Optimal Control of Fuzzy Linear Controlled System with Fuzzy Initial Conditions

In this article we found the solution of fuzzy linear controlled system with fuzzy initial conditions by using $\alpha$-cuts and presentation of numbers in a more compact form by moving to the field of complex numbers. Next, a fuzzy optimal control problem for a fuzzy system is considered to optimize the expected value of a fuzzy objective function. Based on Pontryagin Maximum Principle, a constructive equation for the problem is presented. In the last section, three examples are used to show that the method in effective to solve fuzzy and fuzzy optimal linear controlled systems.