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Receding Horizon Robust Control for Nonlinear Systems Based on Linear Differential Inclusion of Neural Networks

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Abstract

In this paper, we present a new receding horizon neural robust control scheme for a class of nonlinear systems based on the linear differential inclusion (LDI) representation of neural networks. First, we propose a linear matrix inequality (LMI) condition on the terminal weighting matrix for a receding horizon neural robust control scheme. This condition guarantees the nonincreasing monotonicity of the saddle point value of the finite horizon dynamic game. We then propose a receding horizon neural robust control scheme for nonlinear systems, which ensures the infinite horizon robust performance and the internal stability of closed-loop systems. Since the proposed control scheme can effectively deal with input and state constraints in an optimization problem, it does not cause the instability problem or give the poor performance associated with the existing neural robust control schemes.

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References

  1. Kwon, W.H., Pearson, A.E.: A modified quadratic cost problem and feedback stabilization of a linear system. IEEE Trans. Autom. Control 22, 838–842 (1977)

    Article  MATH  MathSciNet  Google Scholar 

  2. Kwon, W.H., Pearson, A.E.: On feedback stabilization of time-varying discrete linear systems. IEEE Trans. Autom. Control 23, 479–481 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  3. Kwon, W.H., Bruckstein, A.M., Kailath, T.: Stabilizing state-feedback design via the moving horizon method. Int. J. Control 37, 631–643 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  4. Lee, J.W., Kwon, W.H., Choi, J.H.: On stability of constrained receding horizon control with finite terminal weighting matrix. Automatica 34(12), 1607–1612 (1998)

    Article  MATH  Google Scholar 

  5. Kwon, W.H., Kim, K.B.: On stabilizing receding horizon controls for linear continuous time-invariant systems. IEEE Trans. Autom. Control 45, 1329–1334 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  6. Ahn, C.K., Han, S.H., Kwon, W.H.: \(\mathcal{H}_{\infty}\) finite memory controls for linear discrete-time state-space models. IEEE Trans. Circuits Syst. II 54(2), 97–101 (2007)

    Article  Google Scholar 

  7. Ahn, C.K.: Robustness bound for receding horizon finite memory control: Lyapunov–Krasovskii approach. Int. J. Control 85(7), 942–949 (2012)

    Article  MATH  Google Scholar 

  8. Ahn, C.K., Song, M.K.: New results on stability margins of nonlinear discrete-time receding horizon \(\mathcal{H}_{\infty}\) control. Int. J. Innov. Comput. Inf. Control 9(4), 1703–1714 (2013)

    Google Scholar 

  9. Ahn, C.K.: Takagi–Sugeno fuzzy receding horizon \(\mathcal{H}_{\infty}\) chaotic synchronization and its application to Lorenz system. Nonlinear Anal. Hybrid Syst. 9, 1–8 (2013)

    Article  MathSciNet  Google Scholar 

  10. Ahn, C.K., Lim, M.T.: Model predictive stabilizer for T–S fuzzy recurrent multilayer neural network models with general terminal weighting matrix. Neural Comput. Appl. (2013). doi:10.1007/s00521-013-1381-3

    Google Scholar 

  11. Kwon, W.H., Han, S., Ahn, C.K.: Advances in nonlinear predictive control: a survey on stability and optimality. Int. J. Control. Autom. Syst. 2(1), 15–22 (2004)

    Google Scholar 

  12. Gupta, M.M., Rao, D.H.: Neuro Control Systems. IEEE Press, New York (1994)

    Google Scholar 

  13. Ahn, C.K.: An \(\mathcal{H}_{\infty}\) approach to stability analysis of switched Hopfield neural networks with time-delay. Nonlinear Dyn. 60(4), 703–711 (2010)

    Article  MATH  Google Scholar 

  14. Ahn, C.K.: Passive learning and input-to-state stability of switched Hopfield neural networks with time-delay. Inf. Sci. 180(23), 4582–4594 (2010)

