Lopez-Caamal, Fernando | Universidad de Guanajuato |
Avilés, Jesús David | Universidad Autónoma de Baja California |
https://doi.org/10.58571/CNCA.AMCA.2024.069
Resumen: In this paper we design a reduced order interval observer for the unmeasured variables of a particular class of discrete-time linear system. By ensuring the cooperativity and convergence properties applied to the estimation error, the observer provides an upper and a lower estimate, despite the presence of unknown, bounded inputs and perturbations. The class of systems is composed of systems with 2n states and n linearly independent measurements. A numerical simulation shows applicability of the results.
¿Cómo citar?
Lopez Caamal, F. & Avilés, J.D. (2024). Reduced Order Interval Observer for Linear Discrete-Time Systems with 2n States and N Outputs. Memorias del Congreso Nacional de Control Automático 2024, pp. 405-409. https://doi.org/10.58571/CNCA.AMCA.2024.069
Palabras clave
Reduced Observer, Interval Observer, Linear System, Discrete-Time
Referencias
- Alcaraz-Gonzalez, V., Harmand, J., Rapaport, A., Steyer, J., Gonzalez-Alvarez, V., and Pelayo-Ortiz, C. (2002). Software sensors for highly uncertain wwtps: a new approach based on interval observers. Water Res, 36(2515).
- Angeli, D. and Sontag, D. (2003). Monotone control systems. IEEE Transactions Automatic, 48(10), 1684-1698.
- Avilés, J.D. and Moreno, J.A. (2014). Preserving order observers for nonlinear systems. International Journal of Robust and Nonlinear Control, 24(16), 2153-2178.
- Avilés, J.D. and Moreno, J.A. (2020). Dissipative Interval observer design for discrete-time nonlinear systems. Asian Journal of Control, 22(4), 1422-1436.
- Bernard, O. and Gouze, J. (2004). Closed loop observers bundle for uncertain biotechnological models. Journal of Process Control, 14(3), 765-774.
- Efimov, D., Perruquetti, W., Raïssi, T., and Zolghadri, A. (2013a). Interval observers for time-varying discretetime systems. IEEE Transactions on Automatic Control, 58(12), 3218-3224.
- Efimov, D., Perruquetti, W., Raïssi, T., and Zolghadri, A. (2013b). On interval observer design for time-invariant discrete-time systems. ECC.
- Efimov, D., Raïssi, T., Chebotarev, S., and Zolghadri, A. (2013c). Interval state observer for nonlinear time varying systems. Automatica, 49(1), 200-205.
- Farina, L. and Rinaldi, S. (2000). Positive linear systems: theory and applications. John Wiley & Sons.
- Gouze, J.L., Rapaport, A., and Hadj-Sadok, M.Z. (2000). Interval observers for uncertain biological systems. Ecol Modelling, 133(1-2), 45-56.
- Hirsch, M., Smith, H., et al. (2005). Monotone dynamical systems. Handbook of differential equations: ordinary differential equations, 2, 239-357.
- Khan, A., Xie, W., Zhang, B., and Liu, L.W. (2021). A survey of interval observers design methods and implementation for uncertain systems. Journal of the Franklin Institute, 358(6), 3077{3126.
- López-Caamal, F. and Avilés, J.D. (2023). A linear interval observer for a class of linear systems of dimensión 2n with n measurements of the state.
Mazenc, F., Dinh, T., and Niculescu, S. (2013). Robust interval observers for discrete time systems of luenberger type. ACC, Washington USA, 2484-2489. - Mazenc, F., Dinh, T., and Niculescu, S. (2014). Interval observers for discrete time systems. International Journal of Robust and Nonlinear Control, (17), 2867-2890.
- Mazenc, F. and Bernard, O. (2011). Interval observers for linear time-invariant systems with disturbances. Automatica, 47(1), 140-
- 147.Moisan, M., Bernard, O., and Gouze, J. (2009). Near optimal interval observers bundle for uncertain bioreactors. Automatica, 45, 291-295.