×

Gain-scheduled control via filtered scheduling parameters. (English) Zbl 1226.93058

Summary: Gain-scheduled control via LPV system models enjoys LMI-based synthesis methods and in particular parameter-dependent Lyapunov matrices have been employed to successfully reduce conservatism. Those controllers derived via parameter-dependent Lyapunov matrices, however, end up with depending on derivatives of scheduling parameters. Though this can be avoided by approximating derivatives or restricting Lyapunov matrices to be partly constant, the former loses guarantee of performance and stability and the latter can cause conservatism. This paper proposes a synthesis method of gain-scheduled controllers that depend on filtered scheduling parameters, instead of derivatives, with a concrete guarantee of a performance level. Moreover, it is shown that the performance level of conventional derivative-dependent gain-scheduled controllers is recovered with arbitrarily small errors.

MSC:

93B50 Synthesis problems
93C10 Nonlinear systems in control theory
93B35 Sensitivity (robustness)

Software:

YALMIP
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Apkarian, P.; Adams, R. J., Advanced gain-scheduling techniques for uncertain systems, IEEE Transactions on Control System Technology, 6, 1, 21-32 (1997)
[2] Apkarian, P., Becker, G., Gahinet, P., & Kajiwara, H. (1996). LMI techniques in control engineering from theory to practice. In Workshop notes in the 35th IEEE conference on decision and control; Apkarian, P., Becker, G., Gahinet, P., & Kajiwara, H. (1996). LMI techniques in control engineering from theory to practice. In Workshop notes in the 35th IEEE conference on decision and control
[3] Apkarian, P.; Gahinet, P., A convex characterization of gain-scheduling \(H_\infty\) control, IEEE Transactions on Automatic Control, 40, 7, 853-864 (1995) · Zbl 0826.93028
[4] Azuma, T., Watanabe, R., & Uchida, K. (1997). An approach to solving parameter-dependent LMI conditions based on finite number of LMI conditions. In Proceedings of the 1997 american control conference; Azuma, T., Watanabe, R., & Uchida, K. (1997). An approach to solving parameter-dependent LMI conditions based on finite number of LMI conditions. In Proceedings of the 1997 american control conference
[5] Feron, E.; Apkarian, P.; Gahinet, P., Analysis and synthesis of robust control systems via parameter-dependent Lyapunov functions, IEEE Transactions on Automatic Control, 41, 7, 1041-1046 (1996) · Zbl 0857.93088
[6] Gahinet, P.; Apkarian, P.; Chilali, M., Affine parameter-dependent Lyapunov functions and real parametric uncertainty, IEEE Transactions on Automatic Control, 41, 3, 436-442 (1996) · Zbl 0854.93113
[7] Löfberg, J. (2004). YALMIP: a toolbox for modeling and optimization in MATLAB. In Proceedings of the 2004 IEEE international symposium on computer aided control systems design; Löfberg, J. (2004). YALMIP: a toolbox for modeling and optimization in MATLAB. In Proceedings of the 2004 IEEE international symposium on computer aided control systems design
[8] Masubuchi, I.; Ohara, A.; Suda, N., LMI-based controller synthesis: a unified formulation and solution, International Journal of Robust and Nonlinear Control, 8, 8, 669-686 (1998) · Zbl 0921.93012
[9] Meinsma, G.; Shrivastava, G.; Fu, M., A dual formulation of mixed \(\mu\) and on the loselessness of \((D, G)\) scaling, IEEE Transactions Automatic Control, 42, 7, 1032-1036 (1997) · Zbl 0892.93028
[10] Oliveira, R. C.L. F.; Peres, P. L.D., Time-varying discrete-time linear systems with bounded rates of variation: stability analysis and control design, Automatica, 45, 11, 2620-2626 (2009) · Zbl 1180.93084
[11] Packard, A., Gain scheduling via linear fractional transformations, Systems & Control Letters, 22, 79-92 (1994) · Zbl 0792.93043
[12] Rugh, W. J.; Shamma, J. S., Research on gain scheduling, Automatica, 36, 10, 1401-1425 (2000) · Zbl 0976.93002
[13] Scherer, C. W., LPV control and full block multipliers, Automatica, 37, 3, 361-375 (2001) · Zbl 0982.93060
[14] Scherer, C. W., LMI relaxations in robust control, European Journal of Control, 12, 1, 3-29 (2006) · Zbl 1293.93258
[15] Scherer, C. W.; Gahinet, P.; Chilali, M., Multiobjective output-feedback control via LMI optimization, IEEE Transactions on Automatic Control, 42, 7, 896-991 (1997) · Zbl 0883.93024
[16] Watanabe, R., Uchida, K., & Fujita, M. (1996). Linear systems with scheduling parameter — reduction to finite number of LMI conditions. In Proceedings of the 35th IEEE conference on decision and control; Watanabe, R., Uchida, K., & Fujita, M. (1996). Linear systems with scheduling parameter — reduction to finite number of LMI conditions. In Proceedings of the 35th IEEE conference on decision and control
[17] Watanabe, R., Uchida, K., Fujita, M., & Shimemura, E. (1994). \( L^2 H^\infty \)Proceedings of the 33rd IEEE conference on decision and control; Watanabe, R., Uchida, K., Fujita, M., & Shimemura, E. (1994). \( L^2 H^\infty \)Proceedings of the 33rd IEEE conference on decision and control
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.