## Abstract

The problem of finite-horizon H_{∞} tracking for linear continuous time-invariant systems with stochastic parameter uncertainties is investigated for both, the state-feedback and the output-feedback control problems. We consider three tracking patterns depending on the nature of the reference signal i.e. whether it is perfectly known in advance, measured on line or previewed in a fixed time-interval ahead. The stochastic uncertainties appear in both the dynamic and measurement matrices of the system. In the state-feedback case, for each of the above three cases a game theory approach is applied where, given a specific reference signal, the controller plays against nature which chooses the initial condition and the energy-bounded disturbance. The problems are solved using the expected value of the standard performance index over the stochastic parameters, where, in the state-feedback case, necessary and sufficient conditions are found for the existence of a saddle-point equilibrium. The corresponding infinite-horizon time-invariant tracking problem is also solved for the latter case, where a dissipativity approach is considered. The output-feedback control problem is solved as a max-min problem for the three tracking patterns, where necessary and sufficient condition are obtained for the solution. The theory developed is demonstrated by a simple example where we compare our solution with an alternative solution which models the tracking signal as a disturbance.

Original language | English |
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Pages (from-to) | 607-626 |

Number of pages | 20 |

Journal | International Journal of Robust and Nonlinear Control |

Volume | 14 |

Issue number | 7 |

DOIs | |

State | Published - 10 May 2004 |

## Keywords

- Multiplicative
- Preview tracking
- Stochastic H tracking
- Uncertainty

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