct adaptive neural control scheme for a class of affine nonlinear systems which are exactly input–output linearizable by nonlinear state feedback. For single-input–single-output (SISO) systems of the form View the MathML source, the control problem is comprehensively solved when both f(x) and g(x) are unknown. In this case, the control input comprises two terms. One is an adaptive feedback linearization term and the other one is a sliding mode term. The weight update laws for two neural networks, which approximate f(x) and g(x), have been derived to make the closed loop system Lyapunov stable. It is also shown that a similar control approach can be applied for a class of multi-input–multi-output (MIMO) systems whose structure is formulated in this paper. Simulation results for both SISO- and MIMO-type nonlinear systems have been presented to validate the theoretical formulations.",
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    note = "Reference text: [1] M. Krstic, I. Kanellakapoulos, P. Kokotovic, Non Linear and Adaptive control design, John Wiley & Sons, Inc., 1995. [2] S.S. Sastry, A. Isidori, Adaptive control of linearizable systems, IEEE Trans. Autom. Control 34 (11) (1989) 1123–1130. [3] M.M. Polycarpou, M.J. Mears, Stable adaptive tracking of uncertain systems using nonlinearly parameterized on-line approximators, Int. J. Control 70 (3) (1998) 363–384. [4] S. He, K. Reif, R. Unbehauen, A neural approach for control of nonlinear systems with feedback linearization, IEEE Trans. Neural Netw. 9 (6) (1998) 1409–1421. [5] K. Nam, Stabilization of feedback linearizable systems using a radial basis function network and its zero-form, IEEE Trans. Autom. Control 44 (5) (1999) 1026–1031. [6] S. Ge, C. Wang, Direct adaptive nn control of a class of nonlinear systems, IEEE Trans. Neural Netw. 13 (1) (2002) 214–221. [7] R.M. Sanner, J.J.E. Slotine, Gaussian networks for direct adaptive control, IEEE Trans. Neural Netw. 3 (6) (1992) 837–863. [8] J.T. Spooner, K.M. Passino, Stable adaptive control using fuzzy systems and neural networks, IEEE Trans. Fuzzy Syst. 4 (3) (1996) 339–358. [9] J.Y. Choi, J.A. Farrell, Nonlinear adaptive control using networks of piecewise linear approximators, IEEE Trans. Neural Netw. 11 (2) (2000) 390–401. [10] F.L. Lewis, S. Jagannathan, A. Yesildirek, Neural Network Control of Robot Manipulators and Nonlinear Systems, Taylor & Francis, 1999. [11] T. Zang, S.S. Ge, C.C. Hang, Stable adaptive control for a class of nonlinear systems using a modified lyapunov function, IEEE Trans. Autom. Control 45 (1) (2000) 129–132. [12] C. Wang, D.J. Hill, Learning from neural control, IEEE Trans. Neural Netw. 17 (1) (2006) 130–146. [13] P. Prem Kumar, I. Kar, L. Behera, Variable gain controllers for nonlinear systems using T–S fuzzy model, IEEE Trans. SMC 36 (6) (2006) 1442–1449. [14] A. Yesildirek, F.L. Lewis, Feedback linearization using neural networks, Automatica, 31 (11) (1995) 1659–1664. [15] S.D. Senturia, Microsystem Design, Kluwer Academic Publishers, 2001. [16] R. Padhi, N. Unnikrishnan, X. Wang, S.N. Balakrishnan, A single network adaptive critic (SNAC) architecture for optimal control synthesis for a class of nonlinear systems, Neural Netw. 19 (2006) 1648–1660. [17] H. Seraji, Configuration control of redundant manipulators: theory and implementation, IEEE Trans. Robot. Autom. 5 (4) (1989) 472–490.",
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    Direct adaptive neural control for affine nonlinear systems. / Kar, Indrani; Behera, Laxmidhar.

    In: Applied Soft Computing, Vol. 9, 2009, p. 756-764.

