[Paper Review] A Symbolic Approach to the Design of Nonlinear Networked Control Systems

Alessandro Borri, Giordano Pola+1 more|arXiv (Cornell University)|Mar 5, 2012

Petri Nets in System Modeling6 references4 citations

TL;DR

This paper proposes a symbolic control design framework for nonlinear networked control systems (NCS) under non-ideal network conditions such as variable delays, packet losses, and quantization. By constructing finite symbolic models that approximately bisimulate the original NCS under incremental stability, the method enables the synthesis of controllers that satisfy complex specifications expressed as automata on infinite strings, validated via OMNeT++ simulation with guaranteed accuracy.

ABSTRACT

Networked control systems (NCS) are spatially distributed systems where communication among plants, sensors, actuators and controllers occurs in a shared communication network. NCS have been studied for the last ten years and important research results have been obtained. These results are in the area of stability and stabilizability. However, while important, these results must be complemented in different areas to be able to design effective NCS. In this paper we approach the control design of NCS using symbolic (finite) models. Symbolic models are abstract descriptions of continuous systems where one symbol corresponds to an "aggregate" of continuous states. We consider a fairly general multiple-loop network architecture where plants communicate with digital controllers through a shared, non-ideal, communication network characterized by variable sampling and transmission intervals, variable communication delays, quantization errors, packet losses and limited bandwidth. We first derive a procedure to obtain symbolic models that are proven to approximate NCS in the sense of alternating approximate bisimulation. We then use these symbolic models to design symbolic controllers that realize specifications expressed in terms of automata on infinite strings. An example is provided where we address the control design of a pair of nonlinear control systems sharing a common communication network. The closed-loop NCS obtained is validated through the OMNeT++ network simulation framework.

Motivation & Objective

• Address the gap in control design for nonlinear NCS under realistic network non-idealities such as variable delays, packet losses, and quantization.
• Develop symbolic models that approximate nonlinear NCS in the sense of alternating approximate bisimulation, ensuring controller synthesis on the symbolic model transfers to the original system.
• Enable the design of controllers that satisfy complex temporal logic specifications expressed as automata on infinite strings.
• Validate the proposed controller synthesis methodology through simulation in the OMNeT++ framework under realistic network dynamics.
• Overcome limitations of existing stability-focused results by enabling specification-driven design for complex, heterogeneous NCS.

Proposed method

• Construct symbolic models of nonlinear NCS using a finite abstraction technique that captures the system's behavior under variable sampling, transmission delays, quantization, and packet losses.
• Ensure the symbolic models are alternating approximately bisimilar to the original NCS by leveraging the plant's δ-GAS (incremental global asymptotic stability) property.
• Integrate symbolic controller design with symbolic model construction to reduce computational complexity, adapting algorithms from prior work on nonlinear systems.
• Formulate control specifications as transition systems over infinite strings, enabling the use of automata-theoretic synthesis techniques.
• Use the notion of alternating approximate bisimulation to guarantee that any controller synthesized on the symbolic model enforces the desired behavior on the original NCS within a user-defined accuracy.
• Implement and validate the closed-loop system in the OMNeT++ network simulation framework, modeling variable delays via hop counts and stochastic delays per hop.

Experimental results

Research questions

• RQ1 Can symbolic models be constructed for nonlinear NCS that accurately capture the effects of non-ideal network conditions such as variable delays, packet losses, and quantization?
• RQ2 Under what conditions can symbolic controllers synthesized on abstract models guarantee correct behavior on the original NCS?
• RQ3 How can complex control specifications expressed as automata on infinite strings be effectively realized in nonlinear NCS with network-induced uncertainties?
• RQ4 What computational strategies can be employed to reduce the complexity of symbolic controller synthesis for large-scale NCS?
• RQ5 To what extent can the proposed symbolic approach ensure robustness and accuracy in the presence of network non-idealities?

Key findings

• The symbolic models constructed are alternating approximately bisimilar to the original NCS, ensuring that any control strategy synthesized on the symbolic model can be safely applied to the original system with bounded error.
• The method guarantees that if a solution does not exist for the symbolic model, no solution exists for the original NCS, providing soundness and completeness in controller synthesis.
• For a two-loop NCS with nonlinear dynamics, the symbolic controller was synthesized in 2,039 seconds with 25,239 integers of memory, demonstrating feasibility despite large model sizes.
• OMNeT++ simulations confirmed that the closed-loop system met the specified trajectory tracking behaviors under a particular realization of network uncertainties, including variable delays and packet losses.
• The approach ensures arbitrarily small approximation error by tuning the model resolution, with the δ-GAS assumption enabling robustness guarantees.
• The integration of symbolic model construction with controller design significantly reduced computational complexity compared to a monolithic approach, enabling practical deployment.