Design of Fuzzy Stochastic Nearly Optimal Control

Abstract

Some large scale systems with a presence of random noises could be described as linear quadratic Gaussian (LQG) model modulated by a finite state Markov chain. This model has a variety of potential applications in the areas of pattern recognition, communication and industrial economics, etc. Its optimal solution is obtained using dynamic programming and the associated HJB equation approach. For the reason of high dimensionality, nearly optimal averaging approach is necessary to achieve consistent solutions to Riccati equations. Here the assumption is that two types of states are available exclusively which are slowly varying and rapidly varying, respectively. In another aspect, this topic is also related to hybrid control issue that indicates continuous attribute inside each rapidly varying group and discrete event attribute upon all transitions among individual slowing varying groups. In fact, real world problems are typically ambiguous and there is not a unique criterion between terms of slow and rapid (such as extremely slow, slightly slow, slightly rapid and extremely rapid). In this case, fuzzy logic has been introduced to formulate a design problem of fuzzy stochastic nearly optimal control. Procedures of fuzzy nearly optimal controller construction have been derived and a simplified case of numerical simulations has been provided as well. This article is the first formulation of fuzzy stochastic nearly optimal control in the literature.