Fuzzy Stochastic Optimal Guaranteed Cost Control of Bio-Economic Singular Markovian Jump Systems

• Published in: IEEE transactions on cybernetics Vol. 45; no. 11; pp. 2512 - 2521
• Main Authors: Li, Li, Zhang, Qingling, Zhu, Baoyan
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.11.2015; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Bio-economic model; Biological system modeling; Computer Simulation; Controllers; Cost function; Economics; finite-time control; Fuzzy; Fuzzy Logic; Fuzzy set theory; guaranteed cost; linear matrix inequality (LMI); Markov Chains; Markov models; Mathematical model; Mathematical models; Models, Biological; Models, Economic; singular Markovian jump system (SMJS); Sociology; Statistics; Stochastic Processes; Stochasticity; Takagi-Sugeno (T-S) fuzzy model; singular Markovian jump system (SMJS); guaranteed cost; linear matrix inequality (LMI); Bio-economic model; finite-time control; Takagi–Sugeno (T-S) fuzzy model
• ISSN: 2168-2267; 2168-2275
• DOI: 10.1109/TCYB.2014.2375957

This paper establishes a bio-economic singular Markovian jump model by considering the price of the commodity as a Markov chain. The controller is designed for this system such that its biomass achieves the specified range with the least cost in a finite-time. Firstly, this system is described by Takagi-Sugeno fuzzy model. Secondly, a new design method of fuzzy state-feedback controllers is presented to ensure not only the regularity, nonimpulse, and stochastic singular finite-time boundedness of this kind of systems, but also an upper bound achieved for the cost function in the form of strict linear matrix inequalities. Finally, two examples including a practical example of eel seedling breeding are given to illustrate the merit and usability of the approach proposed in this paper.