Repetitive Model Predictive Control using Linear Matrix Inequalities

Repetitive systems can be characterized by two time variables, namely, the finite time within each repeating cycle and the cycle index, each embodying a distinct connotation of time. Conventional optimal control theory does not explicitly account for this two dimensional (2D) description of repetitive systems. We propose a new formulation for control of repetitive systems using Model Predictive Control (MPC) that explicitly incorporates a 2D representation of the system. The proposed formulation 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 explicit incorporation of input/output constraints in the controller design. Two examples illustrate the applicability of the proposed approach.