×

Interval observer design for LPV systems with parametric uncertainty. (English) Zbl 1331.93033

Summary: Observer design for dynamical systems with both known and unknown time-varying parameters is of significant interest in a number of real-world applications. This class of systems has been rarely addressed in the existing literature. This paper develops an interval observer design methodology for Linear Parameter Varying (LPV) systems with parametric uncertainty. With information on upper and lower bounds of the uncertain parameters, an interval observer that produces an envelope covering all possible state trajectories is presented. The application of the proposed algorithm in an important vehicle state estimation problem which aims at minimizing the worst-case envelope of the side-slip-angle estimate in the presence of uncertain tire cornering stiffness parameters and varying vehicle speed is presented. The obtained observer is evaluated in simulation using CarSim, a commercial industry-standard vehicle simulation software. The results verify the value of the developed observer design method.

MSC:

93B07 Observability
93E10 Estimation and detection in stochastic control theory
93C05 Linear systems in control theory

Software:

Carsim
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Bernard, O.; Moisan, M.; Gouze, J. L., Near optimal interval observers bundle for uncertain bioreactors, Automatica, 45, 1, 291-295 (2009) · Zbl 1154.93321
[2] Chebotarev, S.; Efimov, D.; Raissi, T.; Zolghadri, A., Interval state observer for nonlinear time varying systems, Automatica, 49, 1, 200-205 (2013) · Zbl 1258.93032
[4] Efimov, D.; Raissi, T.; Zolghadri, A., Interval state estimation for a class of nonlinear systems, IEEE Transactions on Automatic Control, 57, 1, 260-265 (2012) · Zbl 1369.93074
[5] Farina, L.; Rinaldi, S., Positive linear systems: theory and applications (2000), Wiley: Wiley New York, USA · Zbl 0988.93002
[6] Feron, E.; Boyd, S. P.; El Ghaoui, L.; Balakrishanl, V., Linear matrix inequalities in systems and control theory (1994), SIAM: SIAM Philadelphia, PA, USA
[7] Gao, H.; Du, B.; Shu, Z.; Lam, J.; Wu, L., Positive observers and dynamic output-feedback controllers for interval positive linear systems, IEEE Transactions on Circuits and Systems-I, 55, 10, 3209-3222 (2008)
[8] Mazenc, F.; Bernard, O., Interval observers for linear time-invariant systems with disturbances, Automatica, 47, 1, 140-147 (2011) · Zbl 1209.93024
[9] Mohammadpour, J.; Scherer, C. W., Control of linear parameter varying systems with applications (2012), Springer: Springer New York, USA
[10] Moisan, M.; Bernard, O., Robust interval observers for global Lipschitz uncertain chaotic systems, Systems & Control Letters, 59, 11, 687-694 (2010) · Zbl 1216.34050
[11] Nash, S. G.; Griva, I.; Sofer, A., Linear and nonlinear optimization (2008), SIAM: SIAM Philadelphia, PA, USA
[12] Raissi, T.; Efimov, D.; Zolghadri, A., Control of nonlinear and lpv systems: Interval observer-based framework, IEEE Transactions on Automatic Control, 58, 3, 773-778 (2013) · Zbl 1369.93546
[14] Rajamani, R., Vehicle dynamics and control (2012), Springer: Springer New York, USA · Zbl 1268.70002
[15] Rajamani, R.; Phanomchoeng, G.; Piyabongkarn, D., Nonlinear observer for bounded jacobian systems, with applications to automotive slip angle estimation, IEEE Transactions on Automatic Control, 56, 5, 1163-1170 (2011) · Zbl 1368.93055
[16] Raka, S.; Combastel, C., Fault detection based on robust adaptive thresholds: A dynamic interval approach, Annual Reviews in Control, 37, 1, 119-128 (2013)
[17] Rapaport, A.; Dochain, D., Interval observers for biochemical processes with uncertain kinetics and inputs, Mathematical Biosciences, 193, 2, 235-253 (2005) · Zbl 1062.92034
[18] Rapaport, A.; Gouze, J. L.; Hadj-Sadok, M. Z., Interval observers for uncertain biological systems, Ecological Modelling, 133, 1-2, 45-56 (2000)
[19] Rugh, W. J.; Shamma, J. S., Research on gain scheduling, Automatica, 36, 10, 1401-1425 (2000) · Zbl 0976.93002
[20] Scherer, C. W.; Weiland, S., Lecture notes DISC course on linear matrix inequalities in control (2005)
[21] Simon, D., Optimal state estimation (2006), John Wiley & Sons: John Wiley & Sons Hoboken, NJ, USA
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.