Mokhtar Shasadeghi

Alireza Olama, Mokhtar Shasadeghi, Amin Ramezani

There are two main challenges in control of hybrid systems which are to guarantee the closed-loop stability and reduce computational complexity. In this paper, we propose the exponential stability conditions of hybrid systems which are described in the Mixed Logical Dynamical (MLD) form in closed-loop with Model Predictive Control (MPC). To do this, it is proposed to use the decreasing condition of infinity norm based Lyapunov function instead of imposing the terminal equality constraint in the MPC formulation of MLD system. The exponential stability conditions have a better performance from both implementation and computational points of view. In addition, the exponential stability conditions of the equilibrium point of the MLD system do not depend on the prediction horizon of MPC problem which is the main advantage of the proposed method. On the other hand, by using the decreasing condition of the Lyapunov function in the MPC setup, the suboptimal version of the control signal with reduced complexity is obtained. In order to show the capabilities of the proposed method, the stabilization problem of the car suspension system is studied.

Leila Rajabpour, Mokhtar Shasadeghi, Alireza Barzegar

In this paper, we propose a new systematic approach based on nonquadratic Lyapunov function and technique of introducing slack matrices, for a class of affine nonlinear systems with disturbance. To achieve the goal, first, the affine nonlinear system is represented via Takagi-Sugeno (T-S) fuzzy bilinear model. Subsequently, the robust H_inf controller is designed based on parallel distributed compensation (PDC) scheme. Then, the stability conditions are derived in terms of linear matrix inequalities (LMIs) by utilizing Lyapunov function. Moreover, some slack matrices are proposed to reduce the conservativeness of the LMI stability conditions. Finally, for illustrating the merits and verifying the effectiveness of the proposed approach, the application of an isothermal continuous stirred tank reactor (CSTR) for Van de Vusse reactor is discussed in details.