    Research output: Contribution to journalArticle

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    AU - Kar, Indrani

    AU - Behera, Laxmidhar

    N1 - Reference text: [1] M. Krstic, I. Kanellakapoulos, P. Kokotovic, Non Linear and Adaptive control design, John Wiley & Sons, Inc., 1995. [2] S.S. Sastry, A. Isidori, Adaptive control of linearizable systems, IEEE Trans. Autom. Control 34 (11) (1989) 1123–1130. [3] M.M. Polycarpou, M.J. Mears, Stable adaptive tracking of uncertain systems using nonlinearly parameterized on-line approximators, Int. J. Control 70 (3) (1998) 363–384. [4] S. He, K. Reif, R. Unbehauen, A neural approach for control of nonlinear systems with feedback linearization, IEEE Trans. Neural Netw. 9 (6) (1998) 1409–1421. [5] K. Nam, Stabilization of feedback linearizable systems using a radial basis function network and its zero-form, IEEE Trans. Autom. Control 44 (5) (1999) 1026–1031. [6] S. Ge, C. Wang, Direct adaptive nn control of a class of nonlinear systems, IEEE Trans. Neural Netw. 13 (1) (2002) 214–221. [7] R.M. Sanner, J.J.E. Slotine, Gaussian networks for direct adaptive control, IEEE Trans. Neural Netw. 3 (6) (1992) 837–863. [8] J.T. Spooner, K.M. Passino, Stable adaptive control using fuzzy systems and neural networks, IEEE Trans. Fuzzy Syst. 4 (3) (1996) 339–358. [9] J.Y. Choi, J.A. Farrell, Nonlinear adaptive control using networks of piecewise linear approximators, IEEE Trans. Neural Netw. 11 (2) (2000) 390–401. [10] F.L. Lewis, S. Jagannathan, A. Yesildirek, Neural Network Control of Robot Manipulators and Nonlinear Systems, Taylor & Francis, 1999. [11] T. Zang, S.S. Ge, C.C. Hang, Stable adaptive control for a class of nonlinear systems using a modified lyapunov function, IEEE Trans. Autom. Control 45 (1) (2000) 129–132. [12] C. Wang, D.J. Hill, Learning from neural control, IEEE Trans. Neural Netw. 17 (1) (2006) 130–146. [13] P. Prem Kumar, I. Kar, L. Behera, Variable gain controllers for nonlinear systems using T–S fuzzy model, IEEE Trans. SMC 36 (6) (2006) 1442–1449. [14] A. Yesildirek, F.L. Lewis, Feedback linearization using neural networks, Automatica, 31 (11) (1995) 1659–1664. [15] S.D. Senturia, Microsystem Design, Kluwer Academic Publishers, 2001. [16] R. Padhi, N. Unnikrishnan, X. Wang, S.N. Balakrishnan, A single network adaptive critic (SNAC) architecture for optimal control synthesis for a class of nonlinear systems, Neural Netw. 19 (2006) 1648–1660. [17] H. Seraji, Configuration control of redundant manipulators: theory and implementation, IEEE Trans. Robot. Autom. 5 (4) (1989) 472–490.

    PY - 2009

    Y1 - 2009

    N2 - This paper presents a direct adaptive neural control scheme for a class of affine nonlinear systems which are exactly input–output linearizable by nonlinear state feedback. For single-input–single-output (SISO) systems of the form View the MathML source, the control problem is comprehensively solved when both f(x) and g(x) are unknown. In this case, the control input comprises two terms. One is an adaptive feedback linearization term and the other one is a sliding mode term. The weight update laws for two neural networks, which approximate f(x) and g(x), have been derived to make the closed loop system Lyapunov stable. It is also shown that a similar control approach can be applied for a class of multi-input–multi-output (MIMO) systems whose structure is formulated in this paper. Simulation results for both SISO- and MIMO-type nonlinear systems have been presented to validate the theoretical formulations.

    AB - This paper presents a direct adaptive neural control scheme for a class of affine nonlinear systems which are exactly input–output linearizable by nonlinear state feedback. For single-input–single-output (SISO) systems of the form View the MathML source, the control problem is comprehensively solved when both f(x) and g(x) are unknown. In this case, the control input comprises two terms. One is an adaptive feedback linearization term and the other one is a sliding mode term. The weight update laws for two neural networks, which approximate f(x) and g(x), have been derived to make the closed loop system Lyapunov stable. It is also shown that a similar control approach can be applied for a class of multi-input–multi-output (MIMO) systems whose structure is formulated in this paper. Simulation results for both SISO- and MIMO-type nonlinear systems have been presented to validate the theoretical formulations.

    KW - Feedback linearization

    KW - Adaptive control

    KW - Neural network

    KW - Lyapunov stability

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