Output mini-max control for polynomial systems: analysis and applications. (English) Zbl 1290.93036
Summary: This paper presents a solution to a robust optimal regulation problem for a nonlinear polynomial system affected by parametric and matched uncertainties, which is based only on partial state information. The parameters describing the dynamics of the nonlinear polynomial plant depend on a vector of unknown parameters, which belongs to a finite parametric set, and the application of a certain control input is associated with the worst or least favourable value of the unknown parameter. A high-order sliding mode state reconstructor is designed for the nonlinear plant in such a way that the previously designed control can be applied for a system with incomplete information. Additionally, the matched uncertainty is also compensated by means of the same output-based regulator. The obtained algorithm is applied to control an uncertain nonlinear inductor circuit of the third order and a mechanical pendulum of the third order, successfully verifying the effectiveness of the developed approach.
MSC:
| 93B12 | Variable structure systems |
| 93C10 | Nonlinear systems in control theory |
| 93C15 | Control/observation systems governed by ordinary differential equations |
| 94C05 | Analytic circuit theory |
References:
| [1] | DOI: 10.1016/0021-8928(61)90005-3 · Zbl 0108.10503 · doi:10.1016/0021-8928(61)90005-3 |
| [2] | DOI: 10.1115/1.1543174 · doi:10.1115/1.1543174 |
| [3] | DOI: 10.1002/acs.1004 · Zbl 1284.93230 · doi:10.1002/acs.1004 |
| [4] | DOI: 10.1080/00207720701409363 · Zbl 1160.93396 · doi:10.1080/00207720701409363 |
| [5] | DOI: 10.1002/rnc.1055 · Zbl 1105.93056 · doi:10.1002/rnc.1055 |
| [6] | DOI: 10.1002/rnc.995 · Zbl 1100.93012 · doi:10.1002/rnc.995 |
| [7] | DOI: 10.1016/j.jfranklin.2010.08.006 · Zbl 1202.93048 · doi:10.1016/j.jfranklin.2010.08.006 |
| [8] | DOI: 10.1002/acs.1074 · Zbl 1298.93148 · doi:10.1002/acs.1074 |
| [9] | DOI: 10.1080/00207170903390179 · Zbl 1209.93149 · doi:10.1080/00207170903390179 |
| [10] | DOI: 10.1080/00207721.2010.543491 · Zbl 1233.93029 · doi:10.1080/00207721.2010.543491 |
| [11] | DOI: 10.1016/j.ins.2012.01.028 · Zbl 1256.93116 · doi:10.1016/j.ins.2012.01.028 |
| [12] | DOI: 10.1080/00207170601080205 · Zbl 1120.93013 · doi:10.1080/00207170601080205 |
| [13] | DOI: 10.1080/00207720701409280 · Zbl 1128.93309 · doi:10.1080/00207720701409280 |
| [14] | Bellman R., Dynamic Programming (1957) |
| [15] | DOI: 10.1002/rnc.1225 · Zbl 1284.93052 · doi:10.1002/rnc.1225 |
| [16] | DOI: 10.1080/17442508108833174 · Zbl 0458.60030 · doi:10.1080/17442508108833174 |
| [17] | DOI: 10.1080/002071799221118 · Zbl 0943.49017 · doi:10.1080/002071799221118 |
| [18] | DOI: 10.1002/oca.708 · Zbl 1072.49501 · doi:10.1002/oca.708 |
| [19] | DOI: 10.1109/TIE.2008.2005932 · doi:10.1109/TIE.2008.2005932 |
| [20] | Davila J., Proceedings of the American Control Conference pp 2960– (2010) |
| [21] | DOI: 10.1016/j.jfranklin.2011.04.002 · Zbl 1254.93040 · doi:10.1016/j.jfranklin.2011.04.002 |
| [22] | DOI: 10.1016/j.jfranklin.2011.08.002 · Zbl 1254.93142 · doi:10.1016/j.jfranklin.2011.08.002 |
| [23] | DOI: 10.1080/00207720701409538 · Zbl 1128.93312 · doi:10.1080/00207720701409538 |
| [24] | DOI: 10.1002/rnc.1198 · Zbl 1284.93057 · doi:10.1002/rnc.1198 |
| [25] | DOI: 10.1080/02329290309359 · Zbl 1131.93371 · doi:10.1080/02329290309359 |
| [26] | Isidori A., Nonlinear Systems (2001) · Zbl 1049.93562 |
| [27] | DOI: 10.1049/iet-cta.2011.0090 · doi:10.1049/iet-cta.2011.0090 |
| [28] | DOI: 10.1002/oca.795 · doi:10.1002/oca.795 |
| [29] | Juarez-Lopez S., International Journal of Innovative Computing, Information and Control 8 pp 1501– (2012) |
| [30] | Kalman R., Boletin de la Sociedad Matematica Mexicana 5 pp 102– (1960) |
| [31] | Kapitaniak T., Controlling Chaos (1996) |
| [32] | Khan Q., International of Innovative Computing, Information and Control 8 pp 4621– (2012) |
| [33] | Kwakernaak H., Linear Optimal Control Systems (1972) · Zbl 0276.93001 |
| [34] | DOI: 10.1080/00207179308923053 · Zbl 0789.93063 · doi:10.1080/00207179308923053 |
| [35] | DOI: 10.1016/S0005-1098(97)00209-4 · Zbl 0915.93013 · doi:10.1016/S0005-1098(97)00209-4 |
| [36] | DOI: 10.2514/2.4591 · doi:10.2514/2.4591 |
| [37] | Lin T., International Journal of Innovative Computing Information and Control 8 pp 347– (2012) |
| [38] | DOI: 10.1109/81.736558 · Zbl 0957.93042 · doi:10.1109/81.736558 |
| [39] | DOI: 10.1109/81.404059 · Zbl 0845.93040 · doi:10.1109/81.404059 |
| [40] | DOI: 10.1080/00207170210156260 · Zbl 1018.49023 · doi:10.1080/00207170210156260 |
| [41] | DOI: 10.1080/00207720903513384 · Zbl 1209.93129 · doi:10.1080/00207720903513384 |
| [42] | DOI: 10.1080/00207729708929460 · Zbl 0885.93022 · doi:10.1080/00207729708929460 |
| [43] | DOI: 10.1109/TAC.2005.861716 · Zbl 1366.93682 · doi:10.1109/TAC.2005.861716 |
| [44] | DOI: 10.1002/rnc.1348 · Zbl 1166.93363 · doi:10.1002/rnc.1348 |
| [45] | DOI: 10.1080/00207721.2010.550403 · Zbl 1230.93089 · doi:10.1080/00207721.2010.550403 |
| [46] | DOI: 10.1080/00207720500139773 · Zbl 1121.93020 · doi:10.1080/00207720500139773 |
| [47] | Wonham W., SIAM Journal on Control 2 pp 347– (1965) |
| [48] | DOI: 10.1109/TAC.2010.2051090 · Zbl 1368.93669 · doi:10.1109/TAC.2010.2051090 |
| [49] | Wu L., Automatica 48 pp 1229– (2012) |
| [50] | DOI: 10.1080/0020717031000105553 · Zbl 1029.93027 · doi:10.1080/0020717031000105553 |
| [51] | Yau S., Journal of Mathematical Systems, Estimation, and Control 4 pp 181– (1994) |
| [52] | DOI: 10.1016/0005-1098(89)90096-4 · Zbl 0694.49002 · doi:10.1016/0005-1098(89)90096-4 |
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