Publications

@article{BelHajFrej2020b,

title = {Fractional interval observers and initialization of fractional systems},

author = {Ghazi Bel Haj Frej and Rachid Malti and Mohamed Aoun and Tarek Ra\"{i}ssi},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85073555836\&doi=10.1016%2fj.cnsns.2019.105030\&partnerID=40\&md5=79ed72482fa1874d673190eaeaf76737},

doi = {10.1016/j.cnsns.2019.105030},

year  = {2020},

date = {2020-01-01},

journal = {Communications in Nonlinear Science and Numerical Simulation},

volume = {82},

abstract = {In this paper an interval observer is synthesized for fractional linear systems with additive noise and disturbances. The contribution of system whole past to future output is taken into account as an initialization function. Provided the initialization function is upper and lower bounded, it is shown in this paper that the fractional interval observer (FIO) allows to bound pseudo-state free responses by an upper and a lower trajectory. In case interval observers cannot be synthesized straightforwardly, so as to obtain a stable and non-negative estimation error, it is shown that a change of coordinates allows to overcome this problem. The proposed methodology allows to bound fractional systems trajectories when the whole past is unknown but can be bounded. Finally, a numerical example is given to show the effectiveness of the proposed methods on the initialization of fractional linear systems. © 2019 Elsevier B.V.},

note = {Cited by: 6; All Open Access, Bronze Open Access, Green Open Access},

keywords = {A-stable, Additive noise, Estimation errors, Fractional systems, Free response, Initialization, Interval observers, Linear systems, Non negatives, Numerical methods, Pseudo state},

pubstate = {published},

tppubtype = {article}

}

@article{BelHajFrej2020c,

title = {Fractional interval observers and initialization of fractional systems},

author = {Ghazi Bel Haj Frej and Rachid Malti and Mohamed Aoun and Tarek Ra\"{i}ssi},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85073555836\&doi=10.1016%2fj.cnsns.2019.105030\&partnerID=40\&md5=79ed72482fa1874d673190eaeaf76737},

doi = {10.1016/j.cnsns.2019.105030},

year  = {2020},

date = {2020-01-01},

journal = {Communications in Nonlinear Science and Numerical Simulation},

volume = {82},

abstract = {In this paper an interval observer is synthesized for fractional linear systems with additive noise and disturbances. The contribution of system whole past to future output is taken into account as an initialization function. Provided the initialization function is upper and lower bounded, it is shown in this paper that the fractional interval observer (FIO) allows to bound pseudo-state free responses by an upper and a lower trajectory. In case interval observers cannot be synthesized straightforwardly, so as to obtain a stable and non-negative estimation error, it is shown that a change of coordinates allows to overcome this problem. The proposed methodology allows to bound fractional systems trajectories when the whole past is unknown but can be bounded. Finally, a numerical example is given to show the effectiveness of the proposed methods on the initialization of fractional linear systems. © 2019 Elsevier B.V.},

note = {Cited by: 6; All Open Access, Bronze Open Access, Green Open Access},

keywords = {A-stable, Additive noise, Estimation errors, Fractional systems, Free response, Initialization, Interval observers, Linear systems, Non negatives, Numerical methods, Pseudo state},

pubstate = {published},

tppubtype = {article}

}

@article{Ra\"{i}ssi201797b,

title = {On robust pseudo state estimation of fractional order systems},

author = {Tarek Ra\"{i}ssi and Mohamed Aoun},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85017515441\&doi=10.1007%2f978-3-319-54211-9_8\&partnerID=40\&md5=1e73802a102fb9e5603ca4bcffa4ef46},

doi = {10.1007/978-3-319-54211-9_8},

year  = {2017},

date = {2017-01-01},

journal = {Lecture Notes in Control and Information Sciences},

volume = {471},

pages = {97 \textendash 111},

abstract = {The goal of this chapter is to design robust observers for fractional dynamic continuous-time linear systems described by pseudo state space representation. The fractional observer is guaranteed to compute a domain enclosing all the system pseudo states that are consistent with the model, the disturbances and the measurement noise realizations. Uncertainties on the initial pseudo state and noises are propagated in a reliable way to estimate the bounds of the fractional pseudo state. Only the bounds of the uncertainties are used and no additional assumptions about their stationarity or ergodicity are taken into account. A fractional observer is firstly built for a particular case where the estimation error can be designed to be positive. Then, the general case is investigated through changes of coordinates. Some numerical simulations illustrate the proposed methodology. © Springer International Publishing AG 2017.},

note = {Cited by: 3},

keywords = {Continuous time systems, Continuous-time linear systems, Estimation errors, Fractional dynamics, Fractional systems, Fractional-order systems, Interval observers, Linear systems, Measurement Noise, Robust estimation, State estimation, State space methods, Uncertainty analysis},

pubstate = {published},

tppubtype = {article}

}

@article{Ra\"{i}ssi201797,

title = {On robust pseudo state estimation of fractional order systems},

author = {Tarek Ra\"{i}ssi and Mohamed Aoun},

url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85017515441\&doi=10.1007%2f978-3-319-54211-9_8\&partnerID=40\&md5=1e73802a102fb9e5603ca4bcffa4ef46},

doi = {10.1007/978-3-319-54211-9_8},

year  = {2017},

date = {2017-01-01},

journal = {Lecture Notes in Control and Information Sciences},

volume = {471},

pages = {97 \textendash 111},

abstract = {The goal of this chapter is to design robust observers for fractional dynamic continuous-time linear systems described by pseudo state space representation. The fractional observer is guaranteed to compute a domain enclosing all the system pseudo states that are consistent with the model, the disturbances and the measurement noise realizations. Uncertainties on the initial pseudo state and noises are propagated in a reliable way to estimate the bounds of the fractional pseudo state. Only the bounds of the uncertainties are used and no additional assumptions about their stationarity or ergodicity are taken into account. A fractional observer is firstly built for a particular case where the estimation error can be designed to be positive. Then, the general case is investigated through changes of coordinates. Some numerical simulations illustrate the proposed methodology. © Springer International Publishing AG 2017.},

note = {Cited by: 3},

keywords = {Continuous time systems, Continuous-time linear systems, Estimation errors, Fractional dynamics, Fractional systems, Fractional-order systems, Interval observers, Linear systems, Measurement Noise, Robust estimation, State estimation, State space methods, Uncertainty analysis},

pubstate = {published},

tppubtype = {article}

}