Model reference output feedback tracking for nonlinear systems via LMIs. (English) Zbl 07885486
Summary: This work addresses the tracking problem for nonlinear systems with unmeasured variables. We offer a new design methodology that is composed of a two-degrees-of-freedom scheme. The reference model must track a time-varying signal, and the controller employed can be regarded as one-degree-of-freedom. Then, based on the error between the outputs of the reference model and the plant, another controller is designed to ensure that this mismatch converges to zero. The reference model and the system are described as Takagi-Sugeno (TS) fuzzy models with nonlinear consequences (N-TS), which allows for separating measured from unmeasured variables. An advantage of the proposed scheme is that the controller for the reference model can be carried out using several methodologies from the literature, whereas the controller that governs the output error can be static or dynamic, whose design is based on linear matrix inequalities (LMIs). Two examples are used to illustrate the validity of the developed control methodology and to compare it to another recent approach in the literature.
MSC:
| 93B52 | Feedback control |
| 93C10 | Nonlinear systems in control theory |
| 93C42 | Fuzzy control/observation systems |
Keywords:
nonlinear systems; fuzzy systems; tracking; static and dynamic output feedback; linear matrix inequalities; reference modelReferences:
| [1] | Achour, H., Boukhetala, D., & Labdelaoui, H. (2020). An observer-based robust \(\mathcal{H}_\infty\) controller design for uncertain Takagi-Sugeno fuzzy systems with unknown premise variables using particle swarm optimisation. International Journal of Systems Science, 51(14), 2563-2581. · Zbl 1483.93123 |
| [2] | Adil, A., Hamaz, A., N’Doye, I., Zemouche, A., Laleg-Kirati, T. M., & Bedouhene, F. (2022). On high-gain observer design for nonlinear systems with delayed output measurements. Automatica, 141, Article 110281. · Zbl 1491.93044 |
| [3] | Aguiar, A. P., & Hespanha, J. P. (2007). Trajectory-tracking and path-following of underactuated autonomous vehicles with parametric modeling uncertainty. IEEE Transactions on Automatic Control, 52(8), 1362-1379. · Zbl 1366.93393 |
| [4] | Agulhari, C. M., Oliveira, R. C. L. F., & Peres, P. L. D. (2012). LMI relaxations for reduced-order robust \(\mathcal{H}_\infty\) control of continuous-time uncertain linear systems. IEEE Transactions on Automatic Control, 57(6), 1532-1537. · Zbl 1369.93471 |
| [5] | Andersen, E. D., & Andersen, K. D. (2000). The MOSEK interior point optimizer for linear programming: An implementation of the homogeneous algorithm. In H. Frenk, S. Zhang, K. Roos, & T. Terlaky (Eds.), High performance optimization (pp. 197-232). Springer. · Zbl 1028.90022 |
| [6] | Aouaouda, S., Chadli, M., Khadir, M. T., & Bouarar, T. (2012). Robust fault tolerant tracking controller design for unknown inputs T-S models with unmeasurable premise variables. Journal of Process Control, 22(5), 861-872. |
| [7] | Asemani, M. H., & Majd, V. J. (2014). A robust \(\mathcal{H}_\infty\) Takagi-Sugeno fuzzy systems with unknown premise variables using descriptor redundancy approach. International Journal of Systems Science, 46(16), 2955-2972. · Zbl 1332.93191 |
| [8] | Bouarar, T., Guelton, K., & Manamanni, N. (2013). Robust non-quadratic static output feedback controller design for Takagi-Sugeno systems using descriptor redundancy. Engineering Applications of Artificial Intelligence, 26(2), 739-756. |
