Sampled-Data Primal-Dual Gradient Dynamics in Model Predictive Control

Abstract: Model Predictive Control (MPC) is a versatile approach capable of accommodating diverse control requirements that holds significant promise for a broad spectrum of industrial applications. Noteworthy challenges associated with MPC include the substantial computational burden, which is sometimes considered excessive even for linear systems. Recently, a rapid computation method that guides the input toward convergence with the optimal control problem solution by employing primal-dual gradient (PDG) dynamics as a controller has been proposed for linear MPCs. However, stability has been ensured under the assumption that the controller is a continuous-time system, leading to potential instability when the controller undergoes discretization and is implemented as a sampled-data system. In this paper, we propose a discrete-time dynamical controller, incorporating specific modifications to the PDG approach, and present stability conditions relevant to the resulting sampled-data system. Additionally, we introduce an extension designed to enhance control performance, that was traded off in the original. Numerical examples substantiate that our proposed method, which can be executed in only 1 $\mu$s in a standard laptop, not only ensures stability with considering sampled-data implementation but also effectively enhances control performance.