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Stochastic model predictive control using Laguerre function with minimum variance Kalman filter estimation

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Abstract

This paper proposes a stochastic model predictive control using the Laguerre function with optimal Kalman filter state estimation. The controller design uses an ARMAX state-space model, incorporating moving average into the stochastic formulation by a state disturbance matrix in innovation form, which calculates a stochastic term introduced in the control law. Then, reducing the output variance and preserving a better trade-off between the control effort and closed-loop performance. The optimal Kalman filter gain design copes with the minimum variance case, where the Kalman filter weighting matrices are tuned based on the state disturbance matrix and the covariance of estimated states of an ARMAX model. Hildreth’s quadratic programming solves the constrained optimization problem in a stochastic scenario, and it is used with the Laguerre function, simplifying finding the optimal problem in constrained cases. Moreover, we present a highly oscillatory mechanical system, a robotic joint benchmark used for numerical examples, and an experimental test using a circuit representing an under-damped coupled multivariable system with two inputs and two outputs. The proposed strategy results are compared to the Laguerre deterministic MPC approach and the classic MPC approach.

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Notes

  1. http://www.mathworks.com/matlabcentral/fileexchange/50784-daqduino.

  2. https://github.com/tarcioswin/Under-damped-multivariable-system/blob/main/UDMSdata.mat.

  3. https://github.com/tarcioswin/Under-damped-multivariable-system/blob/main/UDMSmodel.mat.

  4. https://github.com/tarcioswin/Under-damped-multivariable-system/blob/main/UDMSgain.mat.

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Acknowledgements

The authors thankfully acknowledge the financial support of the Brazilian National Council for Scientific and Technological Development (CNPq) under Grant 142414/2018-2 and the project 408559/2016-0.

Funding

The research leading to these results received funding from the Brazilian National Council for Scientific and Technological Development (CNPq) under grant Grant 142414/2018-2.

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Authors and Affiliations

  1. Laboratory of Control and Systems, Federal University of Pará, 66075-110, Belém, PA, Brazil

    Tarcisio Carlos F. Pinheiro & Antonio da S. Silveira

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  1. Tarcisio Carlos F. Pinheiro
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  2. Antonio da S. Silveira
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Correspondence to Tarcisio Carlos F. Pinheiro.

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I hereby declare that this manuscript is the results of my independent creation under the reviewers’ comments. Except for the quoted contents, this manuscript does not contain any research achievements that have been published or written by other individuals or groups. I am the only author of this manuscript. The legal responsibility of this statement shall be borne by me.

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Pinheiro, T.C.F., Silveira, A.d.S. Stochastic model predictive control using Laguerre function with minimum variance Kalman filter estimation. Int. J. Dynam. Control 11, 1330–1350 (2023). https://doi.org/10.1007/s40435-022-01029-w

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  • DOI: https://doi.org/10.1007/s40435-022-01029-w

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