Model Predictive Control of Descriptor Systems

While model predictive control (MPC) is widely used in the process industry for its ability to handle constraints and address complex dynamics, its conventional formulations often encounter challenges when dealing with descriptor systems. These formulations rely on system transformations that are applicable only to regular systems in specific scenarios, along with additional index assumptions. This letter formulates the MPC problem of discrete-time linear descriptor systems directly in their original state-space representation. Using the penalized weighted least-squares approach, we derive a quadratic cost function subject to the descriptor system over a finite prediction horizon. Through backward dynamic programming within each horizon, we then solve the constrained optimization problem to construct control inputs for forward-shifted prediction horizons. To accomplish this, we deal with the convergence and stability analysis of the proposed algorithm. Numerical simulations demonstrate its effectiveness compared to traditional techniques, alleviating the need for regularity and index assumptions.