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The piecewise optimisation method for approximating uncertain optimal control problems under optimistic value criterion. (English) Zbl 1362.93061
Summary: In this paper, we introduce an approximate model and propose a piecewise optimisation method to simplify the expression of optimal control for an uncertain linear quadratic optimal control problem. First, we consider an optimal control problem of uncertain linear quadratic model under optimistic value criterion. Based on the equation of optimality, we deduce an analytic expression of optimal control. Then, we study an approximate model with control parameter and propose a piecewise optimisation method for solving the optimal parameter of such an approximate model. As an application, a four-wheel steering vehicle optimal control problem is given to show the utility of the proposed approximate model and the efficiency of the proposed piecewise optimisation method.

MSC:
93B51 Design techniques (robust design, computer-aided design, etc.)
49N10 Linear-quadratic optimal control problems
49N90 Applications of optimal control and differential games
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[1] DOI: 10.1016/j.amc.2006.06.020 · Zbl 1107.65057 · doi:10.1016/j.amc.2006.06.020
[2] DOI: 10.1080/00207721.2011.618646 · Zbl 1307.93371 · doi:10.1080/00207721.2011.618646
[3] DOI: 10.1007/s10700-010-9073-2 · Zbl 1196.34005 · doi:10.1007/s10700-010-9073-2
[4] DOI: 10.1109/9.478328 · Zbl 0843.93091 · doi:10.1109/9.478328
[5] DOI: 10.1109/TAC.1973.1100210 · Zbl 0263.93031 · doi:10.1109/TAC.1973.1100210
[6] DOI: 10.1016/j.mcm.2012.07.003 · Zbl 1286.93202 · doi:10.1016/j.mcm.2012.07.003
[7] DOI: 10.1080/00423119508969086 · doi:10.1080/00423119508969086
[8] DOI: 10.1016/0005-1098(88)90003-9 · Zbl 0637.49017 · doi:10.1016/0005-1098(88)90003-9
[9] DOI: 10.1016/j.automatica.2009.01.019 · Zbl 1166.93030 · doi:10.1016/j.automatica.2009.01.019
[10] DOI: 10.2307/1914185 · Zbl 0411.90012 · doi:10.2307/1914185
[11] DOI: 10.1007/978-3-540-73165-8_5 · doi:10.1007/978-3-540-73165-8_5
[12] Liu B, Journal of Uncertain Systems, 2 (1) pp 3– (2008)
[13] Liu B, Journal of Uncertain Systems, 3 pp 3– (2009)
[14] DOI: 10.1007/978-3-540-89484-1 · Zbl 1158.90010 · doi:10.1007/978-3-540-89484-1
[15] DOI: 10.1007/978-3-642-13959-8 · doi:10.1007/978-3-642-13959-8
[16] DOI: 10.1016/j.amc.2013.09.036 · Zbl 1364.49032 · doi:10.1016/j.amc.2013.09.036
[17] DOI: 10.1243/09544070JAUTO152 · doi:10.1243/09544070JAUTO152
[18] DOI: 10.1016/S0022-460X(03)00812-5 · Zbl 1236.93153 · doi:10.1016/S0022-460X(03)00812-5
[19] DOI: 10.1016/S0895-7177(98)00035-1 · Zbl 0991.49025 · doi:10.1016/S0895-7177(98)00035-1
[20] DOI: 10.1007/BF01397001 · Zbl 0386.34018 · doi:10.1007/BF01397001
[21] DOI: 10.1142/S0218488513400060 · Zbl 1322.93064 · doi:10.1142/S0218488513400060
[22] DOI: 10.1016/j.amc.2013.08.079 · Zbl 1334.93185 · doi:10.1016/j.amc.2013.08.079
[23] Stengel R.F, Optimal control and estimation (1994)
[24] DOI: 10.1016/j.apm.2014.10.042 · doi:10.1016/j.apm.2014.10.042
[25] DOI: 10.1186/2195-5468-1-17 · doi:10.1186/2195-5468-1-17
[26] Yao K., Journal of Intelligent & Fuzzy Systems, 25 (3) pp 825– (2013)
[27] DOI: 10.1080/00207721.2012.745031 · Zbl 1284.93267 · doi:10.1080/00207721.2012.745031
[28] DOI: 10.1080/01969722.2010.511552 · Zbl 1225.93121 · doi:10.1080/01969722.2010.511552
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