Fuzzy optimal control of linear quadratic models. (English) Zbl 1198.93239
Summary: Optimal control is a very important field of study not only in theory but in applications. Based on the concept of fuzzy process, a fuzzy optimal control model is investigated with a quadratic objective functional for a linear fuzzy control system.
MSC:
| 93E20 | Optimal stochastic control |
| 93C42 | Fuzzy control/observation systems |
| 49N10 | Linear-quadratic optimal control problems |
| 60A86 | Fuzzy probability |
| 60H99 | Stochastic analysis |
References:
| [1] | Merton, R. C., Optimal consumption and portfolio rules in a continuous time model, Journal of Economic Theory, 3, 373-413 (1971) · Zbl 1011.91502 |
| [2] | Fleming, W. H.; Rishel, R. W., Deterministic and Stochastic Optimal Control (1986), Springer-Verlag: Springer-Verlag New York |
| [3] | Harrison, J. M., Brownian Motion and Stochastic Flow Systems (1985), John Wiley and Sons: John Wiley and Sons New York · Zbl 0659.60112 |
| [4] | Karatzas, I., Optimization problems in the theory of continuous trading, SIAM Journal on Control and Optimization, 27, 6, 1221-1259 (1980) · Zbl 0701.90008 |
| [5] | Dixit, A. K.; Pindyck, R. S., Investment Under Uncertainty (1994), Princerton University Press: Princerton University Press Princerton |
| [6] | Zadeh, L. A., Fuzzy sets, Information and Control, 8, 338-353 (1965) · Zbl 0139.24606 |
| [7] | Liu, B.; Liu, Y.-K., Expected value of fuzzy variable and fuzzy expected value models, IEEE Transactions on Fuzzy Systems, 10, 4, 445-450 (2002) |
| [8] | Liu, B., Uncertainty Theory: An Introduction to its Axiomatic Foundations (2004), Springer-Verlag: Springer-Verlag Berlin · Zbl 1072.28012 |
| [9] | Liu, B., Uncertainty Theory (2007), Springer-Verlag: Springer-Verlag Berlin · Zbl 1141.28001 |
| [10] | Liu, B., Fuzzy process, hybrid process and uncertain process, Journal of Uncertain Systerms, 2, 1, 3-16 (2008) |
| [11] | Zhu, Y., A fuzzy optimal control model, Journal of Uncertain Systems, 3, 4, 270-279 (2009) |
| [12] | Liu, B., Theory and Practice of Uncertain Programming (2002), Physica-Verlag: Physica-Verlag Heidelberg · Zbl 1029.90084 |
| [13] | X. Chen, A new existence and uniqueness theorem for fuzzy differential equations, http://orsc.edu.cn/online/081230.pdf; X. Chen, A new existence and uniqueness theorem for fuzzy differential equations, http://orsc.edu.cn/online/081230.pdf |
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.
