Approximately bisimilar symbolic models for nonlinear control systems

By Giordano Pola, Antoine Girard, Paulo Tabuada. at - Automatisierungstechnik, 2007

314 citations recorded by the source corpus.

Control systems are usually modeled by differential equations describing how physical phenomena can be influenced by certain control parameters or inputs. Although these models are very powerful when dealing with physical phenomena, they are less suited to describe software and hardware interfacing with the physical world. For this reason there is a growing interest in describing control systems through symbolic models that are abstract descriptions of the continuous dynamics, where each ''symbol'' corresponds to an ''aggregate'' of states in the continuous model. Since these symbolic models are of the same nature of the models used in computer science to describe software and hardware, they provide a unified language to study problems of control in which software and hardware interact with the physical world. Furthermore, the use of symbolic models enables one to leverage techniques from supervisory control and algorithms from game theory for controller synthesis purposes. In this paper we show that every incrementally globally asymptotically stable nonlinear control system is approximately equivalent (bisimilar) to a symbolic model. The approximation error is a design parameter in the construction of the symbolic model and can be rendered as small as desired. Furthermore, if the state space of the control system is bounded, the obtained symbolic model is finite. For digital control systems, and under the stronger assumption of incremental input-to-state stability, symbolic models can be constructed through a suitable quantization of the inputs.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Hardware and Architecture

View Paper: https://www.semanticscholar.org/paper/71057587b50aa9279e63294a36e7cdfd1b57516b

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

In Control and Systems Engineering

In Hardware and Architecture

Citations in the corpus

Review on cyber-physical systems (2017, background): “Reference [55] put forward that, for any differential equation model that describes the physical system, when the assumption of specific stability holds true, an approximate equivalent finite state abstraction can be constructed.”
Temporal-Logic-Based Reactive Mission and Motion Planning (2009, background): “Results, such as the work reported in [22] and [23], where nonlinear dy-”
Cyber–Physical Systems: A Perspective at the Centennial (2012, methodology): “[113], then it is δ-approximately bisimilar [114] to a symbolic model of the original continuous system that can be con-”