# Compositional Construction of Approximate Abstractions of Interconnected Control Systems

Title | Compositional Construction of Approximate Abstractions of Interconnected Control Systems |

Publication Type | Journal Article |

Year of Publication | 2018 |

Authors | Rungger, Matthias, Zamani, Majid |

Journal | IEEE Transactions on Control of Network Systems |

Volume | 5 |

Pagination | 116—127 |

Date Published | March 2018 |

ISSN | 2325-5870 |

Keywords | Aerospace electronics, Approximate abstractions, Cognition, compositional construction approximate abstraction, compositionality, Concrete, concrete control system, continuous control system, continuous time systems, control system synthesis, controller design process, externally stabilizable subspaces, feedback, interconnected control system, interconnected control systems, interconnected systems, linear control systems, Linear systems, linear temporal logic specification, Lyapunov methods, Lyapunov-like function, nonlinear control systems, pubcrawl, simulation function, simulation functions, stability, temporal logic, Trajectory |

Abstract | We consider a compositional construction of approximate abstractions of interconnected control systems. In our framework, an abstraction acts as a substitute in the controller design process and is itself a continuous control system. The abstraction is related to the concrete control system via a so-called simulation function: a Lyapunov-like function, which is used to establish a quantitative bound between the behavior of the approximate abstraction and the concrete system. In the first part of the paper, we provide a small gain type condition that facilitates the compositional construction of an abstraction of an interconnected control system together with a simulation function from the abstractions and simulation functions of the individual subsystems. In the second part of the paper, we restrict our attention to linear control system and characterize simulation functions in terms of controlled invariant, externally stabilizable subspaces. Based on those characterizations, we propose a particular scheme to construct abstractions for linear control systems. We illustrate the compositional construction of an abstraction on an interconnected system consisting of four linear subsystems. We use the abstraction as a substitute to synthesize a controller to enforce a certain linear temporal logic specification. |

URL | https://ieeexplore.ieee.org/document/7496809 |

DOI | 10.1109/TCNS.2016.2583063 |

Citation Key | rungger_compositional_2018 |

- Aerospace electronics
- Approximate abstractions
- cognition
- compositional construction approximate abstraction
- Compositionality
- Concrete
- concrete control system
- continuous control system
- continuous time systems
- control system synthesis
- controller design process
- externally stabilizable subspaces
- feedback
- interconnected control system
- interconnected control systems
- Interconnected Systems
- linear control systems
- Linear systems
- linear temporal logic specification
- Lyapunov methods
- Lyapunov-like function
- nonlinear control systems
- pubcrawl
- simulation function
- simulation functions
- stability
- Temporal Logic
- Trajectory