[Paper Review] Symbolic Models for Networked Control Systems.

Majid Zamani, Manuel Mazo+1 more|arXiv (Cornell University)|Jan 24, 2014

Formal Methods in Verification23 references3 citations

TL;DR

This paper proposes a symbolic modeling framework for networked control systems (NCS) that jointly accounts for communication delays, packet losses, quantization errors, and bandwidth limitations. By constructing abstracted symbolic models, the approach enables the synthesis of controllers that enforce complex temporal logic specifications, such as LTL formulae or infinite-word automata, over NCS with guaranteed correctness under non-ideal network conditions.

ABSTRACT

Abstract. Networked control systems (NCS) are spatially-distributed systems in which communication be-tween sensors, controllers, and actuators is supported by a shared communication network that is subject to variable communication delays, quantization errors, packet losses, limited bandwidth, and other practical non-idealities. This work investigates the problem of constructively deriving symbolic models of NCS by simultaneously considering the mentioned network non-idealities. One can employ the obtained abstracted models to synthesize symbolic controllers enforcing rich specifications over NCS. Examples of such specifi-cations include properties expressed as formulae in linear temporal logic (LTL) or as automata on infinite strings. 1.

Motivation & Objective

• To address the challenge of modeling networked control systems (NCS) under realistic communication constraints such as delays, packet losses, and quantization.
• To develop a unified symbolic abstraction method that simultaneously captures multiple network non-idealities.
• To enable the synthesis of controllers that enforce high-level specifications, including LTL formulae and automata on infinite strings, over NCS.
• To ensure the correctness of synthesized controllers through formal guarantees using the symbolic models.

Proposed method

• The paper constructs finite-state symbolic models of NCS by abstracting continuous dynamics and network-induced uncertainties into discrete transitions.
• It models network non-idealities—such as variable delays, packet losses, and quantization—as bounded disturbances in the system's state evolution.
• The approach uses finite abstractions based on input-to-state stability (ISS) and incremental stability properties to ensure robustness against network-induced uncertainties.
• It formulates the symbolic model as a finite transition system where states represent regions of the continuous state space and transitions represent possible evolutions under network constraints.
• The construction ensures that the symbolic model is a finite approximation of the original NCS with a well-defined simulation relation.
• The resulting symbolic model supports controller synthesis via formal methods, such as game-theoretic or automata-theoretic techniques, for complex specifications.

Experimental results

Research questions

• RQ1 How can symbolic models of NCS be constructed while simultaneously accounting for multiple network non-idealities like delays, packet losses, and quantization?
• RQ2 What conditions ensure that the symbolic model accurately represents the original NCS under such non-idealities?
• RQ3 Can the symbolic model be used to synthesize controllers that enforce rich temporal logic specifications over the NCS?
• RQ4 What formal guarantees can be provided on the correctness of the synthesized controllers when applied to the original NCS?

Key findings

• The proposed symbolic model captures the essential dynamics of NCS while abstracting away continuous state details, enabling formal controller synthesis.
• The method ensures that the symbolic model is a finite abstraction of the original system with a simulation relation, guaranteeing correctness of the controller synthesis.
• The approach supports the synthesis of controllers that enforce specifications expressed in linear temporal logic (LTL) or as automata on infinite strings.
• The framework is robust to multiple network non-idealities, including variable delays, packet losses, and quantization errors, within bounded limits.
• The symbolic model enables the use of formal verification and synthesis techniques on NCS, which are otherwise intractable due to their hybrid and uncertain nature.
• The construction provides a systematic way to derive controllers that are correct-by-design for complex, high-level specifications in networked environments.