Parameter Estimation-Based States Reconstruction of Uncertain Linear Systems with Overparameterization and Unknown Additive Perturbations (2308.10289v3)
Abstract: The problem of state reconstruction is considered for uncertain linear time-invariant systems with overparameterization, arbitrary state-space matrices and unknown additive perturbation described by an exosystem. A novel adaptive observer is proposed to solve it, which, unlike known solutions, simultaneously: (i) reconstructs the physical state of the original system rather than the virtual state of its observer canonical form, (ii) ensures exponential convergence of the reconstruction error to zero when the condition of finite excitation is satisfied, (iii) is applicable to systems, in which mentioned perturbation is generated by an exosystem with fully uncertain constant parameters. The proposed solution uses a recently published parametrization of uncertain linear systems with unknown additive perturbations, the dynamic regressor extension and mixing procedure, as well as a method of physical states reconstruction developed by the authors. Detailed analysis for stability and convergence has been provided along with simulation results to validate the theoretical analysis.
- Carroll R., Lindorff D., “An adaptive observer for single-input single-output linear systems,” IEEE Transactions on Automatic Control, vol. 18, no. 5, pp. 428–435, 1973.
- Luders G., Narendra K. S., “An adaptive observer and identifier for a linear system,” IEEE Transactions on Automatic Control, vol. 18, no. 5, pp. 496–499, 1973.
- Bernard P., Andrieu V., Astolfi D., “Observer design for continuous-time dynamical systems,” Annual Reviews in Control, vol. 53, pp. 224–248, 2022.
- Cho Y. M., Rajamani R., “A systematic approach to adaptive observer synthesis for nonlinear systems,” IEEE Transactions on Automatic Control, vol. 42, no. 4, pp. 534–537, 1997.
- Cecilia A., Costa-Castelló R., “Addressing the relative degree restriction in nonlinear adaptive observers: A high-gain observer approach,” Journal of the Franklin Institute, vol. 359, no. 8, pp. 3857–3882, 2022.
- Kreisselmeier G., “Adaptive observers with exponential rate of convergence,” IEEE Transactions on Automatic Control, vol. 22, no. 1, pp. 2–8, 1977.
- Katiyar A., Roy S. B., Bhasin S., “Initial-Excitation-Based Robust Adaptive Observer for MIMO LTI Systems,” IEEE Transactions on Automatic Control, vol. 68, no. 4, pp. 2536–2543, 2022.
- Jenkins B., Annaswamy A. M., Kojic A., “Matrix regressor adaptive observers for battery management systems,” in Proc. IEEE International Symposium on Intelligent Control (ISIC), pp. 707-714, 2015.
- Limoge D. W., Annaswamy A. M., “An adaptive observer design for real-time parameter estimation in lithium-ion batteries,” IEEE Transactions on Automatic Control, vol. 28, no. 2, pp. 505–520, 2018.
- Prokopov B. I., “On design of adaptive observers,” Avtomatika i Telemekhanika, no. 5, pp. 95–100, 1981 (in Russian).
- Pyrkin, A., Bobtsov, A., Ortega, R., Isidori, A., “An adaptive observer for uncertain linear time-varying systems with unknown additive perturbations ,” Automatica, vol. 147, pp. 110677, 2023.
- Glushchenko A., Lastochkin K., “Parameter Estimation-Based Observer for Linear Systems with Polynomial Overparameterization,” in Proc. 31st Mediterranean Conference on Control and Automation (MED), pp.795–799, 2023.
- Glushchenko A., Lastochkin K., “Parameter Estimation-Based Extended Observer for Linear Systems with Polynomial Overparametrization,” arXiv preprint arXiv:2302.13705. pp.1–5, 2023.
- Wang, L., Ortega, R., Bobtsov, A., Guadalupe Romero, J., “Identifiability Implies Robust, Globally Exponentially Convergent On-line Parameter Estimation,” International Journal of Control, 2023.
- Glushchenko A., Lastochkin K., “Supplement to “Parameter Estimation-Based States Reconstruction of Uncertain Linear Systems with Overparameterization and Unknown Additive Perturbations,” arXiv preprint arXiv:2308.10289, pp.1-8, 2023, https://arxiv.org/src/2308.10289v3/anc/supp.pdf.