| [9] | Boyd, S. P. (1994). Linear matrix inequalities in system and control theory. Society for Industrial and Applied Mathematics. · Zbl 0816.93004 |
| [10] | Byrnes, C. I., & Isidori, A. (2000). Output regulation for nonlinear systems: An overview. International Journal of Robust and Nonlinear Control, 10(5), 323-337. doi:10.1002/ · Zbl 0962.93007 |
| [11] | Chen, M., Xiong, S., & Wu, Q. (2021). Tracking flight control of quadrotor based on disturbance observer. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 51(3), 1414-1423. |
| [12] | Crusius, C., & Trofino, A. (1999). Sufficient LMI conditions for output feedback control problems. IEEE Transactions on Automatic Control, 44(5), 1053-1057. · Zbl 0956.93028 |
| [13] | Esfahani, S. H. (2013). Optimal output feedback \(\mathcal{H}_{\infty } \) -tracking control design for Takagi and Sugeno fuzzy systems with immeasurable premise variables. IET Control Theory & Applications, 7(9), 1300-1308. |
| [14] | Feng, G. (2010). Analysis and synthesis of fuzzy control systems – a model-based approach. CRC Press. · Zbl 1215.93076 |
| [15] | Freeman, R., & Kokotović, P. (1996). Tracking controllers for systems linear in the unmeasured states. Automatica, 32(5), 735-746. · Zbl 0855.93034 |
| [16] | Frezzatto, L., Oliveira, R. C., & Peres, P. L. (2018). \( \mathcal{H}_{\infty }\) and \(\mathcal{H}_2\) memory static output-feedback control design for uncertain discrete-time linear systems. IFAC-PapersOnLine, 51(25), 90-95. |
| [17] | Fu, L., Lam, H. K., Liu, F., Xiao, B., & Zhong, Z. (2022). Static output-feedback tracking control for positive polynomial fuzzy systems. IEEE Transactions on Fuzzy Systems, 30(6), 1722-1733. . |
| [18] | Geromel, J., Peres, P., & Souza, S. (1993). Convex analysis of output feedback structural constraints. In Proceedings of 32nd IEEE Conference on Decision and Control (Vol 2, pp. 1363-1364). Institute of Electrical and Electronics Engineers (IEEE). |
| [19] | Geromel, J., Peres, P., & Souza, S. (1996). Convex analysis of output feedback control problems: Robust stability and performance. IEEE Transactions on Automatic Control, 41(7), 997-1003. · Zbl 0857.93078 |
| [20] | Gong, Q., & Qian, C. (2007). Global practical tracking of a class of nonlinear systems by output feedback. Automatica, 43(1), 184-189. . · Zbl 1140.93380 |
| [21] | Guerra, T. M., Marquez, R., Kruszewski, A., & Bernal, M. (2018). \( \mathcal{H}_\infty\) LMI-based observer design for nonlinear systems via Takagi-Sugeno models with unmeasured premise variables. IEEE Transactions on Fuzzy Systems, 26(3), 1498-1509. |
| [22] | Hu, X., Wu, L., Hu, C., Wang, Z., & Gao, H. (2013). Dynamic output feedback control of a flexible air-breathing hypersonic vehicle via T-S fuzzy approach. International Journal of Systems Science, 45(8), 1740-1756. · Zbl 1290.93077 |
| [23] | Jia, X., Xu, S., Shi, X., & Zhang, Z. (2021). Global practical tracking for nonlinear systems with uncertain dead-zone input via output feedback. Journal of the Franklin Institute, 358(6), 2987-3009. . · Zbl 1464.93025 |
| [24] | Jiang, Z. P., & Kanellakopoulos, I. (2000). Global output-feedback tracking for a benchmark nonlinear system. IEEE Transactions on Automatic Control, 45(5), 1023-1027. . · Zbl 0968.93531 |
| [25] | Kaufman, H., Barkana, I., & Sobel, K. (1998). Direct adaptive control algorithms: Theory and applications. Springer. |
