## Abstract

Does the replacement of the quadratic (H_{2}) predictor by the worst-case (H_{∞}, or cumulative minimax) predictor robustify the predictive control laws? The present work provides a partial answer to this question, positive for the examples considered, representative of three broad classes of systems. The H_{∞} prediction is demonstrated to be a powerful and convenient tool for frequency shaping of the gain of the closed-loop complementary sensitivity function, capable of robustifying the closed loop for systems with different stability properties. The H_{∞}-optimal k-step ahead predictor is derived for an unstable single-input-single-output CARMA model. A BIBO unstable filter for the disturbance rejection is obtained using the internal model principle and included into the closed loop, and the H_{∞} predictor is applied to the combination of this filter with the plant. The sum over a finite horizon of the current and the predicted tracking error and control signal power spectral densities (PSDs) is decomposed into two parts, one induced by the worst-case predicted disturbance and the other - by the known future reference input. A two degrees of freedom algorithm, referred to as the multi-step closed-loop polynomial H_{∞} predictive control law, is obtained that minimizes the peaks of the PSD of the first part and the integral on the unit circle of the PSD of the second. It is demonstrated on several systems that H_{∞} prediction introduces a very intuitive tuning knob in the form of the prediction horizon capable of setting a trade-off between the steady-state disturbance rejection performance in terms of the output error variance and the closed-loop robustness, however the efficacy of the knob strongly depends on the stability properties of the system and its inverse. The trade-off becomes less pronounced or completely disappears when the H_{∞} predictor is replaced by the quadratic one.

Original language | English (US) |
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Pages (from-to) | 1279-1316 |

Number of pages | 38 |

Journal | International Journal of Robust and Nonlinear Control |

Volume | 10 |

Issue number | 15 |

DOIs | |

State | Published - Dec 30 2000 |

## ASJC Scopus subject areas

- Control and Systems Engineering
- Chemical Engineering(all)
- Biomedical Engineering
- Aerospace Engineering
- Mechanical Engineering
- Industrial and Manufacturing Engineering
- Electrical and Electronic Engineering