论文信息 - Fuzzy optimal control with application to discounted profit advertising problem

Fuzzy optimal control with application to discounted profit advertising problem

A fuzzy optimal control model was formulated maximizing the expected discounted objective function subject to fuzzy differential equation for fuzzy control system. We proved that the value function of fuzzy optimal control problem satisfied the dynamic programming principle. The optimality equation in fuzzy optimal control was derived and an example was carried out to obtain the optimality conditions by using the optimality equation. As an application, we used the Bellman's principle of optimality to solve the fuzzy advertising model.

Anton Abdulbasah Kamil | Md. Azizul Baten | A. Kamil

[1] I. Karatzas. Optimization problems in the theory of continuous trading , 1989 .

[2] R. Bellman. Dynamic programming. , 1957, Science.

[3] J. Harrison,et al. Brownian motion and stochastic flow systems , 1986 .

[4] Michio Sugeno,et al. Fuzzy identification of systems and its applications to modeling and control , 1985, IEEE Transactions on Systems, Man, and Cybernetics.

[5] Yuanguo Zhu,et al. A Fuzzy Optimal Control Model , 2009 .

[6] Lotfi A. Zadeh,et al. Fuzzy Sets , 1996, Inf. Control..

[7] L. Arnold. Stochastic Differential Equations: Theory and Applications , 1992 .

[8] Eduardo S. Schwartz,et al. Investment Under Uncertainty. , 1994 .

[9] R. C. Merton,et al. Optimum consumption and portfolio rules in a continuous - time model Journal of Economic Theory 3 , 1971 .

[10] Ebrahim Mamdani,et al. Applications of fuzzy algorithms for control of a simple dynamic plant , 1974 .

[11] Sergei Ovchinnikov,et al. Fuzzy sets and applications , 1987 .

[12] Ioannis Karatzas,et al. Brownian Motion and Stochastic Calculus , 1987 .

[13] W. Fleming,et al. Deterministic and Stochastic Optimal Control , 1975 .

[14] M. Sugeno,et al. Fuzzy modeling and control of multilayer incinerator , 1986 .

[15] W. Fleming,et al. Controlled Markov processes and viscosity solutions , 1992 .

[16] Baoding Liu. Fuzzy Process, Hybrid Process and Uncertain Process , 2008 .