T-S fuzzy modeling and predictive control and synchronization of chaotic satellite systems

In this paper, we present the Takagi-Sugeno fuzzy modeling, predictive controlling and its synchronization of chaotic system. Based on the T-S fuzzy model, predictive controllers for stabilization and synchronization of chaotic satellite systems are designed via linear matrix inequalities (LMIs). To justify the chaoticity of satellite system, bifurcation diagrams with respect to known parameters of satellite systems are analyzed; Poincare section with different sowing axes of satellite are drawn; Lyapunov exponents are estimated. Predictive control technique is applied to synchronize the two identical satellite systems. Analytical and computational studies of satellite systems have been performed by using LMI toolbox. Feedback control gains matrices at the equilibrium points and stabilization gains matrices at initial conditions for satellite systems are obtained. The time to achieve the desired controlling and synchronization of satellite system applying at t = 20 is set by selecting different controller gains. Solutions of equations of motion of satellite system are drawn in the form of three dimensional, two dimensional and time series phase portraits. The qualitative and simulated results are in an excellent agreement.