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**General receding horizon control for linear time-delay systems.**
*(English)*
Zbl 1055.93032

Summary: A general receding horizon control (RHC), or model predictive control (MPC), for time-delay systems is proposed. The proposed RHC is obtained by minimizing a new cost function that includes two terminal weighting terms, which are closely related to the closed-loop stability. The general solution of the proposed RHC is derived using the generalized Riccati method. Furthermore, an explicit solution is obtained for the case where the horizon length is less than or equal to the delay size. A linear matrix inequality (LMI) condition on the terminal weighting matrices is proposed, under which the optimal cost is guaranteed to be monotonically non-increasing. It is shown that the monotonic condition of the optimal cost guarantees closed-loop stability of the RHC. Simulations demonstrate that the proposed RHC effectively stabilizes time-delay systems.

### MSC:

93B51 | Design techniques (robust design, computer-aided design, etc.) |

93C23 | Control/observation systems governed by functional-differential equations |

15A39 | Linear inequalities of matrices |

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\textit{W. H. Kwon} et al., Automatica 40, No. 9, 1603--1611 (2004; Zbl 1055.93032)

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### References:

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