    Article  MATH  Google Scholar 

  15. Chen, F.C., Liu, C.C.: Adaptively controlling nonlinear continuous-time systems using multilayer neural networks. IEEE Trans. Autom. Control 46, 1306–1310 (1994)

    Article  Google Scholar 

  16. Feng, Z., Michel, A.N.: Robustness analysis of a class discrete-time recurrent neural networks under perturbations. IEEE Trans. Circuits Syst. I 46, 1482–1486 (1999)

    Article  MATH  Google Scholar 

  17. Poznyak, A.S., Yu, W., Sanchez, E.N., Perez, J.P.: Stability analysis of dynamic neural control. Expert Syst. Appl. 14, 227–236 (1998)

    Article  Google Scholar 

  18. Suykens, J.A.K., Moor, B.D., Vandewalle, J.: Robust local stability of multilayer recurrent neural networks. IEEE Trans. Neural Netw. 11, 770–774 (2000)

    Article  Google Scholar 

  19. Ahn, C.K.: Delay-dependent state estimation for T-S fuzzy delayed Hopfield neural networks. Nonlinear Dyn. 61(3), 483–489 (2010)

    Article  MATH  Google Scholar 

  20. Limanond, S., Si, J.: Neural-network-based control design: an LMI approach. IEEE Trans. Neural Netw. 9, 1429–1442 (1998)

    Article  Google Scholar 

  21. Tanaka, K.: An approach to stability criteria of neural-network control systems. IEEE Trans. Neural Netw. 6, 629–642 (1996)

    Article  Google Scholar 

  22. Suykens, J.A.K., Vandewalle, J., Moor, B.D.: Artificial Neural Networks for Modeling and Control of Non-linear Systems. Kluwer, Norwell (1996)

    Book  Google Scholar 

  23. Suykens, J.A.K., Vandewalle, J., Moor, B.D.: Lure systems with multilayer perceptron and recurrent neural networks: absolute stability and dissipativity. IEEE Trans. Autom. Control 44, 770–774 (1999)

    Article  MATH  Google Scholar 

  24. Ahn, C.K.: Output feedback \(\mathcal{H}_{\infty}\) synchronization for delayed chaotic neural networks. Nonlinear Dyn. 59(1–2), 319–327 (2010)

    Article  MATH  Google Scholar 

  25. Lin, C.L., Lin, T.Y.: An \(\mathcal{H}_{\infty}\) design approach for neural net-based control schemes. IEEE Trans. Autom. Control 46, 1599–1605 (2001)

    Article  MATH  Google Scholar 

  26. Lin, C.L., Lin, T.Y.: Approach to adaptive neural net-based \(\mathcal{H}_{\infty}\) control design. IEE Proc., Control Theory Appl. 149, 331–342 (2002)

    Article  Google Scholar 

  27. Lin, C.L., Lin, T.Y.: Neural net-based \(\mathcal{H}_{\infty}\) control for a class of nonlinear systems. Neural Process. Lett. 15, 157–177 (2002)

    Article  MATH  Google Scholar 

  28. Boyd, S., Ghaoui, L.E., Feron, E., Balakrishnan, V.: Linear Matrix Inequalities in System and Control Theory vol. 15. SIAM, Philadelphia (1994)

    Book  MATH  Google Scholar 

  29. Passino, K.M., Yurkovich, S.: Fuzzy Control. Addison Wesley/Longman, New York (1995)

    Google Scholar 

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Authors and Affiliations

  1. School of Electrical Engineering, Korea University, 145, Anam-ro, Seongbuk-gu, Seoul, 136-701, Korea

    Choon Ki Ahn

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  1. Choon Ki Ahn
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Correspondence to Choon Ki Ahn.

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Communicated by Jyh-Horng Chou.

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Ahn, C.K. Receding Horizon Robust Control for Nonlinear Systems Based on Linear Differential Inclusion of Neural Networks. J Optim Theory Appl 160, 659–678 (2014). https://doi.org/10.1007/s10957-013-0328-2

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