Finite-time state observation for non-linear uncertain systems via higher-order sliding modes

Abstract

This article deals with the problem of finite-time state estimation for a class of non-linear systems possibly affected by modelling uncertainties and/or unknown inputs. The proposed method, based on the high-order sliding mode control approach, does not require the system to be transformed to any normal form, which can be difficult to achieve in the presence of model uncertainties. The sufficient conditions for observability are derived in terms of certain geometric restrictions imposed on the system's vector fields. Methods for the approximate and exact reconstruction of the unknown inputs are given and simulation results are provided and commented.

Keywords:

• high-order sliding modes
• non-linear observers
• uncertain systems

Acknowledgements

This work was supported in part by Mexican CONACyT (Consejo Nacional de Ciencia y Tecnologia), grant no. 56819, Programa de Apoyo a Proyectos de Investigacion e Innovacion Tecnolgica (PAPIIT) UNAM, grant no. 111206, Programa de Apoyo a Proyectos Institucionales para el Mejoramiento de la Ensenanza (PAPIME), UNAM, grant PE100907, S.R.E. Programa Ejecutivo de Cooperacion Mexico–Italia 2007–2009, DGSCA-DTD-PASPA, Italian MUR Project 930 ‘Real-time Simulation and Control of Combined-Cycle Power Plants’ and by EU 7th FWP, grant no. 224233-PRODI.