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Assessment and Future Directions of Nonlinear Model Predictive ...

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Minimum-Distance Receding-Horizon State Estimation 3570.140.12CRHFRHFPIMDRHF0.1RMSE0.080.060.040.0200 20 40 60 80 100 120 140 160time stepFig. 1. Plots <strong>of</strong> the RMSEs for the considered filtersa reasonable trade<strong>of</strong>f between the performance <strong>and</strong> the computational burden.It is important to point out that the simulation framework considered in thisexample represents a best-case scenario for the CRHF, as the sets W <strong>and</strong> Vare known <strong>and</strong> polytopic, thus ensuring the applicability <strong>of</strong> such an approach, aswell as its numerical tractability. On the contrary, the MDRHF could be appliedregardless <strong>of</strong> the form <strong>of</strong> the sets W <strong>and</strong> V <strong>and</strong>noexactknowledge<strong>of</strong>suchsetsis required.References[1] Aless<strong>and</strong>ri, A., Baglietto, M., <strong>and</strong> Battistelli, G., “Receding-horizon estimationfor discrete-time linear systems,” IEEE Trans. on Automatic Control, 48, pp.473–478, (2003).[2] Aless<strong>and</strong>ri, A., Baglietto, M., <strong>and</strong> Battistelli, G., “Receding-horizon estimationfor switching discrete-time linear systems”, IEEE Trans. on Automatic Control,50, pp. 1736–1748, (2005).[3] Aless<strong>and</strong>ri, A., Baglietto, Parisini, T., <strong>and</strong> Zoppoli, R., “A neural state estimatorwith bounded errors for nonlinear systems,” IEEE Trans. on Automatic Control,44, pp. 2028–2042, (1999).[4] Balluchi, A., Benvenuti, L., Di Benedetto, M.D., <strong>and</strong> Sangiovanni- Vincentelli, A.,“Design <strong>of</strong> observers for hybrid systems,” Hybrid Systems: Computation <strong>and</strong> Control,ser. Lecture Notes in Computer Science, C.J. Tomlin <strong>and</strong> M.R. Greenstreet,Eds., Springer, pp. 76–89, (2002).[5] Bar-Shalom, Y. <strong>and</strong> Li, X., Estimation <strong>and</strong> Tracking, Artech House, Boston-London, 1993.[6] Ferrari-Trecate, G., Mignone, D., <strong>and</strong> Morari, M., “Moving horizon estimation forhybrid systems,” IEEE Trans. on Automatic Control, 47, pp. 1663–1676, (2002).[7] Jazwinski, A.H., “Limited memory optimal filtering,” IEEE Trans. on AutomaticControl, 13, pp. 558–563, (1968).

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