Model predictive control of cyclic systems using linear matrix inequalities

Cyclic processes can be characterized by two time variables, viz, the time within a cycle and the cycle index, each carrying a distinct connotation of time. Conventional optimal control theory does not explicitly account for these two dimensions (2D) of time that characterize cyclic systems. In this paper, we study the control of cyclic process using Model Predictive Control (MPC). The proposed approach uses a 2D Lyapunov function and the stability requirements are established along each time dimension of the system. The resulting controller synthesis problem is expressed in convex form using Linear Matrix Inequalities (LMIs). The approach allows incorporation of input/output constraints in the proposed 2D MPC framework. An example of a cyclic process is presented to establish the applicability of the proposed approach.