`a`
Journal of Industrial and Management Optimization (JIMO)
 

Indefinite LQ optimal control with process state inequality constraints for discrete-time uncertain systems
Page number are going to be assigned later 2017

doi:10.3934/jimo.2017082      Abstract        References        Full text (416.8K)      

Yuefen Chen - School of Mathematics and Statistics, Xinyang Normal University, Xinyang, Henan 464000, China (email)
Yuanguo Zhu - School of Science, Nanjing University of Science and Technology, Nanjing, Jiangsu 210094, China (email)

1 M. Athans, The matrix minimum principle, Information and Control, 11 (1967), 592-606.       
2 K. Bahlali, B. Djehiche and B. Mezerdi, On the stochastic maximum principle in optimal control of degenerate diffusions with Lipschitz coefficients, Applied Mathematics and Optimization, 56 (2007), 364-378.       
3 A. Bensoussan, S. P. Sethi, R. G. Vickson and N. Derzko, Stochastic production planning with production constraints: A summary, SIAM Journal on Control and Optimization, 22 (1984), 920-935.       
4 D. P. Bertsekas, Dynamic Programming and Stochastic Control, Mathematics in Science and Engineering, 125. Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1976.       
5 S. P. Chen, X. J. Li and X. Y. Zhou, Stochastic linear quadratic regulators with indefinite control weight costs, SIAM Journal on Control and Optimization, 36 (1998), 1685-1702.       
6 X. Chen, Y. Liu and D. A. Ralescu, Uncertain stock model with periodic dividends, Fuzzy Optimization and Decision Making, 12 (2013), 111-123.       
7 Y. Gao, Uncertain models for single facility location problems on networks, Applied Mathematical Modelling, 36 (2012), 2592-2599.       
8 M. R. Hestenes, Calculus of Variations and Optimal Control Theory, Wiley, New York, 1966.       
9 Y. Hu and X. Y. Zhou, Constrained stochastic LQ control with random coefficients, and application to portfolio selection, SIAM Journal on Control and Optimization, 44 (2005), 444-466.       
10 D. Kahneman and A. Tversky, Prospect theory: an analysis of decision under risk, Econometrica, 47 (1979), 263-292.
11 X. Li and X. Y. Zhou, Indefinite stochastic LQ controls with Markovian jumps in a finite time horizon, Communications on Information and Systems, 2 (2002), 265-282.       
12 B. Liu, Uncertainty Theory, $2^{nd}$ edition, Springer-Verlag, Berlin, 2004.       
13 B. Liu, Uncertainty Theory: A Branch of Mathematics for Modeling Human Uncertainty, Springer-Verlag, Heidelberg, 2015.       
14 B. Liu, Some research problems in uncertainty theory, Journal of Uncertain Systems, 3 (2009), 3-10.
15 X. Liu, Y. Li and W. Zhang, Stochastic linear quadratic optimal control with constraint for discrete-time systems, Applied Mathematics and Computation, 228 (2014), 264-270.       
16 B. Liu and K. Yao, Uncertain multilevel programming: Algorithm and applications, Computers and Industrial Engineering, 89 (2014), 235-240.
17 R. Penrose, A generalized inverse of matrices, Mathematical Proceedings of the Cambridge Philosophical Society, 51 (1955), 406-413.       
18 L. Sheng and Y. Zhu, Optimistic value model of uncertain optimal control, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 21 (2013), 75-87.       
19 Y. Shu and Y. Zhu, Stability and optimal control for uncertain continuous-time singular systems, European Journal of Control, 34 (2017), 16-23.       
20 V. K. Socgnia and O. Menoukeu-Pamen, An infinite horizon stochastic maximum principle for discounted control problem with Lipschitz coefficients, Journal of Mathematical Analysis and Applications, 422 (2015), 684-711.       
21 Z. Wang, J. Guo, M. Zheng and Y. Yang, A new approach for uncertain multiobjective programming problem based on $\mathcalP_E$ principle, Journal of Industrial and Management Optimization, 11 (2015), 13-26.       
22 W. M. Wonham, On a matrix Riccati equation of stochastic control, SIAM Journal on Control and Optimization, 6 (1968), 681-697.       
23 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.       
24 J. Yong and X. Y. Zhou, Stochastic Controls: Hamiltonian Systems and HJB Equations, Springer, New York, 1999.       
25 W. Zhang, H. Zhang and B. S. Chen, Generalized Lyapunov equation approach to state-dependent stochastic stabilization/detectability criterion, IEEE Transactions on Automatic Control, 53 (2008), 1630-1642.       
26 W. Zhang and B. S. Chen, On stabilizability and exact observability of stochastic systems with their applications, Automatica, 40 (2004), 87-94.       
27 W. Zhang and G. Li, Discrete-time indefinite stochastic linear quadratic optimal control with second moment constraints, Mathematical Problems in Engineering, 2014 (2014), Art. ID 278142, 9 pp.       
28 X. Y. Zhou and D. Li, Continuous-time mean-variance portfolio selection: A stochastic LQ framework, Applied Mathematics and Optimization, 42 (2000), 19-33.       
29 Y. Zhu, Uncertain optimal control with application to a portfolio selection model, Cybernetics and Systems: An International Journal, 41 (2010), 535-547.
30 Y. Zhu, Functions of uncertain variables and uncertain programming, Journal of Uncertain Systems, 6 (2012), 278-288.

Go to top