### Abstract

Finding the minimal bit rate needed for state estimation of a dynamical system is a fundamental problem in control theory. In this paper, we present a notion of topological entropy, to lower bound the bit rate needed to estimate the state of a nonlinear dynamical system, with unknown bounded inputs, up to a constant error ϵ. Since the actual value of this entropy is hard to compute in general, we compute an upper bound. We show that as the bound on the input decreases, we recover a previously known bound on estimation entropy - a similar notion of entropy - for nonlinear systems without inputs [10]. For the sake of computing the bound, we present an algorithm that, given sampled and quantized measurements from a trajectory and an input signal up to a time bound T > 0, constructs a function that approximates the trajectory up to an ϵ error up to time T. We show that this algorithm can also be used for state estimation if the input signal can indeed be sensed in addition to the state. Finally, we present an improved bound on entropy for systems with linear inputs.

Original language | English (US) |
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Title of host publication | HSCC 2018 - Proceedings of the 21st International Conference on Hybrid Systems |

Subtitle of host publication | Computation and Control (part of CPS Week) |

Publisher | Association for Computing Machinery, Inc |

Pages | 217-226 |

Number of pages | 10 |

ISBN (Electronic) | 9781450356428 |

DOIs | |

State | Published - Apr 11 2018 |

Event | 21st International Conference on Hybrid Systems: Computation and Control, HSCC 2018 - Porto, Portugal Duration: Apr 11 2018 → Apr 13 2018 |

### Publication series

Name | HSCC 2018 - Proceedings of the 21st International Conference on Hybrid Systems: Computation and Control (part of CPS Week) |
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### Other

Other | 21st International Conference on Hybrid Systems: Computation and Control, HSCC 2018 |
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Country | Portugal |

City | Porto |

Period | 4/11/18 → 4/13/18 |

### Fingerprint

### Keywords

- Bit rates
- Discrepancy functions
- Entropy
- Nonlinear systems
- State estimation

### ASJC Scopus subject areas

- Computer Science Applications
- Electrical and Electronic Engineering
- Control and Systems Engineering
- Computer Networks and Communications

### Cite this

*HSCC 2018 - Proceedings of the 21st International Conference on Hybrid Systems: Computation and Control (part of CPS Week)*(pp. 217-226). (HSCC 2018 - Proceedings of the 21st International Conference on Hybrid Systems: Computation and Control (part of CPS Week)). Association for Computing Machinery, Inc. https://doi.org/10.1145/3178126.3178150