  Model Predictive Control (MPC) is a versatile approach capable of
accommodating diverse control requirements, holding significant promise for a
broad spectrum of industrial applications. Noteworthy challenges associated
with MPC include the substantial computational burden and the inherent
difficulty in ensuring system stability. Recently, a rapid computation
technique has been introduced as a potential solution. This method guides the
input toward convergence with the optimal control problem solution by employing
the primal-dual gradient (PDG) dynamics as a controller. Furthermore, stability
assurances grounded in dissipativity theory have been established. However,
these assurances are applicable solely to continuous-time feedback systems. As
a consequence, when the controller undergoes discretization and is implemented
as a sampled-data system, stability cannot be guaranteed. 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. Numerical examples substantiate that
our proposed method not only enhances control effectiveness but also
effectively discerns stability degradation resulting from discretization, a
nuance often overlooked by conventional methods.
