Control of an uncertain fractional order economic system via adaptive sliding mode

This paper addresses the design of sliding mode controller (SMC) for an uncertain chaotic fractional order economic system. A new fraction-integer integral switching surface is constructed to facilitate stability analysis of the closed-loop system. A sliding mode controller is developed to guarantee that sliding mode motion exists on every point of the switching surface and any state outside the surface is driven to reach the surface in a finite time. Moreover, an adaptive SMC is designed in the case that the upper bound of the uncertainties is unknown. Numerical simulations are performed to verify the feasibility and effectiveness of the proposed controllers.