| [26] | Kim, J., & Croft, E. A. (2019). Full-state tracking control for flexible joint robots with singular perturbation techniques. IEEE Transactions on Control Systems Technology, 27(1), 63-73. |
| [27] | Krishnamurthy, P., Khorrami, E., & Jiang, Z. P. (2002). Global output feedback tracking for nonlinear systems in generalized output-feedback canonical form. IEEE Transactions on Automatic Control, 47(5), 814-819. . · Zbl 1364.93109 |
| [28] | Krstić, M., Kanellakopoulos, I., & Kokotović, P. (1995). Nonlinear and adaptive control design. John Wiley & Sons, Inc. |
| [29] | Li, Y., Liu, Y., & Tong, S. (2022). Observer-based neuro-adaptive optimized control of strict-feedback nonlinear systems with state constraints. IEEE Transactions on Neural Networks and Learning Systems, 33(7), 3131-3145. |
| [30] | Li, Y., Min, X., & Tong, S. (2020). Adaptive fuzzy inverse optimal control for uncertain strict-feedback nonlinear systems. IEEE Transactions on Fuzzy Systems, 28(10), 2363-2374. |
| [31] | Lian, K. Y., & Liou, J. J. (2006). Output tracking control for fuzzy systems via output feedback design. IEEE Transactions on Fuzzy Systems, 14(5), 628-639. |
| [32] | Lin, H., & Dong, J. (2023). Stability analysis of T-S fuzzy systems with time-varying delay via parameter-dependent reciprocally convex inequality. International Journal of Systems Science, 54(6), 1289-1298. · Zbl 1520.93376 |
| [33] | Lin, W., & Pongvuthithum, R. (2003). Adaptive output tracking of inherently nonlinear systems with nonlinear parameterization. IEEE Transactions on Automatic Control, 48(10), 1737-1749. · Zbl 1364.93398 |
| [34] | Löfberg, J. (2004). YALMIP: A toolbox for modeling and optimization in MATLAB. In IEEE International Symposium on Computer Aided Control Systems Design (pp. 284-289). Institute of Electrical and Electronics Engineers (IEEE). |
| [35] | Mansouri, B., Manamanni, N., Guelton, K., Kruszewski, A., & Guerra, T. M. (2009). Output feedback LMI tracking control conditions with \(\mathcal{H}_\infty\) criterion for uncertain and disturbed T-S models. Information Sciences, 179(4), 446-457. . · Zbl 1158.93024 |
| [36] | Marton, L., & Lantos, B. (2011). Control of robotic systems with unknown friction and payload. IEEE Transactions on Control Systems Technology, 19(6), 1534-1539. |
| [37] | Mehdi, D. (2004). Static output feedback design for uncertain linear discrete time systems. IMA Journal of Mathematical Control and Information, 21(1), 1-13. . · Zbl 1049.93069 |
| [38] | Mozelli, L. A., Souza, F. O., & Mendes, E. M. A. M. (2014). SOFC for TS fuzzy systems: Less conservative and local stabilization conditions. In 2014 IEEE Symposium on Computational Intelligence in Control and Automation (CICA) (pp. 1-7). Institute of Electrical and Electronics Engineers (IEEE), |
| [39] | Nguyen, A. T., Campos, V., Guerra, T. M., Pan, J., & Xie, W. (2021). Takagi-Sugeno fuzzy observer design for nonlinear descriptor systems with unmeasured premise variables and unknown inputs. International Journal of Robust and Nonlinear Control, 31(17), 8353-8372. . · Zbl 1527.93246 |
| [40] | Nguyen, A. T., Pan, J., Guerra, T. M., & Wang, Z. (2021). Avoiding unmeasured premise variables in designing unknown input observers for Takagi-Sugeno fuzzy systems. IEEE Control Systems Letters, 5(1), 79-84. |
