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

Model Predictive Control (MPC) is a versatile approach capable ofaccommodating diverse control requirements, holding significant promise for abroad spectrum of industrial applications. Noteworthy challenges associatedwith MPC include the substantial computational burden and the inherentdifficulty in ensuring system stability. Recently, a rapid computationtechnique has been introduced as a potential solution. This method guides theinput toward convergence with the optimal control problem solution by employingthe primal-dual gradient (PDG) dynamics as a controller. Furthermore, stabilityassurances grounded in dissipativity theory have been established. However,these assurances are applicable solely to continuous-time feedback systems. Asa consequence, when the controller undergoes discretization and is implementedas a sampled-data system, stability cannot be guaranteed. In this paper, wepropose a discrete-time dynamical controller, incorporating specificmodifications to the PDG approach, and present stability conditions relevant tothe resulting sampled-data system. Additionally, we introduce an extensiondesigned to enhance control performance. Numerical examples substantiate thatour proposed method not only enhances control effectiveness but alsoeffectively discerns stability degradation resulting from discretization, anuance often overlooked by conventional methods.