## Abstract

This research concerns fundamental performance limitations in control of discrete time nonlinear systems. The fundamental limitations are expressed in terms of the average cost of an infinite horizon optimal control problem. The control cost is defined by using a certain Kullback-Leibler divergence metric recently introduced by Todorov [1]. The limitations are obtained via analysis of a linear eigenvalue problem defined only by the open loop dynamics. For a linear time invariant (LTI) system the fundamental limitation is shown to depend upon the unstable eigenvalues, as in the classical Bode formula. For a more general class of nonlinear systems, it is shown that the limitation arise only if the open-loop dynamics are non-ergodic.

Original language | English (US) |
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Title of host publication | 2010 49th IEEE Conference on Decision and Control, CDC 2010 |

Pages | 7063-7068 |

Number of pages | 6 |

DOIs | |

State | Published - 2010 |

Event | 2010 49th IEEE Conference on Decision and Control, CDC 2010 - Atlanta, GA, United States Duration: Dec 15 2010 → Dec 17 2010 |

### Other

Other | 2010 49th IEEE Conference on Decision and Control, CDC 2010 |
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Country | United States |

City | Atlanta, GA |

Period | 12/15/10 → 12/17/10 |

## ASJC Scopus subject areas

- Control and Systems Engineering
- Modeling and Simulation
- Control and Optimization