| [41] | Pan, J., Nguyen, A. T., Guerra, T. M., & Ichalal, D. (2021). A unified framework for asymptotic observer design of fuzzy systems with unmeasurable premise variables. IEEE Transactions on Fuzzy Systems, 29(10), 2938-2948. |
| [42] | Peaucelle, D., & Arzelier, D. (2001). An efficient numerical solution for \(\mathcal{H}_2\) static output feedback synthesis. In 2001 European Control Conference (ECC) (pp. 3800-3805). Institute of Electrical and Electronics Engineers (IEEE). |
| [43] | Qian, C., & Lin, W. (2002). Practical output tracking of nonlinear systems with uncontrollable unstable linearization. IEEE Transactions on Automatic Control, 47(1), 21-36. . · Zbl 1364.93349 |
| [44] | Sadabadi, M. S., & Peaucelle, D. (2016). From static output feedback to structured robust static output feedback: A survey. Annual Reviews in Control, 42, 11-26. |
| [45] | Sala, A., & Ariño, C. (2007). Asymptotically necessary and sufficient conditions for stability and performance in fuzzy control: Applications of Polya’s theorem. Fuzzy Sets and Systems, 158(24), 2671-2686. · Zbl 1133.93348 |
| [46] | Sereni, B., Manesco, R. M., Assunção, E., & Teixeira, M. C. M. (2018). Relaxed LMI conditions for the design of robust static output feedback controllers. IFAC-PapersOnLine, 51(25), 428-433. . |
| [47] | Slotine, J. J. E., & Li, W. (1991). Applied nonlinear control (Vol. 199, No. 1). Prentice Hall. · Zbl 0753.93036 |
| [48] | Soroush, M., & Zambare, N. (2000). Nonlinear output feedback control of a class of polymerization reactors. IEEE Transactions on Control Systems Technology, 8(2), 310-320. . |
| [49] | Su, S., & Lin, W. (2020). Global asymptotic tracking for nonminimum-phase nonlinear systems in output feedback form. International Journal of Robust and Nonlinear Control, 30(12), 4485-4502. · Zbl 1466.93061 |
| [50] | Syrmos, V. L., Abdallah, C., & Dorato, P. (1994). Static output feedback: A survey. In Proceedings of 1994 33rd IEEE Conference on Decision and Control (Vol 1, pp. 837-842). Institute of Electrical and Electronics Engineers (IEEE). |
| [51] | Tanaka, K., & Wang, H. O. (2001). Fuzzy control systems design and analysis: A linear matrix inequality approach. John Wiley & Sons. |
| [52] | Tognetti, E. S., & Linhares, T. M. (2021). Dynamic output feedback controller design for uncertain Takagi-Sugeno fuzzysystems: A premise variable selection approach. IEEE Transactions on Fuzzy Systems, 29(6), 1590-1600. . |
| [53] | Tong, S., Wang, T., & Li, H. X. (2002). Fuzzy robust tracking control for uncertain nonlinear systems. International Journal of Approximate Reasoning, 30(2), 73-90. · Zbl 1008.93050 |
| [54] | Tseng, C. S., Chen, B. S., & Uang, H. J. (2001). Fuzzy tracking control design for nonlinear dynamic systems via T-S fuzzy model. IEEE Transactions on Fuzzy Systems, 9(3), 381-392. . |
| [55] | Wang, X., Cao, Y., Niu, B., & Song, Y. (2023). A novel bipartiteconsensus tracking control for multiagent systems undersensor deception attacks. IEEE Transactions on Cybernetics, 53(9), 5984-5993. |
| [56] | Wang, Y., Chai, T., & Zhang, Y. (2010). State observer-based adaptive fuzzy output-feedback control for a class of uncertain nonlinear systems. Information Sciences, 180(24), 5029-5040. . · Zbl 1205.93091 |
| [57] | Zhang, X., & Lin, Y. (2012). A new approach to global asymptotic tracking for a class of low-triangular nonlinear systems via output feedback. IEEE Transactions on Automatic Control, 57(12), 3192-3196. . · Zbl 1369.93267 |
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.
