[1]
|
K. Avrachenkov, O. Habachi, A. Piunovskiy and Y. Zhang, Infinite horizon optimal impulsive control with applications to Internet congestion control, International Journal of Control, 88 (2015), 703-716.
doi: 10.1080/00207179.2014.971436.
|
[2]
|
A. V. Balakrishnan, On stochastic bang-bang control, Applied Mathematics and Optimization, 6 (1980), 91-96.
doi: 10.1007/BF01442885.
|
[3]
|
M. Basin and and J. Rodriguez-Gonzalez, Optimal control for linear systems with time delay in control input, IEEE Transactions on Automatic Control, 51 (2006), 91-97.
doi: 10.1109/TAC.2005.861718.
|
[4]
|
A. Cairns, Some notes on the dynamics and optimal control of stochastic pension fund models in continuous time, Astin Bulletin, 30 (2000), 19-55.
doi: 10.2143/AST.30.1.504625.
|
[5]
|
S. L. Campbell, Singular Systems of Differential Equations II, Pitman, Boston, Mass.-London, 1982.
|
[6]
|
M. Chadli, H. R. Karimi and P. Shi, On stability and stabilization of singular uncertain Takagi-Sugeno fuzzy systems, Journal of the Franklin Institute, 351 (2014), 1453-1463.
doi: 10.1016/j.jfranklin.2013.11.008.
|
[7]
|
L. Chen and Z. Wu, Maximum principle for the stochastic optimal control problem with delay and application, Automatica J. IFAC, 46 (2010), 1074-1080.
doi: 10.1016/j.automatica.2010.03.005.
|
[8]
|
D. Cobb, Controllability, observability, and duality in singular systems, IEEE Transactions on Automatic Control, 29 (1984), 1076-1082.
doi: 10.1109/TAC.1984.1103451.
|
[9]
|
L. Dai, Singular Control Systems, Springer-Verlag, Berlin, Germany, 1989.
doi: 10.1007/BFb0002475.
|
[10]
|
J.-e Feng, P. Cui and Z. Hou, Singular linear quadratic optimal control for singular stochastic discrete-time systems, Optimal Control Applications and Methods, 34 (2013), 505-516.
doi: 10.1002/oca.2033.
|
[11]
|
J. Y. Ishihara and M. H. Terra, On the Lyapunov theorem for singular systems, IEEE Transactions on Automatic Control, 47 (2002), 1926-1930.
doi: 10.1109/TAC.2002.804463.
|
[12]
|
R. E. Kalman, Contribution to the theory of optimal control, Boletin Sociedad Matem$\acute{a}$tica Mexicana, 5 (1960), 102–119.
|
[13]
|
Y. Kang and Y. Zhu, Bang-bang optimal control for multi-stage uncertain systems, International Journal on Information, 15 (2012), 3229-3237.
|
[14]
|
D. E. Kirk, Optimal Control Theory: An Introduction, Courier Corporation, 2012.
|
[15]
|
N. Kumaresan and P. Balasubramaniam, Optimal control for stochastic nonlinear singular system using neural networks, Computers and Mathematics with Applications, 56 (2008), 2145-2154.
doi: 10.1016/j.camwa.2008.03.041.
|
[16]
|
P. Kunkel and V. Mehrmann, The linear quadratic optimal control problem for linear descriptor systems with variable coefficients, Mathematics of Control, Signals, and Systems, 10 (1997), 247-264.
doi: 10.1007/BF01211506.
|
[17]
|
B. Li and and Y. Zhu, The piecewise parametric optimal control of uncertain linear quadratic models, International Journal of Systems Science, 50 (2019), 961-969.
doi: 10.1080/00207721.2019.1586003.
|
[18]
|
F. Liao, Z. Ren, M. Tomizuka and J. Wu, Preview control for impulse-free continuous-time descriptor systems, International Journal of Control, 88 (2015), 1142-1149.
doi: 10.1080/00207179.2014.996769.
|
[19]
|
J. Lian, C. Li and D. Liu, Input-to-state stability for discrete-time nonlinear switched singular systems, IET Control Theory Appl., 11 (2017), 2893–2899.
doi: 10.1049/iet-cta.2017.0028.
|
[20]
|
W. Liu, X. Liang, Y. Ma and W. Liu, Aircraft trajectory optimization for collision avoidance using stochastic optimal control, Asian Journal of Control, 21 (2019), 2308-2320.
doi: 10.1002/asjc.1855.
|
[21]
|
D. G. Luenberger, Dynamic equations in descriptor form, IEEE Transactions on Automatic Control, 22 (1977), 312-321.
doi: 10.1109/tac.1977.1101502.
|
[22]
|
D. G. Luenberger and A. Arbel, Singular dynamic Leontief systems, Econometrica, 45 (1977), 991-995.
doi: 10.2307/1912686.
|
[23]
|
G. P. Mantas and N. J. Krikelis, LQ optimal control for discrete descriptor systems with a complete set of boundary information, International Journal of Control, 47 (1988), 1467-1477.
doi: 10.1080/00207178808906108.
|
[24]
|
D. S. Naidu, Singular perturbations and time scales in control theory and applications: An overview., Dynamics of Continuous Discrete & Impulsive Systems Ser. B Appl. Algorithms, 9 (2002), 233-278.
|
[25]
|
H. Peng, Fei. Li, J. Liu and Z. Ju, A symplectic instantaneous optimal control for robot trajectory tracking with differential-algebraic equation models, IEEE Transactions on Industrial Electronics, 67 (2020), 3819-3829.
doi: 10.1109/TIE.2019.2916390.
|
[26]
|
Y. Shu and Y. Zhu, Optimistic value based optimal control for uncertain linear singular systems and application to a dynamic input-output model, ISA Transactions, 71 (2017), 235-251.
doi: 10.1016/j.isatra.2017.08.007.
|
[27]
|
Y. Shu and Y. Zhu, Stability analysis of uncertain singular systems, Soft Computing, 22 (2018), 5671-5681.
doi: 10.1007/s00500-017-2599-2.
|
[28]
|
K. Wang, L. Xie and Y. Liu, Characteristics of self-excited oscillation in a curved diffuser., Journal of Propulsion Technology, 39 (2018), 1955-1964.
|
[29]
|
W. M. Wonham, On a matrix Riccati equation of stochastic control, SIAM Journal on Control, 6 (1968), 681-697.
doi: 10.1137/0306044.
|
[30]
|
H. Yan, Y. Sun and Y. Zhu, A linear-quadratic control problem of uncertain discrete-time switched systems, Journal of Industrial and Management Optimization, 13 (2017), 267-282.
doi: 10.3934/jimo.2016016.
|
[31]
|
W. Zhang, J. Hu and A. Abate, On the value function of the discrete-time switched LQR problem, IEEE Transactions on Automatic Control, 54 (2009), 2669-2674.
doi: 10.1109/TAC.2009.2031574.
|
[32]
|
W. Zhang, Y. Lin and L. Xue, Linear quadratic Pareto optimal control problem of stochastic singular systems, Journal of the Franklin Institute, 354 (2017), 1220-1238.
doi: 10.1016/j.jfranklin.2016.11.021.
|