Symbolic models for nonlinear control systems affected by disturbances

Abstract

In the last few years, there has been a growing interest in the use of symbolic models for the formal verification and control design of purely continuous or hybrid systems. Symbolic models are abstract descriptions of continuous systems where one symbol corresponds to an ‘aggregate’ of continuous states. In this article, we face the problem of deriving symbolic models for nonlinear control systems affected by disturbances. The main contribution of this article is in proposing symbolic models that can be effectively constructed and that approximate nonlinear control systems affected by disturbances in the sense of alternating approximate bisimulation.

Keywords:

• nonlinear control systems affected by disturbances
• symbolic models
• alternating approximate bisimulation
• incremental stability

Acknowledgements

The authors are grateful to Pierdomenico Pepe, Paulo Tabuada and Antoine Girard for fruitful discussions on the topic of this article. The research leading to these results has been partially supported by the Center of Excellence DEWS and received funding from the European Union Seventh Framework Programme [FP7/2007-2013] under grant agreement n. 257462 HYCON2 Network of excellence.

Notes

Notes

1. Note that since V is smooth, one can choose .

2. The symbols , and indicate the maximal quantisation values guaranteeing that Q _ℙ and L _ℙ are non-empty, as formally defined in Section 2.1.