Infinite horizon fuzzy optimal control: optimality does not imply asymptotic stability

Abstract

In this paper, novel stability result for discrete-time infinite horizon optimal control using fuzzy objective functions is presented. For this class of control, the fuzzy goals and the fuzzy constraints introduced in the fuzzy objective function handle the constraints placed on both the state and the control vectors. We analyze the asymptotic stability of the equilibrium for the infinite horizon fuzzy optimal control law using the minimum aggregation operator. We show that the infinite horizon control with the minimum aggregation operator does not guarantee the asymptotic stability of the equilibrium in general. This is done by deriving an analytical solution of the control law for a simple linear system using a fuzzy dynamic programming approach. An example that shows the novel asymptotic stability result of the equilibrium for discrete-time infinite horizon optimal control with fuzzy objective function problem is given.