A Linear Interval Observer for a Class of Linear Systems of Dimension 2n with N Measurements of the State

https://doi.org/10.58571/CNCA.AMCA.2023.035

Resumen: In this paper an interval observer is designed for a continuous-time plant with an even number of states. We assume that the measured output corresponds to half of the states of the plant. The observer is designed in such a way that the estimation error is a linear cooperative system, whose state matrix can be assigned arbitrarily. The observer’s performance is exemplified by numerical simulations of a mechanical system.

¿Cómo citar?

Lopez-Caamal, Fernando; Avilés, Jesús David. A Linear Interval Observer for a Class of Linear Systems of Dimension 2n with N Measurements of the State. Memorias del Congreso Nacional de Control Automático, pp. 272-277, 2023. https://doi.org/10.58571/CNCA.AMCA.2023.035

Palabras clave

Control de Sistemas Lineales; Control Robusto; Control Clásico

• 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. (2018). Dissipative observers for discrete-time nonlinear systems. Journal of the Franklin Institute, 355(13), 5759-5770.
• 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.
• Avilés, J. and Moreno, J. (2009). Cooperative observers for nonlinear systems. Joint 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference, Shanghai, China, 6125-6130.
• 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., Raïssi, T., Chebotarev, S., and Zolghadri, A. (2013b). Interval state observer for nonlinear time varying systems. Automatica, 49(1), 200-205.
• Gouzé, J.L., Rapaport, A., and Hadj-Sadok, M.Z. (2000). Interval observers for uncertain biological systems. Ecol Modelling, 133(1-2), 45-56.
• Gouzé, J.L., Moisan, M., and Bernard, O. (2006). A simple improvement of interval asymptotic observers for biotechnological processes. In Proceedings of the ROCOND 2006 conference”, Toulouse, France.
• Hirsch, M. and Smith, H. (2004). Monotone Dynamical Systems. Handbook of differential equations: ordinary differential equations. Vol. II, Elsevier B. V., Amsterdam 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.
• Mazenc, F. and Bernard, O. (2010). Asymptotically stable interval observers for planar systems with complex poles. IEEE Trans. on Aut. Control, 55, 523-527.
• 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. 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.
• Thabet, R.E.H., Ra¨ıssi, T., Combastel, C., Efimov, D., and Zolghadri, A. (2014). An effective method to interval observer design for time-varying systems. Automatica, 50(10), 2677-2684.
• Zhang, H., Zhao, S., and Gao, Z. (2016). An active disturbance rejection control solution for the two-assspring benchmark problem. In 2016 American Control Conference (ACC), 1566-1571. IEEE.