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An Adaptive Suboptimal Control Algorithm with Variable Design Parameter for Systems with Stochastic Parameters

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Abstract

A suboptimal dual controller is presented for a class of linear systems with unknown and randomly varying parameters. This work concerns a refinement of an existent suboptimal dual controller for discrete-time systems. The loss function that is minimized contains two parts. The first part is the variance of the output one step ahead of time, and the second part is a function of the covariance matrix of the parameter estimates. The idea is to add simple terms depending on the covariance matrix of the parameter estimates two steps ahead. An algorithm is used for the adaptive adjustment of the adjustable parameter lambda, for each step of the way. The behavior of the proposed controller is evaluated through a Monte Carlo simulations method by three examples.

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References

  • Åström, K., & Wittenmark, B. (1971). Problems of identification and control. Journal of Mathematical Analysis and Applications, 34(1), 90–113.

  • Åström, K., & Wittenmark, B. (2013). Adaptive control (2nd ed.). New York, USA: Dover Publications Inc.

    Google Scholar 

  • Bar-Shalom, Y., & Wall, K. (1980). Dual adaptive control and uncertainty effects in macroeconomic systems optimization. Automatica, 16(2), 147–156.

    Article  MATH  Google Scholar 

  • Feldbaum, A.A. (1960–1961). Dual Control theory, I–IV. Automation Remote Control, 21–22, 874–880, 1033–1039.

  • Filatov, N., & Unbehauen, H. (2000). Survey of adaptive dual control methods. IEE Proceedings on Control theory and applications, 147, 118–128.

  • Flidr, M., & Simandl, M. (2013). Implicit dual controller based on stochastic integration rule. In: Control conference (ECC), 2013 European, pp. 896–901.

  • Hughes, D., & Jacobs, O. (1974). Turn-off, escape and probing in non-linear stochastic control. Preprint IFAC symposium on stochastic control.

  • Ishihara, T., Abe, K., & Takeda, H. (1988). Extensions of innovations dual control. International Journal of Systems Science, 19(4), 653–667.

  • Ismail, A., Dumont, G., & Backstrom, J. (2003). Dual adaptive control of paper coating. IEEE Transactions on Control systems technology, 11, 289–309.

  • Kral, L., & Simandl, M. (2011). Predictive dual control for nonlinear stochastic systems modelled by neural networks. In: Control automation (MED), 2011 19th mediterranean conference on, pp 1277–1282.

  • Kumar, P. R., & Varaiya, P. (1986). Stochastic systems: Estimation, identification and adaptive control. Upper Saddle River, NJ, USA: Prentice-Hall, Inc.

    MATH  Google Scholar 

  • Lee, J. M., & Lee, J. H. (2009). An approximate dynamic programming based approach to dual adaptive control. Journal of Process Control, 19(5), 859–864.

    Article  MATH  Google Scholar 

  • Lindoff, B., Holst, J., & Wittenmark, B. (1999). Analysis of approximations of dual control. International Journal of Adaptive Control and Signal Processing, 13, 593–620.

  • Maitelli, A., & Yoneyama, T. (1994). A two-stage dual suboptimal controller for stochastic systems using approximate moments. Automatica, 30, 1949–1954.

  • Maitelli, A., & Yoneyama, T. (1999). A multistage suboptimal dual controller using optimal predictors. IEEE Transactions on Automatic Control, 44(5), 1002–1008.

  • Milito, R., Padilla, R., & Cadorin, D. (1982). An innovations approach to dual control. IEEE Transactions on Automatic Control, 27(1), 133–137.

  • Wittenmark, B. (1975). An active suboptimal dual controller for systems with stochastic parameters. Automatic Control Theory and Application, 3(1), 13–19.

  • Wittenmark, B., & Elevitch, C. (1985). An adaptive control algorithm with dual features. In Proceedings of the 7th IFAC/IFORS Symposium on Identification and Systems Parameter Estimation (pp. 587–592).

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Authors and Affiliations

  1. Programa de pós-graduação em engenharia elétrica e de computação - ppgeec, Universidade Federal do Rio Grande do Norte (UFRN), Campus Universitário Lagoa Nova, Natal, Rio Grande do Norte, 59072970, Brasil

    Aderson Jamier Santos Reis

  2. Departamento de Engenharia de Computação e Automação, Centro de Tecnologia, Universidade Federal do Rio Grande do Norte (UFRN), Av. Senador Salgado Filho s/n - Campus Universitário Lagoa Nova, Natal, RN, 59072970, Brasil

    André Laurindo Maitelli

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  1. Aderson Jamier Santos Reis
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  2. André Laurindo Maitelli
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Correspondence to Aderson Jamier Santos Reis.

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Reis, A.J.S., Maitelli, A.L. An Adaptive Suboptimal Control Algorithm with Variable Design Parameter for Systems with Stochastic Parameters. J Control Autom Electr Syst 26, 215–224 (2015). https://doi.org/10.1007/s40313-015-0176-4

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  • DOI: https://doi.org/10.1007/s40313-015-0176-4

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